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LANDOLT-BORNSTEIN 

Numerical Data and Functional Relationships 
in Science and Technology 

New Series 

Editor in Chief: K.-H. Hellwege 
Group III : Crystal and Solid State Physics 

Volume 4 
Magnetic and Other Properties 
of Oxides and Related Compounds 

Part a 

J.B.Goodenough • W.Graper • F.Holtzberg • D.L.Huber 
R.A.Lefever -J.M.Longo • T.R.McGuire • S.Methfessel 

Editors: K.-H. Hellwege and A. M. Hellwege 



Springer-Verlag Berlin • Heidelberg • New York 1970 

BEST AVAILABLE COPY 



N LANDOLT-BORNSTEIN 

,s Zahlenwerte und Funktionen 

aus Naturwissenschaften und Technik 

Neue Serie 

Gesamtherausgabe: K.-H. Hellwege 

Gruppe III: Kristall- und Festkorperphysik 

Band 4 

Magnetische und andere Eigenschaften 
von Oxiden und verwandten Verbindungen 

Teila 

J.B.Goodenough • W.Graper • F.Holtzberg ■ D.L.Huber 
R.A.Lefever - J.M.Longo • T.R.McGuire • S.Methfessel 

Herausgeber: K.-H. Hellwege und A.M. Hellwege 




1970 i SpringerA^rlag Berlin • Heidelberg • New York 1970 



3.0 Einleitung 



[Lit. S. 275 



Ref. p. 2' 



3 Crystallographic and magnetic properties of perovskite and 
perovskite-related compounds *) 

3.0 Introduction — Einleitung 



The perovskites form a family of compounds 
having a crystal structure similar to that of the 
mineral perovskite, CaTiOa. There are two classes 
of materials crystallizing with this general structure 
type: primarily ionic materials having the ideal 
chemical formula ABX,, (A - larger cation, B = 
smaller cation, X = anion), and alloys havmg the 
ideal formula M^^XM^ , (X = interstitial atom, 
and Mf are metal atoms). Of these two classes, the 
former is much larger and the more important. 

The stabihty of the ABX3 perovskite structure 
I is primarily derived from the electrostatic (Made- 
lung) energy achieved if cations occupy corner- 
shared octahedra. Thus the first prerequisite for a 
stable ABX3 perovskite is the existence of stable, 
polar octahedral-site building blocks. This, in turn, 
requires that the B cation have a preference for 
octahedral coordination and that there be an effec- 
tive charge on the B cation. Since any A cation 
must occupy the relatively large anionic interstice 
created by corner-shared octahedra, a second pre- 
requisite is an appropriate size for the A cation. 
Where it is too large, the B-X bond length cannot 
be optimized, and hexagonal stacking with face- 
shared octahedra becomes competitive. Where the 
A cation is too small, A-X bonding stabilizes struc- 
tures having a smaller anionic coordination about 
the A cation. Thus ABX3 perovskites are common- 
ly found in fluorides and oxides having B cations 
with a preference energy for octahedral coordina- 
tion. By contrast, the chlorides and sulfides, havmg 
larger anions, not only require the largest A cations, 
but also form layer structures, where the A cations 
are missing, because they have anionic d orbitals 
energetically available for orbital hybridization. 



There are many perovskite-related structures, 
and these have been included in these tables. For 
example, the structure can tolerate mixed systems 
such as A,_,AiBX3 and AB^-^B^X,, A-catiomc 
vacancies □ as in Di-z^^^Z' and cationic order- 
ing as in A^BB'Xfi. Although anion-deficient 
perovskites have been reported many times, the 
anion vacancies ® are probably not distributed 
randomly. In compounds containing Fe3+ ions, for 
example, they appear to condense in pairs at indi- 
vidual B-site octahedra to convert the local anion 
interstice from an octahedron to a tetrahedron. In 



3.0.1 General remarks - Ailgemeines 

Die Perowskite sind eine Gruppe von Verbin 
dungen mit der gleichen Kristallstruktur wie das 
Mineral Perowskit. CaTiOj. Man unterscheidet zwei 
Klassen von Substanzen. die in diesem allgemeinen 
Strukturtyp kristallisieren : in erster Linie lonen- 
verbindungen mit der idealen chemischen Formel 
ABX3 (A ^ groCeres Ration, B = kleineres Kation, 
X = Anion) und Legierungen mit der idealen 
Formel M^XMJ (X - Zwischengitteratom. M^ und 
W = Metallatome). Von diesen beiden Klassen 1st 
die erstere wesentlich umfangreicher und wichtiger. 

Die StabiUtat der ABXj-Perowskitstruktur be 
ruht in erster Linie auf der elektrostatischen (Made 
lung-) Energie, die dann zustande kommt. wenn 
Kationen Oktaeder mit gemeinsamen Ecken be- 
setzen. So ist die Existenz von stabilen, polaren 
Oktaeder-Bausteinen die erste Vorbedingung fiir 
ein stabiles ABX3-Perowskit. Dies wiederum er- 
fordert daB das B-Kation die Oktaeder- Koordma- 
tion bevorzugt und daB beim B-Kation eine effek- 
tive Ladung existiert. Da ein jedes A-Kation die 
relativ groBe Anionen-Lucke besetzen muC, die 
zwischen Oktaedern mit gemeinsamen Ecken ent- 
steht ist die passendc GroBe des A-Kations die 
zweit'e Vorbedingung. Wenn das A-Kation zu groB 
ist. laBt sich der optimale B-X-Bindungsabstand 
nicht erreichen, und eine hexagonale Packung von 
Oktaedern mit gemeinsamen Flachen kann ebenso 
auftreten. Wenn das A-Kation zu klein 1st, ergibt 
die A-X-Bindung Strukturen mit einer kleineren 
Anionen-Koordination urn das A-Kation. Daher 
sind ABX3-Perowskite gewohnlich unter den Fluo- 
riden und Oxiden zu finden, in denen die B-Kati- 
onen Oktaeder-Koordination energetisch bevor- 
zugen. Dagegen erfordern Chloride und Sulfide, 
die groBere Anionen haben. nicht nur die groBten 
A-Kationen. sondern sie bilden, weil sie aniomsche 
i-Elektronenbahnen mit der richtigen Energie fur 
eine Bahn-Hybridisierung haben. auch Schicht- 
strukturen, bei denen die A-Kationen ganz fehlen. 

Es gibt viele dem Perowskit verwandte Struk- 
turen, die in diese Tabellen aufgenommen wurden. 
Zum Beispiel konnen gemischte Systeme wie 
A,_;,Ai,BX3 und AB,_,BLX3 mit dieser Struktur 
auftreten, weiter A-Kationenliicken □ wie in 
□ ._^A,BX3 und geordnete Kationen wie in 
A BB'Xg. tJber Perowskite mit Anionenlucken 
ist schon haufig berichtet worden, vermutlich 
sind die Anionenleerstellen © nicht wiUkurhch 
verteilt. In Verbindungen, die Fe^^-Ionen enthal- 
ten. scheinen sie z. B. paarweise im Oktaeder ernes 
einzelnen B-Platzes zusammenzutreffen und die 



*) This work was sponsered by the U. S. Air Force. 



126 



Goodenough/Longo 



c< 


Dmpoui 


it 


is mor* 


a 


nions 1 


d 


eficieni 


c 


ations, 


c 


ontain 


a 


cross 


e 


dges (] 


c 


Aencies 




lUoys. 


] 


B-occui 


] 


jerovst 


< 


:ation ^ 




an intei 




(Fig. 23 




stackin 




nal stai 




cies (F 




(AX)^( 




rocksal 




stackec 




also oc 




an A a 




struct! 




with i: 








and E 




rather 




for ex; 




18). & 




of the 




Tt 




ing pi 




BaTi( 




ferror 




condi 




ducti 




lator- 




tor a; 




patib 




trans 




ture 




ab:k 




mult 




[Sm 




ferro 




ed f 




Ba, : 




pero 




and 




mag 




of t 




mas 




app 




tura 




thai 




*ri 




c 




1 



.275 



Ref. p. 275] 



3.0 Introduction 



compounds containing Ti*+ ions, on the other hand, 
it is more probable that local rearrangements of the 
anions form trigonal bipyramidal sites. Anion- 
deficient, ionic materials in which there are no A- 
cations, such as DWOs-j;, have been shown to 
contain DBXj blocks connected by "shear" planes 
across which the occupied octahedra share common 
edges (Fig. 22). On the other hand, anion defi- 
ciencies may occur randomly in the WX^-JAl 
alloys. B-cation defects cannot occur, because the 
B-occupied octahedra form the basis of the ABX3- 
perovskite structure. Where there are apparent B- 
cation vacancies, as in A^B^-iX^^, there is either 
an interleaving of perovskite layers with A^X^ layers 
(Fig. 23) or an interleaving of cubic (perovskite) 
stacking of AO3 layers with regularly spaced hexago- 
nal stackings at which are located the B-ion vacan- 
cies (Fig. 24). Similarly, the series of compounds 
(AX)„(ABX3)„ crystalhze with an interleaving of 
rocksalt layers (Fig. 25). Interleaving of cubic- 
stacked AO3 layers and hexagonal-stacked layers 
also occurs in ABX3 compounds having too large 
an A cation to be accommodated by the perovskite 
structure (Fig. 3). Finally, there are a few alloys 
with interesting magnetic properties that can be 
classified as AgBB'Xg compounds if the symbols B 
and B' are allowed to represent atomic clusters 
rather than single cations. These are illustrated, 
for example, by the alloy Al2(AlCOi2)(Co8)B6 (Fig. 
18). Sections 3.1 and 3.2 are devoted to descriptions 
of the perovskite and perovskite-related structures. 



The ABX3 perovskites exhibit several interest- 
ing physical properties such as ferroelectricity (as in 
BaTiOg), ferro magnetism (as in BrRuOg), weak 
ferromagnetism (as in LaFeOg or HoFeOg), super- 
conductivity (as in SrTiOs-a:), a large thermal con- 
ductivity due to exciton transport (LaCoOj), insu- 
lator-to-metallic transitions of interest for thermis- 
tor applications (as in LaCoOj), fluorescence com- 
patible with laser action (as in LaAlOgiNd), and 
transport properties of interest for high-tempera- 
ture thermoelectric power (as in La2Cu04). A few 
ABX3 perovskites have been found that are si- 
multaneously antiferromagnetic and ferroelectric 
[Sm 16, Mi 7, Sm9]. The simultaneous occurrence of 
ferroelectricity and ferromagnetism has been report- 
ed for systems like Sr^ asLa^ ^gMnOj-ATiOj (A = 
Ba, Pb, Bio.5Ko.5) [To3, fo6l *Many of the M^XM| 
perovskite alloys are ferromagnetic or ferrimagnetic, 
and a few exhibit first-order ferrimagnetic- to-ferro- 
magnetic transitions. Nevertheless, the significance 
of the entire perovskite family for the field of 
magnetism*) lies not yet in their technological 
applications, but in their provision of an isostruc- 
tural series of compounds having outer d electrons 
that are localized and spontaneously magnetic in 



*) The technologically important dielectric properties arc 
outside the scope of this summary. See Vol. 111/3 of the 
New Series of Landolt-Bornstein. 



dortige Anionenlucke von einem Oktaeder in einen 
Tetraeder umzuwandeln. Bei Verbindungen, die 
Ti'*'''-Ionen en thai ten, ist es dagegen wahrschein- 
licher, daB die lokale Anordnung der Anionen tri- 
gonale Doppelpyramiden-Platze bildet. Fiir lonen- 
verbindungen mit Anionenliicken, die keine A- 
Kationen haben, wie DWOa-j, ist gezeigt worden, 
dafi sie □BX3-BI6cke enthalten, die durch „Gleit"- 
ebenen verbunden sind, in denen die besetzten 
Oktaeder gemeinsame Kanten innehaben (Fig. 22). 
In M*^Xi_3,M^-Legierungen konnen jedoch Anionen- 
liicken auch beliebig auftreten. B-Kationenliicken 
konnen nicht vorkommen, weil die von B besetzten 
Oktaeder die Basis der ABXg-Perowskitstruktur 
bilden. Wo scheinbare B-Kationenleerstellen auf- 
treten, wie in A^Bm-iXj^n, sind entweder AgXg- 
Schichten zwischen Perowskitschichten eingescho- 
ben (Fig. 23), oder kubische (Perowskit-) Anord- 
nungen von AOg-Schichten wechseln mit regel- 
maBig verteilten hexagonalen Anordnungen, in 
denen die B-Ionenliicken auftreten, ab (Fig. 24). 
Ahnhch kristallisieren die Verbindungen der Reihe 
(AX)„(ABX3)„ mit einer Einschiebung von Stein- 
salzschichten (Fig. 25). Einschiebungen von ku- 
bisch gepackten AOg-Schichten und hexagonal ge- 
packten Schichten treten auch in solchen ABX3- 
Verbindungen auf, deren A-Kation fiir die Perows- 
kit- Struktur 2u groO ist (Fig. 3). SchlieBlich gibt 
es einige wenige Legierungen mit interessanten 
magnetischen Eigenschaften, die als AgBB'Xg- 
Verbindungen eingeordnet werden konnen, wenn 
man unter den Symbolen B und B' Atomgruppen 
statt einzelner Kationen versteht, Dies gilt z. B. 
fiir die Legierung Al2(AlCOi2)(Co8)B5 (Fig. 18). Die 
Abschnitte 3.1 und 3,2 sind der Beschreibung der 
Perowskit- und verwandter Strukturen gewidmet. 

Die ABXj-Perowskite weisen einige interessante 
physikalische Eigenschaften auf, wie Ferroelektrizi- 
tat (in BaTi03), Ferromagnetismus (in BrRuOg), 
schwachen Ferromagnetismus (in LaFeOg oder 
HoFeOj), Supraleitfahigkeit (in SrTiOg-J, groCe 
Warmeleitfahigkeit durch Excitonentransport (in 
LaCoOg), fiir Thermistoren interessante Obergange 
zwischen Nichtleiter und metallischem Leiter (in 
LaCoOg), fiir Laser- Anwendungen geeignete Fluo- 
reszenz (in LaAlOsiNd), und Transporteigenschaf- 
ten, die fiir ThermospannungenbeihohenTempera- 
turen von Interesse sind (in La2Cu04). Einige wenige 
ABXg-Perowskite wurden gefunden, die sowohl 
ferromagnetisch als auch ferroelektrisch sind [Sfn16, 
Mi7, SwP]. Das gleichzeitige Auftreten von Ferro- 
elektrizitat und Ferromagnetismus wurde bei 
Systemen wie Sro,25La(,.75Mn03-ATi03 (A = Ba, 
Pb,Bio.5Ko.5)[T(?i, T06'] beschrieben. VieleM^^XM^- 
Perowskitlegierungen sind ferromagnetisch oder fer- 
rimagnetisch, und einige zeigen t)bergange erster 
Ordnung von Ferri- zu Ferromagnetismus. Trotz- 
dem liegt die Bedeutung der gesamten Perowskit- 
Familie fiir den Magnetismus*) noch nicht in der 
technologischen Anwendung, sondern im Vorhan- 
densein einer isostrukturellen Reihe von Verbin- 



*) Die technologisch wichtigen dielektrischen Eigenschaf- 
ten liegen nicht im Rahmen dieser Zusammenstellung. 
Siehe Band 1 1 1/3 der NeuenSeriedcs Landolt-Bornstein, 



Goodenough/Longo 



127 



3.0 Einleitung 



[Lit. S. 275 



one member, collective and spontaneously magnetic 
in another, and collective and Pauli paramagnetic 
in yet another. This permits a systematic experi- 
mental investigation of the properties of the d elec- 
trons on passing through the transition from a 
localized character, where crystal-field plus super- 
exchange and/or double-exchange theories apply, 
to an uncorrelated (except below a superconducting 
transition temperature) collective-electron charac- 
ter, where the conventional band theory applies. 
In addition, the simplicity of the perovskite ABX3 
structure minimizes competitive magnetic inter- 
actions between neighboring magnetic cations. 
Therefore from a study of magnetic order, as re- 
vealed by neutron diffraction, together with de- 
tailed structural information, as revealed by x-ray 
diffraction, it has been possible to test the semi- 
empirical rules for 180° cation-anion-cation iso- 
tropic superexchange interactions between localized 
electrons, the double-exchange hypothesis, anti- 
symmetric exchange, and predictions of magnetic 
order and spontaneous atomic moments due to 
collective electrons. 



Section 3.3 presents the general phenomenologi- 
cal exchange Hamiltonian for localized electrons 
and summarizes the microscopic models for iso- 
tropic superexchange, double exchange, and anti- 
symmetric exchange. From these models, general 
rules for the interactions responsible for magnetic 
order are developed for comparison with the tabu- 
lated magnetic data. 



Section 3.4 presents the fundamental physical 
concepts needed to construct a quahtative phase 
diagram for the outer d electrons as a function of 
the number ni of electrons per relevant orbital, the 
magnitude of a nearest-neighbor transfer energy 6, 
and the temperature T. It also summarizes the 
various characters of several physical properties 
imparted by outer electrons to show how they can 
be used to distinguish the electronic phases in differ- 
ent perovskites. Information from the tabulated 
data is used to show the influence of covalence and 
intra-atomic exchange, which help determine the 
parameter b, on the character of the electrons. 
Spontaneous collective-electron magnetism is seen 
to occur only in a narrow transitional interval of b 
between localized -electron magnetism and collec- 
tive-electron Pauli paramagnetism. 



Section 3.5 provides schematic energy diagrams 
for the alloys M^^XM^. These are shown to be useful 
guides to predictions of the magnitudes of the 
atomic moments and the magnetic order. 



dungen mit auBeren ^Z-Elektronen, die lokalisiert 
und spontan magnetisch in der eincn Verbindung, 
kollektiv und spontan magnetisch in einer ande- 
ren, und kollektiv und PauH-paramagnetisch in 
noch einer weiteren sind. Dies erlaubt system a- 
tische experimentelle Untersuchungen der Eigen- 
schaften der ^i-Elektronen, indem man von einem 
lokalisierten Zustand. in dem Kristallfeld plus 
Superaustausch- und/oder Doppelaustausch-Theo- 
rien gelten, zu einem Zustand unkorrelierter KoUek- 
tivelektronen (auCer bei Temperaturcn unterhalb 
des t)bergangs zur Supraleitung) ubergeht, in dem 
die konventionelle Bandertheorie anzuwenden ist. 
Weiterhin fuhrt die Einfachheit der Perowskit- 
ABXg-Struktur zu minimalen konkurrierenden 
Wechselwirkungen zwischen benachbarten magne- 
tischen Kationen. Aufgrund der Untersuchung der 
magnetischen Ordnung, die man durch die Neutro- 
nenbeugung kennt, und einer genauen Kenntnis der 
Struktur, wie man sie durch Rontgenbeugung 
gewonnen hat, war es deshalb mdglich, die halb- 
empirischen Gesetze uber die isotrope 180°-Kation- 
Anion— Ration— Superaustausch— Wechselwirkung 
zwischen lokalisierten Elektronen, die Doppelaus- 
tausch-Hypothese, den antisymmetrischen Aus- 
tausch und Voraussagen fur magnetische Ord- 
nung und spontane Atom-Momente, die von Kollek- 
tivelektronen herriihren, zu prufen. 

Der Abschnitt 3.3 enthalt den allgemeinen pha- 
nomenologischen Hamilton-Austausch-Operator 
fur lokalisierte Elektronen und faBt die mikroskopi- 
schen Modelle fiir den isotropen Superaustausch, 
den Doppelaustausch und den antisymmetrischen 
Austausch zusammen. Aus diesen Modellen werden 
allgemeine Regeln fiir die Wechselwirkungen, die 
fiir die magnetische Ordnung verantwortlich sind, 
zum Vergleich mit den tabellierten Daten ent- 
wickelt. 

Der Abschnitt 3.4 enthalt die grundlegenden 
physikalischen Ideen, die fiir die Herstellung eines 
qualitativen Phasendiagramms fiir die auBeren d- 
Elektronen als Funktion der Elektronenzahl ni pro 
betreffenden Bahnzustand, der GroBe einer tjber- 
tragungsenergie b zwischen nachsten Nachbarn und 
der Temperatur T notwendig sind. AuBerdem wer- 
den hier verschiedene Charakteristika einigcr durch 
die auBeren Elektronen gegebenen physikalischen 
Eigenschaften zusammengestellt. um zu zeigen, wie 
man mit ihrcr Hilfe die elektronischen Phasen ver- 
schiedener Perowskite unterscheiden kann. Auf 
Grund der tabellierten Werte wird der EinfluB von 
Kovalenz und intra-atomarem Austausch, die 
den Parameter b mitbestimmen, auf den Charakter 
der Elektronen gezeigt. Spontane Magnetisierung 
der Kollektivelektronen tritt, wie man sieht, nur in 
einem schmalen Obergangsintervall von b zwischen 
dem Magnetismus lokahsierter Elektronen und dem 
Pauli-Paramagnetismus der Kollektivelektronen 
auf. 

Der Abschnitt 3.5 enthalt schematische Energie- 
diagramme fur die Legierungen M^^XM^ . Es wird ge- 
zeigt, daB sie zu brauchbaren Voraussagen iiber die 
GroBe der Atom-Momcntc und die magnetische 
Ordnung fiihren konnen. 



128 



Coodenough/Longo 



275 



ert 

le- 
in 
la- 
an- 
em 
lus 
eo- 
ek- 
alb 
em 
ist. ! 
dt- 
ien 
ne- 
der 

TO- 

der 
ing I 
lib- 
on- 
ung 

lUS- 
lUS- 

)rd- 
lek- 

)ha- 
itor 
opi- 
sch, 
hen 
den 
die 
ind, 
ent- 

iden 
lines 
n d- 

pro 
ber- 

und 
wer- 
urch 
:hen 
. wie 

ver- 

Auf ! 

von 
die 
.kter 
rung 
ur in 
chen 

dem 
onen 

:rgie- 
dge- 
:r die ] 
ische 



Ref. p. 275] 



3.0 Introduction 



In the introductions to the sections 3.2 — 3.5 
we have referenced the principle theoretical contri- 
bution discussed, but no attempt was made to do 
this systematically for the experimental contribu- 
tions, which are thoroughly referenced in the ta- 
bles. — In the crystallographic tables, the crystal 
parameters quoted either represent the most com- 
plete analysis, in our judgment, or belong to the 
most complete set of parameters for a series of 
similar compounds. They do not necessarily re- 
present the historical reference that estabhshed the 
unit-cell dimensions. 



Literature was considered up to 1969. 

Finally, we would like to thank David Maho- 
NEY for his willing assistance, the library and pubh- 
cations personnel of Lincoln Laboratory for their 
efficient support, and Mrs. G. E. Boyd for her help 
with all the foreign references. 



In den Einleitungen zu den Abschnitten 
3.2 •"3.5 haben wir die grundlegenden theoretischen 
Beitrage, die diskutiert werden, mit Literaturhin- 
weisen versehen; fur die experimentellen Beitrage 
haben wir dies nicht systematisch durchzufiihren 
versucht, da die entsprechenden Tabellen voll- 
standig mit Liter aturhinweisen versehen sind. — 
In den kristallographischen Tabellen stellen die an- 
gefiihrten KristaUparameter entweder die nach 
unserer Beurteilung voilstandigste Analyse dar, 
Oder sie gehoren zum vollstandigsten Satz von 
Parametern f iir eine Reihe ahnlicher Verbindungen, 
Sie geben nicht notwendigerweise den historischen 
Literaturhinweis, der die Dimensionen der Ein- 
heitszelle festlegte. 

Die Literatur wurde bis 1969 beriicksichtigt. 

SchlieBlich mochten wir David Mahoney fur 
seine bereitwillige Hilfe, den Angestellten der Bi- 
bliothek und der Veroffentlichungsabteilung des 
Lincoln-Laboratoriums fiir ihre wirksame Unter- 
stiitzung und Mrs. G. E. Boyd fiir ihre Hilfe bei der 
auslandischen Literatur dan ken. 



symmetry 



a, h, c [A] 
a. y [deg] 

0tran8> ©ord [°Kj 

^* X 
''A,B,B' [A] 



magnetic order 



Weff 

[°K] 

©p [°K] 
& [°K] 

[emu °K mole-^] 
Xy [emu/g], [cmVg] 
Xm [emu/mole] 

d 

(^w [erg/cm^J 



3.0.2 Symbols and units used in tables and figures 

Crystallographic structure 

symmetry classification for perovskite structures : C = cubic, H = hexagonal, 
R = rhombohedral, O orthorhombic (a < c/Vl), O' = orthorhombic 
(c//2 < a), T = tetragonal, M = monoclinic, Tr = triclinic 
lattice parameters 
angle between crystallographic axes 
crystallographic transition and ordering temperatures 
Debye temperature 
melting temperature 
elastic constants 
crystalline strains 
radius of A, B, B' cation 

Magnetic properties (static measurements) 

see magnetic structure type from Fig. 26 

atomic moment and component of atomic moment parallel to net ferromagnetic 

moment in numbers of Bohr magnetons: = _ 
net magnetization per molecule in numbers of Bohr magneton: p^^ = t^mt^B 
7ieff = j/gCm is the effective paramagnetic moment: p^n = y-B 
Curie temperature 

N6el temperature; extrapolated N6el temperature 
temperature for spin reorientation 

paramagnetic Curie temperature (0p < 0 if antiferromagnetic coupling) 
temperature below which parasitic nf deviates appreciably from 0.05 
molar Curie constant determined from Curie-Weiss law Xm = ^m/l^ — ^p) 
specific paramagnetic susceptibiUty 
molar paramagnetic susceptibility 
atomic moment, atomic moment of element A 
molecular moment (of molecule xy) 
effective paramagnetic moment : p* = Vxm ^ 

isotropic exchange constant of Eq. (16) for near-neighbor interactions 
Ln-Fe interaction parameter defined by 

^ (^^(0) B(t) [1 -h WO], where / = T/Oc and B(0 is the Brillouin function 
domain wall energy density z 
net near-neighbor Weiss molecular field constant: ^ Wi^M^ 



i-ajidoU-Bornsleiii. Neue Serie 



Goodenough/Longo 



129 



3.0 Einleitung 



[Lit. S. 275 



magnetic moment per gram = specific magnetization 
specific parasitic (weak) magnetization as obtained from o = a^-\- Xs^^ 
spontaneous specific magnetization 

cJti^l^'ue? Mdlor antiferromagnctic-ferromagnctic transition or for spin- 

flop transition 
cocrcivity 
cant angle 

magnetoelectric coefficients aj ni. r \ 

magnetostriction constant for [100] direction: A^oo - " 3^,- ^.-nn 

components of the tensor describing the quadratic dependence of magnetization 

on applied field: Eq. (36) 
the Bohr magneton 5585 cmu/s 
torque : T — oxH^ 

Magnetic properties (resonance measurements) 

effective crystalline-aiiisotropy field 
exchange field 

spin-canting field (Dzialoshinskii field) 
internal magnetic field at the nucleus 
axial hyperfine field arising from nuclear polarization 

hypS field /-A-S, where / ^ nuclear spin S - net ^to-ic spin, and the 
components of the interaction tensor are A3, Ans. hnndine- 
fraction of unpaired s, p. or electron spins involved m covalent bonding. 



i [Gauss cm'/g] 
^ \[emu/g] 
[emu/g] 

Ha [Oe] 
Hcrit [Oc] 

He 

(X 

bi, 62 [dyn/cm^] 
^100 

T [crpj/R] 



Ha 

Hex 

Hd 

Hint 

Hn 

Hhyp 



[Hz] 
Av[Hz] 
Ti [sec] 
Tz [sec] 
r,e [sec] 



Q [°/cm] 
VTO. "LO [Hz] 



Q [Qcm] 
S [jxV/°K] 
I e [esu] 

I c, Mj, n± [cm~^] 
fi [cmVVsec] 
: [sec] 

I Wi* [g] 

Dq [cm2/sec] 



T [°K] 
P 



J 



racoon 01 Uupauc;Li ^, ya " ^ . „ . , TvTa 12 

■A = 2SA,/A^ = i NlAi, /A = 2SA„/A,p = i N|A|. = 2SA„/A,p i N,A„. 



See Eq. (4) for Ng, Nt, Ag. Aa. 
nuclear quadrupole coupling constant and quadrupole splitting^ 

dipolar and quadrupolar magnetoelastic coefficients: =.£^U' 

dx - EGx^Ei, where ^spin-lattice = I^B'^a • <5g • S' h ' d • S 
i = i 

resonance frequency for NMR 
half-line width 

nuclear spin-lattice relaxation time 
nuclear spin-spin relaxation time 

nuclear spin-lattice relaxation time during a locking pulse 

Optical measurements 

index of refraction 
low-frequency dielectric constant 
Faraday rotation 

frequency of transverse and longitudinal optical modes 

Transport measurements 

superconducting critical temperature 
Fermi energy 

activation energy for a small-polaron hop 

electrical resistivity 

Seebeck coefficient 

magnitude of the electronic charge 

charge-carrier density 

charge-carrier mobility 

charge-carrier collision time 

charge-carrier effective mass 

charge-carrier diffusion coefficient at £a " 

density of unoccupied states: lilnmlVTIh^f'"- 

General properties 

temperature 
pressure 

specific heat at constant pressure 



and 



130 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABXg perovskite structure 



AFMR 
APR 
BPW 
C, cub 
DS 
DTA 
ESR 
fx. 
FMR 

H, hex, hex (nL) 
LR. 
Ln 
MF 

M, moil 
NAR 
NMR 
ncub 



O. O' 
P&S 
Prep. 
Prop, 
pscub 
psmon 
R, rh 
RW 
S. G. 
S.S, 
T, tetr 
Tr, tr 



orth 



Abbreviations for text and indices 

aatiferromagaetic resonance 
acoustic paramagnetic resonance 
Bethe-Peierls-Weiss method 
cubic 

Danielson- Stevens method 
differential thermal analysis 

electron spin resonance = paramagnetic resonance 
face-centered permutation 
ferromagnetic resonance 
ferromagnetic with reduced 
hexagonal, hexagonal n-layer structure 
infrared 

Lanthanon = any of the rare-earth elements 
molecular field approximation 
monoclinic 

nuclear acoustic resonance 
nuclear magnetic resonance 
noncubic 

orthorhombic (O: a < O' : cjn < a) 
reference to preparation and structural mformation 
reference to material preparation 
reference to material properties 
pseudocubic 
pseudomonoclinic 
rhombohedral 
Rushbrooke-Wood method 
space group 
solid solution 
tetragonal 
triclinic 

3.1 Descriptions of stoichiometric ABX, and M^XM's structures 

3.1.1 The ideal perovskite structure 

The ideal perovskite structure has the cubic unit cell of Fig. 1 with space group Pm3m Fig. 1 (a) 
shoifthe corn'Tr-sharing octahedral units (BX. array in ABX, and XM^array in M'XMj). which form the 
JaWe skeleton of the steucture. The A cation (or M« atom) occupies the body-center position. Fig. 1(b) 
shows the uSt cellwith the A cation (or M« atom) at the origin, or corner position. This shows the fao^- 
cSrered cubk character (with Cu,Au-lype order) of the AX, or M«=]S^^ subarrays. Fig. 1 (c) ^hows the cubic 
;:rSte on'an hexagonal basis. withSie . axis along the cubic [111] 'i--t'-/3^^.^^^^^^^ 
ionic layers each have cubic stacking. Also indicated is the ordering of B and B layers m the ordered 
A(B;/,B,/s)X3 structures. 




Fig. 1. ABX„ M=XMf. Ideal perovskite structure: a) B cation (or X atom) at origin, b) M= atom (or A cation) at origin. 

c) A cation at origin in hexagonal basis [GaW]. 



Goodenough/Longo 



131 



3.1 ABX 



Perowskit-Struktur [Lit. S. 275 



The allovs M'^XMf are stabilized by covalent M-X bonding and by metallic M-M bonding, so that they 

aescnoea oy ^i""^ ^ ^^j..u'^ [T a2^ theory of phase transitions, it may be argued [Hal, CoJ\ 

lT:t\^^col/JA!^^^^^ one norma, .ode becomes zero^ Thus tje 

modes are involved, and these displacive transitions are first-order. 1 1 n ok R^5^ 

in the cubic phase- For T < ©trans, it splits into two ^ouc symmetry is further 

J r\o.3i rF/?1 In the presence of an external electric tieiQ tilt; b> iiiin^:; 1.1 y 

I dence co ^ trans - T) if ^^r 1^1 i c axis and the critical modes have the same symmetry as 
reduced to C^v if ^a 11 c-axis, or Cjv if £a ± c-axis, ana tne cnuc 

electrons- 

3.1.2 The influence of relative ionic sizes 
3 1.2.1 Tolerance factor 

fbe "Kn™ bordetlin.. bemg sUMe in lo»r. live or coordmahon. How.v„. Ga", G. * and V 
of the A cation via a tolerance factor . 

i = (^A + »-x)/l^(''B + '•X) 

;r5.r.^/o»idi'^°.noTntrs:^'r.=^^^^^^^^ 
rsifaSnrsrroi:^?::,;™"^^^^^^^^^ 



Goodenough/Longo 



275 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



Fig. 2. General - phase diagram for A'+B'+Oj com- 
pounds based on ionic-size considerations. Exceptions may 
occur where considerations other than ionic radii r 
become important, as in the case A = Bi. A similar plot for 
A*+B«+0, perovskites is not useful because secondary con- 
siderations are amplified by ferroelectric distortions and the 
possibility of different layer sequences where larger A cations 
are present. [Adapted from Sc13]. 



to 



0.8 



Q£ 




OS 



OB 



A type rare eorfh oxide 
B type rore earth oxide 
C type rare earth oxide 
Corundum relattd 
Ferovstiite 

Perovsti 'ife at high pressure 



W 



Given smaller A cations, however, electrostatic screening between face-shared octahedra can be 
achieved by displacements of the cations away from the shared face, and the structure competitive with 
perovskite is generally built from an hexagonal-close-packed anion array, which has octahedral holes 
sharing common faces along the c-axis. With one octahedral hole per anion and a cation/anion ratio 2/3, 
the cations are ordered among these holes so as to minimize the electrostatic energy. If the A and B cations 
carry the same charge, as in A^+B^+Oa, only pairs of cations share common octahedral-site faces and there 
is no ordering of A and B within the cationic array. This allows the electrostatic force between two cations 
sharing a common octahedral face to be reduced by displacements of the cations away from each other, 
thus distorting the octahedra. The result is the corundum structure of AI2O3. If the cations A and B carry 
different charges, as in A^+B^+Oj, then the A and the B cations order into alternate puckered cationic 
(111) planes of the rhombohedral corundum structure to form the ilmenite structure. However, where 
there is a large difference in the cationic charges, as in Li+Sb^+Oj and Li+Nb^+Oa, two other alternatives 
become competitive: (1) The A+ ions order in strings of face-shared octahedra so as to permit the 
B*+-ion octahedra to share only edges with near-neighbor occupied octahedra. This structure is illustra- 
ted by LiSbOj \_Ed1\ (2) After ordering and Li+ ions whithin each cationic (111) plane of the corun- 
dum structure in such a way that B^^ and Li+ ions share common octahedral-site faces, each A+ cation 
is then displaced into the far face of its octahedron, where it is equally spaced from B5_+ cations above 
and below so long as the B^-*- cations remain in the centers of their octahedra. This is the structure of 
paraelectric LiNbOg and LiTaOa \Ah3\ t_ xi, • 

Where the A cation is too large [i > 1.0), the close-packed AX3 layers of Fig. 1 (c) tend to change their 
stacking sequence from cubic to hexagonal. However, the change from the all-cubic stackmg of the 
rhombohedral perovskite structure to the all-hexagonal stacking of the hexagonal (hex. 2L) CsNiCls 
structure goes via the three intermediate steps shown in Fig. 3 \Lo1\ The first step is the hexagonal 
BaTiOj structure of Fig. 3 (c). It is a six-layer structure with stacking sequence a-b-c-a-c-b-a, correspondmg 
to one hexagonal stacking out of three. In this structure (hex. 6L), two-out-of-three B cations form pairs 
sharing a common octahedral-site face, and one-out-of -three B cation shares only common octahedral-site 
corners as^in the perovskite structure. Many ordered compounds AgBgB'Og are known to have this 
structure. ^The second step, illustrated by the hexagonal BaMnOs structure of Fig. 3 (d), alternates hexa- 
gonal and cubic stackings with the sequence a-b-c-b-a. This four-layer structure (hex. 4L), contains only 
B-cation pairs sharing common octahedral-site faces. The electrostatic forces between paired B-cations m 
Figs. 3(c), (d) displace the paired cations from one another along the c axis, exactly as in the corundum 



1 / A ' 










m 





























a 1) c ^ ^ , 

Fig 3 Stable structures intermediate to a) cubic perovskite and b) the two-layer hexagonal CsNiCl, structure, c) six-layer 
hexagonal BaTiO, structure, d) four-layer hexagonal BaMnO, structure, e) nine-layer hexagonal BaRuO, structure, 
[Adapted from Ca2\ 



Goodenough/Longo 



133 



3.1 ABXg Perowskit-Struktui- 



[Lit. S. 275 



structure The third step is the nine-layer (hex. 9L) structure of BaRuOg, which has two hexagonal 
stackings out of three in the sequence a-b^c^b-c-a^c^a-b-a. Here the B cations form strings of three sharing 
common octahedral-site faces along the c-axis. Electrostatic forces displace the two end-member B cations 
away from the center B cation of each string, as shown in Fig. 3(e). Because cubic stacking is stabihzed 
by hydrostatic pressure, it is possible to convert under pressure and high temperature the hexagonal 
structures to the perovskite structure through the successive sequence of steps. This is well illustrated by 
the Ba.-^Sr^uO, system as shown in Fig. 4(a). These particular intermediate structures appear to be 
stabilized by the cation displacements, but at the cost of alternating the stacking sequence. The (hex^4L) 
structure, which has the maximum alternation of stacking, is not always found, and the intermediate 
structures tend to be stabilized by smaller B cations, as illustrated in Fig. 4(b)- 



• Perovshife 


80 


o $ layer 


kbar 


© H laytr 




® S layer 


SO 





Fig. 4. a) Ba^.^Sr^RuO,. p - x phase diagram where p is 
hydrostatic pressure [Lo/], b) structural phase diagram of 
0 QZ OM as 0.8 7.0 CsBFj compounds [Lo/6]. 

a BqRu03 

3.1.2,2 O-orthorhombic structure 

Cooperative buckling of corner-shared octahedra, although indexed on a monoclinic pseudocell in 
earlier work may produce the orthorhombic primitive cell of Fig. 5 containing four formula units. It was 
first identified in single crystals of GdFeO, [Gel] and later confirmed [Co2/]. Powder photographs taken 
with CrK^ radiation could be indexed on the monoclinic pseudocell containing a single CdFeOj molecule, 
which is the origin of the earlier classification. The pseudocell dimensions of CdFeO^ are a = c = 3.87 A, 
J _ 3^83 A, i? = 92.8°. where 26psendoceii = ^trueceii- The true orthorhombic cell is referred to in the tables 
as O-orthorhombic and is distinguished from the O' -orthorhombic structure by a lattice-parameter ratio 




Fig. 5. GdFeOs. O-orthorhombic structure. 

^ol, = < B.XnB.. 0, = < B.XiB.. 

Fig. from structure [Gel], coordinates[Co2/J. 



ion 


position 


X 


coordinates 

y 


z 


Gd»+ 


4(c) 


-0.018 


0.060 




Fe»+ 


4(b) 


4 


0 


0 


0}- 


4(c) 


0.05 


0.470 






8(d) 


-0.29 


0.275 


0.05 



134 



Goodenough/Longo 



275 



Rcf. p. 275] 



3.1 ABXj perovskite structiS 



c/a > I' 2, where a <h. The O'-orthorhombic structure, which has c/a < Vl, is the result of a super- 
posed Jahn-Teller (with or without spin-orbit coupling) distortion. It is also to be distinguished from ferro- 
electric OB-orthorhombic and 0|-orthorhombic distortions in which each B cation is removed from the 
center of symmetry of its interstice. Other orthorhombic distortions have been reported for NdGaO 
[Br26] and NaCoFg [Ok5l ^ 

The 0-orthorhombic unit cell has the probable space group Pbnm with A cations in positions 4(c): 
ib(^, J - i -f % I), the B catjons in 4(b): (i 0. 0; J, O.J; 0, i. 0; 0, J. h), eight anions Xn in 

^(^) '- ±(x, y, z\ ^ ~ X, \ y, ^ — z\ X, y, \ -\- z\ \ -\- X, ^ — y, z), and the remaining four anions Xi in 
4 (c). Coordinates for the ions in GdFeOj arc also given in Fig. 5, 

The buckling of the corner-shared octahedra decreases the cation-anion-cation angle O from 180°, If 
the B cations and the anions are distinguished as B^(^. 0, 0). 62(0, i, 0). Bgfi. 0, \), Xii(J x, ^ — y^J) 
and Xi(J — J y, \), then the two representative angles are (P^b = (Bi — Xjj — Bg) and 0^ = 
(B2 — Xj — B3). GiLLEO [Gi4] has estimated that in La(Coo ^Mn^ 5)03 these angles are = 150° ± 3' 
and 0, = 177° ± 3° with B, - 0„ = 1.95 A, Bg - 0„ - 2.10 A,' B^ - Oj - B3 - Oj 1.96 A. The 
angles in GdFe03 are similar. 

3.1,2.3 Rhombohedral structures 

Where there is no buckling of the octahedra, the perovskites ABX3 may have a small deformation 
from cubic to rhombohedral symmetry. Where this deformation does not enlarge the unit cell, it is 
possible to index it either on a unit cell containing two formula units, as shown in Fig. 6, or on a unit cell 
containing one formula unit. The corresponding rhombohedral angles are a 60°orc( 90°. In the early 
literature, detailed anion positions were not known, and it w^as common to use the smaller cell with 
(X ^90°. However, the anions are generally displaced so as to require the larger unit cell of Fig. 6, 
which has oc ^ 60°. 




a 0 ' ^ ^ 

Fig. 6. Rhombohedral ABX, structures: a) anion shifts for symmetry R3c; b) the simplest ionic displacements, corre- 
sponding to symmetry R3m for ordered A,BB'X, structures having r-Q'> {Ra3]. 

Anion displacements from their ideal positions may be of three different types: (1) AX3(111) planes 
remain equidistant from neighboring B-cation (111) planes, leaving all the B-cations equivalent. Within 
these planes, three A — X distances are reduced and three are enlarged via cooperative rotations of the 
B-cation octahedra, as shown in Fig. 6(a). (2) The anions may move within pseudocubic {110} planes 
including the B-B axes so as to create two distinguishable B positions : B positions having a shorter B-X 
separation and B' positions having a larger B'-X separation. This gives the symmetry R3m, which allows 
the A cations to be displaced along the [111] axis so as to make the Reparations B-A B'-A. (3) In the 
most general case, the anion displacements may be decomposed into R3c and R3m components. The result- 
ing symmetry R3 also gives distinguishable B and B' positions via its R3m component. 

Although the distinction between these possibilities has been determined in only a few cases, it appears 
that R3c can be anticipated unless there is a physical reason for creating two distinguishable positions B 
and B'. This conclusion is based on the fact that LaAlOg has been shown to have the symmetry R3c by 
neutron diffraction, [Del 4] nuclear quadrupole resonance [MuS], electron-spin resonance, [Ki3] and x-ray 
techniques [Ge 4b, Del 7]. It is strongly supported by the observation [Ra3] that LaCoOs has the symmetry 
R3c at low temperatures, where all of the trivalent cobalt are in their low-spin state, but has the symmetry 
R3 at higher temperatures where thermal activation creates a nearly equal population of high-spin and 
low-spin cobalt ions. These are crystallographically distinguishable, via different ionic radii, as B and B'. 



Goodenough/Longo 



3.1 ABXs Perowskit-Struktur 



[Lit. S. 275 



3.1.3 The influence of localized-electron ordering 
3.1.3.1 Crystal-field theory 

Crvstal-field theory rests on the assumption that the outer electrons to be described are localized at 
discS lmIc ^."^7ons. This assumptio^n is valid for outer / electrons xt .vahd '^^'^'^^^^^^^^ 
fluorides and in many oxides. Given this assumption, the Schroedmger equation = £ v that describes 
the locaUzed orbitals and their energies contains the Hamiltonian 

= + F„ + Fe„b + (Vls + Vncub + V,+i: Vii) (2) 

i,.r. 3^ ;<= the Hamiltonian for a hydrogen-like, spherical potential. is the atomic correction for 
I where ^ . is thkn one outer d electron, and V^^ is the energy correc- 

Zl ui^.. I» the c^ ol 3l el«.r,». .h. pe,.u,ba.,o„s .jKd ^^t^.l'Zi 

and azimuthal-angular-momentum quantum number m denved from L,/ ^ ^ih^m - mhf. 



/a 

(/d ± ih) 
(/b ± ifc) 



2(zx ± iyz)lr^ = sin 26 exp(±i^); 
f^x^^y2j^i2xy)lr^== sin^ 0 exp (±i2^) ; 



m = 0 
m = ±2 



(3) 



or*. r^Wf-d to as / orbitals The principal contribution to the cubic-field spiitung i"/^4 
i S £ enerS fsTfdu: " cSvatnt mixing.'not to electrostatic energies as calculated on a pomt- 

' cLrg'e modd' H covalent mixing with the near-neighbor anionic and A-cation.c orbitals is introduced, 
then the crystalline localized orbitals of t,^ and symmetry become 



Ve = ^e{/e 



-1- Aa^a) 
h<i>>- ^ah) 



(4) 



where /. and /. are linear combinations of the atomic U fu.h and A. /b "'"i' Wofal'eS 
lanioniclsaVorbita^are, jan^^^^^^^^^^ 

1 SEn^onsTn^^^^^^^^ energy separation. Initially, the energy separations of 

' ca'LS airrorVaregiv'^nby^ - E, the difference between the Madelung energy and lomzation 
potentials for the "effective" ionic charges, so that by symmetry 



lODq = zIm + (^a - 4) (£m - ^i). < 



(5) 



1 where Au is any electrostatic contribution to 10 Dq. The one-electron crystal-field 'P^^^^'^f.fJ^^^-^^^ 

occupancies by unpaired spins of the 2s. 2p^. and 2p„ orbitals are: 

fx, ^ 2SAJA,, ~ NU. fx„ = 2SAJA,, ~ NUl fx„ = ISAJA^^ ~ N^^^ 

where is the isotropic component and A„. A„ the anisotropic components of the ^y^^^^^^^^l^^^^^ 
tensor A^ entering the nuclear spin-electron spin coupling energy S.^ • A,j - Interpretation 
phenomenological parameters A.. A, and 10 Dq has been discussed f^^'^fl^" responsible 
With more than one outer d electron or d hole, it is necessary to introduce 7ei, which >s r«2°trons 
for Hund' highest multiplicity rule (highest net S and Z.) for the ^ree atoms^ For four ou^^^^^^^^ 
the atomic ground term is therefore 'D. In a crystal, this rule may break down as a result of the crystalline 



136 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABXg perovskite structure 



fields. Schematically, the Hund splitting Jei ^or states of different spin and the one-electron splitting 10 Dq 
may be represented on the same energy diagram, as sho\vn in Fig. 7(b). It follows from this figure that 
with four to eight outer d electrons, the magnitude of the net ground-state spin depends upon whether 
(Jei — 10 Dq) is positive or negative. If A^x > 10 Dq, the ion is in a high-spin state; if A^x < 10 Dq, 
Pa 




4 



'3 



r 0 along carksion axes 
maxima on cartesian axes 



Afom 



Effech'ye 
point 
ckrge 



IS 

Crysfal 
field 



Fig. 7. 



One-electron crystal-field splitting of the d-state manifold of a transition -metal B cation in a cubic perovskite: 
= 0 and b) schematically for ^ei 7^ ^* corresponding to more than one outer d electron. 



Hund's rule breaks down and the ion is in a low-spin state. Since Zlei decreases with larger radial exten- 
sion of the crystalline wave functions, it decreases with increasing covalent-mixing parameters X^, Ajj. 
Simultaneously, from Eq. (5) it follows that 10 Dq increases with increasing covalency. Therefore there 
is a critical amount of covalent bonding beyond which Hund's rule breaks down. Covalency with a 
particular anionic sublattice increases with cationic charge and on going to the right through any long 
period of the periodic table. In oxides with the perovskite structure, only divalent and trivalent ions of 
the first long period are high-spin. Of these, trivalent nickel is low-spin and trivalent cobalt exhibits a 
variable high-spin to low-spin population as a function of temperature. 

In general, it is necessary to use a multi-electron notation for the outer d electrons. Whereas atomic D 
states are split by the crystalline fields as shown in Fig. 7, atomic F states are split as shown in Fig. 8. 



Jigiei^ cos^or + //sin ^cc ) 




JjQ ( t^^zQs^cc- e'^i^sln^ccj 



Fig- 8. 



a 2 Electrons b Z Holes 

Octahedral-site splitting of atomic F states: a) two-electron 'F states and b) two-hole states. 



Because the operator = -~ihd\d^ is imaginary, the crystal-field splitting of /g and /c quenches the 
orbital angular momentum associated with these orbitals, so that the orbitals have m = 0, 0 and the 
orbitals have m = 0, ± 1. An isomorphism between /c, /d. /e and atomic F orbitals simplifies calcula- 
tion of Vi,s* It is possible to treat the t^^ orbitals as atomic P orbitals if the sign of the spin-orbit-coupling 



Goodenough/Longo 



137 



3.1 ABX., Pcrowskit-Struklur 



[Lit. S. 275 



parameter A is reversed [Gr9]. Therefore ground states having an orbital degeneracy and m 0 arc spUt 
by Vls irit^ (2/ -f 1) multiplet states corresponding to states of different / = -f S. However, the 
order of the levels is inverted (largest / lowest for less than five d electrons, smallest / lowest for more 
than five d electrons) because of the change in sign of A. According to the Lande interval rule, the separa- 
tion between states / and / + 1 is | A | (/ 1). The first-order multiplet splittings, which do not include 
mixing of higher states of similar symmetry, are shown in Fig. 9 for Fe^+ and Co^^ ions. Note that the 
term is now identified by its symmetry character or 7,^ rather than by its atomic orbital-momentum 
character D or F. Tab. 1 summarizes the various symmetry notations for different spin states. 




I'ig. 9. Schematic spin-orbit plus trigoiial-ficM, or tctraguual-ficld, splittings of cubic-field levels as a function of the 
ratio 6I{ - A) for a) 'T^^ level of Fe*- and b) *T,^ level of Co'^". 

Spin-orbit coupling introduces an axial symmetry to the charge distribution, where the spin (or 
atomic-moment) defines the axis. Therefore, if there is a noncubic component to the crystalline field 
(Vncub 7^ 0), then there is a spin-lattice interaction via the orbital-lattice interaction that introduces a 
magnetic anisotropy. For localized electrons, this is a local, one-ion anisotropy. Conversely, if the spins 
are ordered below some transition temperature, then the local interstices have time to relax about the 
noncubic charge distribution, thereby distorting the octahedral site. Therefore there is an intimate 
connection between the noncubic symmetry and the magnitude of the multiplet splitting. The noncubic 
component is usually parametrized as 

Kncub - '5(^1 - I). W 

and I'ig. 9 includes the total j^crturbation Vj^s + l^'ncub of the oiic-elcctron and two-electron ground states. 

With one or two holes in a half-shell, the one-electron and two-electron energy diagrams are inverted. 
In these cases = TiWi = 0., so that V^s = ^> and there is no multiplet splitting. 

Tab. 1 also displays the general ground-state wave functions for a magnetically ordered phase having 
collinear spins. The coefficients a^, a^, of the Kramers' doublets and b^, of the singlets all depend 
upon the relative magnitudes of the five perturbation terms Vj^s + ^ncub + + -^z where is 
the Zeeman energy due to the internal molecular field resulting from magnetic order. The molecular- 
field approximation is used for the first-order, isotropic magnetic-coupling energy J^f' ex, which is the 
dominant term in E [see discussion of Eq. (13)]. This gives 

y^z «2/p <5>S, (7) 

where /p. the sum of all near- neighbor exchange parameters, can be determined from the temperature 
dependence of the magnetic susceptibility and z is along the axis of the average spin <S> on the neighboring 
cations. This term contributes to the spectroscopic-splitting factory, and hence to the net atomic moment, 
if Vls ^ 0- III Tab. 1, the components of the wave functions are designated by the notation \Mi, Mg >, 
where M^, Mg are the azimuthal quantum numbers for the net orbital and spin momenta. 



138 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX;j perovskitc slructur" 



13 
O 

-d 

O 

o 
d 

d 

*> 
aJ 

jci 

O 



d 
o 

o 
d 

0) 

> 



•d 

d 
o 



d 



o 



H 



A 



+ 

CO 



V 



CO 



3 



A 


A 


A 




T— < 




4- 




7 


7 


7 


7 









A + 
A 
l_o 

o 

^ o 

+ A 
A - 

+ ^- 

o + 



eg 

+ A 



A + 



A 

I 

T— < 



coHm O" ^ 'f*« - 

+ — o • ^ 



o - 
. A + o 



A A 

+ A + 



+ ^ O 

+ A 



_ o 



+ — ■ 

A 



o 



I 

T— < 



A ^ 

o + 



+ 



A A 



A 

+ 
7 

Af 
A + ^ A 



- - + 
+ + o (iq 



A 
o 

7 

CO 

A A 

o ' + 
£ + H — 

^ O - 8- 



+ - <r + 

+ A 

A <N 



A 



+ 

A 
4- 

, o o 
o ~- + — 

— ^ if 
« Dq o PQ 
4- « — « 



H5» Hw 

+ A + 



A 

I 

7- 



4- 



il 11 II II II II II II II II II II II 



m .n m ni ... >J _a CJ n fM 



Q [i< Q 



o 



d 



> 

in 

o 



+ 

s 

^" i K 

^ « R d 
> cj c5 ^ 



+ + I b \^ > 



^ CM CO t4- 



Goodenough/Longo 



139 



3.1 ABXg Perowskit-Struktur 



[Lit. S. 275 



3,1.3,2 Jahn-Teller distortions 

If the cubic-field ground state of the B cation is an orbitally two-f old-degenerate Eg state, then the 
t^g orbitals are either full or half-filled, so that Mi = 0, and there is no spin-orbit coupling (Vj^s = 0)* 
Jahn and Teller [Ja6] have shown that, if there is no perturbation available to remove a ground- 
state orbital degeneracy, then there will be a spontaneous distortion to lower local symmetry below some 
transition temperature ©trans < ^meii where Tmeit is the melting point. Since the energy gained by a local 
distortion is reduced by the work done against the elastic restoring forces of the crystal, transition tem- 
peratures 6^trans are small for isolated ions. However, if all of the B cations are similar, then cooperative 
distortions are possible, and the net energy gained per ion is much greater because of the elastic-coupling 
energy of Eq. (2). Such a cooperative phenomenon is characterized by thermal hysteresis and a definite 
(usually first-order) transition temperature. Since they are due to electronic ordering, such transitions 
are martensitic. 

Van Vleck [Fa/i] pointed out that the normal vibrational modes that split an electronic state 
are themselves twofold-degenerate with symmetry Eg. One mode gives the interstice a tetragonal distor- 
tion, the other an orthorhombic distortion. It follows that, from first-order theory, there is no static 
distortion of the interstice, only a dynamic coupling between the electronic charge density and the 
vibrational modes. Moreover, this dynamic coupling greatly enhances the two Eg vibrational modes and 
gives a dynamic splitting of the electronic Eg state. This mechanism has important consequences for the 
acoustic properties and, as discussed in 3.3, for the sign of the magnetic superexchange coupling. 

Inclusion in the theory of higher-order coupling terms and anharmonic elastic terms shows that a 
static, tetragonal (c/a > 1) distortion of the interstice is stable below some ©trans [KalO]. This sign for 
the static distortion was first established experimentally through the interpretation [Go/5] and further 
study of cooperative tetragonal- to-cubic transitions in spinel systems. However, application to the perov- 
skites requires a solution of the lowest-energy cooperative distortion via inclusion of the elastic-coupling 
energy V^. Goodenough [Go6] proposed that individual tetragonal (c/a > 1) octahedra order their long 
axes alternately along [100] and [010] axes of the pseudocubic cell. Kanamori [KalO] generalized this 
solution to include an orthorhombic component to the local-octahedron distortions. This gives B-B 
separations within (001) planes having a long (1) and a short (s) B-X separation and along the [001] axis 
two intermediate (m) B-X separations where s < m < (1 -f- s)/2. This prediction was later verified by 
Hepworth and Jack [He9] for □ MnFg and by Okazaki [Okt] for KCuFj (see Fig. 10). Superposition 
of this distortion on an O-orthorhombic cell stabilizes the unique axis along the orthorhombic c-axis, and 




140 



Goodenough/Longo 



Ref. p. 275] 3.1 ABX3 perovskite structur^ 



the axial ratios of the O-orthorhombic cell are transformed from a < < a. To signal the fact 

that a Jahn-Teller distortion (with or without spin-orbit coupling) has been superposed on a distortion 
due to relative ionic sizes, the notation O'-orthorhombic is used in Tab. 2 wherever cjVl < a. 

The important B cations that exhibit dynamic and static Jahn-Teller stabilizations in the absence 
of spin-orbit couphng are: Cu2+ Cr2+andMn3+ ''E^(tl^e\), Ni^^ 4). where Roman numer- 

als are used for the valence state of a low-spin cation. Tab. 2 shows that O'-orthorhombic symmetry 
above a magnetic-ordering temperature is associated with these ions, provided the electrons arelocaUzed, 
and only with these ions, with the exception of LaVOg and CeVOj, where sharply enhanced distortions 
appear abruptly below 9^ [RoS; G0IO]. The cubic ^T^^ state of V3+ is orbitally threefold-degenerate, so 
that it may induce small distortions above 0^- larger distortions below 0^ (see discussion Go/ 4). LaNiOg 
remains R3c because thee^ electrons are collective. In LaaLi^.jNio.jO^ crystals, on the other hand, the 
ordered Ni^^ ions have localized electrons, and there is a tetragonal [c/a > 1) distortion. The sign of 
this distortion is manifest by the large cja ratio. Strictly speaking, this is not a Jahn-Teller distortion, since 
the K2NiF4 structure is tetragonal, but ordering of the localized electron of unpaired spin in the tetragonal 
field distorts the Ni"^ octahedra to tetragonal symmetry with axes parallel to the unique axis. Pure 
Jahn-Teller distortions can be distinguished from distortions associated with spin-orbit coupling because 
they are independent of magnetic order and generally occur at a ©trans above the magnetic-ordering 
temperature. 

3.1.3.3 Spin-orbit coupling 

B cations having cubic-field ground-state terms T^g or Tj^ are orbitally threefold-degenerate with 
Ml, = 0, ±1, so that Vis 7^ 0. The combined perturbations Vj^s + ^ncub separate into secular equations 
for different Mj, as shown in Fig. 9. With a single outer electron, the ^To^ cubic-field term is split in two, 
the energies for different Mj shifting by 

^3/2 = 3 ^ — i ^- /g\ 

= -id -f jA ± i{<$^ + + iixy-v^' 

where A > 0. In a cubic field 

■£^3/2 = ^1/2 = ^1/2 — t^' 

and spin-orbit coupling leaves an orbitally twofold -degenerate ground state. Therefore it is necessary to 
consider an additional Jahn-Teller stabihzation via Kncub + l^A + -^^z* Goodenough [Got 4] has 
shown that it is necessary to consider two temperature regions: T > 6>n and T < 9^, where 9^ is the 
temperature below which the spins order collinearly. In the paramagnetic domain T > 0^. the molecular 
fields vanish (<S> = 0) and, from Eq. (7), Jffz = 0. In this case, the ground-state energy varies as 
(<52/A). Since the work done against elastic restoring forces is q^S^, there is a spontaneous Jahn-Teller 
distortion, corresponding to ^ > 0, at a ©trana > 6>n only if the product Xq^ is relatively small. In the 
magnetically ordered state (T < 9^), on the other hand, there is an internal molecular field Hint at each 
atom, which produces a Zeeman sphtting of the orbitals of different spin. The magnitude of this splitting 
depends upon the spectroscopic splitting factor, which has the components 

- 2 - 2g^(S|X) and ^j. - 2 -f g,{SIX) (10) 

where gi > 0. Therefore the Zeeman splitting in the molecular fields is maximized by making 6 <0 and 
having the spins parallel to the unique axis defined by S. Further, this energy is linear in 6, so that a 
spontaneous distortion should occur at some e^trana < A similar argument holds for the orbitally 

twofold-degenerate / = 1 and / = i states of octahedral-site Fe^^ ^T^g and Co^+ ^T^g. 

In summary, if multiplet splitting leaves a ground state with a twofold, accidental orbital degeneracy, 
then there is a spontaneous Jahn-Teller distortion at some ©trans that removes this degeneracy. If 
6>traiis > 6>N» then <5 > 0. However, this alternative requires special crystallographic conditions that do 
not appear to be met in perovskites. On the other hand, a Otrans < 9^ and d < 0 can be generally anti- 
cipated wherever the spins order coUinearly and the d electrons are localized. Further, from Eqs. (3) and 
(6), it follows that T^^ states (one outer t^g electron) have ^ < 0 if the site symmetry is tetragonal (c/a > 1), 
whereas T^^ states (two outer t^^ electrons) have 6 < 0 if it is tetragonal (c/a < 1). Alternatively, distor- 
tions of the site symmetry may be to trigonal symmetry. A <5 < 0 corresponds to <x < 60° for T^g states, 
to a > 60** for T^^ states. These relationships are also summarized in Tab. 1. Experimentally, Fe^^ ^T^^ 
octahedra become trigonal (a < 60°) below 9^, as exhibited by KFeFs, whereas Co^+ *T^g octahedra 
become tetragonal (c/a < 1) below ©n. as exhibited by KC0F3. Where 6^ = ©n, the magnetic- 
ordering temperature may be first-order. In addition, the spontaneous distortions introduce large magne- 
tostriction and magnetic anisotropy. 

The cubic-field ground state of ^Ti^ is orbitally threefold-degenerate. As a result, any sponta- 
neous distortion must correspond to 6 < 0, i.e.. tetragonal (c/a < 1) or trigonal (a > 60°). However, as 
in the other cases a ©trans < 6^ is to be expected in the perovskite structure. The V3+ ion generally 
occurs in an O-orthorhombic perovskite, and superposition of a tegragonal (c/a < 1) distortion with 
coincident unique axes again results in O'-orthorhombic symmetry. The perovskite LaVO, exhibits an 
abrupt contraction of the c-axis on cooling through ©j,- 



Goodenough/I.ongo 



141 



3.1 ABX, Perowskit-Struktur [Lit. S. 275 



3.1.4 The influence of collective-electron ordering 
3.1.4.1 Band theory 

Conventional band theory rests on three principal assumptions: (1) A description of the outer electrons 
may be built up from solutions of a single electron moving in a periodic potential. (2) Multiplet structure 
on individual atoms may be disregarded. (3) Electron-phonon interactions may be treated as a small 
perturbation. For an infinite crystal, the unperturbed solution of running waves in a periodic potential 
gives the Bloch functions and energies 

y>km = exp(i/c . r) «fcni(r); £ic = + ^=AV2m* (11) 

where hk is the momentum of an electron of effective mass m* and Wfc(r) is a periodic function. In the 
tight-binding approximation appropriate for narrow bands, the Bloch functions arc 

N 

VkW = ^IV^ ^'^'^P {^'^ • "~ 

u- 1 

whore w(r - il^) is a localized wave function for the atom at defined by 

zv(r~n,,) - \I^N~Eoxp [in - (r - M 

n 

and Uk(r) is a localized crystalline orbital. At the Brilloin-zone boundries defined by 

21c- K + |K|2 = 0, (12) 

where K is a reciprocal lattice vector, there are energy discontinuities in energy-momentum space. In 
polar insulators, this introduces an energy gap between occupied, primarily anionic states and empty, 
primarily cationic states. Cooperarive displacements d of the cationic sublattice relative to the anionic 
sublattice may increase this gap, thereby stabilizing the total energy of the occupied states by e^d\ Since 
the resultini? elastic- strain energy is q^d-. there can be a spontaneous displacement only for the exceptional 
case ^2 < £o and a ground state corresponding to a small distortion parameter <5, In this case vibrational 
entropy may stabilize the higher symmetry at the higher temperatures. This differs from the usual 
criterion for spontaneous distortions, where a term linear in 6 is identified. There appear to be two situa- 
tions occiiring in perovskites where the requirement < is met: (1) Where B-cations have empty d 
orbitals there is a critical range of covalent-mixing parameters through which the site preference changes 
from octahedral to tetrahedral. In this range q^ is very small for B-cation displacements withm an octa- 
hedron that reduce the coordination number from six towards four. The origin of the small is a balance 
of the electrostatic energy lost and covalent-bond energy gained on going to smaller anion coordination. 
(2) The high polarizability of the outer core electrons of Pb2+ and Bi3+ ions makes 7, relatively small, so 
that displacements that permit a relatively large can occur spontaneously. 

What distinguishes these spontaneous distortions from those due to an ordering of localized electrons 
is the displacement of the cations from the centers of symmetry of their interstices. (The Jahn-Tellcr 
distortions, with or without spin-orbit coupling, leave the cations in the centers of symmetry of then 
interstices.) Unlike the structures, such as corundum, where pairs of octahedra share a common face, 
these cationic displacements from the centers of symmetry of their interstices do not follow from point- 
charge electrostatic arguments. In polar insulators, these displacements lead to ferroelectricity or anti- 
ferroelectricity and they often induce displacements of neighboring cations. Further, where the require- 
ment q.. occurs just above etntns, there must be a strong interaction of the bonding (mostly amonio) 
electrons with those vibrational modes that anticipate the cooperative ionic displacements below 6>tran3. 
These "soft" vibrational modi.-s im])art several anomalous physical properties, incl^^<li^.^- a hif<h electric 
SMSceptibilily. 

3.1.4.2 Distortions due to B-X bonding 

Transition-metal cations having no outer d electrons have the following site preferences: 
Sc^i Ti*+ V^*" Cr«' Mn'^ 

Y3i Zr^+ Nh^+ Mo«+ Tc'+ 

Hf*+ Ta^'- W^ Re':^; 

where cations at the left of each row have definite octahedral-site (or larger anion coordination) preference 
and those to the right have definite tetrahedral-site preference. Those underlined by a solid hne may be 
stabilized in the octahedral sites of a perovskite-type structure, but they tend to induce spontaneous 
ferroelectric or antiferroelectric distortions, the ions moving cooperatively out of the centers of symmetry 
of their interstices. The ions undedined by dashed lines only occur in ordered perovskites AgBB and 
A3BB2O9. In general, they are found in tetrahedral sites or in strongly distorted octahedral sites. How- 
ever, in the ordered perosvkites they are able to strongly polarize the anion near neighbors so as to stabilize 
the octahedral symmetry. 



142 



Goodenough/f .ongo 



275 



Ref, p. 275] 



3.1 ABX3 perovskite structure 



It is significant that spontaneous^ ferroelectric distortions are only induced by B cations if these are 
transition-metal cations having empty d orbitals. It is also significant that the change from octahedral- 
site to tetrahedral-site preference is associated with a relative stabilization of the d orbitals (larger atomic 
number in any long period) as well as with a decrease in ionic size. (The ionic radii decrease in the order 
YS+ Sc3+ Hf^+ Zr^+, Ta^+. Nb^+, Ti*+, W®+. Mo^"'-, Re'+, Tc'+, Cr®+, Mn'+). The greater the relative 
stability of the d orbitals, the larger are the parameters and of Eq. (4), and these are enhanced by 
any displacement that decreases a B-X separation. Such an enhancement stabilizes the occupied states 
at the expense of the d states, and a net stabilization can occur if the d states are empty. Also the smaller 
the cationic size, the smaller the elastic resistance to displacements within an octahedral interstice. (Pho- 
nomenological ionic models for the ferroelectric distortions have also been given \_Me7, Ha33\) 

There are three B-cation displacements relative to their octahedral interstices that would simulta- 
neously stabihze the occupied anionic p^, orbitals relative to the unoccupied t^^ orbitals: (1) Tetragoiial 
symmetry. Displacements along an [001] axis that create alternate long and short B-X distances along 
this axis would stabilize s, and the two p^ orbitals per anion on this axis and strongly polarize the 
charge density toward the short B-X separation. (2) Orthorhombic symmetry. Displacement along a [110] 
axis that created two shortest and two longest B-X distances would stabihze the s, p^ and the two pj, 
orbitals per anion on tvs^o out of the three cartesian axes. (3) Rhombohedral symmetry. Displacement 
along a [1 11] axis would stabilize the s, p^ and the two p^ orbitals per anion on all the anions. These three 
possibilities are illustrated in Fig. 11. 

Such distortions also induce changes in the A-X separations, and the particular cooperative distortion 
that is stabilized depends upon the character of the A-X bonding. The covalency contribution to the A-X 
bond increases with formal A cationic charge; for a fixed charge it decreases with increasing atomic 
number of the A cation down any column of the periodic table. If A-X covalent bonding is relatively 
strong and the perovskite is distorted to O-orthorhombic symmetry, all ferroelectric distortions may be 
quenched because the p^ orbitals are stabilized by a-bonding with the A cations. This appears to be 
illustrated by CaTiOg, and almost so by SrTiOa. On the other hand, if the A atom is stabilized by a 
polarization of its outer core electrons (Pb2+ and Bi3+ as discussed in 3.1.4.3), then a tetragonal, ferro- 
electric distortion is stabilized so as to allow a cooperative displacement of the A and B cations, the A 
cation moving along the [001] axis to stabilize two p^ orbitals per anion not on [001] axes. This is illustrated 
by the PbTiO, structure of Fig. 12. If the covalency contribution to the A-X bonding is relatively weak, 
then the B-X covalency contribution should dominate. For large A cations (t > 0.9). this would stabiUze 
a ferroelectric, rhombohedral distortion at lowest temperatures, as illustrated by BaTiOs- As the tempera- 
ture increases, successive distorted structures (R^-^ Og Tg C) introduce incremental additions to 
the entropy. However, a small A cation and weak A-X covalency contribution may lead to a ferroelectric 
distortion superposed on the O-orthorhombic structure to give the OJ-orthorhombic structure of CdTiOj 
orNaTaO^showninFig- 13. Even more complex distortions arc found in NaNbOj [Vo6\ The room-tern- 



9 
6 

Cubic 



9 



Jehagonol 



9 



9 



Mho- 
rhomtic 



Rhombo- 
hedral 



4<— -ol — 




Fig. 11. Possible B-cationic displacements within tlicir 
octabctlra in ferroelectric or antiferrfK^lcctric distortions. 




00 0 Cd • Ti 
a 



O 0 ® No • To 
h 



0^1 

ink 




Fig. 13. Ionic displacements in a) Cd TiO^ and 
b) NaTaO, \Ka22\, 



Fig. 1 2. Tetragonal PbTiO, : a) environment of Ti 
and b) environment of Pb [S/t2/]. 



i 



Goodenoiigh/I.ongo 



143 



3.1 ABXs Perowskit-Struktur 



[Lit. S. 275 



perature form has parallel pairs of (001) NbO, planes coupled antiparallel to give an antiferroelectric phase, 
as shown in Fig. 14. The Na atoms are also displaced antiparallel to one another. 

3.1.4.3 Distortions due to core polarization : Pb*+ and Bi*+ 
Lead and bismuth are heavy ions, and the 6s orbitals are sufficiently more stable than the 6/> orbitels 
that Pb»+ and Bi^+ ions are commonly stable. However, the outer 6s^ core electrons have a relatively 
large radial extension, making the ionic radius large, and this reduces the overlap of the 6^ orbitals with 
the orbitals on near-neighbor anions. This reduction in overlap reduces the strength of the A-X bond. 
However hybridization of 6s and 6p orbitals. which costs the energy separation of 6s and 6/. orbitals, 
produces'a polarization of the outer-core electrons, so that the effective ionic radius is much smaller on 
one side of the cation than on the other. This permits the formation of a much more stable bond on one 
side of the cation, and the energy gained in this bonding may be greater than the hybridization energy 
required to polarize the core. It is for this reason that Pb«+ and Bi'+ ions are stabilized in many crystals 
with an asymmetric anion coordination. ,j ^ , ... ... ■ >, „.-k;+,1c 

There are three possible displacements of the A cations that would stabihze the amon p orbitels 
(which a-bond with the A cations) : (1) Tetragonal symmetry. Displacement of the A cations along [001] 
axes to stabilize the two/., orbitals per anion not on [001] axes, as found for PbTiO, (see Fig. 12). (2) Ortho- 
rhombic symmetry. Displacement of the A cations along [110] axes to stabilize strongly one p orbital per 
anion on [001] aies and less strongly one p„ orbital per anion not on [001] axes The sma est induced 
distortion of the B-cation octahedra occurs for an antiferroelectric displacement of the type illustrated by 
PbZtO, Fig 15 (3) Rhombohedral symmetry. Displacement of the A cations along [111] axes to stabilize 
strongly one orbital per anion. To be cooperative, such a distortion must be ferroelectric, as m BiFeO,, 
Fig. 16: Further, since the A cation is moved toward a B cation, there is an electrostatic repulsion between 
them that displaces the B cation from the center of symmetry of its interstice 

Given spontaneous distortions due to A-cation displacements, there remains the possibility that elec- 
tron ordering among localized d electrons on B cations can superpose an additional distortion. Whether 
this is the origin of the triclinic symmetry reported for ferromagnetic BiMnO,. where Mn»+ is a Jahn- 
Teller ion, is not known. 






^\^^ O 0 • Nb ® Na 

X 

Fig. 14. Ionic displacements in orthorhombic NaNbOj. The 
shifts of the anions in NbO, planes and the small t shifts of 
the Nb ions have been omitted for clarity {Vo6\, 



Fig. 15. a) Pb-ion shifts ( f«0.26 A) in a (001) plane of anti- 
ferroelectric PbZrO,. b) Distorted Zr octahedra as a result of 
simultaneous anion displacements, Zr-0 distances are given 
in [A] \Sa8, Jo5l 



144 



Goodenough/Longo 



Ref. p. 275] ABX3 perovskite structure 



3.1.4.4 Competitive phases 

A few compounds have atomic radii compatible with the formation of a perovskite phase and yet 
are stabiUzed in other structures at ordinary temperature and pressure. Two important competitive 
structures of this type are represented by YAIO3 and PbRuOg. Both of these compounds convert to 
the perovskite structure under hydrostatic pressure. 

The hexagonal YAIO3 structure of Fig. 17(a) consists of close-packed layers havmg the sequence 
b-a-b'-a-b-c-b'-c-b. where b is an A-cation layer, 6' is a B-X layer with anions stacked beneath A cations 
(6 stacking) and B cations in the trigonal bipyramids formed by face-shared tetrahedra in the hexagonal 
a-b-a or c-b-c anion-stacking sequence. The structure apparently forms because both the A cations and 
the B cations simultaneously approach the lower limit for cationic size: = 0.51 A, = 0.90 A, The 
small AP+ ion is relatively stable in the five-fold coordination of the trigonal-bipyramid sites, and the 
small Y3+ ion is more stable in an eightfold (or 6 + 2) coordination instead of a twelvefold (or 9+3) 
coordination. These site preferences reflect an increased stabilization of the bonding, anionic orbitals as a 
result of closer cation-anion distances. 

The antiferromagnetic. ferroelectric compound YMnO^ has a similar structure, but with an a-axis K3 
larger than that of YAlOsto give six molecules per unit cell. The Mn'+ ion can be stabilized in a trigonal- 
bipyramid site because it has four outer electrons with configuration ele^al where the empty a, orbital 
is directed along the c-axis to bond covalently with the two coUinear oxygen ions. The larger unit cell 
and the ferroelectric! ty are reflected in the complex magnetic order shown in Fig. 17(b). Below 
exchange striction favors antiferromagnetic Mn-O-O-Mn interactions. The ferroelectric transition that 
occurs above 600 X is apparently due to the relatively large size of the Un^+ ion, which creates a large 
enough interstice for the ion that it is stabilized by a displacement from the center of symmetry of its 
interstice so as to lower its near-neighbor anion coordination from eight toward seven. 





• Bi ■ Fe O 0 

Fig. 16. Structure of BiFeO, showing displacements 
in perovskite subcell [MiO]. 



QO @Y •Al.Mn 



Fig. 17. a) Comparison of the unit cells of YAIO, (solid lines) 
and YMnO, (dashed lines), b) Magnetic structure of VMnOj 
[BeS6, BeS9]. 

a = 3.678 A, c = 10.52 A for YAIO3. 



Cubic PbRuOa gives an x-ray pattern of the pyrochlore structure, corresponding to chemical formula 
AaBgOy and therefore may be written as PbgRuaO^©. This structure is competitive with the perovskite 
structure in several PbB*+ O3 compounds. It has been shown [Lo4] that the anion vacancies © are located 
at the centers of Pb^^-ion tetrahedra sharing common corners and that the electrostatic repulsion between 
the Pb ions may be counteracted by a transfer of the two outer-core electrons per Pb ion to the © sites, which 
act as traps for four electrons per vacancy. Thus, the outer core electrons at the Pb«+ ions induce a com- 
pletely new structure rather than a ferroelectric-type displacement of the A-cations within the perovskite 
structure This new structure contains B cations in corner-shared octahedra, as in perovskite, but the 
B-X-B angle is reduced to about 135°. This structure is also stabilized in AgSbOg [Sc22] presumably 
because there is a small effective charge on the Ag+ ions. The pyrochlore AgB^O, structure itself is compet- 
. itive if attempts are made to force a low valence state on one of the cations. 



LandoU-Bftrnstf^in, None Scric; Tll/'la 



Goodenough/Longo 



145 

10 




/ 



3.1 ABXg Perowskit-Struktur [Lit. S. 275 



3.1.5 Structures encountered with ordered B, B* cations 

3.1.5.1 Same B atom 

There are three ways of creating two different cations from the same atom : 

(1) Two A cations of different valence can create two different valence states of the same B atom, 
and these may order at lower temperature as a result of different cationic charge. The ordering temperature 
may be quite low. since only electron transfers are required for cationic ordering. This is illustrated by 
(LaojCaos) (MnJt Mn*+)03, which has the Mn^^, Mn<+ ordering in a rocksalt-type array. Because 
Mn3+(/JgeJ) is a Jahn-Teller ion having localized outer d electrons, there is also a cooperative distortion 
to tetragonal (c/a > 1) symmetry of the Mn^^-occupied octahedra, and the ordering of these distortions 
gives a macroscopic distortion to tetragonal (c/a < 1) symmetry (see Fig, 26). 

(2) Where the energy difference between the high-spin and low-spin states of the B cation are nearly 
equal, the populations of the tw^o energy states approach each other at higher temperatures. In LaCoOg, 
high-spin Co^^ and low-spin Co™ are separated by only - Em ^ 0.08 eV, and the populations of the 
two spin states are nearly equal at 400 °K. This temperature is sufficiently low that ordering ofjhe two 
different spin states occurs above this temperature, and the symmetry changes from R3c to R3 [Ra3]. 
In this case, it is the difference in ionic size and covalent bonding, which results in a difference in the 
effective ionic charge -not the formal ionic charge— that is the driving force for the ionic ordering. 

(3) Disproportionation of B°^+ cations into B^"*-!*-*" and 3^°^+^'+ cations may create ions of different size 
and charge that become ordered. This is illustrated by DPaFa, which has been shown by magnetic 
susceptibility measurements to be Pd2+Pd^F6[i?a/ 5?]. (The A cation is missing.) Such a disproportiona- 
tion permits the formation of (PdFJ^" clusters in which the anionic orbitals are stabilized by strong 
covalent mixing with the a-bonding orbitals of % symmetry. This is accomplished by a shifting of the 
F- ions toward the Pd^+ ions and away from the 'Pd^+ ions. Simultaneously, the anionic shift reduces 
covalent mixing in the occupied, antibonding 4d orbitals of symmetry at the Pd2+ ions. These orbitals 
are therefore localized and further stabiUzed by intra-atomic exchange (Hund spUtting), so that each Pd2+ 
ion carries an atomic moment of 2yL^. Were there no disproportionation. the single electron per-low-spin 
Pd™ ion would occupy antibonding orbitals that were more unstable than the occupied, localized 
orbitals at the Pd2+ ions. However, the transformation 2 Pd"^ Fd^+ -f Pd^^ costs ionization energy, 
and this is usually too large (as in LaNiOj) for disproportionation to occur. 

3.1.5.2 Different B atoms 

There are many examples of ordered B, B' structures in compounds having different B atoms: 
AfB+B'^+Fg; A|+B3+B'^+Oe, Ai+B^+B'^+Ofi. A^+B+B'^+Oei Al+B^+B'^+O^, Af+B+B'^+Oe.and Ai+B^+B'^+O^. 
IntheAgBB'Xg group, ordering is on alternate (111) planes of B cations, in the AgB^B'Xg group the B' 
cations occupy every third B-cation (111) layer. Fig. 1 (c). The probability for an ordered arrangement 
of the B. B' cations is determined by the differences between their ionic charges and their ionic radii 
[Fe22 Fe23, Gal, GalO]. To first approximation, the order-disorder transition temperature ©ord induced 
by the charge difference = (q' - q) at cations B' and B is Oord - (A?)'- Thus superstructure has 
been observed in all the known compounds having ( A^)^ = 36 and 16. whereas those having {^qY = 4 are 
disordered unless there is a relatively large difference in ionic sizes. The minimum difference 
in ionic size that results in ordered Ai+B^+B'^+Og compounds is I^b - ^^b'I/^b ^ 0 09, and this has 
been achieved where B* - Nb or Ta, having empty d orbitals for the formation of stable (E'C^)' 
clusters, while the B cation has no relatively stable, empty d orbitals. 

Given the formation of (B'X^) octahedra. a confusion arises as to where the structure corresponds to an 
ordered AgBB'Oe perovskite built up of corner-shared octahedra plus A cations and where it corresponds 
to the isostructural (NH4)3FeF6 structure, which consists of discrete (B'X^) octahedra separated by A and 
B cations. (The cubic K^NaAlFg structure with space group Tj(Pa3) is similar to (NH4)3FeF6. but has a 
lower symmetry because there are very small rotations of the (B'Xe) octahedra.) Some authors [Fe22] 
select as a criterion for the perovskite structure the cationic radius ratio ^b/^'a < 0.8 where > rg. . This 
decision is based on the observation that a plot of the cubic lattice parameter vs. B-cation radius is a 
straight line for t^/rj, < 0.8. but bends over for r^/rj, > 0.8. However, this probably reflects the ratio at 
which electrostatic forces inhibit (or reverse) any A-cation displacements rather than the ratio at which 
discrete (B'Xg) octahedra are formed. For most physical properties this criterion is probably arbitrary. 

Without electron-ordering distortions superposed on the size effects, ordered AgBB'Xeperovskitescan 
be described by either the 0-orthorhombic cell of Fig. 5 or by the rhombohedral R3 (or R3m) cell of Fig. 6. 
Where oc = 60°, a tetramolecular cubic cell may be chosen provided the A cations are not displaced from 
their ideal positions. Like cubic (NH4)3FeFg, the cubic cell has the space group 0| (Fm3m) with B cations 
in 4(b) (iii); fx.. A cations in 8(c) ± (J. J. J); f.c. B' cations in 4(a) (0, 0. 0); f. c. and X-anions in 
24(e) ± (u. 0, 0; 0, u, 0; 0. 0, u); f.c. with 0.2 < u < 0.25. However, even where a = 60°, motions of the 
A cations along the [111] axes may occur, thereby destroying the cubic symmetry. 



146 



Goodenough/Longo 



Ref. p. 275] 3.1 ABX3 perovskite structure 



If an electron -ordering transition superposes a distortion at every other octahedron of Fig. 5, either the 
B or tlie B' octahedra remaining cubic, cooperative elastic interactions between the distorted octahedra 
give a further reduction in symmetry. The resulting monoclinic cell [Fi9, B18], which is pseudotriclinic, is 
not to be confused with the pseu do monoclinic symmetry reported in early work for the O-orthorhombic 
structures. The origin of the superposed electron-ordering transition could be either a Jahn-Teller ordering 
of localized electrons or a ferroelectric-type displacement of the anions about a (B'X^) octahedron. 

Several CaaB^+Ta^+Og and SraB^+Nb^+Og perovskites having B = rare-earth atom exhibit the mono- 
chnic symmetry of a distorted O-orthorhombic cell [FiS]. Since the 4/ electrons at the rare-earth ions are 
localized, it is tempting to attribute this to a Jahn-Teller distortion with spin-orbit coupHng. Although 
Fig. 9 shows that the octahedral site splitting of one-electron 4/ orbitals gives orbitally threefold-degene- 
rate levels having an accidental degeneracy that is not removed by spin-orbit coupling, nevertheless there 
are two reasons why this explanation cannot be correct: (1) There is no magnetic ordering of the 4/ elec- 
trons at room temperature and (2) SrgGdNbOe shows the distortion even though Gd^+ has a half-filled 4P 
shell, which has no orbital degeneracy associated with the ground state, Itis therefore concluded that the 
additional distortions are due to the potentially ferroelectric cations Nb^^ and Ta^+. 

3.1.5.3 Complex alloys AgBB'Xg, where B = M^g, B' := Mg 

Several complex interstitial alloys have a formal structural relationship to the ordered perovskite 
AjBB'Xg as well as interesting magnetic properties. In this group, having space group Fm3m, the B posi- 
tion is occupied by a thirteen-atom cluster consisting of a metal atom at position 4 (a) at the center of a 
cubo-octahedral, twelve-atom cluster of M atoms at positions 48 (h) ; the B' position is occupied by a simple 
cube of eight M' atoms at 32(f). The three principal axes of each cluster are along the cubic axes of the 
perovskite cell, as shown schematically in Fig. 18, so that each X atom at positions 24(e) has eight near 
neighbors. The eight A atoms of the tetra- molecular cell are at the 8 (c) positions. The 4(b) position at 
the center of the MJ clusters is empty. Alloys with this structure include the ferromagnetic borides 
Al2[(AlMi2)(M^)]B6, where M = Fe, Co, Ni, as well as Cr^fis- 




B-Mj3 B'^M^ B^Mfs 

Fig. 18. One quadrant of the A^BB'X, structure showing 
the atomic positions of the B = M13 and B' = m; clusters 



3.1,6 First-order magnetic transition in M^XMJ perovskites 

Many perovskites M^^XMj exhibit first-order phase changes at magnetic-ordering transitions. Most of 
these are reported to be cubic-to-cubic transitions, but in ZnCMng it is a tetragonal (ferrimagnetic)-to- 
cubic (ferromagnetic) transition. These crystallographic changes are induced by a complex interplay of 
collective electrons in overlapping bands. Because of the intimate connection with the magnetic proper- 
ties and because of the necessarily speculative character of any model at this time, discussion of these 
compounds is deferred to 3.5. 



Goodenough/Longo 



• 147 

10* 



3.1 ABX3 Perowskit-Struktur 



[Lit. S. 275 



3.1.7 Data: Crystallographic properties of ABX3, AgBB'Xg, AaBiBXg and A(B^B^B,)X3 
compounds with perovskite or perovskite-related structure (Tab. 2) 

Tab. 2. 

Within any section, the compounds are in general first ordered according to the atomic number of the 
B cation and then by the basicity of the A cation. For the ordered perovskites of Tab 2 b, c. d the com- 
pounds are further ordered by the atomic number of the other B cation. The order of the sections is as 
follows : 

Tab. 2a - ABX3 
A^+LiH^ 

A(Ufi) (Li,/3)3; A = l'\ Br-i 
A+B2+X3; X = F-^ Cl-i, Br-i 

A+B^+O,' B = V, Nb, Sb, Ta, I, Pa. U tt 
A2+B*+03; B = Ti, V. Cr. Mn, Fe. Co. Ni. Ge. Zr. Mo, Tc, Ru, Sn. Ce. Pr. Hf. Re. Ir. Pb. Th. U. 

Np. Pu 

A2+B*+X3 or A^+B^+X,; X = S or Se, B - Ti, Zr. Ta. In. Ga 

A^+B^+Og; B - Al. Sc. Ti. V. Cr, Mn, Fe. Co. Ni, Ga, Y. Nb, Rh, In. Ho. Er. Tm, Yb. Lu 
Tab. 2b - AjBB'Xs 

A BB^+X ; X = F-\ Cl-\ = Al. Sc, Ti, V, Cr. Mn, Fe. Co. Ni. Cu. Ga, Ag. In. Ce. Pr. Au, Tl 
A^+A^+B^+B^+Oe; B*+ = Ti. Ir 
AgBB^+Oe: B*+ = Ti. Mn, Ge, Zr, Ru, Ir 

B5+ = V. Nb. Sb. Ta, Bi. Pa. Pu 

B«+ = Mo. Te. W. Re*+.5+^ Os«+.5+, U«+'S+, Np«+, Pu«+ 
B'+ = Tc, Re. Os, I 

Tab. 2c - A3BBJO9 

AgBBl+Og; B^+ = Nb, Ru. Sb. Ta 

LagCogBs+Oe; B^^ = Nb, Sb 

AaBgB^+Og; B«+ = Mo. W. Re. U 



Tab. 2d - a2+(b^b;b;)03 



148 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



-a 

a; 

•§ 

6 



B - 

J3 '-' 



H 



li g 



CO 



o {3 

O 0) 

■5 0^ 



O 

■a 



d 
o 

a 

o 
o 

pct 
< 

H 



C3 *<1 



a 



O 

o 



2 



e 

c«-) 

a 
d 

en 

O 
Xi 



o 



O 

*^ 

^ ^ 



N 
c 



^^^^ 

I — irO O I — t 
C/) a +i C/) 



CM 
CM 

o 
CO 



CO C/3 

a P. 

ID (U 

U. 1-1 t-l 

tf) Cft r— < — ' 

K * y 

rilj ^ 

bO bp o 

rj C\| O 
CM 

w-1 oq .t: 

S S £ 

m c/i 



t; s o 

CN| [x. O O 

^Plh pu h ffi <d 



in 
[A 



^ 



CO 



1-1 



'^a- 

^ fN ^ ^ 



1^ 



lr^ u^ lr^ oo rt 

^ J5 ^ -s2 ^ 

O O O O >^ 



0\ ^ 
OQ >H 



o 



00 



in fO cvi GN 

t-4 r-; r-J 

Tt csi 06 cx5 



(N 



O 



T— < 

06 



O 

in 



o 



fTj vO vO 

<N m CN 

o 00 r~~ 

r«S r<S r<S 



T^- VO O ON 

O ^ T-< 

O ^6 CN 06 



C7\ 



CO c<» in ^ 00 ^ 
v£> Tf in ^ r-- Ln 

CN O (N CN 

in fo to ^ 



CN} lO \0 CTn 

in r- rn 
''j^ 06 uS 



pq 



t3 
C 

O 
P. 

a 

o 
U 



u 0000 00 o 



OHoaffio oouo ffi 



I 



-I 2 

s« CO 

< pq 



3 a u 3 

pq c)5 w pq 



X 
+ 

Cl 



bO 

;4 



bo 



|0D 

Sis 



o 

H 



Goodenough/Longo 



149 



3.1 ABXg Perowskit-Struktur 



[Lit. S. 275 



'tt) 



B 

>^ 
CO 



C 

O 
Oh 

S 
O 

O 



o 

u 
P. 



tuo 



CO O CO 
PL, g^PM 



- - - C\4 

O 



H^l J J 

X X 

O) O 4) °0 

ffi ffi ffi fx, 



X5 
O 



a) 
C 

o 

•-^ o 

CO Td 

^ g 



CO 



o 
o 



<a ■+J 

to ^ t/} 
1^ ^ rrC 

II o 



o o ^ 



X 2 - ^ 



r— . O 
I I ^ 

CD 

^ CO 



O 



1^ 



O 



05 



8 H 



oo 
A 



oo 
V 



fin 



V 

_ (in > ^ 



O 0^ o « 



o 



o 



JO 
CM 



CO 



\0 CX) 



CO 



CO 

< 



^ tn lo 



A 



Oo 
V 

to o ^ 



Oq Oq to 



^ 



00 



00 00 C^ ^ 00 

m 00 oor-i ofOiovocMoo 

oocN oo OnOCnOCMO o 

xoouS o6o6 r-^t^r^ooo^o lo 



\o o o 
ro o 

ro c<^ O 
o6 00 00 



oo CM 



00 

in 



in o o 

00 O o 

00 r- 

in in in 



CN oO"^ln^NT^c^ m 
ro-^o Ti-TfinTfcNmcN-^cn ^ 
csocN r-<o*-iinvocMi-<ojo 



00 



00 



inooo 00000-^ 

ooo^o cnmooo cs) 

oocNin cscMC^T-H o 

ininin rf-^r^K o 



Q K K K 



o oo ooPdffi H 



I 



X 
+ 

CI 

+ 



«H fly 

p:^ 



Z 5-HO« 



c 

CJ 



p^i 



c 



&HCJP:h 



150 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structu^ 



(L> 4-1 



Id 

B 

0) 



bo 



C! 
O 

S 

o 
U 



vo vO vO 



On 
o 

1 — I 

o 

O 



' — '00 



5^ A 



" — ' (0 *- - 



t-i ^ 



r— , O 
>- ri 

o O 
u 

in 



A V c 



W CO - 
* CO 

^0 



o CNi 

A 



o 

V 



' to 



ffi 



oo^C2 



o o 

00 

t-^ I — I 

II ^ 



to 
CO 

Oh 1-^ i-» 
^ X X 



O 0) ^ <N 

^ S to o - 

•43 (t> CO Ox H 

° QrC t3 V 

ct; Siti « 00 

S S " 

ffi ffi a, ^ 



a. 
o 



c 
bo 

e 



o 

II 



I 

^ ^ ^ ' 

>^ CN| < 

^ c| I 



<2) 



1^ 2 



6^ 



6 ^ 
o o 
-co 



<N CO 

;s 1^ -T — 

ft; cj ft; to t-l 

L_.i__n — i(M 0) C^J 

CO CO C/) W t M 

c« cy £ o £ 

pi, Plh K ffi 



CN, 

0 CO I — t ^ 

-3^.^01 CO 

t-J h-3 h-? 0) 
c^j <:7\ \o vo CL, 

W W « X ^ 

4) OJ (l> (D 

K ffi K K 



^ fyv tj 



o 



O ,'^r^t2, 

o Si; ^ " 
1^) ^- 

CO «^ 
CO oo" 

< .0 CO 



> CO ^ 

5 <^ ^ 

t I 

bo 4i" 

e 2 TT- 



•c 5 =^ 

O "h 00 
) ^ bp^ ^ 11 



d 

o 
o 



pq 



I 

it 

r. to 
< U 



Kef 9 
Lolb 
Wa12 


0 


0 fti N CO oq .3 0 


Vr. >- 

S ?^ s 5 ::t3 


til 


:S ;S ^ 
^ 0 0 ?2 

^ ft; 


15 ^ 

K 0 


0 






in 


















0 

00 


















II 














in 
in 

00 




0 in 0 

00 0000 


0 t-- 


ro 
0 


so 
On 
CT; 


in 

(N CM Tj- ^ 
CM fO in CO 






t— ( 








vd 


viS 


in oi rt^ 

T-H 










(N 

r- 


m 
0 

VO 
















in 


in 












00 CO ro 

in 00 
T-< T-i 


eg 


ooinr-oor^o^l- vocn 

OC\t~-OOcO>OCNCNT-iv£) 

T-JTl-T-Hi^CN)Or-<OT-iO 


0 

in CM cs) 

0 Tl- 


CO (N 
CO 0 
^ <N 


SO 
Cs 
Cs 


vO ro 
fO in tn '<4- 
CM th 0 00 


Tf in 
0 0 


c^^ 
0 
0 


VO Tj^ ^ 




Tfinr^-^Kt^NOvOTt^ 


Ti- in r- 


v6 


so so so in 






ffi 0 0 


0 




H 0 0 CJ ffi 




W ffi ffi ffi 


0 0 


0 . 



(It , " 
So 



o 



ti7 

c3 



Good enough/Longo 



151 



3.1 ABX3 Perowskit-Struktur 



[Lit. S. 275 



4) 



o 

I ( » — I 

CO cn 



t — ■ o 



<l> to 

=3 Cu 



CM 



PkCq ^ CM o 



K K ffi 



P I 



o 



O t 



' CD _ 



O ^ - 

2 ^' 



'—'00 ct; 
.2 II ^ 



o « 

o 
o 



o 

in 



I 

^ a? 
s +^ 



Oh 
S 

u 



s 



o 



c 
bo 



i5 ;5 ^ 



' 0) 



O ■ «* 



o ^ 



o o 



1-1 



» I - 

D >^ 
r: CJ U< 

E o 

^ " ^ 
o d 

lis 

S -d 



bo S 

do 



^ oq 



<^ Or! 



C o 

d 'oj 
o o 

R 

CL,o 

2 ^ 

12, O 



Oo U-v Xj. >^ 

s ;s o o 'ti 
ct; ft^ 



5^ 



c\ \o 

« s s 
oq ft^ (1^ 



V3 ^ >^ ^ ^ 



>^ ^ 

S o « « 

»^ cq CP tic; 



^^^^ 

S sL ^ o 



bo 
d 



Cn cn 



00 OCNO Tl-vOcO^vO vOfO 

00 r- ^ 000 \ocN'^ t-hcnoo\oo ro 00 int-- 

\o ro CN inoooo CNiTtr-ooo r- oco ono 

r-^ '^i^ uS N£?(N T-Jr-^r^ rnr-^r-^Koo 06 cicN cnt^ 



in 



t3 
0) 

d 



com CN CN 00 
gvOTj-r^ONO T-Hoo 



^ in T-t rn 
mom cnt-hcnooo 
mooo T-tooocM 



^ m 00 m Tj- r- 
t 

W 



1— ' v3 vo 



CN NO o NO m 

CM Nom oc\»-HCNm 

O 00 C^O^COO 

T^Tj^ <jNNO'<J-in'*1^ 



Tj- m Tj- 

o 00 m 

tJ- T— I Cn Cn 

in rn in 



Tt- m 



3 O O K O K 



I 



O U U K Ph o 



T3 

d 
a 
o 

S 
o 
o 



X 

ra 



a 
o 



u 
a 



D 1- 



to 

d 
Nl 

c3 



to 

d 
N 



to 
d 



nto « 

d p<i d 7 



152 



Goodenough/Longo 



. 275 



Ref. p. 275] 



3.1 ABX3 perovskite struct! 



bo 



S 



13 

a 
o 

6 



o 



o 

I — I 



o 

u 
+ 



O CM 
' — ' o 



-5 



C 0\ 

o ^ 

^ ^ § ^ 



CO 



O 



11 ^ vo:^ 

C/) ffi ^ 



to 

o o 

si 

CO 



>^ w> 



r5 o i:: 

CN CNj C\j fY^ - 

O O U^ to 



^ ^ ^ 
000 



« « *S ^ ^ ^ 
^^^^^^ 



10 



00 

in 



in T-< 

0^ O 

CO T-. 



00 O 00 
O O O T-t o 

(T) (N Tj- r-- 



00 r- 
in CN r- 



O CN 

00 r- th c\ c^ 
00 r- 00 in in 00 



OOH HOOKO OOU OOOHOO 



bo 



-C C/) 

o 



II o CI, 

cn to ' — • CX 

^ ^ 1^ 

O O Jh 

u 3 ^ 

<u rj ir* 

12; c/D 



OA 

HcM^in 
m II C/3 II 



o 

o « 

I + 

II ^ 

h< CM 



S to ^ 



00 



o 



o 
o 



CM ^ 

O O (M 



H O 0^ O 



X 

. CO 

CO CO 

0 U 



to 



CO 



cth X) X) 



HO O 



„ CO 

O ffl txj 

0 a ^ 
in t/mi 

cn c/3 CO 

u u u 



O fP ti^ O FQ 

ffi ffi Oh fl^ (1, 

cn cn CO CO to 

O O U U U 



o 

pq 
+ 



nXl O 



o 



Goodenough/Longo 



153 



3.1 ABXg Perowskit-Struktur 



[Lit. S. 275 



■ 0) 



be 
C 

nJ 



d 

O 

e 

o 
O 



IrC ^ 125 I— ^ 

' in 



V-t » - 

53 ^ « 



(-1 e 

I 

o 



^ OS 



1-. t-j • 



o 
o e 

^3 to 

o 



. . 1-1 
to 3 



*^ Q 
^ to 



O *N 



.6 



O p 



O o «i * 



CO ^ t/i Q 



^ cy 



S - - 
'^^^ 

^^.^ 

H <o ^ 
o O O 

G) . , 
'OJ ^ 



a 

o 



CO 

r— I 

o 

:^ 



o 

o 

O 

A 
h. 

A 
o 

CO 



3 c 

to 3 



O CO 

I, — r"" 



o 

.9-0, 



6 



C4 • — 



. .O 

hs. (O 

„ to vO 

a a> . Al 

^ 5 



So 



^=^gco 



00 

A 

hi 

o 

O 

O 



CO 

0, 



^ 

CO CO o ^ 
pL, dl PLh 



S ^ (i, CO 



o 



o 



Tt CM lO O 
^ M (N 

o o o o 
O CN C\ 
00 00 OO OO 

II !l II II 



CD 
3 

G 
O 
o 



O 
+ 

in 

PQ 
+ 



15.518 


LLL 


7.782 
13.8631 
15.660 


4,51 


7.751 


13.783 


3.914 
8.94 


5.568 


5.57 


5.582 
7.888 




5.513 




7.862 
8.94 


5.505 


5.51 


ro 

OO oo 00 in 
(N oo Cv CM 

in T-i OO in co 
tn in cn o 


3.92 
3.9885 


5.494 


3.929 
5.154 


CM O O oo 

\o^r^"^"^^'~'00NO 
oocNomoN'^in^cn 

r-^fOTfTfooTtTfCN'^ 


O 


O 


o ffi § u o 


H O 


O 




^OCjp:iSp:^P^UO 



o 



o 

XI 



o 

XI 
CO 

< 



nj O 
H 

Sh 

p:^ W 



o 

H 



H M H H 

:z; t-i o < 



« 

o t! o 

^ XI HH 



y E 

H ;z. o 



154 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABXg perovskite structure 



EL s 



CI) 

B 



0) 



bo 



en 



a 

o 

s 

o 
O 



III 

' — o 

<^ 

S 5 ^ 

{fi m 
oy c« 
^ Pk 



C\j CN| CN) 
« (O <*1 



3 

d 
-43 
d 
o 



O 

+ 

pq 



Pk 5 ^ ^3 



V . 



V 

o ' 

o 
o 



V 



o 

I 



o 

! ^ 



C3 
ctJ 



M CO 



. A 



o 

o 
o 

CM 



■ ' t 1 o 

^ II 



B 

o 

u 
O 
Xi 

o 



0) 
OS 

B 



X! 5 



bo 

CD 



P. ^ 



P. 

o £2 



O d 



> 7 U 



II- 



V 

^ V 
in 



T 
o 

- CO QJ 

O 
„ O HH 



3 

fX4 



> d P 

i-i t-" 

o ^ o 

'bn o o 
d bp _ 

O oJ o 

- 1/) ^ 



o 
O 



O 
O 



* OO 

On 

O 

1-1 



in ,£> 

so g 

in to 
m g 

Pli 



^-1 



00 



m CM 




O 


o 

CN 


in 
o 




.8991 






00 00 






C<S 






m 






in 

r- o 

Cs 


















in in 






in 












t-i CO O lO 

c^ o3 CN r- 

ro 00 C<1 (N 


o 


CTN 


(N 
00 

NO 


00 in 
CN m 


in 

o 


.8972 






in liS 




CO 


in 




cn 








ooooo 


O 


H 


o 


0^ K 


O 


H 


O 





o 

+ 

pq 
+ 



O 
H 

CO 



cn or; o ^ 



rt 

u :s ^ 



bo 



o ^ ^ to .-- 
X rt oc ^ ^ VI 

« s « £ 
j= 'A ^ f7 ^ 



rt 



- :5 5: , 



{/) o 

Si *-d 



:^ :t: 

ii: ^ 
- ^- > p 



^5 s J ^ > 



13 cn' 



j:: c; trj 

2J 2 :2 K 

— ci *j — . 

5 ^ ^ 0) o 

o rt «^ ST' ii 

•-^ » ^'5 c « 

^ J ^ t3 

O 2 ^ a ^ 



^^^^ 



u 
O 



rt Q 



S «^ 

rt 

t>0 , 



■ ^ ^ C? ^ 'n ^ " 



2^ 

^ t: S3 ^ 

^ Ci. rt rt 

g)&rt^5S^ + 
e 8 rc § a 

o cj s t; G N 

U OJ 00 rt o o 

» C rt 12 ^ 
a> tN, o< c ^ jr* 

a* « o rt i ^ 
5) K *H rt o 



5 ^ 






^ "ul 



Goodenough/Longo 



155 



3.1 ABX3 Perowskit-Struktur 



[Lit. S. 275 



S 



C 
D 
O 

8 



o Co 



^ Q 
« C 



.5 V 



o ;s ^ 
— o ''^ oo~ C/) OC 

I? 'I^ cnT 



^1 



^ 



o o 



rt Q) O O XI 

•2 9 « .1! "1 

g-a^ S ^ 



^ r"" ^ 



in 



to 



^ r-A 



o 

o — 

. A i_ 

c/) - m o Cu 

^-^ il :S 

g in O Cf."— 

ri II II f-O 



to to 

CO t/) 

o 

-SJ Xi 

■r' 

a a > 
0) <u ^ 



to to 

to Co ^ 

. - On 
<u 

(U <u H 
)-< « 

o o H 

U l-t j_i 

Oh 

• H XI 
u u •*-> 
4J +j -r; 

00^ 
(U <u 

t/i 

5 i5 







Sh21 


CN ^ 
^ til 

^oQ 


(NO 00 °o °o w 

0 0 0 0 ^ ^ »C 










m 










0 

00 










1! 












in 


in 


in 




rj- rn 

NO 










r-^ rn 


5.443 


5.417 






5.443 


5.381 


5.348 


3.904 


0 

cn r-^ 

I 


Tj-NOrO^t--0O0O 

oocNOOCNOOtncNOCoocooo 
r-^cnrocnro»nrnr<Srorotn 


0 


00 


H 


u 0 


OOOOOOHf^OOU 



T3 

a 

o 



+ H 



o 

H 
O 



XI 



„ P « o ^ ©O •« o 

o V #v :^ V -5 M 



o 

< 
o 



« ^ K CS< 
in I — I ' — ' ' ' ^ 

o -"i ° ^ 

■ V 



rt 

V- £V 73 'Tx ^ 

•J? *t « ?^ « -5 

^ t) bo 
^ rt -d « 

- X ^ 

-9 o 3 S P 
^ O +J CX Q> 

^ e ^ " « c 

D- S *3 ^ « 
^ — • * . _ - 



^ S -Sii 
shot's ^ 



o ^" 



rt ^ o d 
S ^"-^ rt 



O < — ' ^ (rt 

C 02 O 

- 43 ^ - g 
3 s "5 o « 
§£'5 I 

^ ^ 

V ^ a> •- 
<^ ^ " c > 

.t; >^ rsj ^ 

Q 00 ^ S3 

3 no" £ cn O 

« o ^ ^ S « 

CX „ "t3 iS C 
,5 + C ui bp 
CO >^ « rt C rt 

r^S g 8 e 

« rr: rt « 



156 



Goodenough/Longo 



Ref. p. 27S] 



3.1 ABXg perovskite structurllP 



L> ^ 



a 

o 



^ H 



o 



00" 
I — I 

CO 



0) 



o 



o 

d 



0) <v 



tn ID 



O re '.-< 



O <U (U <u 

U Ut i-< 

3 3 3 3 

[/) t/1 t/J (rt 

cn tn to trt 

0) <u <u 0) 

u tx u 

ci^ Ph a. p^ 



C/1 

- 0) ri 

P. Ph^ ^ 



3 3 

to CO 

cn to 

CD O 



^p.ai^> 
^ ^ X ^ • 

;rpM ;5 (/5 

C\| ^^^^^ 
Q h3 H-i t-4 t-1 

;_icvj ^ ^ 



X X! X 43 



.0 ~ o ^ 



IM II 



H-) )-l 1-1 

\o c^i r-- 



w *— 'cq 

P.C/5 
X! ^ ^ 

o g ^ 



CIO 



- o 

5i 



o 

I — I 



9. is 5 ^ 



00 ocs) «^ 



:::: ^ V 
-* 3 • 



c 

2 
ffl 



JO 



CO 

\0 lO o 

m (N T-i 



^ X X X 



4; ^ 



£ 000 



II <U >s 

H 'C O r^- « 

. a 



CO 5 
• o 

CO p 



^ 3 



^ S o 
^ 11:5; 



H H H 



X ^ I! ^ 
: ffi PQ ^ P. 



^ — ^^N 
CO CO O 

Ph Ph 



to 

<::>" 
^^ 

oq 
I— 

o - 
s ^ 

t-i "TV o 

' ' 

Ph Ph 



^ :C 
^ ct; o 



^ o c> o o J. 
« o o o o 't; 



^ CN, 



o <N m o 

CN m ■«-< O 00 

\o V- 

fo r-^ (N CN) K 

T-i CM CO NO 



00 in Tj- m \o Tj- 

T-H r- ^ 00 CN NO 

CN CO <N O ro 

O CN CN CN r<S 



NO 

o o 

O CN U-> 



00 

NO CN) 

00 in 



CN 



NO 
CO 

iri 



o 
m 



00 

Cs 

NO 



00 

NO 



o 



NO o 

NO (N 00 CM 

ro 'O 
rn uS rn LO 



r~- CN (N CN 00 csr-CNincNT-HO 
CN)vomTj-T-*ooot^vOvOTj-Ti-ror^ 

nOnOOvOOOCMOnOnONOnO'^"^<N 



CM C> NO (N o 

ocNCNinr^fomiTj 

rnOCNCNNOOOr-iCX) 



00 NO 



oOuW X D^ffiS^KoOoWKffiK^CffiO OP^OHffiOOO HO O OH 



0) 

3 
a 

o 
o 



O 
+ 

+ 



o 
a 



O Vh 

> y 



C/^ O Oh PQ 



O 

c 



O 

i 



o 



art O 



pq 



O 



S S 
w ci 
00 

(-1 

CO C/) 



s :5 



5 



6^ 



Goodenough/Longo 



157 



3.1 ABXg Perowskit-Struktur 



(Lit. S. 275 



n! 

B 



o 

e 

o 

O 



o :5 

g ^ 



CO 



CO 

(A 



0) 

3 

O 
03 



o 



w to 



.Si XI 



•li 4-> ^ 



p 



X! Xi > o ^ 

tfi m ^ 
[ft « o 

Ph p^<-^ 
^ x: c/) 

3 wpk 



IE o S *-g ^ 

- ph>? 



O r-^ 
O 

o to 

CM 



^ 

^ « hi 

o to 

(J § o 

o 

Co 



o o CM cn 

o ^ e 
J3 T3 ;5 ^^ 

^ ^ 5 

^ a> 



A 

O XI 



cop 



pq 



^7 C ti XI 

5 o o I 

^ dt tn ^ 

^ OJ 4) ^ C/3 

Pu Ph Pu Pu 



2 X 



V5 

PM 
o 



^ u 

CN x: 
o +; 

I — r 

9 t^ 
v> - 

( — » 
.So 

•sa 



XI 



o 



jj CTN CSi 



1 I - — , 



»x ^ ^^ oo »o 

2 w -r* .vl 

5 >. ct; ft: ti: 



o ^ 



^ ^ °o 
hi tt, 00 



oo 
o 
o 
oo 



O 



^0 

r-- o 



NO o 
CO -r-I 



oo 
in 



00 

in 



in ro CM 

CNCMOOCMOO vOCN 

Lnr^inr^r-;CM 

inr-^inrorOTi- Tfin 



CM 

oo 00 o t~- 
in in 



CN Cn 

-^i- CN 

-rt O 



OO 
O CN 



OO o o 
m in ^ in NO in 
Tt- t-H ON OO CO r- 



in in 00 tn m o in 



o O o O 



a a 



O 
+ 

+ 



« as ^ « 

OqOOOo 
cd ri 'O 

pq (/) PQ O O PQ 



en 



O O 

rt XI 
U PM 



o w 
W pq pq PQ c/) 



90 
o o 

si 
o m 



CO O PLh PQ 



158 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structij 



rt 

e 



o 

6 
o 
U 



pq 



to 



- cn XJ O 
OS S O 



o 
o 



tin O 



k4 ^ O 
so uZj'— ' 



0) 



K PL( 



M cn Q 

I — I PL, I — I 

m j:^ (Tt 

O. Pm 



nJ 

-t: V ^ H 



in 

PU 3 



in ^ (f) 



3 O 
(U in 

II 



CO -c 
t/) 

o u 

CN ^ ^ 



n 

O 



o 



O ^ 



P^ O 
in 

in A 
c/2 



^ CN4 u ^ 

3 CO CO 

^ ^ ^ S 

K ^ PL| pin CM pL^ pL, PUi CO Ph fl, 



T3 
0) 

t: 

o 

o ,^ 



Cn C/^ 



« 2 y 

g 2 S ; 

s " 

0,0 0 

K ?5 a 



o ^ 

CM y 



^ (U O 

T3 pti b 

(I) > — ' 

^ CM'" 



CM 
O 
u 
Pi. 



5 ii ^ CO 
O P CAi 



4-( *A 

2i .-ti ^ 

O UJ W > « 

S^c^ 

qu, K Pm Szi CM 



^o ^ ^ ^ 

0) ci ^ o o 

^ tti ft: 0^ ^ 



in Co 



CN 

S 5 ;s H 
Co CO Co to 



to 



> '(J. tr^ , 



^:^;:^;:^;^o^t:Q^^o^o^Q 



v- v^ CN 



00 



CO 



li 



o 

o 00 \o 00 
K r-^ 



r-- fO 
00 O 



00 
00 



(N 

00 ^ G\ 
CN CV O 



Cv 
t-i 00 



cv 



VO 

cn 



r-~ m 00 
in in in 



in o 



rO 00 

r- cv 



in c\ 
(NO in 

\0 v£> 00 Cv 

Cv in Cv in 



<r> VO in in VO -r-* 
in ro m cj in ^ 

in in in in o in 



o Cv VO 

in r- r- Cv 
o in Ti- o o m 
06 in liS ^ ^ 



r-^ 00(NCN00OJvOTl-in 

^ OincMor-vovoTtfOtOCvivo 
o r-vovor^i-<ou^cvT-"t-iTi-r- 



^ in in Tt- 

o 00 VO vo 

\0 in <M (N 00 



[-^r-^r^oori^rt*info^^c>in inmoro^m 



ffi o o o u o o 



00 oSoo o oooouooShooK ^ooooo 



o 



W ^ u u 

<; pq c/) o c/^ Plh 



o 

c 

CO 

p:; 



09 
t/l O 



09 
C/) t/) 



o 
o 
pq 



O 
(J 



Cj o pq pq C/) O U 1^ 



P^ ►i^ 
PMpq 



cr> 



Goodenough/Longo 



^ ^ 
PM a pq c/) 

159 



3.1 ABXg Perowskit-Struktur 



[Lit. S. 275 



o 



e 



bO 



c 
o 

e 

o 
O 



CO ^ 



< — 1 ^ 

^ oq 

CS| « » 

to ^ 

"a c/i 
^ 2" 

^ Si 



H 

-♦-> 

c/i 



1 ^ 



2 ^ 

:3 3 :3 o 

rj O O CO 

o o o llL 

TJ -_ 
r3 3 r3 C/} 

pL, CM Pm 



o o 
o o 

CD (D 

Pm 



c:^ u> u^ lr^ 

^ :5i IS; ^ t< 



in o 

OOTl-Ti-Tj-\OOOOOiOOO 



_ uaaoacjooo 



73 
oJ 



B 
O 

o 



o 



ctJ 



o 2 o 



'+-> 



CO 
,P^ 



0^ nJ 



3 §j 

tn 

> W 

it! S<^:J 

g 3 r^ ^ 



'3 



trt tn 



§ ^2 



x) 



(l> 4J (U (u bO J .2 4) 



X X ii 



o 
o 



if) 



11 11 



^ _ _ ?^ - 



^S; to o ^ o o ^ 2; ^c; 



rn<N iniriOJminTj-oo oo 
r-- ooo ^-ooc^^or^c^c^c^ cm 



oo 



00 



00 

00 



(D 
C/) 

11 



Tj- o 00 r- 

or- ■(-to-<-«'^oooT-<oc\ 



«K WW HOWOOffiWOO W 



+ 
+ 



d'o'd'd'Q 

pqcouuPHPQp:5PQc/) 



+ 

n 

+ 



+ 
pq 



^ pq PQ c/5 o p:5 p:^ <; 



O 



OJ 

: 73 



C/) 



o 
c 

.a E 

^ !3 O « '? 



PQ 



5 3 
^ P^ O 



^ oC c/) im O 

^ -s Q 2 II 



CM Pk 



m CM 



O O 

\0 vO 



00 
00 



CM O 



P^ 



P^ p:^ 



pq :t5 



oo 

O P4 



160 



Goodenough/Longo 



275 



Ref, p. 275] 



3.1 ABXg perovskite structure 



t-i 

0) 



bo 



13 



a 

o 

a 

o 
U 



T3 



C3 

a> c3 

I 2! as 

(1) ra 



> I 



O r\ 
eft 

5 PM 



o 



CM 



. O 
O > - 

'bcO 
2 »\ o 

3^ II 

CD iHi " 



hp CO 



Dq K) 
PM Pk 



(5 



Si o 

to ..-r 



CO 



O M-t 

^ 2 



to 

r Q 
bb - 

to - <N 
TJ o O 

0,0 fr^ 
P, V i— . 



<D 

s 

p. 

O 

o 



O 

oJ 











r- 










bb 




bb 


E 


S 


E 






a? 




(U 


<D 


tft 


tft 


Cft 


O 

o 


o* 

o 


o" 

o 



-J « O CN - 



V. V V 



O oo O oo 
O cSj O c\| 



PmPLhPM 



I 1 CO 

to ■** 

S,co 
o ^ 
^Pu 



o 

a - " 

|i? 

S V2 



O a> ^ 



o , 
d ^ 



to 



=^ 

CO S to uo 

1 1 Q 1 II 1 

C/5 ^ CO CO 
c« O ^ <^ 

Pm ^ pu, pu, 



13 

.s 

o 



O 

+ " 

pu 



Ma27 1 






CN ^ 'l^ ^ 
O O OQ O 


CM 
to •** 

oq oq 


oq 


^ ^ r»N ^ rrN Oo 

^ >!j *A CN 

oq to oq Co oq CO 




^ rrv 

oq o ^ o to 




LTl 

CM 


















V bo 

OJ OJ 






o 

O 
O 




o 














o o 

o o 

II II 






11 




11 






















OO r- 
in CM -(J- 
-■4; in 


m 
in ''J- 


-.-t o 
in 


o o 
in CO 


^ CO O C\ 

in CO in <N 


r- 

T— I 

CO 


o 
r- 

CO 


00 

OJ Tj- c\ 

in c\ o 


00 

OJ CN in 

O CN 








r-^ o 

r— ( 


d 


d 


d 


d r-^ d 




r-^ 


d r-^ 00 


00 






o 


(N 

Cn O 
CSj CO 


00 

o 
fO 


T-I 


CO 
CO 


fO 

CO CO 


(M 
CO 
CO 


C^ 
OJ 
CO 


00 


\0 rH 

h~. vo 
^ ^ *^ 








LO vn 


in 


in 


in 


in in 


in 


in 


in 


in in in 




00 
(M 


in 

00 


o ^ o r- 

r-l r- so 

cn OJ r-; (N 




o 

CO CO 


o 

O 00 


o o 
o NO in 

\0 yf^ \o T-* 


00 
04 




00 

00 T-< 00 in 
vo \o r- r-~ so 


in 

T-< CO 
vo in in 


rn 


in 


vn r-^ 


in in rn in 


c<i in 


fO in 


fO in 


CO in CO m 


m 


in 


CO CO CO in 


in in m 


H 




OO 


OHIO 




SO 


ffioffioffioo 


O 


SHPt^ PhOOOOO 



o 



o 
B 

CO 



O Q 



o 
< 

H 



O 
P 



o 
X 



o 

u 

w 



H >^ h^l >^ 



LandoU-liornstein, Nenc Serie ni/4a 



Goodenough/Longo 



161 

11 



3.1 ABXg Perowskit-Struktur 



[Lit. S. 275 



IS 



bo 



a 

>> 

C/5 



fl 

O 

o 



"vO \0 vO \0 \0 



o 

(^1 



a. 
o 



Oh 



<0 E-H 



o 



00 CO 



to 



H 

r1 CO 



rO "-H «H 
C_j I It I 



CO CO 
pin Pm 



u CO 

CO ^ 
<yC 
'a O 

cq oq 
CO to 

Oh Ph i 



to 

pq ^ 

CO (- 

? S 



' — o 
O 

X! ^ 

. ^ oq 



^ ^ ^ ^ 

O O O fv 

. - . ^ 

Oq Oo Oo ^ 

<a «o <u o 

ft; 1^ ct; OQ 



<^ r— .f— . " 
(y>^ fr^ Pr\ Oq C>o ^ 
^ ^ ^ ^ <0 CO O 

oq oq qq cq tt^ fc; 
^ I — 1 1 — 1 1 — 1 1 — 1 1 — 1 1 — ) I — 1 1 — I 

co^^cocococococncoco 
Pm pkpM(iHfX,P4P^pL,Ci, 



<N ^ <N Q 

U ^ O 'si 

to to to O 



>^ V*. >^ >^ >^ 



in Ti- 

<M c\ o 

ON G\ OO OO OO O 

r-^ r-^ K 



O CM OO T-t vo 

SO csi in T-H 

t-- so 

r-^ r-^ 1^ K r-^ 



\or-vomr--oooTi- 
voso^osooinmsooo 



^ ^ (N r- oo 
Tfinmr-coor-oovooo 



^0 

\o m -r-t 

r- r-- 

in in uS in in tj^ 



(vjsoin TtinsoinTj-cofOOTf 
inmso \osososoo\Ososoin 
iriuSin vniniriininminmin 



sO(NC7sOO^(N'^Ln 

oovor-oOfHOOOooT-' 
r:^-lnlnln^oso^O'OLnso 
ininininiriLfSiiSLnLnin 



•rH 00 fO <M fTl Tj- 

in Tf Tj- Tj- o 
in uS uS lo i/S tj- 



Tfr^ mcocMoorno oo-t-'C\oo\om'^oo 

rOOO lOOOCNtn^ OOsOrn^OCNr^"^"^ 

inm^^cocnoo rommfOcocNCMrnin 

r<Sf<S ininininiiSr- u-iinininiriiriininin 



vOr-^fOcOCMCM-^ 

ooooinCN-^Osoooinoo 
inuSiiStnininLnminm 



oooooH ou HHOOoo ooooooooo bboooooooo 



s 

0 

o 
o 



O « « n o _ 

t O O O O «n 

5? CO CO CO c/D o ^ 

^ pa O P Jrl fQ 



?9 
h-) _) 



ddoood 

u pui CO o w 



9000-QQOO-0" 



" — PS " « M 

cjpM;zicoOQW>^PU<ii 



162 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



o 
a. 

S 



H 



PI A 



o a 



- o 
cs o 



a 



2 o 
S <N 

4j • rj 00 

O ^ (D 

.a ^ W5 

CO 



o 

O 



V 

V 

o 
00 

CM 



r-, O 

W*> o 

. O 
CN (M ^ 

^ It II 



o O 
II 1 



I — I 

o 



O CO 



01 O 



+J -M 13 r-n 



u est 



^ est -d 



;2 



CO to [T 



da da . 



Ley . 



J* 

•A I ( 

« o 
o o ^tl 

X) 

C\| i__Ji__» o 
ii^da ca S 

CM ^ 



O 

(U o ^ 

bp-- 



II « 

« CO [=1 

B 

,^ CO >^ 



O 



CO 
CM 



o 

'5 . 



13 Tl 



O 



o ^ 



10 



C\ p 

^L 2 ^ 



CO 



o 
CM 



-2 o 
^" ^, ^ 



iJ O 

1 — t (D 



P^+3 



+> Csj 
So [^Ij I p. 



CO ^'^ 



■ Ph P^ 



;2 ;S » S 



ro 



O 



O 00 



crj CM O vO <N 
Tj- (M o r-- in 
\c> vo in in 



00 
m 
in 



o o 
o c^ 
in 



in 



in 



in G^ 

o r- 
in 



00 
o 



in in 00 o 

T-t CM T-t CM 

in in in m 



\o 00 o 

T-t O t-< 

in in in 



CM 

in 



in 
cn 



Tj- in 00 
(N r- in r- 
Tj- c^ 

in in in in 



CM 



CO 



o CM '<-< in 

Tt- -r-i C7\ O 
CO CO CM CM 



CM 



CM o c\ 

CM CM ^ 



\0 o 
r-. 

T-< tN 



p:^ O O O O O O 



000 O 



00 



0) 
C! 

o 

m 

o 

+ 

PQ 

4- 



20 



00 
U U 

O O 
a> u 



U 



CO 



000 

u u u 

^ y ^ 

WO H 



o 
o 



pa 



00" 



9 

u 



O 



a 
a 



Goo denougb /Longo 



163 

II* 



3.1 ABX3 Perowskit-Struktur 



[Lit. S. 275 



6 

C/} 



a 
o 

a 



\0 O vO O vO O 



2 ; 



o 

s 

+j 

'5 

o o 
^ h 

»-< u 

CO , 



; (Si o f*N CM 

Csi - 

^ o 



0CP4 o 



?»5 



X) ^ >^ 



o 



-3 Pi 



^ - On fx " 



43 <D 



- 1 — I 

rr^ <Y\ f*f^ 
Pr^ <y^ 
^ <^ U 

Dq 



O 
o 
O 
nJ 
h4 



o 



. 'jlj T-H "C 

bo+i . hi 

flj pH 0) 



O 



to a 

M <li <D 

to 



I ) I 11 Ir^ « 1 



^ -z* PQ f** 



C/D C/) t/) 

08 

Ph 



C/) CO 



^ <N C/) t/) CM 

b ^ ^ 

^ +3 o "-^ ^ o ' 



cm Oi S 



at 



CM 

Osi* ^ 

:^ « 

O 

3 t-( *41 

at) S3 

Kg 



o 

o - 
o 

CM *^ 

cm" 
US tu 

£ S 

0) 



O 



■'5 

in 



Dq 



ni fli ™ 'J^ 



^ t: o 



So-. 



ft 4J O 



On ^ 

to to 



CM 



CM 



§ i:^ t>o N ^ >i ^ >^ :s >^ 



in 




ro _ 

0 0 


CO 


0 




0 




0 


11 s 




N 11 


11 


tl 









7.647 
3.90 


7.76 
7.694 


oomr-oicoc^Jcnin 

,-er-ioooincoor-cncs 

coininTj-Ti-TfT^-cn'^^ 


7.35 
11.41 


7.335 
11.40 


7.32 
11.40 


7.30 
11.37 


7.31 
11.41 


5.405 

3.87 


5.51 
5.722 


inooiO'^'^mcoc^ 
inr-cocx5oooooqoo 

intninioiOinuSin 


5.84 


5.82 


5.81 


■ 5.80 


5.79 


5.302 
3.90 


5.46 
5.533 


<Mr-inocrvoocrir^inr-NO 
c\^0'^oolnm•<-*c^r-^~fO 
ooin'^cocncOcn<NcST-j'<-; 
coinininiiSiiSinuSinNO^o 


5.26 
6.115 


5.24 
6.062 


5.23 
6.062 


5.22 
6.042 


5.205 
6.125 


u 

OH 


00 


^oooo'oo'ooXX 




OX 


OX 


OX 


b X 



<L> 

c 

■•a 

o 
o 



O 

+ BO « 

Si HP 



eo n n n « 

00090000 
||l|lllt 
cSpM^c^WOHft 



O 

CI' 

o 



o 

a 
W 



O 
H 



o 



o 
t-l 



o 



164 



Goodenough/Longo 



Berichtigungcn zu Band ni/4a 

S. 177, letzte Zeile: statt BagTdPaOe lies BajTbPaOe 

S. 219. Zeile 16 von unten: statt KMgi.^Ni^Fca lies KMgi.j-Ni^Fa 

S. 252, Zeile 26 von oben (Uberschrift) : statt SrgFeaUOg lies SrjFegUOj 



Errata in Vol. in/4a 

p. 177, bottom line: instead of BasTdPaO^ read Ba^rbPaOe 

p. 219. line 16 from the bottom: instead of KMgi.^Ni^j-Fe, read KMgi_^Ni^F3 

p. 252. line 26 from above (headline) : instead of SraFejUOj read SrjFeaUOc, 



Landolt-Bbrnstein, Neue Serie III /4a 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



> 

o 

u 

o 



in 

C/5 



to 



O 



^5 ^ 00 <a 



o 
CO 



A' 



O «H 



Co u— I 



PU 



o ^ 



^ f\ ^ 



i5 ^ C/2 
(1> . » O 

+^ 



4-» 



u O 
a o 






O 

O 



43 
CM 



C/5 
CO 



Pm 

X! 
CO 

I — I 
o 



- - o 

I — I ■*-< 
« <N 



^ o 

I—I • 



(2 



o ^ 



.-H c/) en 

W e« 
Pm P4 



cn 
PM 



jO irv 

OQ 

W <« 

PUPk 



I ( 

•si- 

^ w W) 



C/j 
C/3 



Pk 



5 I 

U cn 



« CO 



CO 



ft: 



>0 - . 

ft; ts cn 



05 



•ti cn o) cn 
PM Ph PU 



O o ^ 
CI (Jh (V 

M ^ 

K ca 



O 

»2 



CO ^ 

^ nJ t — • 

to ft^ 



ctf ) — I 1 1 

^ w 



C/D CO XI 

pq o« oy ^ 
Pm Pu 



>^ so 



00 



CM 



00 



00 

CO 00 r- 



vO 00 
00 \o 
>0 VO 



ro (M 
CO (S o 

VO O \0 



VO O 

in \o 



00 



in 
o 
in 



00 
in in 



'T-t VO CM 00 T-H 

VO VO \o "in m 



00 
in 



VO 



(M 

Cv 

in in 



00 



VO 



Cv 



VO 

VO in 
00 in 



in 



Cv 

'^l- cn 



^ VO 

CO cn 



vO cv) 00 

CM o 
tn CO (M 



t-t CO CO CO 

in CO ' C30 

CM CM ^ 

LiS in in in 



00 



00 



00 000.0 



O O 



0 



3) ^ 



o 
I 

s 



00 
O PL^ 



O 



O 

CO 



00 

WO 



o o o 

o O 



tl4 



o 

B 
H 



O 

X> 
>< 



o ^ 

5>< 



H 



Goodcnough/Longo 



165 



3,1 ABXs Perowskit-Struktur 



[Lit. S. 275 



I 45 

1° 



fn xi 



B 

a> 



bo 



CO 



a 

O 



-J 

hi 3 

o 



o to 
CM 



I » ) — I C\| I — I 

^ ..^^ 



u - 



o 3 s r^" 

« H ^- 
^^■^^"^^ 

to O 5 

^ O O cs; 

u k4 
ttn iJ CA3 I/) 



0 g 

158 

1 ^ 



T3 

^ 

ft; ^ ^ 

^ CO 



• ^ to ^ 



CO 



\o ^ 
c\ >^ 
= " o *— ' 
■^5 in ^ ^ 



o 
o 



B 



C 

O 

a 

o 



O 
H 

VH 
O 

> 



H 

7-^ 



8f^ 



o 'Sen 



^ ^ ^ [T" 



.2 



d n3 

P. O 
p U 



I in 
x> 
A 
fx 

u 



^ „ ^ CO 



o o 



:2 . ^ ?^ ! 



CO CO 



CO ^ o 

^ 5 

Ph CO 



X! CO 



^ CO 



- 

CD 

^^ - 

^f^ >- 

t — I t__j 

CO CO 
CM CM 



o 
o 

Xi 

CO +3 
CO S 



c c; 

o o ,o 

'+3 +j 

nJ nJ 

b b 

TO nj CO 

CM ft 

tt> <U <U 

u u u 

PU( ft ft 

0) <l> O 

u u u 

3 3 3 

tn ai V) 

tfl W CO 

<U <U !> 

1-. (-1 l-r 

ft ft ft 

^ ^ ^ 

tio bO bo 



in QU W UO W 

S S iS iS 



MiO 


o 




<Y^ cy^ <y^ 

(V^ (y^ 
to u u ^ 

OQ flq pq 


Tollb 

Wo8 

Tollb 

Ge2 

Ge2 

Ke2 

Ge2 

Ge2 


l^ Ir^ 
Cm Cs| CN( CS4 

"3 54 13 « 

^^^^ 


r-* 


00 


o 






Th 

CM 






o 

in 

li 


o 

o 

II 


o 

O 
VO 

li 




o 

O 


o 

O 














1! 


li 
a 












t-- ^ 

CO ^ ^ 

in in m 




oo 
r- 


C\ \o 
Csl O 


o oo O 00 
in cs o r-- 
VO NO VO in 








r-^ 1^ r-^ 








r-^ 








m \o Tf 
r-- m in o 
rn m fO ^ 




c^^ 
in 


in 

c\ o 
in 


o 00 r-- T-H 

CM cn CD 

in in in in 








in uS in in 




in 


in in 


in in in in 






CM 

m 


•TH -o C\ 00 

m CO 00 
m m cs» o) 


00 •(-< 
(N ^ 


m ^o 
r- CN 

lO 


in 

\o <M 

00 Tj- Tj- 


CN ^ CM 

VO in CM o 
CO cn m m 


in 


in 


in 


in in in in 


in Tj- in in 


co in in 


in in in in 








oooo 


CJ p^; O O P:^ O o o 


OOOO 



o 

n -1-1 



o 

o 
U 

t-3 



CM Iz; CO o H 



92oS 

PQ J PQ 



oo^ 

O Cm ;2; 



c« 

S 3 'O 

CO W O H 



166 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



(-2 



r3 d I=! 

000 



cti cJ 

CX| Ph Oi 

0) dj (L> 

M )H tH 

CM CM 

0) 4) <U 
l-i 

P J3 SI 

tn m to 

CO cn cn 

O 0) <1> 

t-i M Ui 

pL, 

J^i A 
bo bO 



3 



O O rt o 

^ '4=1 +5 *-ti 
nJ rt rt rt 4J 

P^ i;;; 

oJ pJ oJ o S 

PU p., . P^ 

03 (D (L> (U r— « (L> 

p^ Pm o CM 



a d 
o o 



(U 4) a> 03 ^ 0) ^ 



CO tft tn otCN ot^v^„ cn - 

P^ P^ Ph Pm' — ' 0-^3, ' — " — " — ' — 
bo bJD bo bpc^ bp ^ 0^ 



CO 



C/3 CO 
CM 



Cm 



d d d c 

0222 
4J '43 *^ 
cd nS gJ d 
t-i H H b 
nj TO TO TO 
p^ CM 
a> a> o o 
t-« »-« M n 
p< pL^ Cm CM 

a> 0) <i> <i> 
M v-i v-« (-< 
0 ;3 

eft 0) CO CO 
to CO CO to 
(D (D 0) <D 

*-< l-* fc! 
p^ Ph CM CM 

^ ^ ^ ^ 
bo bo bo bo 

M S S 2 



2^ 

3 o 

V, II 
iJ s 

O f— . 
u ^ 
- S 

^ NO ^ S 
O O O lH. 

^^-^--^ 

f^" <^ d 
't- ^ 
ti Pm 

to to to ^ 



CO C/^ C/5 



Cm PM Pm 



o ^ 

II 



cnI c>J N <N (N CN (N ^ ^ (2 cS (S t§ «S 00 Ox ^ ^ Ox 0\ On o ^ ^ 



r^r^t-^t-^r^t^t-^Kr-^t~^i^t-:r^o6o6ooooooooooooooc)oco 0000 



i.n i-D lT) lo lO lO o 
uS lO lO lO i-H O 



o o 



(N (N CN CN CN T-^ v*^ , . . . . . .1-. .r^ li-i 11^ 10 iTi in in LTi 10 



--------- 



in T-i 

OJ 
CO 00 

in in 



_oooooooooooooooooooooooooooooo^oooo 



o Y d 



Go odenough/Longo 



000 



90 



167 



3.1 ABXj Perowskit-Struktur 



[Lit. S. 275 



O 



s 



a 

o 
ft 

B 
o 
o 

W 

<N 

H 



in 



a 

O 
Oh 

fi 
O 













ski 




CM 


> 






S 


:ex( 


:ex( 





o 

A 



I — I 



O 

S 

(n u) 
CM fUi 



ft 
O 

ft 

o 



ft ° ^ 

I a 11 B a 

^ CO ft 2 cn 
.^cy ^ I cy 
pL, (Xi f-s K pu tnpH 



^ 00 

ft ft V 



CM 



o 

O 

O r~. 

va 

o 

oo i 

s 11 

ft . 

O C7N 
^ft, 

dj ctJ ^ 

Kg 



3 

c<l fin § 

K Cu ffi 



C\j C\| C\| f\ 

O •< O O K 

oq hn 0^ oq oq 



« « ^3 «3 (3 

t\ tN. ^ 

V « e « e Q 

Dq oq Dq oq oq Qq g:i 



««««««« 
oqa,cqoqcqqqoqqq;:c;ct| 



o 



o 



o 
III 



On 
CM 



OO 

CM ^ LO 

o vo r- 

oc) CO cfS 

OJ r-H ^ 



CM in 



CM 



T-H CM 

\0 NO 



o 



00 
CM 



oo 



fo 

oo 



oo CM LO 

vOGNOt--T-<OiOvOO 

t-^cMooirjxo^vOTj-cN 
oodiriiTiLriododinod 



O O vO 

so CM in 
tn o cS 00 



r-- ^ 
so rO vO 00 <;^ 
CO m o CM 00 Tj- 00 

00 iri c\ vd ocJ 00 uS 



coor-*CNCMooTfooiom 

OOCNGNOONOOOCOirioOOO 



ooooPcloaKHo 




> 



^ « dfl J 

< (f « « « 



« « « -Q XI w 

^ o o p:^ 0^ ft; 



> o CJ u ^ ^ 
*^ U 0) V »5 -1 o o 

•^Cr « *• ®» JQ J^l « N 



168 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structur^Bl 



o 



03 



bo 
C 



X) 

a 
o 

o 
O 



CO ^ 



.g 



00 
to 



o 
t-l 



o 
CM 
o 



no 



CM 

V 
V 

CN 

wi" 



r— .CM 



V 1 



O ° V 

^ (M 



1 — I 



CM 



10 o 

' in 



00 

•r* O • 

PI S s 

II ^ --^^ 

4-» CM 
O OJ 

If 5 V 



o 

CM 

V 

V 
o 



o 

o 



0) 



OJ ® 

Vo So 
_ CM P.CM 



in 



O^in 
O I 



(J) 



^ It S 11 

ex. . n . 
o 00 -00 



-in ' 



!i ti: I! 



03 II 
bo «s 

O 

V i2 



f 



o , 

o V vo 

3 o 1^ 

(L» Cn I— J 
Oh 



ON •—'lie; 

<D 00 

a. 53 11 
2^ fc: 



go 
Ho s 



cs « « s e M. 



5 « is 



iJT ^ fc-Z 



o 



o 
0 



00 
CM 



3 

V 

o 
o 



00 r- 
r- 0 
00 0 in 




0 


in 

r- CM 
^ cv 




0 
m 














r-^ vo 06 




CO 




















vo 






t-H 


















in 
























vo CO ^ 
vo vo T-H 0 
CM 0 10 


vo 


0 

in vo 00 r- 
0 CM 00 00 Tj- 


^ m vo 

C7V 00 CM 0 

00 in co in 


00 
00 


CO T-H 


CO 
CM 


0 

CN 


in 


CM T-H 

CM Cv 




m vo T-( m 
0 Tj- 
in cv <N 0 Ti 


06 in c\ K 06 




cv vd 00 06 06 


in 06 06 uS 


06 


vo CTv 


cS 


06 


06 


06 r-^ 


06 


00 00 00 Cv C7V 




U 


HO 


0 


0 


0 


00 


0 


00000 




pq 
+ 

pq 



p4 





























0 


0 
0 




5. 


m 




0 


0 

ot 

a 





o 



mh o 



Goodenough/Longo 



169 



3.1 ABX, Perowskit-Struktur 



[Lit. S. 275 



I 
Id 

a 



bo 



CO 



PJ 

o 

B 
o 
o 



C/) 



2. 



a d 



(D <D 
O O 

:3 :3 



Oh 

O 



d 



o 



bo 



^3 «t3t3t3<3'3t3<3t3« 



O 00 



00 



PI 

S 
'+3 

a 
o 

o 



o^o^o^o^lnTJ-^£)ooa^or-oo^ooooc^^oo^Ov^^c^^cNlnv^oooo^vo^ 
ioc^ojr-t-H(>)vor^oornoTfTfcvJO'^^CNT-iCN(XJOcooooooorn 

<Sc^C^r-^C^cK(:7ic^C^C7i<:7^C^<7^C^C^<^ 



t OOOOOOOOCJOOOOOOOOOOOOOOOUOUHOHCJO 



o 

CO 



O 



5o 

J-H O 

A 



A! 



O 



r\| C\| c\) c\| c\ 

^ <A ^ 

Q « « « 

^i:: ^ tt: 



o o 



O (N rO 

vo t-t <N m 

C^ C^ 00 CO 
cS rO viS rO 



o p=; o 



I 

I! 

4- 



^5 ^ c 

« t> D:i n 

u o Ph !^ 



to 

« 

o 

I 

0) 




PQ 
+ 

PQ 



o 5 5 ^ ^."^ ^..^c^z, i^«:z; <<^^^ 



<j'dd-<3 d S « S d"« cfS S d" « cfS cfS c3 o c3 <3 w 



t-t ^ J >^ 
PQ CO a O PM 



170 



Goodenough/Longo 



Ref. p. 275] 



3. 1 ABX3 perovskite structure 



2 



B 

<1> 



bo 



I 

O 

O 



CD Xi 



Oo oo 

5 s s 



CM m Tj- 

G\ ON CN 



000 



O 

+ 

h S 

oJ ctf 
h-l h4 h4 



I I cs 

O CO 

tn D 
ay 

^ t! 



CO 
Oh 



2 2 



0 o o 



O 



o 

S 
o 



C CD 

-J c G O • rj 

W S O O J-; 

'"^ t, .2 p. 



CN O 

cn -^^H ^ 



+J W 

CO O 



SB 6 

10 CO CO 

S E S 

CO trt cn 
>> 

tn i/i CO 

« n « 

00 o 

CO c/3 c/) 



ft; 



o 



o 



I — I 

0C| 



> 
o 



O +J 

CO o 



) 1 (.^ I 



0) 
CM 



bo 



:3 

a 

o 
o 



CN 



o 



a. 
O 



O flj 

S B 

Oh 5 



+3 1: +^ 
i-i h 

<D ^ <V 

a CM 
o £ o 

p. Oh 

o ,0 O 
+3 +3 *43 

OJ <1> 0) 

G C 

tub tuo bo 
ri 

6 a fi 

X « X 
^ ^ ^ 

Pt P( Ph 

a a B 
000 

u o a 



00 Q 

Cm csi ir> ^^5- rx. r\ i\ 

O O ?t 'tt 

0^ ct; to ft^ oq fi^ 



« e 

^ e « « Jo ir* IT^ 



Vr>, Oq Oo 

e> Oq oq 



00 

NO 
ON 



CM 

ON 



ON 



ON 

O <N 00 rO 

ON ON ON 00 

c<S r<S CO 



NO 00 ^ 

ooovor-ON^-^or-CNicMOT-i 
ONooO'TimONOOcTNONOONONO 



<N NO O O O 
On 00 VO CTN 00 

tn r-^ in 



0000 



' — ' at 



P. 
O 



^<=> 
,CM 
ftN CO 

S A 
) 1 



Csl 
CM 

NO 



rO CM 

CM r-- 



ooooOooooocjoH uoooS 00 



H 



<1 
+ 



C/5 (/) C/) 



o 
w 

PQ 
+ 

CON 



H 
bo 



'U c3 ^ N oJ a! 
^ h5 m >^ h^l h4 




cii oiciC«e4e4MC«e40««cie«cae)NC4ci 

^J^J>^^Jl-^l-ll-ll-^^Jt-^^-ll-l^-^l-l>-l^-^l-l^-l^-l^-l 



> > 



Goodenough/Longo 



171 



3.1 ABXg Perowskit-Struktur [Lit. S. 275 



0) 



5; op 



• ■ o 

^ o o 



(1, 1^ Ph fl^ Oh PL, Ph Ph (l^ PLh PM PL, fin fin IX, PM fL, Pu fL, p^ t-H O Pli 

o <:^ o 

\o 7) in 



o f o 

C^ 00 
\0 CTn 



a 

cn 



O 
Ox 

E 
o 
O 



CMlr^C^t^^^O Ti-C0r^r--00OC\C0'Tt-<-HOC7\Cslc<^C<^C<)OI^\0Ca0000O^r^r^v0v0c^ 



O 
+ 



2o-S2'22|o2o0^oo-dooo-ddooo-2oo-o-^ ddo-o-o- 

PQc/}>§p:4c3;z;t}5>^p:i£pqHj|OPLH:z;tJ5wOHPffiWH>^K:iH«^c3> uOcJ3>^£ 
< pq pQ pq pq pq pQ pq pq pq w pq pq pq pQ pq pq pq pQ pQ pq pq pq pq pQ pq pq pq c/) c/D cTi c/) (/) c/) c/5 cd c/: c/) 



172 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perov'skite structure 



in 



a 



0) 



a 



Id 
a 
3 
o 

a 

(3 



CO w^ 



Oh 



O O 

'^3 Tj- 

^ A A 
^ ^ 
£ 

tn o O 



3 
W 



tuO 



tH t-t 

a a 

a a 

CO tfi 

<U 0) 

o o 



to to 
to to 
O O 
ft 



00" 3 

+J .S; HH TJ 

cj i_r -5 

8 p^H i 
CM -a PM 0) 

^ m 



o 



H 

O 1—1 
O <N 

+J I— • 



Cm C\j C\i C\i 



^ ^ 



00 On 00 
-Si 



CN CM lO _ _ . ^ - - , 

■rlK-tT-IOOCNVOT}- 
O O O O o o o 

0000000 

C-\ Cr\ G\ C\ C\ C\ C\ 



t? ;^ 
K 



11 li II 11 II II II 

CQ^ <ax ctx QQ. CO. QQ_ OCX 



mvooooor^vocofo 
000606000606060606 



00 •r^vOrOOO'^OOCS)<NOOO rO 

't^LOTi-ooTj-T-<TfT-»ocNoor^OLn(No 00 

vor^oor^oooc^^^^ooooooo o 
I^r^ror^f0o6r^o6o6o6o6o6o6o6o6o6o6 



T*- ^ o 00 

GN C^ 00 00 00 00 
un liS uS LT) uS in iri 



00 T** ^CxmvOv£>OOOT-HOC\CNTj-CN 

Tj-inTj-ininoor^oooooooooooooooor~-r- 



Csl o vo 

Cv)OOlOTl-rOCNlr-<^OOCNC\CNiriO 
00r-00 00 00 00 00 00 00<Nt-HT-rCNO00 



cvi 00 i-HOtMc^mcNOCNti-HootnTH Tf 
ooTt^Tt-inoofr»io<N'r-<CNr^r^oooor-r-coi^ 



O CO 

VO Tl- OJ 

o in o 



mioioijOiomiTimLooooooor-r^r^ mLOLniriminmiriirimmirtmiriiriinmo'^ '<4-0'^ 



hhSSSSSSSooouuh ooooooooooSSooooouh ooo 



C/5Cnc/){/2COCOt/)COC/3t/5Cnc/)t/3V)COi-JUOOUOOOOOOOU(J(jCj 



w >4 <(; c/) 

' " « « M 

O O PU 



o 

c/) O S 

CM <N Cvl 

J3 jO XI 

FM PM 



Goodenough/Longo 



173 



3.1 ABXa Perowskit-Struktur 



[Lit. S. 275 



H 

■ 0) 



3 
O 

a 

o 
O 



\0 vO VO \0 



o c/) a, 

^^^^ 

p "2 



pQ s; 

t/5 ^ 



I — l"^ 



CO J 

OS OJ 



-J ^ 

hjO 



QJU 

o 



C\| 

^ o 

to h-i 
I — 1 1 » 

-.W o 
o 



- d 

i-i 
+^ <t> 

a> rv 

^ 
S 2 

t-^ to 
o to 

h ^ 

o *^ 
<v ^ 
'a3 to 



5 S 



O 0) <U 

a. 

t>> o o 

(0 P^ P^ 
O O O 

o i3 

H <U 4J 

pLi Q P 



0\ 



t5 c/) 

O 

O 



0) 

p. 

o 



O 

S s s s 

V V V V 

a\ ^ ^ U ^ 

^ ^ :^ 
I 1 1 — 1 1 — I ' — ' 

CO tn t/j tn 
O <u <u D 

'ij +J 4J '-P 

1-1 t-< J-« 

" 03 OJ 

a p 
o o 

P^ Ph 

o o 



0) ^ 

tn 

O (U 

o 



p^ p^ 
o p 



C30 '(^ OO 

A^f^ A 

Cj (3 PPPP 



P 
o 



p^ Pt 

o o 

•a • 

U O 



13 ^ 
CO cn 
> > 
O O 
u u 

P ft 



CO 



0) 0) 

pp 



tn 

— P. — 

X X P* X 1. 
o o o o o <u *^ 
:z; 12; ffi K Iz; ffi ^ 



to 

I — I 

PL, 



en 
0^ 



P^ 



o 



On >^ ^ 

s s s 



^ ^ ft; 



is 
to 



CO 



O 



00 VO 

-<-» r- oo 

O) r-< ir-< 



o 



\0 00 

^ rn ^ 

0\ C\ 



o 



O 



O 



-^J- O O 00 00 

CO CO in T-< vo ir> 

O O VO ^ 00 00 oo 

00 o Lfi uS 



r- 00 o 00 00 o 

^ CM ^ <N vo 

r-- o o o o o 
d rt^ ^ ^ 



00 vo o o 00 
r- CM 00 oo CN oo 
in 00 o6 r-^ r-^ 



o u a o o o o 



o ^ o o o o u 



o 

+ 
+ 



M CM « 



P^P^pL^PL^p^P^P^P^ 



O 

Xi 

Pu 



• • w « 

2 S-l s s s 

PQ S o iz; N o 

C« C4 N C4 M d 

XI XJ X) XI ^ XI 
pU, pi, Ph p^ PL^ pL, 



f 9 d 2"o oVo o-2V2°Q d d 



pq pq pq.pq pqpqpqpqpqcnc/3c/}c/)c/) 



W CJ <N 



174 



Goodenough/Longo 



Ref. p. 275] 



3,1 ABX3 perovskite structure 



o 



c: 

e 

o 
c 



Ref. 


OQ <>D ^ ^ 

Jo S S 5 S S S 


angle 






-<-• C7\ m 
C\ CN ro 

r^: r-: 06 




5.77 
5.54 




rj- uD r~~ rO 0 

00 in 0 c» 
in uS r-^ K r-^ 


Sym 


H 0 0 0 0 H 

(L> — 


Compound 


3 

C! 
0 

+ « « «M h-I h-l h-l 
«« w t-t TO l-< t-» V-t 

< {/) If) {J U) (n 



CO 



0:1 



o 



P. 

o 



o 

I — I 



I,... I 



12; p 



' o 

(-1 IT} 

i\0 I — 



C/) rt 
fin 



V o 

*j 



o 

o 
o 

CO 

A 



3 



(U 

c 



•«» 

^ 

o o o 

O O o 
O O O 
ro rn rO 

AAA 

K< f-s 

000 

o u o 

■«J 



C3 

I r 



^ ^ 

CO S CO 
c« ^ 

^ 0^ 



Cq r-n 

c/) t/5 

c« l^i 

P4 PL^ 



i^ ^ 
>^ >w +j 
^ ^ ^ <s 

^ o 



CO CO I 
<^ . 
Oh PU( I 



ax: 

u 'd 

:5 & 

Irsj lr>^ l^ Vr>y lr>, 

^ 

o o o o 

CO CO CO CO C/) t/) 

<^ cy cy 

fx, pL, pL^ PL, pL, 



I — I 0) 

-I o 
P Ah 



^ ^ ^ , _ , ^ *^ Y». >^ 

-^^ it; -c* •** « c3 -T* -t* -t* •** -IS* -t* ^ ."ii -t* 

OotoU^tt, tOl^ lJ^(^e> ^ tt, tin ^ CO N 



>^ ^ ^ 



in 



000 

O 



« « 45 



in 

o 

o 



o 

CM 



o r- ^ in 
T-H 00 

06 Tf 06 06 



00 o 
<M r- o 

06 06 vb 



voooovoooooootj- r--vo 
inTtT-<oor-Tf(NT-<c\oor^in<N'<4-oo 

\ovovoo6o6o6o6o6o6o6o6o6o6^5r^ 



o uWou 00 OOP^ P=J O O O O O O O O O O O 



O 

H 

PQ 



09 
HH 

5 CO 

p:^ W 



91 C4 01 

rt ct3 ct 

pqpQ p:^ PQ 



c» CI 

PQ p:^ 



5 pa k4 

CO <N (N 

n} nJ c4 

p:^ PQ PQ 



n O Q o O o O O qO o o r^n^ 
pqpqpQpqpQpqpQpqpQp:5pqp:5pqfflco 



Goodenough/Longo 



175 



3.1 ABXs Perowskit-Struktur 



[Lit. S. 275 



^3 
•Hd 

o (d 
- H 



I I 



C/5 

c/i 



0^ 



to c/i 



CD 

? o 

o 



I/) 



, ,Jj >^ >>. 

S 5 S 

V, ■ \ I • • « ( I f 

c/3 c/) c/) cn 
cy cy oy dy <^ 
PL, ^ Pm 



o 

o 
.2 



c 
o 

o 



•a 



CO 



e a 



o ^ 



5 e ?s s 



oo oo oo 
■«* 

ti, 



00 
C7N 



ooooooooo 

ooooooooo 



QQ. CQ. QCi. QQ. ^ QCl QCL <^ ^ 



06060606060606060606 



oo-rHvoir)r-ooTt-<S'*^oc\ 
<Nor-oooooooc?;^'-;'<-;o 
oor-^r^fOcncooor^QOoooooo 



ooofOr-tooor-i^^ 



Tj-^'^-'^mLnoor-ooooQOoo 



inmiTjiriioiOLniriiriintn 



r- o 

\0 vO 
C^ C> CN 
c<S fO rn 



O O U H 



oooc^oohSSS^^SSSSouooohooooooooooo 



73 

o 
"+3 

c 

o 



o 

to 

H 
+ 



> O S P^l 

U Ui 

< (f) in (/) ^ 



rt O O ,aJ 

H H 
t H X 
O >^ 
»r ;r u t:' 

{/) (/5 [/) tn C/) C/) C/D 



0*99 
^ ^ tl 



d o oTo d'd'd'do do S § § o o-d^^oVo o do 



Goodenough/Longo 



S. 275 



Ref. p. 275] 



3.1 ABX3 perovskite struct! 



CD 



a 

CO 



ri 
3 
o 

B 

o 

a 



CO ,6 



> 

'So 



00 



CO o 

bo 



73 



CO as 
o s 

4-» f — I ^ W 



. cx, 

^C P 



Oi P< 
X 

4-> +» +J 



0) ^ ^ 



g CO 



2 -t: ;r a 



8co 2 



2 " 

Qj o CO a; 
Q (In Q 



S 2 2^ 

^ ^ o 

s s 2 : 

o a o 
000 

a< &t D^ 

4-> +J +J 

000 
dj (u 0) 

MH *4H < 

O Q) <D 



0(1)0 

2 

A 

+^ 

^ .2> -g 



pu. — •< — > 
J" 

I-< ^ _ 

^ Ir^ 1^ 

o 



a a. 
o o 

u u 

Oh Ph 

O O 

-M 4-> 

o o 

4) 0) 



CO 0) 0) 
SSS 



't* ■«* •«* •** -t* 



^ >^ -.^ >^ 

;s ^ ^ — 



"r* i,^ *^ ■*» ■«* 

^ ^ tl. tin tin !icj ^iC; N ^ 



^ 



o o 

II II 



O vO -"d- rO <N 

00 SO ir> ro o 
000000 

00 00 06 06 00 06 



(N ^ ^ 
(N 01 00 



T-< ro O •<-< 

m ■r-< c\ r- 

00 00 00 00 r- 

IT) liS LO uS to 



o C\ 
c\ 00 



(M -^d- OJ \£> OJ O O 

r^r-oooooor^-t-Hoo 
lOioirjiominioo 
uSiiSuSiiSuoLnoTj^ 



r-* CO 00 VO 10 CN 

CO r-troomoootn-^i-oO'rHO 
oor^r-sor^oooovooo 
o •^^ooooioino'^Tf 



« 

3 



o 



o 



i 



S ^ ^ U^^ U>, Ir^ Irs 

cocoJ^t^^:^^fcc;:^ji^tx;tx^:^^;:< 



O C\000\0<Mir>OCSIOMrOOcO 

JO Tt-vot-HCNcoooovOTi-CNOor-io 

^ inoot^ioosooooQOcx)r-r^r-r- 

06 06060006060606060606060000 



SSOOOOCJO CJ CJOOUOOOOHOO 



nJ UOOOOUC^CJOOOOOCJO 

PM 



+ odooo-oo-o 

« O H P ffi W >^ <^„t/^ 
<i OOCJOOOCUiPh 



O 
H 



pi^o>^PM;zito><HjPQ 

pL^fl^pL^pl^a^p^pI,(l^fl^ 




X5 XI 
Ph P4 



L.iiidoU rVirnstejn, Neuc 5>eric IT 1/4 a 



Goodenough/Longo 



177 



3.1 ABX3 Perowskit-Struktur 



[Lit. S. 275 



CO jq 



ctJ 



c 
o 

B 
o 
U 



U3 
:3 



o 
Id 



1^ 



o 
o 

+ 3 



(3 <N 
t — ' 

C u 
3 CO 

CL, J3 

O > 

o . 



2 2 

u u 

o o 

O O 



X! ^ 

I — I 

c/i c 

- U 

>- O 
O 

CN, 

fin >^ 



00 3 

^ of 
>> II m 

^ bot/i 

.Sc/5 

2 p > 

C C (U 

to +^ O 



o 
ni 

o 
'C 
o 



o 

•A 
o 

.0 



^ 



pLn di 0 



00 

o 



E 
o 



O 

a 
o 

o 

O 
CM 



3 



^ yf ^ ^ ^ ^ 

Q V ^ Q 

a, oq oq oq oq o 



Oq Co 

;2 ;s ;s 



00 

=1 



O ^ 



00 
00 



OS 



+J OOOCSOO^OOfOCvlTf 

ooo6o6o6a6oSo6o6o6c6c6c6oSo6c6o6o6c6 



m 
06 



rO (N CO 

00 Tj- CSl T-< 00 00 

O o O CN 00 

06 



T-< 00 O 

00 T-< 

in cn lo 



NO 10 

in CN 



3 



1(j u o o o o o o o u o o o u o o o o o 

+" " 



OOOUOH HUH 



O HO 



» u (& e to — ? «. 

o o o o o o"9 o 



pq o ^ a S ^ ^ e ^5 eg >S ^^3. *^ 2 r c f? 

PQ QffiWH>^^-lP^<^^^5g^5K-lOI^;H^^PM 

+ e>i « « e» w « M CI cMcatMciciMMci 

<j pqpqpqpqpqpqfripqt/)pqpqfqpqpqpqpqpq« 



+ J" J* «r « «^ 
< pqpqpqpqpqcnc/icT) 



O 
o 

o 
O 



O 
o 



o 

o 



178 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



B 



6 



C 
C 

e 

O 

U 



CO 



\o ^ 



C3 



|2i 



I 1 1 I 

if) CO 



13 



o o 
I-t J-( 

ft ft 

o o 

ft ft 

00 



ft*^ 

o •— ' 

CD 

O) Co o 

I 1 1 t f-t 

cy ^ o 
ft ft Iz; 



a; 

00 

d 
il 

O cn ft^ 

P OJ 



B 5". 

3 r-.CL, 

o to o 



ft ft 



o 2 ^ S 

6 Sen 
^^cn 0*5 

2 g >o o 



o 



cn 
cn 



ii^a ^< oq ii; 

cn cti CO cn cn cn 
ft ft ft ft ft 



O 

o 

o 

o 
00 

A 



Xi 

p 

o 

t: 

o 

, . 

■ >.to 
cn 



d 

O 



<L> 

2 I 

(a TD -•-» tJ 
01 ^ 'g ^ 

cn o ft O 

« § « 



.2 

o 

3 .S3 
S 

O CN 

^ T3! 
*« CO ^ 

1^' 



ft ft 
O O 



Cnft ftQOpOftP Q^Q^ 



a 

c 

o 





cocoOqcqoqct^ctiftiDq 


S ^\ ^ ^ 


> 


(Xik,oqoqLoaicotoft50^oqDqQ:|ft;QqK; 




0 CO 


LO 

SO 00 
















06 


0 CO 

Tf in 










KTi uS 










5.36 
5.42 


CO in 0 
coc7\ooTfininooincN 

T-<cOOC^C^O^^£)lnC^ 

ododoot^r^cot^uSr^ 


8.099 
8.390 

8.133 
8.098 


8.066 


VO CO CO 

00r-iCO0O(NCN00<7*vOr-00 CSJ'tHvO 

oor-4incovoqcO(Ncooeoooc>Joooc\ 
r^o6o6o6o6o6o6o6o6o6o6r^odr^o6r^ 


0 0 


OOOOUOHOU 


0 u 00 


0 


HOUCJOOOCJOUOUOOOO 



<cjo <iPQPQ(X|cncncncncjft <;pqpq(ppqpci 



O 



„ „co ^cn L 

i3 i3 i$ i3 ^ ffi n! ri u' iJ' C 

fPfElpqpQpqpqfnpqpqFPPQcyScncncncn 



Goodenough/Longo 



179 

12* 



3.1 ABX, Perowskit-Struktur 



[Lit. S. 275 



2 



a 



0) 



a 



a 
o 

6 
o 
o 



CO XI 



o . 

^ rv- 

^ ''3 CO 

A 



03 

PQ 

o 
Tl- 

A 



o 

fS fii . 
^ K 



• o o 

> +^ CT) 
• — <u 

c/) *Xi ^ 

rt c/3 cn 

^ II 

PM 



■$ 

CO 

u 

o 

o 
o 

1— < 

A 

o 

a 3 

o 



o 

(J; 

\ — J 

a 

o 

O 



C/) 
o 

O 

o 
m 
Y-i 

V 



3 



3 C3 KJ 

cn 

^ o o 



cn c/) CO c/) 
cy cy <^ ^ 

^ 



t3 



trt t/5 
^ - - 

. crt ( — I 
*jj 

^ £ .ti 



to 

. bo <u 



TJ XJ rTJ 

t: -g 

o o o +i 

4-» 5 

tn cn cn ? 



QPQP 



J; > o 05 

cu o :zi p 



o 

o § ^ > 



t.—i o 



tuO 



^ B 
(3 



g 2 ^ « 

Pk Pm Pm t-s 



bo 



« <^ ^ 
>r (sj ct; 

t-s O CJ 
Db C 2 

o a. 

-r- +J +3 
^ 1 



ft. 



•CP'S 

<U I. CD 

i5 5 



SO 



o • 



O 



u 



'^^^ Oo 



S <M ^ 
oq oq 00 CO 



Dq :^ 



. ^ NO >^ 

^ O o <a 



1^ 



O t-H 

^ o 



o m o 
r~ 



o 
oo 



o 

CsJ 



r- o 
Tf \o in 



CN O NO 

oo CN 00 

K 



O vO CS 
C\ NO (7; 

1^ 



CO 
00 



00 T-H o 

00 oo 



iTt o 

ro 

liS uS uS 



o 

00 



in 



so ■<-« CN o 
vo o CTN o ■<-; 
in o6 r-^ oo 



H O H 



O H H 



o o a a o o o 



oo 



U O H O 



T3 

OJ 






:3 






+3 
G 






O 






o 

+ 


o 


«> 


PQ 
+ 


O 

O 

M 




MM 


in 


C/} 



oo 

O M 
« »■ 
u u 
cn CO 



So 



if} 



CO CT) O O 



N C« C« M 

rt rt rt rt X> 
O O O O fi< 



dodd 

« ei M « 
XI XI J3 ^ 
PU Oh P4 Pk 



ooo 

Ct M &I 

X3 J3 ^ 

P^ PM Ph 



o 
o 



180 



Goodenough/Longo 



Ref. p. 275] 



3.1 ABX3 perovskite structure 



4) 



bo 
C 



.0 •<) 



a 



a 
o 

a 

o 
O 



tf> CO 



to CO 

a PI 

a a 



o o 



a 

o 

'to 

a ^ 
^ :^ ^ 



-M '-i3 
a> S <u 
£^ 

pop 

t! 

Cl< Pi 



^ Cm 

CD' .Si 

.2 



, ^ 

;^ 



to to to 

d a a 

o .0 o 

'"to 'm w ^ 

d CI ^ 

a a a^. 

^ ^ ^ 

o o u !^ 

o o o « ^ 



e '-g '-6 1, 



CJ o o o 0 -3 



+* +J 4J 

iH l-l 

<D O (D 
Ph P< Ph 
000 

IH 

Pi P< P^ 
000 



t: t 

(D dj <D a> tu 

p^ P, P, P, P, 
00000 

t-< b fcf h? * 



p^ Ph P, P, P, 

■S IS I 'I I III 



(1> o 



000 

OJ W 4) 



U/ VL/ Vl/ 14/ ^ I4i/ U.f V I*/ w w -a^ -^f 



> > 
^ di ^ 

N ^ ^ ^ U 



^ ;^ ^ N ^ ct; 



'(i- 00 
o ^ 
T-I o 

06 06 



CM (N 
O 00 
CM o 

06 06 



00 <n o 

O 'tH O 

000^ 

06 06 



<M CO 

T-H O 



CO 
I I 



bo 



to CO 

+ + r 
^ & t 

O O <D 

-5 ^ CQ 
« *M ^ 

CO 

Kri ■* 



+ d 

o ^ 
bo CO 

-a t 

to o 



o o _ 

1^ CO 
I 1 1 1 1 — ) 

c/3 tn cn 
<=y cy 
fXt Ah 



c/) cn to 



C\| CNj C\| 

o O O ti 

to 

L_J • '» II 1 

o« c8 0^ cy 

PM 



:3 

Oj 

O 
P^ 

a 

p. is 

Ph I 
to (0 

. r 

o ^ 

->-* M 
« fP 

r-iCio 00 O _d ^ 

^ ^ ;^ 0 1; SfL 

c/5 c/) 

c« dy a> CO fLi 
a, fl( 



10 

Pu 



o 

o 



Oo Oq Oq Oq Oo 
t-^ "~<» 1^ 

Co to to to to 



cototototototocoCq 



CO Pq CO cq 



06 



CO 
06 



vO fO 

00 in vo 00 in 
-i ro T-i T-^ O 



o vD 04 00 r~ 
ooTtoor-c^inmTj- 

OOT-iSDcOCO<M^Om 



0606060606 060606060606060606 



00 00 T-l ON 

T-t in rO rO CN 

in -^j; CO 
06 06 06 cd6 06 



H H 0000 



00 + OUOUO OOOHOtJOHtJ 



o 00 O (J 



P4 



+ 
< 



10 10 10 w'Ts 
c# cf ^ (f 

« M N C9 C9 

XI J3 ^ XI 

pu, ^ PM 




k^ ^ SI ffi £f 

IZi H^l t-J K-l >^ 

X>^XijQ^XlXlXlXlXi 
pMpMPLnPkPl^fXiplipMpLHflH 



s pt^ (2 

PQ g o CO § 

^ C4 CM tM <N CI 

nj cil n] nS 

< pq pq p:^ pq pq 




;z; SI to u M pq 
pq pq pq pq pq pq pq PU pq 



10 <0 <o «o 

o o o o c? 

« «J O QJ 0) 

p^f^pc^gfs 
TJ a ^ 

wo H 

M C« CI e« C4 

cd C4 (4 (4 

pq pqpqfp W 



Goodenough/Longo 



181 



3.1 ABXj Perowskit-Struktur [Lit. S. 275 



Magnetic 
Data 




Remarks 


Prop, [Lo2], P&S [Sc18] 

X = 1.2, small positive deviation from Vegard's 
law 

Prop. [S18, Lo2] 

Single crystal [S/7], Prep. [Sc18] 

distorted 
distorted 

P&S [Lo^ WalS] 
P&S[Sc/<?] 

P&S [Sc/<?] 
P&S [Sc/<?] 

P&S [Lo2] 






angle 






r: 00 r^r^r^cx) o6 o6 r- oo t- r- t- r- t- 




^ lOoSii-liniotrlin. 




^ S252o6o6 r^^o6r^o6r^r^t^r^r^o6o6^ooaoooooooooooooin^inu^^i/^u^ 

s 

+3 — 


Sym 


d — — ■ — 

o 

^ OOOOOO HOOUOHHHHOHOOOOOOOOOOOOOOOOO 

pci ^ 


Compound 


T3 

+ O 

5 III! 1 1 immmmMMMM^ 



Goodenough/Longo 



Ret. p. 275] 3.1 ABX3 perovskite structurl 



6 ^ 



2' 



I ^ 



1-4 

r— 1 

in S3 



1^ 00 00 



to S 

06 



S2 EoS^ 



in t~- tJ- u-> 
in r-; 
iri m iTj m 



o 

00 IT) 



6 



c 

o 
P. 

s 

o 
O 



8, 

+ 

d 



15 S S vS 

IT) uS tri 10 



00 NO ir> <N 

(x3o6o6uSioodo6o6o6o6r^o6odKi^ 



in in Tj- 

C7\C<-l(N(NvOO^CMTj-invO<N<N'OcOOOI^ 

0'^^<^c^^voooc^^ooooooooo^^o^-f0'^ 



00 00 lo m in 



060606060606060606 



0000 oaoffiffiOHOOHHOOOOHUHOOOO ooooooooo 



tM « « « 

CJ o ^ 




<j pq pq pq pq pq pq pq pq pq c« cA» CO c/3 c/5 CO c/) CO cri (J o o 



pq pqScjc/iHoSPMU 

+ MM M C* M « J* W M 

<: fqppqpqfqpqpqpqffl 



Goodenough/Longo 



183 



3,1 ABXg Ferowskit-Struktur [Lit. S. 275 



ytagnetic 
Data 


in 3.3.4. 
Tab. 

6 
6 


Remarks ^ 


Optical properties [Re4a] 
Doubtful 

Distorted. P&S[Ru4] 
Distorted 

Hex (6L) 

Complete structure determined, P&S [SIS, Ru4] 

Distorted 

Ce*+ 

Distorted 

Doubtful 
Doubtful 

Distorted 

Distorted 
Distorted 
Distorted 
Distorted 

Distorted, optical properties [Re4a] 

Complete structure; P&S [SIS, Ru4, Be2S; Ip1] 

Distorted; Prop. [KeU] 


Ref. 




angle 


o 

o 

C7S 

i! 




8.84 

14.9 
8.64 

8.943 

8.46 

8.553 
8.42 

8.36 




6.13 

6.06 

6.179 
6.03 

6.01 




SSSSSSo6uSvoo6aivdo6aio6c6o6oda3o6o6c6ooa>ooo^ 


Sym 


UHOOOOOKOOOHUOUUOOOOUOUOOUUUOOOOOaSOOO 


Compound 


c 

VP 

c 

o «, » 


184 


Goodenough/Longo 



Ref. p. 275] 



3.1 ABXj pciovskite slruclui 



e 



bo 



C/) 



o 

o 
o 



ft; 

CO 



5 

2 ^.t: 



0) 



CD u^ 

o 

a 



O 



> 

o 
o 



CO 

I — 1 1 — I " 
Os On . 



to 



<^ ^ .2 
1^ ^ Q 



3 ^ o 
I Ah ^ cA) 



o ^ 



CM 
to 



^ ^ 
(a «tt <ti <tt <to <tt ^ 

t< fcc^ t< E< 



vo *o 

>^ 

K K. ""^ "-^ 1^ t-^ 

ti^SSS CrjCoCOCOCoC^CoCoO^CoCoCo 















o 




O 




11 








r-l 




O 






(M 


00 


00 


OO 




iO 


VO 




rO 


uS 








CO 






T— » 






tri 


to 








O 



o o o r-- 

O CD OO Tf -rH 

r-- 00 r-; OO t-; 
o6 00 00 00 o6 00 



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3.1 ABX3 Perowskit-Struktur [Lit. $. 275 



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189 



3,2 Perowskit-ahnliche Strukturen 



[Lit. S. 275 



3.2 Desctiptions of perovskite-related stmctutes 
3.2.1 A-cation vacancies 
3.2.1.1 No A cations 

Because a skeleton of shared-comer octahedra is stable, it is possible to remove all the A cations from 
the perovskite structure without collapsing the BX3 subarray. In the case of □ ReO, for example, the 
structure remains cubic. However, a partial or a complete collapse of the skeleton is found in many □ BX^ 
compounds. The completely collapsed structure has hexagonal-close-packed X layers with one-third of 
the octahedral sites occupied by B atoms, as indicated in Fig. 19. This results in a simple-cubic array of 
B cations with comer-shared octahedra having a B-X-B angle of 132°. For comparison, Fig. 19 also shows 
the corner-shared octahedra across a close-packed □ X, plane of the cubic □ ReOa structure, where the 
B-X-B angle is 180°. It is possible to go from one structure to the other by a simple increase of the B-X-B 
angle, the B cations forming a simple-cubic array in all structures. In the partially collapsed structure, 
represented by CrFg, and B-X-B angle is intermediate, 150°. Trifluorides of the first-row transition 
metals have the partially collapsed structure, those of the second- and third-row transition metals have 
the ReOj structure where the number of outer d electrons per cation is S 3, but the completely collapsed 
structure where it is ^6. The B cations of the latter group either have no atomic moment (Rh^ and 
Ir^^ have /|g^2) disproportionate into magnetic and nonmagnetic ions (Pd^^, t\^e\ and Pd^, ^|g«g), so 
that there are no magnetic interactions between neighboring cations. The other trifluorides, on the other 
hand, are all antiferromagnetic, and coupling between like atoms of the second and third long periods is 
stronger than that between Uke atoms of the first long period . Since the B-X-B superexchange interaction is 
enhanced by a larger B-X-B angle, it is reasonable to assume that the interactions between neighboring 
B cations stabilizes the ReOj structure. These interactions may be either weaker interactions between 
localized electrons, as in the magnetic fluorides, or stronger interactions, as in metalhc ReOg. In this 
connection, stabilization of the cubic structure in the tungsten bronzes AJ^^WOj tor mx > 0.3 is signifi- 
cant. The conduction electrons introduce cation-anion-cationinteractions while simultaneously reducing 
the energy gained by a ferroelectric distortion. 

Electron-ordering distortions may be superposed on the array of comer-shared octahedra. MnFj, for 
example, exhibits the Jahn-Telier distortions shown in Fig. 10(a) superposed on the partially collapsed 
structure. WOj, on the other hand, exhibits several low-temperature phases characteristic of an interplay 
of antiferroelectric distortions and different degrees of the collapse of the B-X-B angle. 

3.2.1.2 The bronze structures 

Although □ BX3 compounds with the ReOg structure and cubic ABXg compounds have the same BX3 
array, complete solid solutions [Jx^i-x^^z^ 0 ^ x ^ 1, are not possible. Although there is no ordering of 
the vacancies for larger x, except for Nao.ysWOg [Ail], for smaller x there is ordering accompanied by 
a collapse of the BX3 array within basal planes perpendicular to a unique axis. Such a collapse creates the 
tetragonal and hexagonal tunnel structures of Fig. 20. The tetragonal structure contains three types of 
tunnels; one containing cubic, twelve-coordinated A* sites, one containing pentagonal-prism, fifteen- 
coordinated A " sites, and one small tunnel containing nine-coordinated A'*' sites, which are only occupied 
by Li+ ions. Without Li+ ions, all these sites are filled at Aj gAi'^BXg. This phase, which may occur for a 




Fig. 19. Projections on B-cation planes of two DBX, Fig. 20. Bronze structures found in A^Q^.^BX, systems, 

structures. Triangles in full and dotted lines represent faces a) Tetragonal (H) structure occurring for x ^ 0,6. b) Hexagonal 

of octahedra below or above the B-cation plane, a) Cubic structure occurring for x ^ 0.33 [Wat], 

□ ReO, structure DO,. Arrows indicate cooperative atomic 
motions that collapse the structure, b) Completely collapsed 

□ RhFj structure. 



190 



Goodenough/Longo 



Ref. p. 275] 



3.2 Perovskite-related structure! 



-range of x ^ 0.6, is labelled tetragonal {II) in Tab. 3 to distinguish it from the antiferroelectric tetragonal 
(I) phase of WO3. The hexagonal structure contains hexagonal-prism, eigh teen-coordinated A sites and is 
restricted to the range of composition x ^ 0.33, An orthorhombic tunnel structure has also been identified 
for ABjOe compounds [Gal So]. 



Tab. 3. Color vs. x for Na^WOj and compositional 
ranges for the bronze structures in the AJ-^WOj 
perovskites. Adapted from [Di3] 





royo/ blue 

dark blue 
dark gray 
green, WO3 



cub. 



kin m fefr.E 



hex. 



Q) K in plane 

or al ± 1I2 
% X ol ± ijif 

% K al ^ 



O A in plane 
O A qI ±7lE 
O B al ± ifz 

• B inplane # ^ + ^/^or - /A 

a b 

Fig. 21. Projections onto {110} planes of a) cubic perovskite 
and b) brown miller ite structures. Brownmillerite structure is 
formed by removing alternate [110] strings of oxygen from 
central row of a) and regrouping remaining oxygen into the 
tetrahedra shown in b) [W^a/]. 



3.2.2 Anion-deficient compounds 

3.2.2.1 Conipounds ABXa-^. 

'Several systems ABXg-^, where 0 < x < 0.5, have been reported as anion-deficient perovskites. 
SrTiOa.s and SrVOa.s, for example, both give simple x-ray powder patterns in qualitative agreement with 
the assumption of a perovskite structure having one-sixth of the anions missing at random. Further, the 
homogeneity range of SrTiOg-, is reported [Wal] to extend over 0 < a: < 0.5 without any change of lattice 
parameter. However, if an anion is removed from a close packed structure, the metal atoms to which it was 
formerly bonded will have highly unsymmetrical coordination, and some local rearrangement of the 
anion can be expected. The nature of this local rearrangement depends upon the character of the B 
cation. In order to learn what rearrangements may occur locally, it is necessary to examine those 
special cases where long-range order occurs, since local changes of cation coordination are difficult to 
detect by x-ray diffraction and have not been investigated by other methods. 

In the system SrFeJJFeJljxOa-a;, 0 < x < 0.5, it is known that the Fe^^ ions are stable in either tetra- 
hedral or octahedral coordination. Therefore, it is reasonable to anticipate the creation of fourfould co- 
ordination about half of the Fe®+ ions in the system. This is possible because the d electrons of Fe^^ ions 
are localized, so that Fe3+ and Fe*+ ions are distinguishable, even though the d electrons of the end member 
SrFe*+Os appear to be collective. Support for the creation of tetrahedral sites, as well as a suggestion of how 
the tetrahedra might be arranged, is given by C^^^fi^, which has the brownmillerite structure [Be41] of 
Fig. 21. Within every other (001) BXg plane of the cubic perovskite, alternate [110] rows of anions are 
removed. The remaining anions in these planes are displaced alternately along [110] and [TlO] directions 
toward the anion vacancies, the B cations shifting slightly also to maintain equal B-X distances with all 
four near-neighbor anions. The result is fourfold coordination for all B cations in these (001) BX planes, 
sixfold coordination for all B cations in the alternate (001) BXg planes. 

The x-ray pattern of KgTigOg has a strong resemblance to that of perovskite. However, KTiOg.s is not 
an anion-deficient perovskite, but is completely ordered, each Ti*+ ion having five oxygen near neighbors 
forming a trigonal bipyramid [An3]. It has little similarity to perovskite. 

The oxygen-deficient, tetragonal compounds (B^^x^i^^^j^BiO^-^, 0.22 < x < 0.5, retain an octahedral 
grouping for Bi in the B sites, but the A positions have only six oxygen near neighbors, two each at 2.7, 3. 1 
and 3.6 A [Aul]. 

These examples indicate that a variety of orderings must occur in anion-deficient perovskites. Further 
structural work needs to be done. 



Goodenough/Longo 



3.2 Perowskit-ahnliche Stnikturen 



[Lit. S. 275 



3.2.2.2 Alloys M^'Xi-^Mj 

Since the alloys M*^XMj are generally considered to represent interstitial X atoms in an ordered, face- 
centered-cubic M*^Mj alloy, it is not surprising that the phase is stable over a considerable range of anion 
deficiency. Since these alloys are metallic, it is probable that the X-atom vacancies are randomly distri- 
buted. 

3.2.2.3 Shear structures DBOa-,. 

Ranges of composition have been reported for BOa-^;, where B = Mo or W. Magneli lMa74] has 
shown that these compositional ranges consist of a series of discrete phases having an x-ray diffraction 
pattern dominated by a cubic □ ReOj-type (DOg) subcell, but exhibiting superlattice lines. The super- 
lattice of any discrete phase is not due to an ordering of anion vacancies within this basic structure, but to 
a regular interruption of the DOg structure by planes of discontinuity across which octahedra share edges 
rather than corners. In these structures the oxygen vacancies condense into regularly spaced planes and 
are then eliminated by a shear displacement of the type shown schematically in Fig. 22. These "shear" 
planes may be constituted in different ways ; For the series of phases B„05„-2» six octahedra in a group 
share edges, and for the phases B„03„_i groups of four octahedra share edges. In both cases the discon- 
tinuities continue in two dimensions throughout the structure where they separate DOg blocks n octa- 
hedra thick. The ^-WOg-^ phases, 0.10 < x < 0.17, belong to the series B„03„_2 with 12 < n < 20. 
The observed compositional range (W, Mo)Os_^, 0-07 < x < 0.12, contains six discrete B„03rt_i phases 
corresponding to n = 8, 9, 10, 11, 12, and 14 [Mat 7a]. The origin of the shear planes appears to be an 
interplay between electrostatic and elastic forces: Electrostatic repulsive energies between B cations 
sharing common octahedral-site edges is minimized by cationic displacements (of ferroelectric type) away 
from the center of symmetry of the interstice and the shared octahedral edge. These displacements can be 
cooperative, costing a minimum of elastic energy, if the shared edges are coplanar. The origin of the 
regular spacing between planes is not established. Presumably it is primarily due to elastic energy, 
although collective-electron effects [Goll] probably play a contributing role. 

3.2,3 Structures deficient in B cations 
3.2.3.1 Bismuth compounds 

Bismuth compounds with chemical formula (BigA^-ajB^-jOs^ have the structural formula 
(Bifiz)^'^ (A„_iB„03„+i)^", n = fw — 1. These compounds consist of a regular intergrowth of the perov- 
skite structure with BijOa sheets consisting of Bi04 square pyramids sharing edges [Au2], as indicated in 
Fig. 23. Between the Bi202 sheets are n layers of corner-shared octahedra and (w — 1) layers of perovskite- 
type A cations in the twelve-coordinated interstices. Where w = 1, the pyramidal sheets alternate with 




Fig. 23. One half of the pseudo- tetragonal unit cell of Bi^TijOi, (from x 0.25 J ^ 

toz ^ 0.75). A denotes the perovskite layer (Bi,Ti,0,o)*", C the (Bi,0,)*^ layers, 

and B the unit cells of the hypothetical perovskite structure BiTiO, [AuS]. # Bi • Ti Q 0 



192 



Goodenough/Longo 



275 



Ref. p. 275] 



3,2 Perovskite-related struct urel 



J 



single octahedral layers, and no sites are available for A cations. This particular phase has been prepared 
in a large number of oxides and oxyfluorides, where B — Ti, Nb, Ta and the 0/F ratio depends upon the 
valencies of the A and B cations (see Tab, 4). 

Many of these compounds are reported to exhibit ferroelectric distortions within the perovskite 
layers, and they will certainly be important for technical applications in the future, 

3.2.3.2 Hexagonal A„B„_iX3„ structures 

As shown in Fig. 1 (c), the cubic perovskite may be indexed on an hexagonal basis. It consists of cubic 
stacking of close-packed AX, layers with B cations in the all-anion octahedral interstices. Within a (110) 
plane, B-cation octahedra share common comers as shown schematically in Fig, 3(a). In the BajTa^Ois 
structure [GaSa], the stacking sequence of the AX3 layers is a-b-c-b-c-a, as shown in Fig. 24, and the B-cation 
vacancies are where the stacking is hexagonal. Thus the structure consists of perovskite blocks n AX3 
layers and {n ~ \) B layers thick, separated by a stacking fault at a layer of B-cation vacancies. These 
hexagonal structures appear to be stabilized where the tolerance factor is / > 1. 

3.2.3.3 AX (ABX3)„ structures 

Materials having compositions intermediate between ABX, and A2BX4 may have similar diffraction 
patterns. However, this compositional region contains several phases having the structural formula 
AX * (ABXgjn. Each phase contains perovskite sheets w units thick separated by AX (NaCl-type) sheets. 
The limiting composition AjBX^, corresponding to w = 1, is shown in Fig. 25. It is important for the 
theory of magnetism because, if A is nonmagnetic, then by symmetry there is no net molecular field within 
an antiferromagnetic layer from cations in adjacent antiferromagnetic layers. This permits the study of 
two-dimensional antiferromagnetism. The AjBX4 structure also permits the study of cations in oxides 
with a smaller B-X-B separation (hence stronger interaction) than is found in the BO compounds with 
rocksalt structure. The possible significance of this is illustrated by La3Ni04. The Ni*+ electrons of Cg 
symmetry appear to be collective in LagNiO,, localized in NiO. 









V /\ 

A / \ 












Y\ / 


• B cof/on 



Fig. 24. Schematic (110) projection of the BajTa^Ou struc- 
ture. Horizontal lines refer to BaOj close-packed layers with 
stacking a, b, or c. 




Fig. 25. Comparison of ABX, and A^BX^ structures [Tri]. 



3.2.4 Data: Crystallographic properties of non-ABXg compounds of composition Aa-BXg, 
□BX3, (AX)„(ABX)^ and BigOsCA^^iB^Og^+i) with perovskite-related structure (Tab. 4) 

Tab. 4. 

See Fig. 20(a) for the tetragonal II bronze structure with a 12.5 A, c 4 A 
and Fig. 20(b) for the hexagonal bronze structure with a 7.4 A, c 7.5 A. 

Within any section, the compounds are ordered by B-cation atomic number, and the order of the 
sections is as follows : 
Tab. 4a - A^BXg 

A^BOg; B = Nb, Mo, Ta, W, Re 

AxFeFj 
Tab. 4b - □ BX3 
Tab. 4c - □ BB'Xc 
Tab. 4d - (AX)„(ABX3)„ 

X = F-^ Cl-^ B2+ = Mg, Cr, Mn. Fe. Co, Ni. Cu, Zn, Cd 

X = 0-2; B = Al, Ti, Cr, Mn, Fe, Co, Ni, Cu, Ga, Ge, Zr, Nb. Mo, Tc, Ru, Rh, Sn, Hf. Ir, Pb, U 
Tab. 4e - BiA(A„-iB„03„+J 

« ^ 1 ; B = Mo, W « = 2; B = Nb, Ta « = 3; B = Nb, Ti n = 4. 5 and 8; B = Ti 



TandoU-Bornstein, None 51crie TIl/4a 



Goodenough /Longo 



193 



3.2 Perowskit-ahnliche Strukturen 



[Lit. S. 275 



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3,2 Perovskite-related structure 



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o 
ft 

B 
o 
O 



T3 

I S = 5 . 

4; §12-2- 



U 0) 

SI 



2, r 

it 



CO 



5 lo o • 



o 

o 



ft; 



o 

o 

o 



o9 



Goodenough/Longo 



195 

13* 



3.2 Perowskit-ahnliche Strukturen 



[Lit. S. 275 



'i $ 

Br. ^ 



B 



CO 



O 

c3 



c: o 
o - 



I — . tn 

■ - t-l 
- +J 



o 
no 

d 
o 



rn 



O 



JO 
00 



o o 

t; +^ 

S3 S - 

0) <D Ut 



O (N 
D > 



u O 



w =3 3 

^ tf) tn 
- w tn 



bo bo 



M CO 

o 



<N 
*^ 








rn 




o 




r-- 


o 




(M 




o\ 


11 


il 







Qq c:) CO 



00 



u~i r- 

OO 00 U~i 



S O O S 



O 



o 

o 



o 

o 



ooo 

o o o 

nJ nJ 

12; ^ ;z; 



C/5 



ex. 



CO 



00 to 



CX, PL, 
<D <U (U 
t-. 



^ o 

2 p. 



( — i 
.-t^ 

■> ■> 

CD <V 



4J CL 

O CN ^-^ - 



00000 



o -s; 
o to 

CO "—J 



m in if) m 
<^ oy 
Oi p^ pL^ fit pLi 



oo 00 Qo 
CO C/) C/) 

=y °y 

Pu, Pu 



O 



O 



CO CO CO 
PL, PL, PU 



C3 
O 
bO 

a 



^ ^ ^ 

55 52 to 



, ^ vii ^ ^ y> 00 



o 

<^ 

i! 



r-00 moo\ocNu^c<)ioocNO"^CNOo 

LOOO r-<r-^^^<NOOC^C^OOvOm»i~>fOl^ 

r~-r- CNOOoooor~-t~-r^t~-r--r^r~-oor-; 



00 r- in m vo 
r- r- 00 c^ 
r-^ r-^ r-^ r-^ c<S 



o ^ 10 

T-t t-H C> 00 

C\ 00 00 

cn c<S CO 



vOlo csiootntnvOCv)T-irt-'r-<r--T— (lOOO'^O c^ •^c^c> 

^oornr-HC^^^CNr-oor-r--tnTfTtolc^CNi't-*r--rnoinoovo 
T^oovor-u^CN<>ooooooaDoooooooooooooooor~-r^r~;V5ooin 



HK HOOHOHHOOOOHHHHHl^HaHHHHHH 



O 
H 



00 



I — « — f a n to n n con 

" "r<'/-?^«0 rTo O O o O O O O o O «0 O 
H H H H H H H H S^S 8 S^g SH ^a^aE-, S 



iaS£o.3o(i;;2icowOHQKw>H>^HPL.P^ 



196 



Goodenough/Longo 



Ref. p. 275] 



3.2 Perovskite-related structure 



B 



8 



^ o <l> 
O ^ 

0) t! CO 
c/3 H PM 



O C/} 

U I — I 

VP 00 

o > 

.T; -M 4J -^J 

g o nJ o 



a. 



3 

O 
o 



o 



9 OJ ^ 



^ ^ to C/) 
: S.| 

' P ^ 



0\ 

Co 
I 



2 
a. 



^ II a 



C! 

— aJ ^ 

+J un O 

_. <D H o 

;^ o ^ — +j 

3 « a 

^ o 



H oq 



o c! o 
P, -j:; j3 
d o Pi+j +^ 

S 3 



awl 

.JJ ® ? ~ 
^ ^ 

5f II ^ 

^- fl <l> ^ 



^ <^ r— . 

^ to 5 

<-> 



- tn 

> ^ 



+^ Pi 

I T-t c\ 



_T r— « 

00 nj ^ll^ 



^ o 



^ C! 

So 

Pi CO , 



V 

s 

<2) 



, H V 



' to Q 



m O +^ III ^ H-i ^ 
^ p< * ^ 



Oo 



to 

is 

P. 



v2 53 8v 



o \o ^ 
II o to 



o ^ bo 
-Co 

- oo 



4-> ^ 



-M O 1 — I 



H <M y ^ ^ - 



ill 

Ph ^ a? 

T* O -r* 

5 to 

— 

^ t; P. 



oq 



ei to 



to 
K r-^ 



•o in in 



in 

CM \o 
in m 



00 



in 



in 
1^ 



00 



in 

oo 



CN 00 00 

fO m 



m vo 

On O CM 
CO O 



<N 
CO 



o 



00 



o 



oo 

CN 



O -rH 



to 



-a 
o 

Ph 

o 
U 



po 



O 



o 

u a Ph 



o 



-p 

p^ 



o o 



o 



o 



o 

O 
1^ 



o 



d o 



O 



Goodenough/Longo 



197 



3.2 Perowskit-ahnliche Strukturen 



[Lit. S. 275 



•I 



o 



c 

l-< r 
><^ 

d 
o 



0) fO 

> ^ 

^ II 

G .tl 
> 

o Q 



P. 
3 



I — I 0) 

U rrl 
+-» 

O 0) 



2o 



o g 



I ^ 

'o no 
O OJ 

11 

^ CO 



-tJ V - 



O O ni 



tn o 



P. 

J-l - 



. o 

'go s 

o "-^ 

0 o 

1 11 V 



C 

o 



o £^ 
II 



^ O u 
O O 3 



<2> 

c 



3 
o 



5 V 



in 



It 



oVI^ 

vS ^ 

V o 



o 
o 

O 



T/ - - 



o > 

5 o C t-« op 



in 



*4-» o 

'HS .bJ 



2 



o 



4-* 



13 

a. 

X) 
<1J 



lO \0 00 
(N fO CO ^ 

II li II II o 

^ § S §^ 

s ?; s 5s 



CO 

(l4 



XI 
0) 

CI. 
XI 
0) 



H 



C3 



o 



o 

I — I 

X! 

o 
1-1 
bo 

to 
o 

^ g ^ b b ^ 
-i^ ON T-i i-( CN 



45 to 
o 



II II 11 II II 

S S S S 

^ s s ?; ?; 



o o d 



CN, 



O O 

pq oq pq O O O O OOOO OOOOO 



bo 





3.88 

3.84 
3.843 

' 3.834 
3.840 

3.854 
3.832 

7.581 

3.774 
3.767 
3.782 

3.89 




7.502 
7.420 

j 




rotn o o <N o ^mr-cs oor-oir- oomooo ooiOT-tr-^Ti- 

OJiOC^l Tl-\0 OlTf ''d- C^ rO tJ->OOCSCM(N<S<Nt-( (N^O^ OOOOOs 

r-^r-^oj tNt-H -r-fcn cm cm '^t cM^(Nootnoooooooo oooc5oc>co oc)oooc)r^t~^ 

rOfOuS t^oi oir-^ lO in CMCMCMrOt-^cncncOcn c*Sr*ScOrO cOcncOcOfO 


Sym 


UOH OH HO H H ffi HHHUHOUOO OUOO OUOOO 


Compound 


0) 

c; O 

^ o -n" "O" 1 » o dd'd o o>o-o"o oVo o" dddn-o 



198 Goodenough/Longo 



Ref . p. 275] 



3.2 Perovskite-related structure? 



■2- 



0) 

0^ 



in 

^ o 



C 
3 

. , sh 

O CO 

:s t 

8° I 

V ^ 

^ o o o 

O o 



o 



55 ?; H 



I o ^ 



CN4 ^ 

o o 



A 

H 

o d 

vf-g 

Vg 

2 S 

o c/5 



o 

0) 

I 

o 



CO 



XI 



d 

bo 



ft, o 

L_J(M 

0. V 



o 

o 

S II 



a. 

0) 



Q4 



> 

o 

o : 
^ *^ 



v: 



O O CN LO 

3 o o o 
'good 

" O <M r-« 
O O O O 



o o o 



H H H H 



CO O ^ 
O OT • S I I 

: 1^ NO ^ g 
d g>d b -Ji 



o a V ^ 

a a a Q 

« « 

O O O X) 
+J +j +j O 

> ;> > S 

CO CO 

X! 



> 
O 

« ,^ 
d to 

o ^ 



>H lH »H ^ 

TJ 'O 

d d d ? 

aJ . 

d d^ 

w ni oJ ^ 

Oh Oh P. 0) 

X « X 

0) (D 



d 
o 

CO 

d 



^ ^ ^ oS 

flj oj rt 

(U (U (U 'M 

xi X! X! d 

H H H W 



O 



- Cm 
?5 « « o o 
CO Op QQ 



CO CO 



^^ ^j- 



to 



li £^ 

2 

1w 



nJ ■- 



d 

d 

o 

O U (J 

'rt XI 'rt 

SMS 



^2 « 



o-2^ 

9 o ^ 
: — o 
00 <=? ^ 

■TH ^ O 

d : : 



a - 



\0 o 



II lO o 

^d d 
X il II 



: o o 

2 ; II 

• o . 



X. <a <tt V V 

q Q Q h h 



in o r~ 
m 



bo 

d 



Tj- fO 

CO C\ Cn 

II II II 



OO CO 

00 



00 r- CO 00 
in \o \o o 
CO 00 00 00 in 

r-^ CO CO CO 



^ in in 

(N T-t 00 o 

00 vo c\ 

r-^ r-^ K CO 



in 1-H 

00 Tj- 

00 



in 



o o 

CO T-H Cs) 

o^ in in 



Ti- oo in 

OO VO 



CM 

in CO 
00 in 



OO O OO 
00 O ^0 

r- r- CO ro 
CO en CO K 



00 CO in 
m 00 



vo ""t CO 

CO r-t Tt- CO OO 
CO CM CO 

ro K in in r-^ 



o ^ 
in CO 



(N ^ O <N CO 

*-t (N in CO \o 

00 00 CO CO CO 

CO CO r-^ r-^ csi 



in 00 in 
c\ ^ Cs) 
00 CO 00 



vo T-t o 00 r- in 

CO 't-f vo CO CO CO 
K (N 1^ in r-^ 



OOOO OOH OOHHffi KH O O K ffi ffi H oKH ffi O H ffi K 



d 
d 
o 

o 
U 



d 

d 
o 
u 



^ O =^ H 



o o 



3°^ 



5 » 

bOTj 



oo 



do 

« B 



g S « 

O O op 

ID ID (3 P^!^^ 



2 8 rt 



(£4 flH QJ I 
a> (1> O [34 

o g s s ^ « 



I fx, 



Goodenough/Longo 



199 



3.2 Perowskit-ahnliche Strukturen [Lit. S. 275 



H 



>^ 
















d 
o 






O fX( 











- - ^ d <N oj > CI 

" ^ ^ -5^1 £2t 

- o ^ -5 > 3 a, 



^ P ^r^p^p'^pZl, i-i oo Or—, Z2j'~^ 5 d Oh J l_:!jLZ, 

^ ^o^^^^^^^^^ ^ -S^ dd IS^E c/)2g|c/)c/^ 

^ Ss^gS^S^Scy ^ gg gu, ^^^^ 





CM cn 




r- 


r- 








o 


O LO 


in 


To 


in 


in 


CO 


CO LO 


CO 


co 






o 


o 


m 


CN CM 


in 


y—t 


(N 


in 


o 


o o 


o 


o 




o 


o 


C) 


o 


o o 


o 


O 


o 


o 


QO 


0\ OO 


r- 






CM 


00 








CO 


\o 


SO 


O 


in 

II 


iri u-j 
II II 


in 
11 


11 


u-j 
II 


II 


in 

11 


in 
II 


m 


in in 


in 


in 


in 


cr\ 




a 8 


8 


8 


8 






« 


II 
« 


II II 
« 8 


fl 
8 


li 


II 
« 


II 



in 



o in 



cvoocNoocnTj- (Nti- csj c\ cncsooooom <s(Ot-H\or-~ t^r^ oovo 

fno so r--ovooocNOfOCM oooocno ioti- 'r-iin 

pr--inr^cn(N f^*^ rn r>)cMCNC\c\ooTtcnin r-T-iCNoo<N r-r- '^'th 

inminroinm moo uS ininrncnroroininin inuScnc<Sr-~ corn in^ 



Goodenough/Longo 



275 



Ref. p. 275] 



3.2 Perovskite-related struct' 



d 

O 

a 

o 



XI 
pq 

□ 



o 
H 



bo 

a 



d 

o 
p. 

6 

8 



00 



0\ 



0) 
'> 

u 

O 

u 



o oo 
oo 



OO 

S II 



II II 



CM 

00 



0\ 



04 



o ^ 



a, 
o 



CD 

II ^ 
fa ^ 



O 



o 

O 
O 

V 

S7 



o 
o 
m 

V 



Oo tfl r^, 
^ 111 '— ' 



II 



CO 



S Q p; 5S rv 



On 
o 

O -+2 



P.® 
O , 

o 



5) o 
OiO 

22 
P. I 

o ' 

'■g II 



CM 



"^J- 

>^ ty^ 
ttt O O w to 

t< |:q ti^ tic^ ^< 



Oo Oo Oo 

C\| 

o o o e 
cq flq OH 



oq 



>^ f\ >^ >^ 

Dq ^ Jicj t:^ ^< 



Oo Oo Oo Oo 
o o o o « o 
PQ pq 0^ pq CXl tc: 







































o 


oo 




ri- 






CO o 
















CM 


o 


CM 






X— t 


rr> 


in 








o o 


m 




o 


o 


o 




T-< 




T— 1 


o o 


-* o 


o 


o 


o 


o 


o 


o o 


o o 


o 


o 


o 




o 


o 


O 


0 


o 


o o 


vO 


\o 


in 


vO 


oo 




in Tj- 






CO 






oo 




in 


in 


in 




in 
It 


in 
II 


in 
II 


in 

H 


in 
II 


in 

11 


tn in 

II 1! 


in in 
II II 


in 
II 


in 

11 


in 

II 


m 
II 


in 

II 


in 
II 


in 
II 


in 

II 


in 
II 


in in 
II II 


*S 


« 




« 




8 




« 8 


« 


« 


8 


« 




« 


8 




8 


8 8 



O \o r- c^ 

so m in CM CM T-t 



rn r~- o c\ ro 
00 CO in 



CM O 

in r- 



CM 

00 vo oo 00 oo 

^ Tl- -^t CM ^ 



in oo 



o rn o I m 

00 GO in Td- 



mmmmooinoo mmmmin 



00 in 00 00 in 00 



m m in tn in 00 



04 c/i 



tX4 
04 

+J 

04 



12; ^ cj ;z; 



•to 



^ H-1 h-1 04 O 



Goodenough/Longo 



201 



3.2 Perowskit-ahnliche Strukturen 



[Lit, 275 



C 

;=( 
o 

B 
o 



X 



o 
a, 

B 
o 



vO -O 



>0 SO O VO 



so 



o 
'53 

6 



CM 



'% 

CO 



o 



o 



to 



3 



O 



Vi CN 

du <^ 

---- 
;r c/) c/) 

fin Ph 



o 



to 



oo 
I I ' — ' 



1 I 

CM O 



-9 



I ft: CO 

^ o o a<«i 
Ph PM 



o c/5 
o - 

• in ' • Jj 

O t:^ J 
^ 



CD <U 

PL^ Pi^ 

o o 



Qi Qli" r-i 
(N CV, ^ 



PL^ (X, Pk PL, 



PU PM Oh 



^ oo 



O >^ O Dp Q q t:. Pc^ D:; Ct! ft^ Pq 



ft^ ct; ft^ 0:; ctt cti tS ^ oq c)5 cci 



o 



C7\ o oo c*^ m \o ro 
oo vo 

r<S CO lO vO lO 



ooT-<fOCNi-«c\\oo or-o 



oo(NoocNJO^c>vovrioor--Loc>l 

^^^^ ^ ^ ^ ^ ^ OS, 



o ^ 
(N iri ''t- 



lo lo Tj- in ro 

Lo lo r~- o ^ tj- 

O O O O CO CsJ r-H 

r<S CO iri lO 



00 o o lo r-- 



T— I oo m T-H c7^ tri rO 

OOiOrOTt-\0<:7\OOiO(N(NO 
00<NT-*CNT-<CSIcncOr-iOO 



hhhhShh hhhhhhhhhh hhh hhhhShooohhh 



no 



^ x's 4.U s § ^"(j; ^ ^ "«(3 



1 g 



tin 



3 ^ ^12; ^ c ^ 
«0 «^ ffi hr' Ph «fs) fo 



202 



Goodenough/Longo 




Goodenough/Longo 



3,2 Perowskit-ahnliche Strukturen 



[Lit, S. 275 



CO pQ 

a 



\^ \0 \0 vO O 



















o 






CVJ~ 












to 












CO 






o 












O 
























-M 






CO 




















1 
























o 








to 




& 














d 


d 


il 


O 

















to 



to 

d 
o 



CO 



O 
t-i 



00 



o ^ ^ 

Pm fit P-i 



o 

o 

O 

, .in 

^ A 



CO 



3 



o o 



a, 







o 










<N CN 


CM 






1 1 1 — 1 




03 


to 




1 — 1 


c/) c/) 












o 
o 




Plh Pu 






Pm 



C3 

O 



P. 

o 



to 

PM 



« 

O 
I I 

d 
o 

1-1 

PLH 



tN fN Ll, 
C/) C/) 

^ o 

PM Iz; 



0\ 

<^ 0^ Os *^ 0\ 



Os ^ 



0\ ^ CNj 



, , ^ ^ ^ ^ ^ ^ "2 ^ ^ ^ 

t^QqQq^3^;t^[?^(5aif^ioa.PL,a,cSDci:<:s^G^D;:a:i^^ 



(N lO 

inooc^^ovooo ooo>)m 

oc4cvi(N<N<N oic^oi csioic^)^oc<S(^j<^iT-IT--It-^cSl--«fOojoc^c^^ moi 



00 Tl- 

O -r-. 
00 00 



c\ Tt \o o oo 
00 00 00 00 



CM to in 

00 OO CO 



r^-r-«oom -'-'CNo or- 

,-ioin\OT-HvoTf^T-<CNTfooooc^CN^ocN)i-Hor---incMcorr» 

00 00r--^000C^C^G^0^ 00 00r--r-^00^-•r^C^C^OC^0000C^»-*O 



< OJ o o 
^ o r- in CO CO m 



r— * CS 
VO GO 

t-H O 



C/5 



HHHHOHHHHH HHHOHHHHHHHHHHOOHHHHHHHHH HH 



c 

O 

S 
o 
a 



c o 



O 



bo o 

^ tin O o o t/1 t/5/jg^;c5-^:3 



^^66^66% do odd 

(£:z;(^WOc))OPQc)5t))c)3^tJ0pqt/)c)3coc/)pqc/)omco 




204 



Goodenough/Longo 



Ref, p. 275] 



3.2 Perovskite-related structurJ 



Pi 



0) 



o 



(3 ^1 — lO 

P ^ ^ 

Ci II 



CD 
Oh 



CM C^ O m O OO 

CN I-" CO r- 00 r-t -O 

oi rn CO 



Td- fr> cn 



H 



m so m to LTi 

C^ CSI On 00 m CTn 

00 (N fo rO CO r- 

en CS Tj- Tt Tl^ liS 



C/) 



H ffi H H H H O 



a 
o 

o 



Id 



fin ?? D R,^ 
u rt to 5 I 



Goodenough/Longo 



205 



3.2 Perowskit-ahnliche Strukturen 



[Lit. S. 275 



O 

e 

o 
o 



q 

r 
o 

s 



C 



c/) 



o 
p. 
£ 
o 

a 



I/) 



to 

O 

c 



4-> 



o I — ' 

5 5 2^" 

13 . to 

^ i— . 



CO _ 
- On 



. CO <U 



I 1 1 I 

(f) CO 



>- r\j 



CO s 

..CO 
Ov 

CO to 

CO ID 

oa ^ " 



o 



CO CO 

On" oC 
00 00 



9. ^ 

»-! o CO 



O NO 



CO CO 

^ ^ 

Q t-s p^ 



S .Si 
■c a 

+J o 
o u 

s ^ 

0) (J 
On ^ 

Ql 

15 

cn^oo 

CO C/) 

^ PM 



^^^^ 

CO ^ 

^i; cn 



o 
o 

o 

6 



WO 



On 



o 



00 
to 



<D t 1 

OJ CO 



+J ^ CN~ 



00 



o 

u 

0^ 



^ r \ 

u O 

2?^ 



5?Os On" O 
>^ ^ o 



' h « £ It" 

PM 



o 



On |3 



g g g 

CO 00 CO 

<N Sr^' A 'otn' *A 

cococ/^co ^cococo 
f^PMPLipuHPHpL^PL^ 



a 

o 
xi 

u 
o 

^ C/) 

PM ^ 



*^ Cm c\| <N tN 

r: ::: s 5 s s 
cq cq ^ ^ ^ 



C\4 CN -^j. <N 



^ fN (N ^ (^f^ 



^ 00 ^K^*^00^^00CO^ 



^ ^ ^ ^ 

cocooococoi^cooo-^»-iCoco»-H 



m m fO 

CM (N vi-> O 00 10 

NO vO uS lO 

Oi CM OJ CN) 



csvo-sfo^r-oooT-HiooLOTj- 
r-csjcNvoocNO'^T-Hr-ir--Lnoo 
lOiOvOiOLnTj-iTiiTiiniornrocsi 



coaNr^roo(^t-'Orr»'<-'oor--cs 



rO m rr> 

o o cn o 00 o 

Lo u-» m iri in 

m lO uS liS lO LiS 



\o vo 00 

o m o o 

Lo in un 

liS in to uS Lfi 



NO (N 0 
C\ -^l- ro 

^ ^ ^ 



00 



10 



NO O 

CM O 

in in 



m in CM 

C> CN rO O rn C\ 

Tt- in in ^ Tj- 
liS in tn in in i/S 



m^o \OGNioc7v^OLncM^r--o 
fnor-momr-c\oor-vOT-f 
inmTj-minTi-Tf'^Ti-Tfoooo^ 
ininiiSioinintnioiriiiScnrnin 



1— "oooor~-ooinor--"^o^T-'T-i 

OCMT-*fnOTj-'^CM^C7NNO'OC\ 

^^^'^'^^'^'^^^'^^^ 
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Goodenough/Longo 



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III Figuren871-877 



Fi^. 87t. CaBi Mu ^ 

(ceramics). 













n 




mm 



i ^ 

« vs. r {61SU\ Fig. 872. CaBUTa.O, (ceramics) 



• tceramics). « vs. T (623 f 7}. 








1 — a?i?kHr — 






( 



Fig. 874, SrBi,Ta,0. (ceramicsl 





©fit ®Pb 

Fig. 877. PbBi,Nb,0,. Schematic dra - 
ture. One haU of the pseudotetragonal n^-'*^ °' ^V^tsl struc- 
to 2 0.75 is ffiven. ^ denotes the perx>v*L ""^^^ ^^"^ x ^ 0 25 
B denotes a unit ol hypothetical ptcov^l-!^^ ^^^^^ PbNb.Of- 
and C denotes (Bi,0,)»+ Jayers jj^^^^-^ucture PbNbo' 



Ill Figures 878-883 


























"A 
















r 
\ 













































m 



m 



m 
J- 



soo X soe 



Fig. 87 B. PbBi,Nb,0, (ceramics). Lattice parameters vs. T 
[6011]. 























\ 


a 










mk 

1 





Fig. 879. PbBi.Nb.O. (ccramitfs). jc vs. T [62S17]. 



heudo-erfhoHiomic 



m 300 

Fig. 880. PbBt,TatO, (ceramics), x vs. T [525 f 7]. 




Sed'm shoma tysfe- 
rtsis (for fitla in her^ 
diitch'on) 



Hon showing Hthd 
exHncfm dincHoos 
imwtd along dof^) 




Fig. 881. Bi4TiaOi». Relationship between the throe sets of 
crystallographic axes [67CS\, 



A 



U.9 
317 























































— 1 

pscffdo 


1 — 

'Orfhor 


1 — 

^om6ic 








n 














1 


ht^ooal 














1 
1 
1 





Bi • Ti O 0 



Fig. 883. Bi4Tt,0„. Lattice parameters vs. T [61S16\, 



Fig. 882. Bi«Ti,Oj(. Schematic drawing of crystal structure. 
One half of the pscudo tetragonal unit cell from * « 0.25 to 
z A* 0.75 is given. A denotes the perovskite layer Bi,TijOJ^ , 
a denotes a unit of hypothetical perovskitc structure BiTiO, 
and C denotes (Bi,0,)*+ layers {62StS], 



LandoU-Bfinutehi, Neue Serie in/3 



25 



377 



Ill Figures 890 :"895 




Fig. 890. BaBuTuOi,. Schematic drawing of crystal struc- 
ture. One half of the pseu do tetragonal unit cell from x « 0.25 
to I Af 0.75 is given. A denotes the perovskite layer 
BaBi,TijO|J, B denotes a unit of hypothetical perovskite / 
structure (Ba, Bi)TiO,, C denotes (Bi,Ofc)»+ layers [62SiS]. 




Fig. 893. PbBi^Ti^O,, (ceramics), x vs. T[6tS1S]. 




2 



















c 0 » 















Fig. 894. SrBijTi^Ojj {ceramics), s vs. 2' [S2Str], 



Its 



Fig. 892. BaBi.TuO„. Ba.Bi.TUOi,. Bi^Ti^On. vs. 
/] . ( J : swi tchin g time. 



Fig. 895. CaBi^Ti^Ou (ceraniics). x vs. T [tf/S//]. 



25* 



379 



HI Figuren896-'901 



01 




Fig. 896. BaaBi4Ti,0|,. Schematic drawing of the crystal 
structure. One half of the tetragonal unit cell from x « O 25 
to I = 0.75 is given. A denotes the perovskitic layer of 
BatBiaTitOii"^ B denotes a unit cell of the hypothetical 
perovskite stractore (Ba, Bi)TiO», and C denotes the laver* 
of {Bi,Oa)»+ [6^AS], 




-£00 -m 



Fig. 898. BajBi^TijOu. x' and «" vs. T \67AS\. 



1 - ■ 

mm 



















Fig. 900. Sr,Bi«Ti,0„ (ceramics). « vs. T \jS2S^7\, 




SO m m m &o m ssoxm 

^^ig. 897. Ba^Bi^TisOu. Lattice parameters vs. T {6315]. 
10^ 




m 300 mxm 

Fig. 899. Pb,Bi4Ti|0x. (ceramics), x vs. T {62S17]. 



mmm 




mmm 



o Bi 



cMedm 



Pig- 901, BijTiiOii. Schematic projection of structure on 



380 



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