Laboratoire de Cristallographie aux Rayons X, Université de Genève, CH-1211 Geneva 4, Switzerland
Contents
1. Introduction 114
2. Survey o f the compositions o f ternary
c o m p o u n d s 114
2.1. The four-digit composition code 115 3. The different crystal chemical
approaches to the classification of the ternary crystal structures 115 3.1. Classification according to the
types o f polyhedra a r o u n d the
smallest a t o m s 118
3.2. Ternary structures interpreted as ordered derivatives o f binary types 119 3.3. Interrelation o f different crystal
structures o f the same composition which can be regarded as stacking variants o f a c o m m o n structure
slab 119
3.4. Structural seiles Of c o m p o u n d s having different composition 119 3.5. Classification o f struetures accord-
ing to the type o f h o m o n u c l e a r linkage o f the M a t o m s 120 3.6. Changes in structure type u p o n a
systematic exchange o f one o f the c o m p o n e n t elements for a given
composition 120
4. The strueture types o f the ternary phases in R - T - M systems 121 5. Recent structure determinations 285 6. Survey o f structures found in R - T - M
c o m p o u n d s and concluding remarks 287 Appendix. A t o m coordinates for the
structure types f o u n d in ternary R - T - M c o m p o u n d s 294
References 326
Symbols
a, b, c = lattice constants AH = change in enthalpy h.t. = high temperature
LC = linkage coefficient (see page 130) l.t. = low temperature
M = m a i n g r o u p element from the b o r o n or silicon group (carbon not included) R = rare e a r t h element, Y, Sc
rR3+ = ionic radius o f a trivalent rare earth a t o m
T = transition element from Ti to Ni group V = unit cell volume
x, y, z = a t o m coordinates
X E'~+"1 = crystal-chemical formula (see page 122) [] = vacancy
5' = part o f crystal chemical formula (see page 122)
= part o f crystal chemical formula (see page 122)
113
1. Introduetion
In a survey on the crystal structures of ternary metallic rare earth (including Sc, Y) compounds written 13 years ago (Parthé, 1970) the few known structures could be interpreted as ordered derivatives of well known binary structure types. Since that time phase diagram studies have shown that the number of ternary phases is surprisingly large (for example 21 phases in Ce-Ni-Si according to Bodak et al.
(BoMTKG, 73)) and a large number of ternary structures are not derivatives of binary structure types. With a few notable exceptions most of the early structure determinations were made at Lvov University (USSR) under the guidance of Prof.
Gladyshevskii, Prof. Kuzma and the late Prof. Kripyakevich. However, recently it was shown that some of these ternary rare earth compounds are superconductors (Matthias et al., 1977; Vandenberg and Matthias, 1977; Yvon, 1981; Braun and Segre, 1981; Johnston and Braun, 1982) which led to a wider interest in these compounds, and now a number of different laboratories are engaged in structure studies on metallic ternary rare earth compounds.
2. Survey of the compositions of ternary eompounds
This survey is centered on the phases found in ternary R-T-M systems where R is a rare earth element including Y and Sc,
- T is a transition element from the Ti to the Ni group, and
- M is a main group element from the boron or silicon group (carbon not included).
These phases can be grouped into three categories:
a) Truly ternary stoichiometric phases R«TyMz, where the different elements occupy different crystallographic sites. The structures of these phases are the main object of this paper. Frequently but not always they correspond to ternary derivatives of binary structure types.
b) Truly ternary phases, where certain crystallographic sites are occupied by different atoms at random. These phases can have extended homogeneity ranges. In nearly all the compounds ofinterest here, the content of rare earth element of a given ternary structure type is generally fixed; however, the ratio of the number of T atoms to the number of M atoms may vary. The composition given in the literature may correspond only to one point in the homogeneity domain in a ternary diagram. We shall denote these compositions by
Rx(TyMz).
Here we are often confronted with insufficient data in the literature. In most cases the homogeneity ranges have not been investigated. Furthermore there is always the possibility that the phase studied was not in thermal equilibrium. A reinvestigation of certain supposedly disordered phases, allowing for a sufficient annealing time, has shown that these phases are fully ordered.c) Extension of binary phases into the ternary phase diagram. These phases shall not be discussed here, except for the special case where, at special compositions, ternary ordering variants of the binary structures occur.
CRYSTAL STRUCTURES AND CRYSTAL CHEMISTRY 115
The compositions of all ternary RxTyMz compounds which shall be discussed in this paper are plotted in the ternary diagram of fig. 1. There are about 80 composition points to be found in fig. 1. With this great number of different ternary compositions, we encountered difficulties finding enough space in fig. 1 to denote the complete chemical formulae and opted to write only x, y, z instead of RxTyM~. This applies to compounds which are stoichiometric. In the case that a certain homogeneity range has been reported or that different atoms occupy a given crystallographic site at random the composition listed is that which has been found in the literature and for which the structure has been determined.
2.1. The four-digit composition code
We use, in this paper, a four-digit composition code to simplify the comparison between different formulae and as an aid in a quick search of a particular ternary compound in the ternary diagram. Since in nearly all compounds with variable composition the content of rare earth element is constant, it was found advantageous to characterize the composition of a given phase first with the content of non-rare- earth elements and secondly, with the M/T ratio or an equivalent value. In the proposed four-digit composition code the first two digits correspond to the (rounded- oft) atomic percentage of non-rare-earth elements and the second two digits to the (round-off) atomic ratio, in per cent, of M element to the sum of T and M elements.
Thus for a compound RxTyM~ the four-digit composition code is calculated as follows:
first two digits: rounded-off value of y + z
x 100, x + y + z
last two digits: rounded-off value of - - z x 100.
y + z
Examples of the composition code: 6750 for RTM, 9170 for RT3M»
Fig. 2 corresponds to fig. 1 but with the composition points identified by the four=digit eomposition code. In the case of a compound where T and M atoms occupy a structure site at random the last two digits of the composition code have to be placed between parentheses. However, for simplicity these parentheses have been omitted in fig. 2.
3. The different crystal chemical approaches to the classificaüon o f the ternary erystal structures
Many of the composition points in figs. 1 and 2 correspond to two, in some cases even to six, structure types. There are more than 125 structure types for approxi- mately 80 composition points. With this many crystal structures it becomes a
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