R. G . GooncrrrLu et al.: Crystal Structure of I I 1 1 I V Se, Compounds 239

phys. stat. sol. (a) 68, 239 (1951)

Subject classification: 1.1; 22.8

Department of Physics, University of Ottawa’)

Crystal Structure of I 111 IV Sea Compounds

R. G. GOODCHILD, 0. H. HVGHES~), and J. C. WOOLLEY

Polycrystalline samples are produced for 13 different compounds of the form I I11 IV 0 Se, where I is Cu, Ag, I11 is Al, Ga, In, and IV is Si, Ge, Sn. Debye-Scherrer powder photographs are taken for each compound and all found to have tetragonal symmetry. The ordering lines are analyzed and i t is found that all of the compounds have the same structure. Intensity ratios for the 103:112 and 211:220 lines are detcrmined and compared with predicted values for various ordered arrangements. It is found that the compounds have the chalcopyrite structure with the lattice vacancy and the group I atom arranged a t random on one cation sublattice and the group I11 and group 1V atoms a t random on the other, i.e. (I

Es uerden polykristalline Proben fur 13 cerschiedene Verbindungen der Form I 111 IV Se, Iiergestellt, wobei I Cu, Ag, I11 Al, Ga und I n und TV Si, Ge und Sn darstellen. Es 11-erden Debye- Scherrer-Pulverdiagramme von allen Verbindungen gemacht und festgestellt, daJ3 alle tet,ragonale Symmetric besitzen. Die Ordnungslinien werdcn analysiert und gefunden, daB alle Verbindnngen dieselbe Struktur haben. Intensitatsverhaltnisse fur die 103: 112- und 211 : 220-Linien werden bestimmt iind mit vorhergesa.gten Werten fur unterschiedliche geordnete Anordnungen verglichen. Es wird gefunden, daB die Verbindungen Chalkopyrit-Struktur mit Gitterliicke aufweisen und das Atom der Gruppe I statistisch auf ein Kationenuntergitter und die Atome der Gruppe I11 und Gruppe IV statistisch auf das andere verteilt sind, d. h. (I c] )(HI IV) Se,.

) (111 IV) Se,.

1. Introduction

Previous work [I to 31 has established that many of the 1111 I V 0 Se4 compounds are adaniantine with a tetragonal structure. It has been indicated that the c/. ratio for some of the compounds is approximately two and that the coinpounds probably have chalcopyrite structure. However, no detailed investigation of the structure has as yet been described. Here the X-ray diffraction results for 13 compounds of the form I 111 I V Se, have been considered in order to determine conclusively the c / u values and hence the detail of the atomic arrangement.

2. Experimental Methods

Except for the case of CuCaSnSe, [4], single crystal samples of these compounds were not available and hence the analysis has been made using the results of Debye-S c h errer powder photographs. The I I11 I V Se, compounds investigated were the twelve formed by combinations of I Cu, Ag, 111 Al, Qa, In, and IV Ge, Sn plus one silicon compound AgGaSiSe,. These were prepared by the melt and anneal technique described previously [3] and for each compound, Debye-Scherrer powder photographs were taken using a Philips 114.6 mm camera.

l) Ottawa, Ontario K1N 6N5, Canada. 2, On leave from Physics Department, Nottingham University, Nottingham, England.

240 It. G. GOODCHILD, 0. H. HWHES, and J. C. \TOOLLEY

3. Analysis of Data

The 1 TI1 TV Se, compounds are adaiiiantine and can be considered as being devel- oped froiu the cubic 1 I-V1 coinpoimds with zincblende structure, the tetragonal dis- tortion being due to ordering on the cation sublattice. Thus the lines observed in the powder photographs can be divided into two types: ( i ) those corresponding to thc cubic lincs, called, for convenience, ‘structure lines’ and (11) those not occurring in the cubic case, caused by the ordering on the cation sublattice, i.e. ‘ordering lines’. With the tetragonal structure, most of the cubic structure lines will be split, e.g. the cubic 220 and 202 lines will be separated and the separation of the structure lincs gives a good indication of the c/a ratio.

For each coinpound, the positions of the structure lines have been irieasured and pseudo-cubic values obtained for the lattice parameters ( ~ 0 ~ and cot) using the Nelson- Hiley extrapolation nicthod [ 5 ] and imposing thc condition in each case that the slopes of the lines of (1 and c against the function 1/2 (em2 0/sin0

The true tetragonal paranicters can then be written as m i O c arid nco, where na and ra are siiiall integers. Values of nz and n can then be deteriiiined from measurements of the ordering lines. For all compounds considered, the ordering line values indicated that 778 : 1 and n = 2, i.r. that a0 = uoc and c0 = 2 ~ 0 ~ . One effect of this i s to double the value of the 2 parameter of the Miller indices froni that for the cubic case, so that, for exaniple, the 220 cubic structure line becomes the 220 and 204 lines in the tetra- gonal case. Ordering lines were considered only at low Bragg angles and were the same for all compounds considered, viz. 101, 103, 105, 211, 213, and 301. I t was found diffi- cult to try to detect ordering lines at higher Bragg angles, but the lines listed above were found sufficient for the analysis to be carried out.

Having determined the cell dimcnsions, the next problem to be considered is the ordcring of the atonis on the lattice. Effcctively, here there are four types of cation to be considered, viz. the T , 111, and JV atoms and the lattice vacancy. The first step is to consider what arrangement of these will produce the combination of ordering lines, and hence absent spectra, listed above. The intensity of the line hkl can be written as l(j1

cos2 O j O ) be the same.

where g(0) - (1 + cos2 2B)/sln2 8 cos 0, 21 is the niultiplicity factor for hkZ, A , is an absorption factor and

3’2 = C f i L cob 2n(/un + h j n + lz,) + C fn sin 2;z(hsn + kiyn + Zzn) 2 (2)

the suinination being over onc unit cell, and fn the atoniic scattering factor of the atom at the coordinates xn?j,z,?.

I n the first part of the analysis, it is necessary only to determine whether 1 is zero or not and hence the variations of 9;(8), A , and fn with 0 can be neglected. Thus f n has been assumed proportional to thc atoniic number of thc atom concerned and ~ ( 0 ) and A , have been ignortd In (1).

Since the same ordcring lines are obtained with all of the compounds investigated, i t is convenient to consider firstly thc case of CuC+aGeSe,. Tn this case, the three cations can be taken as equivalent and the ordering lines will depend only upon the arrangement of the lattice vacancies. Initially, an analysis has been made to see whst arrangement of lattice vacancies will give the observed ordering lines and absent spectra. T o do this, eight different cation sites in the tetragonal lattice need to be considered - for convenience these will he labelled in terms of the cell coordinates

[ % l 2 [ a I

Crystal Structure of 1111 IV Se, Compounds

x,y,z, as follows:

341

A 0 0 0 , B L1-L 2 , C O O ; , D + + 0 , E + 0 + ,

F 01-1. 2 4 ) G + O $ , H O + $ .

Calculations of I from (l), (3) have been made with one vacancy kept on the site A and the second vacancy placed successively a t each of the other sites. However, the cornbinabions AC and AD were not considered since these appeared to be structurally impossible, so that five combinations, viz. AB, AE, AP, AG, and AH, were analysed. Table 1 shows bhe 'ltkl' values of the low-angle ordering lines for which non-zero values of I are obtained in each case. It is seen that no combinat'ion of A with a second site gives the observed combinat>ion of ordering lines and absent spectra. Thus the vacan- cies can not be completely ordered in t.hese compounds.

Table 1 Ordering lines produced by the va.rious indicated ordering of vacancies

AB AE, AG AF, AH

001 001

003 003 005 005 010 100

101 101 101 102 012

103 103 103 014 104

105 105 105 110

111 111 113 113

115 115 201 201

203 203 205 205 210 120

211 211 211 122 212

213 213 213 214 124

215 215 215 221 221

222 223 223 225 225 030 300

301 301 301 302 032

303 303 303 305

002

114

202

16 physica (a) 68/1

2 42 R. G. GOODCHILD, 0. H. HUGHES, and J. C. WOOLLEY

Another possibility is that the vacancies are arranged a t randoni together with one of the cations on a cation sublattice. Thus the possible structures of stannite, thio- gallate, and chalcopyrite have been investigated. For stannite, there are three cation sublattices, given by the combinations (1) AB, (ii) CD, and (iii) EFGH sites. The posi- tioning of the vacancies on the AR and CD sublattices has already been considered in the above analysis but there is still the possibility of the vacancy and a cation a t randoni on the EIXH sites. Calculations have been made for this combination again in the case of CuGaGeSe, and the resulting ordering lines are listed in Tahle 2 . Again it IS seen that this does not agree with the experimental values.

T a b l e 2 Ordering lines produced by vacancies arranged on stannite, thiogallate, and chalcopyrite structures. Vacancies arranged a t random on sites indicated

stannite thiogallate chalcopyrite EFGH CDFG ABEH

002 002 101 103 105

110 110 114 114 202 202

211 213 215

222 222 30 1 303 305

101 103 105

21 1 213 215

301 303 305

For thiogallate there are again effectively three cation sublattices viz. (i) A R , ( i i ) FJH, and (iii) COFG sites and again there is the possibility of random arrangement of vacancies on the CDFG sites. The ordering lines calculated for this case are shown in Table 2 and again they do not agree with the present experimental results. Pinallj, the chalcopyrite structure has two cation sublattices viz. (1) ABEH and (ii) CI)F(+ sites, and the vacancies could be arranged at randoni on one of these sirhlattices. G I - culations for this case give the ordering lines listed in 'I'ahle 2 and it is seen that these arc the same as those observed for the present quaternary cornpounds. Thus it is con- cluded that the I I11 IV 0 Se, cornpounds have a defect chalcopyrite structurc.

The final question which arises is the arrangement of the cations on the two cation siiblattices. Thrcc coinbinations are now possible, viz. ( i ) (I C) and (I1 1 1 V), (i i) (1 1 I c) and (I IV), and (iii) ( IV 0) and (I 111). To see which of these occurs, it is necessary to consider intensities of the ordering lines. It is convenient to consider these relative to the intensities of the structure lines, since the latter intensities will be the same for any of the three combinations indicated above. Thus in thc powder photographs of the 1 3 cornpounds investigated, the 103 and 211 ordering lines have been used, the ratio of the intensities of the 103 to the 112 structure line and that of the 211 to the 220 line being deterniined. These ratios have been estimated by visual observation, two observers separately making the estiniates. For each componnd, the average of the four values thus obtained was determined and the resulting average valiies noritinl-

Crystal Structure of 1111 IV Se, Compounds 243

T a b l e 3 Relative values for the ratio of the intensities of ordering to structure lines. Mean values for ratios 103:112 and 211:220

CuInSnSe, CuInGeSe, AgInSnSe, CuGaSnSe, Cu AlSnSe, AgInGeSe, CuGaGeSe, AgGaSnSe, CuAlGeSe, AgAISnSe, Ag GaGeSe, AgAIGeSe, AgGaSiSe,

exp.

10 7 7 6 3 3 2 2 0.5 0.5 0.5

< 0.5 <0.5

- (I11 0) (I IV) (IV 0) (I III)

10.0 6.2 4.7 6.2 3.0 2.1 2.9 2.1 0.7 0.5 0.4 0.05 0.05

2.1 0.4 4.7 6.2

12.9 2.1 2.9

10.0 8.0

18.0 6.2

12.9 3.0

2.1 6.2 4.7 0.4 0.05

10.0 2.9 2.1 0.7 0.5 6.2 3.0

12.9

ized to a value of ten for the CuInSnSe, case, this having the niaxiniuni observed value. The normalized intensity values thus obtained are given in Table 3, the coin- pounds being listed in order of the intensity values.

These values are to be compared with values calculated from ( l ) , (2). Since each pair of lines, 103, 112 and 211, 220 are very close together in Bragg angle, again it was not necessary to allow for variation in g j ( O ) , A , and fn with Rragg angle in calculat- ing the intensity ratios and so the calculations have been made as indicated above. In these calculations, the scattering factors of cations in the same row of the Periodic Table have been assumed equal, i.e. A1 and Si taken as R,; Cu, Ga, and Ge as K,; and Ag, In, and Sn as R,; R,, R3, and I1, being taken as the mean of the appropriate atomic numbers. Calculations have then been made using (l) , (2) of the intensity ratios for 103, 112 and 211, 220 lines for all possible combinations of cations obtained with one vacancy and any three of the R values. Again, the two intensity values were averaged and normalized to a value of ten for the case of (Cu 0) (InSn)Se,, i.e.

Table 3 shows these calculated intensity ratios for each conipound and for each of the three possible cation arrangements. Coniparison of these values with those deter- mined experimentally shows a very good agreement of the experimental values with those calculated for the case (I 0) (I11 IV) . The values for the compounds CuInSnRe,, CuInGeSe,, AgGaSnSe,, CuAlGeSe,, AgAlSnSe,, and AgAlGeRe, rule out the possibility of (111 0) (I IV) ordering, while those of CuGaSnSe,, CuAlSnSe,, AgInGeSe,, AgGaGeSe,, and AgSaSiSe, similarly eliminate the (IV 0) (I 111) case.

(R3 0) (R,R,)Se,.

4. Coilelusions

The results given above show that all 13 quaternary selenides investigated have a tetra- gonal structure with a cia ratio of the order two. The same ordering lines occur in all cases and indicate that the structure is chalcopyrite with the vacancies arranged at random on one of the cation sublattices. The values in Table 3 indicate that the order- ing is the same for all of the compounds with the vacancy mixed with the group I element on one sublattice and the I11 and I V elements mixed on the other, i.e. all compounds can be represented as (I 0) (111 IV)Se,. 16*

244 R. 0. GOODCHILD et al. : Crystal Structure of I 111 IV Se, Compounds

One other effect which occurs with chalcopyrite ordering is the displacement of the anions, the selenium atonis in this case, from the ideal + f etc. positions. This dis- placeuient is small in the corresponding ternary chalcopyrite compounds and a similar result can be expected for the quaternary compounds. However, accurate intensity measurements on a large number of reflections, such as are obtained, for example, in a U’eissenberg photograph, are needed in order for any calculation of the exact posi- tions of the sclenium atoms to be carried out and so that question has not been con- sidered here.

References

[l] H. HAHN and G. STRICK, Naturwissenschaften 64, 225 (1967). [2] B. R. PARIPLIN, T. OHACHI, S. MAEDA, P. NEGRETE, T. P. ELWORTHY, R. SANDERSON, and

131 0. H. HUGHES, J. C. WOOLLEY, S. A. LOPEZ-RIVERA, and B. R. PAMPLIN, Solid State Commun.

[4j J. -4. LOPEZ-RIVERA and B. R. PAMPLIN, to be published. / 5 ] J. B. NELSON and D. P. RILEY, Proc. Phys. SOC. 67, 160 (1945). [6] 3. F. N. HENRY, H. LIPSON, and W. A. WOOSTER, Interpretation of X-Ray Diffraction

(Received June 25, 1982)

J. H. WHITLOW, Ternary Compounds, Inst. Phys. Conf. Ser. 35, 35 (1977).

35, 573 (1980).

Photographs, MacMillan Co., Ltd., London 1960.