Nonstoichiometric Compounds

18 Investigations of Nonstoichiometric Sulfides II.

The System In S .MgS 2

3

Downloaded by CALIFORNIA INST OF TECHNOLOGY on September 22, 2017 | http://pubs.acs.org Publication Date: January 1, 1963 | doi: 10.1021/ba-1964-0039.ch018

JACQUES BENARD, GÉRARD DUCHEFDELAVILLE, and MICHEL HUBER Ecole Nationale

Supérieure de Chimie, Paris, France

The stoichiometric compound MgIn S , as well as 2

the

terms

of

the

4

nonstoichiometric

phase

In S .xMgS, has the spinel structure. X-ray diffrac2

3

tion on this series and extrapolation for χ = 0 present a simpler approach to the problem of the position of the vacancies in the lattice than direct investigation of the pure In S , which has a super 2

3

structure of the spinel structure.

A careful study

of the diffraction intensities of MgIn S , of several 2

4

members of the In S .xMgS series, and of dis 2

3

ordered In S indicates the tetrahedral nature of 2

3

the vacancies for members of the series that are low in magnesium and for In S itself. 2

3

A concise

comparative study of the patterns of ordered and disordered forms of In S suggests a mechanism 2

3

for the order-disorder transition.

j^t the present time, the structures of I n S are rather poorly understood; two forms have been reported, and it appears that impurities have an influence on the crystallographic structure. O n l y the so-called "β" form is w e l l established. 2

Ordered Form,

3

fi-In S 2

3

The structure of / ? - I n S is not yet known w i t h certainty. T o a first approxi mation its structure is identical w i t h that of the spinels, but additional lines i n the x-ray pattern imply the existence of a superlattice whose origin must be sought i n the ordering of existing vacancies. This superlattice is tetragonal, and results from the stacking of three spinel unit cells (7). The assumed arrangement of vacancies deduced from the determination of the space group b y powder x-ray diffraction (7) requires for its confirmation a comparison of the observed and calculated intensities. This is difficult to accom plish directly on the powdery ordered product for two reasons : 2

3

1. I n the powder method, except at very small angles, there is considerable overlapping of superlattice lines w i t h each other, or w i t h primary lines, as is shown b y single-crystal spectra, and this renders unreliable an interpretation of intensity measurements. 204 Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.

7 8. BENARD ET AL.

70S

Indium-Magnesium Sulfide Systems

2. T h e displacement of atoms i n passing from the spinel structure to the superlattice structure may introduce a considerable error into any calculation based on the atomic coordinates of the spinel structure. T h e determination of these dis placements, considering the large number of position parameters, is out of the question except b y Fourier analysis of measurements made on a single crystal. Disordered

Forms

a - I n S , a form reported b y H a h n and Klinger (3) as having a cubic struc ture, and i n w h i c h the vacancies should be disordered, w o u l d be suitable for x-ray study, but we have not succeeded i n reproducing i t ; its existence, moreover, is debatable. B u t we have obtained, b y quenching l i q u i d I n S , a product w i t h a strict spinel structure. T h e interpretation of its pattern leads to a clear rejection of the hypothesis of octahedral vacancies.


2

3

2

The Phase In S . 2

3

3

xMgS

T h e trial and error method used for disordered I n S cannot account quanti tatively for observed intensities, since it offers no w a y to correct the systematic deviations that tend to restrict considerably the significance of precise measurements. A comparative study of the variations of intensities i n the I n S . x M g S system makes it possible to evaluate these corrections and to draw conclusions about pure I n S b y extrapolation to χ = 0. O u r study has therefore centered primarily on this nonstoichiometric phase, I n S . x M g S . 2

3

2

2

3

3

2

3

Preparation of Samples. A l l samples i n the series were prepared between 950° and 1000° C . b y direct combination of the constituents i n a silica tube sealed under vacuum. The disordered form of I n S was prepared b y heating to 1200° C . and very fast quenching to room temperature. X - R a y Patterns a n d Calculations. W e used, under the same conditions, the apparatus previously employed i n studying M g G a 0 and C d G a 0 (6), and our calculations were carried out i n the same manner. Intensity measurements were made w i t h a Geiger-Muller counter. T h e wavelength used was that of CuKa. Lattice parameters were measured w i t h a relative precision of ± 5 X 10 ~ A . 2

3

2

4

2

4

4

W e have referred all measurements to the series limit, M g I n S , as a stand ard. T h e structure of the latter was precisely determined, w i t h the following results: T h e degree of inversion (percentage of i n d i u m atoms i n tetrahedral positions), β, is 78 ± 3 % ; the sulfur position parameter, u (=2?r x), has a value of 93° ± 0.5°, rather far from the ideal value, u = 9 0 ° . T h e criterion for the convergence is the continuity of the curve of l o g (I /h) function of sin #. The refinement showed the need for a correction i n the / factor for i n d i u m given i n the tables. This correction allows the factor R — 2 | A F | / 2 | F | to be reduced from 8% to 3.5%. This corrected value of / was used i n a l l remaining calculations. 2

c

The Series In S . 2

s

a

s

4

a

2

xMgS

T h e fundamental assumption about this type of structure is the existence of a single k i n d of defect: metal vacancies. W e set out, first, to determine qualitatively the nature of the metal vacancies. The results are shown schematically i n Figure 1, where two triangles, F F F , represent the domain of F values that could be observed i n one case w i t h tetraX

0

Ward; Nonstoichiometric Compounds Advances in Chemistry; American Chemical Society: Washington, DC, 1963.

N

C


206

ADVANCES IN

CHEMISTRY SERIES

Figure 1. Comparison of measured structure factors of x-ray diffrac tion lines with those calculated on basis of octahedral and tetrahedral vacancies Values of F vs. number of vacancies

hedral vacancies, and i n the other w i t h octahedral vacancies. Subscripts I and Ν refer to the inverse and normal structures. T h e occurrence of vacancies requires the adoption of two definitions of the degree of inversion, depending on the hypothesis made about the vacancies. Tetrahedral hypothesis: β measures the concentration of i n d i u m i n tetrahedral positions w i t h respect to the maximum possible concentration. Octahedral h y pothesis: β measures the concentration of magnesium i n octahedral positions w i t h respect to the maximum possible concentration. T h e average of the experimental points corresponding to four lines among those most sensitive to the distribution of cations and vacancies indicates u n i formly a tendency, at all compositions, toward a very marked inversion, and for phases lowest i n magnesium, shows the tetrahedral nature of the vacancies. T h e experimental point representing disordered I n S is located almost on the exten sion of the straight portion of the average curve, near the corner of the triangle w h i c h is theoretically its only possible position. 2

3


IS. BENARD ET AL.


207

The quantitative study was made w i t h the aid of the function =

VF'(hkl) Ί

/VFW)

LF'(440)J/

Ί

L^(440)J

STANDARD

used previously i n the study of nonstoichiometric C d G a 0 . This function has the considerable advantage of eliminating the systematic corrections that are necessary i n direct comparisons—for example, i n the previous diagram. Its graphical representation consists of two families of straight lines corresponding to each hypothesis and to every composition. T o each observed value of Z , there corresponds a value of β for each of the hypotheses, both on the same horizontal level. A graphical solution is very easy; it leads to a single possible solution for phases l o w i n magnesium, that of the tetrahedral hypothesis (Figure 2 ) . T h e results of these graphical solutions are shown i n Figure 3.


2

4

Ζ

/ /

1/6

Figure 2. Ζ as a function of β for 620 reflection Deviations from Vegard's law are also shown i n F i g u r e 3. Beyond six vacancies (for a tripled cell) only the tetrahedral hypothesis is possible and Vegard's l a w is sensibly followed. W i t h a single vacancy, both hypotheses are possible, a n d the two types of vacancies conceivably could co exist. I n the intermediate region, it is not possible to proceed w i t h certainty. However, considering the results of V e r w e y (8) on the series M M 0 (where M is F e , N i , C o , etc.), relating the cell edge to the degree of inversion, and those of Baffier and H u b e r (1) on the strict correspondence between the curves of lattice dimension and the distribution, it can be supposed w i t h some con fidence that the degree of inversion increases or at least varies little. T h e product I I

2 I I I

1 1


4

ADVANCES IN CHEMISTRY SERIES

208 pi

Tetrahedral

100

100Ï

Hypothesis


90

76

K-H-K

60

Octahedral Hypothesis

50

40

Mgln S 2

4

1 1,6 2

3

Figure 3. Comparison of hypotheses of octahedral vs. tetrahedral vacancies in the system MgS.In S 2

3

Deviations from Vegard's hw thus remains inverse i n the intermediate range, as the qualitative graph (Figure 1) suggests, and the tetrahedral hypothesis w i l l be equally valid. Compounds Low in Magnesium

Content

These compounds are spinels up to very l o w concentrations or can be obtained as such b y quenching. T h e existence of the a form is perhaps due to the presence of impurities. Discussion In S 2

3

The tetrahedral nature of the vacancies predicted b y Rooymans (7) for is thus confirmed b y our study. I n addition, this suggests a physical ex-


78. BENARD ET AL.


planation for the residual difference between the characteristics of the structures of / ? - I n S , of disordered I n S , and of the idealized extrapolated structure, agree ing w i t h the crystallographic data and the irreversible nature of the order-disorder transformation at l o w temperature. Indeed the disordered compound becomes ordered rapidly and irreversibly at temperatures as l o w as 250° C , w h i c h leads one to suppose that the ordering occurs without m u c h movement of the metal atoms through the sulfur lattice. O n the other hand the pattern of disordered I n S is between the idealized structure and / 3 - I n S so far as the intensities are concerned, w h i c h means that the majority of the vacancies are already at the sites they occupy when the struc ture is ordered. The nonappearance of the superstructure lines w o u l d be due i n this case to the rather small size of the zones i n w h i c h the vacancies are i n phase, and to a statistical distribution of the metal atoms among their positions i n the superstructure. T h e appearance of the latter w o u l d require only small displace ments of the metal atoms w i t h i n the sulfur polyhedra, whereas the domains i n phase generate homogeneous superstructure zones, those out of phase generate twins w h i c h have been observed both b y microscopy (2, 4) and b y diffraction from crystals and from whiskers ( 5 ) . This multiply-twinned state of crystals of / M n S is probably very stable and is an example of antiphase domains (2, 4). This equilibrium state justified i n a certain measure the ratio c/a — 3.0000 between the axes of the / 3 - I n S lattice w h i c h the structural data appeared to forbid. 2

3

2

3

2

2


209

2

3

3

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Literature

3

Cited

(1) Baffler, N., Huber, M., Compt. Rend. 252, 3586 (1961). (2) Goodyear, J., Steigman, G. Α., Proc. Phys. Soc. 78, 491-5 (1941). (3) Hahn, H., Klinger, W., Z. anorg. allgem. Chem. 260, 97 (1949). (4) Harwell, H., Offerfeld, G., Herinckx, C., Van Cakenberghe, J., Compt. Rend. 252. 3586 (1961). (5) Huber, M., Ibid., 253, 471-3 (1961). (6) Huber, M., J. Chim. Phys. France 57 (3), 203-27 (1960). (7) Rooymans, C. J. M., J. Inorg. Nucl. Chem. 2, 78 (1959). (8) Verwey, E. J. W., Heilmann, E. L., J. Chem. Phys. 15, 174-87 (1947). RECEIVED September 6, 1962.


Nonstoichiometric Compounds

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