Structure of amorphous and glassy Sb2S3 and its connection with the structure of As2X3 arsenic chalcogenide glasses

Journal of Non-Crystalline Solids 48 (1982) 231-264 North-Holland Publishing Company

231

STRUCTURE OF AMORPHOUS AND GLASSY Sb2S 3 AND ITS CONNECTION WITH THE STRUCTURE OF As2X 3 ARSENICCHALCOGENIDE GLASSES

L. ( ~ E R V I N K A a n d A. HRUB~( Institute of Physics, Czechoslovak Academy of Sciences, Prague. Czechoslovakia Received 24 December 1980 Revised manuscript received 25 August 1981

Two types of amorphous and glassy Sb2S 3 were studied: amorphous orange-red powder obtained by precipitating a SbCl 3 solution using a stream of hydrogen sulphide in a bath of boiling water and a glassy material in the form of thin platelets obtained by the method of rotating cylinders. It was found by DTA that there is a great difference in the crystallization entropy and temperature between the powder and glass. Radial electron density distribution curves were measured for both modifications and a difference analysis showed that they can be considered to be much the same. From the distribution curves it follows that the basic unit is a trigonal SbS 3 pyramid which forms in the case of SbES 3 glass, a covalent random network while for the amorphous powder a random ordering of crystalline-like and band-like (Sb253) n molecules can be considered as an appropriate model. A comparison of radial electron density distribution curves for As/X 3 ( X = S , Se, Te) and Sb2S3 shows that Sb2S 3 belongs to the class of glassy A s 2 X 3 structures. A rule is found that in this class of glasses the mutual ratios of diameters of corresponding coordination spheres are constant. On the basis of coordination numbers and of broadening functions for individual coordination spheres it is shown that in the series As2Sa-As2Se3-As2Te 3 a gradual transition from a layer-like to a random network takes place and that glassy Sb2S3 can be put beside As2Te 3. This process is a result of the difference between orpiment-like configurations and As 2X5 ones, which evoke chain branching and interconnecting. This leads finally for As2Te 3 and Sb2S3 to a random continuous covalent network. This process is confirmed by increase of both occupation numbers and the widths of broadening functions corresponding to individual coordination spheres.

1. Introduction I n f o r m a t i o n a b o u t local o r d e r i n g in glassy a n d / o r a m o r p h o u s Sb2S 3 is o f p a r t i c u l a r i n t e r e s t : firstly it e n a b l e s a c o m p a r i s o n to b e m a d e w i t h o t h e r a m o r p h o u s 2 - 3 m a t e r i a l s ; s e c o n d l y , t h e c r y s t a l l i n e a n a l o g u e has i n t e r e s t i n g s t r u c t u r a l (local) p r o p e r t i e s ; a n d , thirdly, b e c a u s e o f t h e m e t h o d o f p r e p a r a t i o n o f the m a t e r i a l . A s a result o f the c h a r a c t e r o f the b o n d s in c r y s t a l l i n e SbES 3 it is r e l a t i v e l y d i f f i c u l t to o b t a i n an a m o r p h o u s s t r u c t u r e for this p a r t i c u l a r c o m p o s i t i o n a n d h i g h c o o l i n g v e l o c i t i e s a r e n e c e s s a r y [1]. T h e r e are t h r e e p o s s i b i l i t i e s for t h e p r e p a r a t i o n o f Sb2S 3 in a n o n - c r y s t a l l i n e f o r m : as an a m o r p h o u s t h i n film; as 0022-3093/82/0000-0000/$02.75

© 1982 N o r t h - H o l l a n d

232

L. Cervinka, A. Hrubf, / Structure of amorphous and glassy Sb,Sk~

an orange-red non-crystalline powder; and in the bulk. While the methods of preparation of amorphous Sb2S3 as a thin film and as a non-crystalline powder have already been reported (see later) we succeeded recently in the preparation of this material in "bulk" form by the method of rotating cylinders (section 2). Amorphous Sb2S3 thin films are usually obtained by evaporation in vacuum on substrates with temperatures lower than 130°C [2]. Zacharov and Gerasimenko [3] have presented a comparative study of Sb2S3 and Sb2Se3 thin films. They reported the positions of the first and second coodination spheres R I = 2.5 and RII ----3.9,~ and the number of S(Sb) atoms surrounding a Sb(S) atom as 4(2.7). The higher coordination numbers than in the corresponding crystalline phase were explained as a result of the absent atoms at distances of 3.15 and 3.20,~ which reflects the manner of joining S b - S - S b - . . . chains into bands. This conclusion was used to argue that the local ordering in the amorphous state was different from the crystalline one. However, in contradiction to their quantitative results (their relation R I I / R I -- 2 j/2 and R I I I / R I ~ 2 provides a basis for the consideration that the angles between covalent bonds in the film are close to 90 and 180 °) they proposed a structural model of an amorphous Sb2S3 thin film as pyramidal (trigonal) SbS 3 units bound by S b - S - S b bonds. In the crystal (section 4) similar pyramids are formed on the edges of double bands (forming a layer). Contradictory results were presented by Tatarinova [4]. A radial distribution of a Sb2S3 thin film calculated on the basis of an electron diffraction pattern under simplified conditions was presented. The number of S(Sb) atoms surrounding a Sb(S) atom was 6(4). A dense octahedral packing of Sb and S atoms was proposed. In another paper [5] values of R I = 2.6, R ii = 4.0 ,~ and coordination numbers 5.9(3.95) were reported for an amorphous Sb2S3 film. In connection with amorphous thin films it is worth mentioning the results on the measurement of the IR spectra of amorphous Sb2S3 films by Poltavcev et al. [6]. The position of the maximum of the intense absorption band (275 cm-1) practically coincides with the position of the maximum of a group of very intense high frequency modes in the IR spectra of the corresponding crystal. The authors considered that the absorption band of the amorphous film was a result of vibrations of similarly bound Sb-S pairs of atoms having equal distances to those in the crystal. As a consequence the observed absorption bands were attributed to vibrations in SbS 3 pyramids. The nonexistence of the complicated system of interatomic forces in amorphous films was suggested by the fact that in the IR spectra of antimony chalcogenide films the high frequency band corresponding to the shortest (SbnS I = 2.46 ,~) distance of the crystalline structure was missing. Amorphous powder can be obtained by precipitation of an aqueous solution of SbC13 by passage through H2S. In ref. 7 it was considered that this powder has a certain similarity with corresponding glassy materials. The shortest interatomic distance was found to be R I ----2.54,~ and coordination numbers were given as 3(2). From 'these measurements it was deduced that the structure of this amorphous powder was more similar to the crystalline powder of Sb2S3

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy Sb2S¢

233

than to a hypothetical amorphous material of the same composition. Recently Diemann [8] presented RDF of orange-red amorphous Sb2S 3 powder in a study of the difference between this material and SbzS3 prepared as a thin film. He obtained R I =2.54, Rn =3.80 and RIII z 5 . 8 0 , ~ . The interpretation of the area of the first maximum peak is in favour of a Sb-3S coordination, where Sb-S distances correspond to the same spectrum of distances as in the crystal (i.e. varying from 2.46 to 2.60 ,~). The interpretation of the second peak of the RDF can be given in close analogy to crystalline Sb2S 3, i.e. by the shortest interband Sb-Sb distances. However, the comparison of the calculated first peak with the experimental one on the basis of the crystalline short-range ordering is not convincing. Moreover, quantitative details on the analysis of the areas of the first and second peaks (coordination spheres) are missing. It was further pointed out that the RDF did not obtain distances in the range of 2.7 to 3.2 ~,, which are in the crystalline phase responsible for the mutual binding of (Sb4S6) n bands. The author therefore concluded that the short-range order of this non-crystalline substance was almost analogous to that of the crystalline variety, however, the characteristic connections of the (Sb4S6) n ribbons parallel with the b axis (section4, fig. 4) appeared to be absent. Because crystalline Sb/Se 3 is isostructural with Sb2S 3, studies of amorphous SbzSe 3 could be of interest in this connection. An atomic radial distributon function of this substance has been determined by electron diffraction [9,10], and the authors have deduced that the short-range order distribution is close to that in crystalline Sb2Se 3. According to ref. 10 the position of the first peak was 2.58 ,~, and of the second 3.90 ,~. The first peak coordination number was given as 2.63. From the above published work we may therefore conclude that while on the one hand there are strong indications that the local structure in amorphous Sb2S 3 consists of SbS 3 pyramids bound via sulphur atoms, on the other hand it is less obvious that the amorphous powder is formed by disconnected (Sb4S6) n layers (double-bands) and finally that there are still uncertainties concerning the structure of this compound and its classification a n d / o r comparison with other non-crystalline A s 2 S 3 arsenic chalcogenides. Moreover, as pointed out in ref. 11, there is still considerable debate concerning the structure of A s z X 3 glasses and thin films (the presence of layers in the bulk glasses of this type is still an open question) and therefore a comparison of non-crystalline Sb2S 3 and A s 2 X 3 might also help to elucidate this problem.

2. On the glass forming of Sb2S3 According to Hansen and Anderko [12] there exists only one compound in the Sb-S system, i.e. Sb2S3, which solidifies congruently at a temperature of 546°C (fig. 1). According to ref. 13 the melting temperature is (566 -+ 2)°C and the neighbourhood of the liquidus for the composition of Sb 2S3 has the form of

L. Cervinka, A. Hrubj~ / Structure of amorphous and glassy Sb2S3

234

700

/

i

I

615"

,I~J 600

520"

~

t

I

!~.546~,

530"

500 :D I-<~

,,- 400

IJJ O.

~r

300 ,,a

200

110" 100

o Sb

1'0

20

30

iO 5'0 60 7'0 8'0 ATOMIC PER CENT SULFUR

9'0

100 S

Fig. 1. The equilibriumphase diagramof the Sb-S systemaccordingto ref. 12.

a sharp peak. The authors also found a narrow (0.5%) miscibility region of sulphur in Sb2S 3. The preparation of glassy stoichiometric Sb2S 3 in massive form is very difficult and is only possible at high velocities of cooling the melt (section 3). A conventional method [14] that we have used in previous works (material in an evacuated thin-walled quartz ampoule, quickly quenched into water) was not successful, though a similar method was perfunctorily reported in ref. 15, but the material thus obtained was not thoroughly analyzed and its crystallization temperature (230°C) was questionable. We succeeded in the preparation of this material in glassy form only when we put it in ampoules having a sharp needle-like form at their end. We obtained, however, only small quantities (about several mm 3) which were insufficient for the present study. Finally we used the method of rotating cylinders (50 mm diameter). The melt heated to 700°C was dropped between rotating cylinders in an atmosphere of pure argon. As a result we obtained thin (0.1 to 0.2 cm) platelets of transparent glassy material with a dark red colour and having an area of about several cm 2 (material A). Very often there were dark regions at the ends or sometimes in the middle of these transparent platelets which according to our X-ray analysis could easily be attributed to crystalline Sb2S 3. We estimate that the velocity of the cooling of the melt between rotating cylinders was 103 to 104K s-1. The density of this material, measured by the pycnometric method, was 4.21 g c m -3. In order to have a better understanding of the structures of non-crystalline Sb2S 3 of different forms, amorphous Sb2S 3 was also prepared in the following way: antimony of a purity 6 N was dissolved in concentrated HC1 (with an

L. Cervinka, A. Hrubf~/ Structure of amorphousand glassy Sb_,S~

235

addition of several drops of HNO 3) and heated for several hours in a bath of boiling water. Then the excess HC1 was evaporated and the remaining volume was diluted with water to 11 so that the solution of the obtained SbC13 had a weak acid reaction. This substance was further precipitated by a use of stream of hydrogen sulphide in a bath of boiling water (material C), and in a bath at room temperature (material B), see section 3, table 1. These precipitated materials were then washed three times with distilled water and filtered and finally dried in a vacuum (10 -5 Torr) at room temperature for 5 days. Later a fourth modification (material D) was prepared as complementary sample for the DTA (see section 3). It was obtained by grinding (pulverizing) an originally crystalline Sb2S3 material which was prepared by melting the components in an evacuated and sealed quartz ampoule and by normal cooling of the ampoule in air. The crystalline material was then pulverized in a mechanical mill. During grinding X-ray diffraction showed a gradual broadening of the crystalline peaks. After six hours of grinding the half-widths of the strongest hkl-reflections were twice as large as at the beginning. At this stage DTA analysis was undertaken. Thus we produced several modifications of non-crystalline SbzS3 for further studies. The study of the differences in the structures of some of these modifications might help in solving the general problem of the structure of non-crystalline Sb2S3.

3. DTA of glassy and amorphous

Sb2S

3

The as-prepared modifications of non-crystalline S b 2 S 3 w e r e thermodynamically characterized by DTA (table 1 and fig. 2). In line A are given the data of the material prepared by rapid quenching of the melt. In order to find the region of glass transformation (Tg = 174°C) a standard rate of heating (2°C to 10°C/rain) is sufficient, however the development of heat is so abrupt (for some amorphous materials such as Ge and Sb it is even similar to an Table 1 DTA of glassy and amorphous Sb2S 3 (see also fig. 2). Tg is the temperature of glass transformation, To, is the temperature of the first crystallization and To2 the temperature of the second crystallization; A H i a n d A S i is the crystallization heat and entropy. The temperature is given in °C. Sb2S 3

Tg

Tc~

Tc2

AHt

AH2

A - glassy B - precipitated from aqeous solution at room temperature C - precipitated from aqeous solution in a bath of boiling water D - grinded (pulverized)

174

174

-

3.45

-

76

81

0.86 0.12 0.98

76 120

-

0.43 0.90

ASI

AS2

1.45

-

0.49 0.07 0.56

0.23 0.46

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy SbeSs

236

C

\

amorphouspowd,

/

IZ

~T

;o

1 76"81"

120"

174"

T [C °1

Fig. 2. DTA of several non-crystallinesamples of Sb2S3 for cooling rates 0.5 to l°C/min. A Sb2S 3 glass prepared by rapid quenching of the melt (between rotating cylinders), here TA coincides with TA, TA = 174°C; B - amorphous powder prepared by precipitation in a bath at room temperature; C - amorphouspowder precipitated in a bath of boiling water; D - crystalline Sb2S3 ground for 6 h. Tc are crystallizationtemperatures(see table 1).

explosion) that the DTA peak has the form of a thin and sharp maximum the area of which cannot be quantitatively evaluated. Therefore slower heating rates (0.5 to 1° C / m i n ) are necessary, but then the glass transition temperature T~ characterizing the glass transition interval practically coincides with the temperature Tc (sensitivity of the apparatus - 2 ° C ) , see fig. 2. Hence finding the region of glass transformation and taking in account Roy's definition [16] according to which "glasses are solids obtained by the cooling of a liquid with the very special condition that there is a congruent change of phase, i.e. that the melt can be completely transformed to the non-crystalline solid", we can consider the material A as a glass. For samples B, C and D we did not find the region of glass transformation and because these samples were prepared by precipitation a n d / o r grinding we shall call them amorphous. Line B represents the data obtained from measurements on amorphous SbES3 powder obtained by precipitation in a cool bath (at room temperature). Line C represents the data for the amorphous powder obtained by precipitation in a bath of boiling water. Data in line D correspond to a material obtained by the grinding (pulverizing) of an originally crystalline S b 2 S 3 material. For case A - glassy Sb2S3 - the region of glass transformation coincides with the beginning of crystallization (Tg = Tc = 174°C). This observation is in agreement with general knowledge that the difference Tc-T~ is a good estimate of the glass forming tendency. For very small differences (in this case T~ - Tg 0) the glass forming tendency is weak and high cooling velocities are necessary. The rotating cylinder method enabled a cooling velocity of about 103 to 104K sec-1. The crystallization occurs here in one stage at a temperature of 174°C and the developed crystallization heat and entropy are many times higher than

L. Cervinka, A. Hrubf / Structure of amorphous and glassv Sb, S¢

237

for samples B, C and D. Thus we find here an indication that in the glassy sample A the individual units which combine during crystallization are much smaller than those obtained by precipitation a n d / o r grinding as in samples B, C and D. In the case B - amorphous Sb2S3 powder prepared by precipitation in a bath at room temperature - the crystallization passes through two stages at 76°C and 81°C. However, this sample has a very large surface with a great adsorption ability and holds greater quantities of other substances which are present in the aqueous solution. Neither by careful decantating nor by washing were we able to remove admixtures. After drying the sample was not homogeneous, i.e. it was proved by X-ray diffraction that it contained not only already crystallized particles of Sb2S3 but about 5% of other different admixtures (oxides and chlorides). For this reason this sample was excluded from further X-ray studies. In case C - a m o r p h o u s powder prepared by precipitation in a bath of boiling water - there is only one crystallization process at 76°C and the crystallization heat and entropy are approximately a half of the value observed for sample B. It is remarkable that we observed a crystallization process at all because in this case the sample was precipitated at approximately 90°C, i.e. at a temperature considerably higher than the crystallization temperature found in sample B. The reason that sample C did not undergo crystallization during the precipitation might be attributed to the formation of large Sb2S 3 molecules surrounded by O H - and H ÷ ions which are relatively very stable in the aqueous solution and thus hinder complete crystallization during precipitation followed by the drying of this material. On the basis of the preceding considerations we conclude that this sample approaches the state of a real Sb2S 3 crystal more than sample B does. Moreover we were able to prepare it in pure form. For these reasons we decided to choose this material for further X-ray analysis. In fig. 3 is shown a scanning microscope picture of this powder illustrating its homogeneity and amorphous character at the limits of the resolution. It is very improbable that the observed thermal behaviours for samples A and C could be associated with the impurities in these samples. Great attention was paid to the preparation of different modifications of Sb2S3; starting materials were of purity 6N. It was proved by X-ray analysis that only sample B contained about 5% of impurities (chlorides and oxides) after precipitation. The reason for this was that in contrast to sample C, sample B (precipitated from a solution at room temperature) consisted of clusters (particles) of precipitated Sb2S3 which were smaller and less homogeneous. Therefore material B had a larger surface and could adsorb a greater quantity of impurities (admixtures) which could not be perfectly washed out. In the case D - pulverized (ground) crystalline Sb2S 3 we observed a higher value of T~ (120°C) than for samplesB and C (76°C). It is not easy to give a complete explanation of this increase. We suppose that this increase is probably connected with distortions, defects, a n d / o r deformations which are pro-

238

L. Cervinka, A. Hrubf, / Structure of amorphous and glassy Sb_,S3

Fig. 3. Scanning electron micrograph of the amorphous orange-red Sb2S 3 powder prepared by precipitation in a bath of boiling water, see section 2 for details; 1 cm corresponds to 5 #m.

duced during pulverization and which modify the structure more than could be expected. This idea is supported by recent results from the study of the amorphization of a-quartz by grinding [30,31] which show that the structure of amorphized a-quartz is essentially different from the structure of the SiO2 glass: the grinding process influences not only the mutual orientation of two corner bound tetrahedra but also produces considerable distortion and deformation of the lattice. Moreover oxygen defect centres are formed in the presence of 02. That there is a greater number of defects in the microcrystalline sample D than in the amorphous powder C can also be explained by the total measure of disorder characterized by the crystallization entropy AS which has for pulverized Sb2S3 a greater value (0.46) than for the amorphous powder (0.23). The question also arises concerning why all the DTA curves shown in fig. 2 are similar in shape. The explanation is that in all cases we have a crystallization process of a glassy or amorphous material. Because this process is from the thermodynamical point of view a transformation of the first order (bound with development of heat) it is understandable that the course of the DTA curves must be similar.

L. (ervinka, A. Hrub~ / Structure of amorphous and glassy SbeS3

239

crystalline $b253

f

-,~,~,

1/,

1/4

NI _Z-'~3/~

o=11,31 ~,

Fig. 4. The orthohombic structure of Sb2S 3. Large circles - Sb atoms, smaller circles - S atoms. Interlayer distances between atoms are given.

Sb2S3

crystallinelayer ~.o~ouble band)

I i

,

i

: i

i i

I: - ~ I i i

'i

i

i

4,

Fig. 5. The structure of a S h 2 S projection of the double-band.

c

3

layer (schematic). Intralayer distances are given together with a

240

L. (Tervinka,A. Hrubf / Structure of amorphous and glassy Sb, S~

4. The crystal structure of Sb2S3 The crystalline structure of Sb2S3 is quite a complex one; we use here data of the latest structural refinement by Bayliss and Nowacki [17]. The structure is orthorhombic (Pnma, D~6, a = 11.3107, b = 3.8363, c = 11.2285 ,~, Dm = 4.64, D x -- 4.63 gcm-3). Its projection along the b-axis is shown in fig. 4. Atoms form thread-like molecules, neighbouring molecules are coupled to form a band along the b-axis. The bands themselves are combined into layers (doublebands), which are parallel to the b-axis, fig. 5. In the book by Krebs [18] a description of the structure is also given. In general a Sb atom has three S atoms as nearest neighbours and S has two Sb atoms when taking an account only the strongest S-Sb bonds. The Sb-S bond distance is 2.57,~.

5. Comparison of the amorphous SbzS3 powder with glassy Sb2S3 In order to find whether there exist structural differences between amorphous Sb2S 3 powder and glass, we calculated for both materials the radial electron density distribution (REDD) curves (fig. 7a) and the reduced REDD curves (fig. 7b) from the diffracted X-ray intensity distribution (fig. 6a). In fig. 6b is presented the dependence of the interference intensity function s . i ( s ) on s. A difference curve of both REDD curves is presented at the bottom of fig. 7a. It shows that there are only very small differencies in the positions of the coordination spheres. Within the accuracy of the analysis the two REDD curves can be considered to be identical, Fig. 6 shows that amorphous powder (sample C) has a slightly weaker first diffraction peak at approximately 1.2 ,~-1. This peak measures the spacing of layered molecular clusters a n d / o r can be associated with certain forms of long-range order in the structure [32]. There could therefore be in sample C more disorder than in the glass (sample A). However, when we compare the difference in the height of these peaks (in our case 10%) with differences in the height of the first diffractions peaks in cases where real structural transitions were observed (difference in the height was more than 20%) [33,34], it is obvious that conclusions that depend on the analysis of the first diffraction peak of glassy and amorphous SbES 3 c a n n o t be convincing. On the other hand the intensity interference function of amorphous powder (fig. 6b) shows fine structure in the region from 7 to 9 ,~ and the REDD shows a peak at 7.5 ,~ (fig. 7), i.e. at approximately twice the value of the crystalline c-parameter. These observations indicate a more perfect ordering in the amorphous powder C. The results of the DTA support this idea because they show that both materials differ substantially in their crystallization entropy (see table 1 difference of about 1.22) and this difference cannot be explained in any other way than by the supposition that the structures of both materials are different.

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy Sb2S~

241

12001~", 1000"', 8001,'

Sb2S~

"~

~orphous 0[

~a

J

I

powder 1

20

30 8

40 1'0

5~ 12

6'0 1'4

70 16

'

1500 SbzS3

1000 glass amorphouspowder.....

A

500 iIj

" (- /-)

I

i

0

2V

Z

6L]/ 8

- 500 -1000 Fig. 6. (a) Corrected and scaled diffracted X-ray intensity as a function of the BragS angle 0 (s :4~r sin 0 / ~ ) for amorphous powder and SbES 3 glass. The diffracted intensity was measured using MoK~ radiation and a monochromator between the sample and the counter. (b) The interference intensity function s. i(s) for amorphous powder and glassy Sb2S 3.

L. Cervinka, A. Hrub) / Structure of amorphous and glassy Sb,S 3

242

20000

Sb2S3

5.95

>,. I-Z

3.85

10000

Z 0 (Z: I-¢,J LI.I ,-I

/"

gloss 2.50

/

"--

~8/

.

/

I.IJ

//."

amorphous powder

5000

t

r 0

I

-f: i " ~

v 1,0

2.0

3.0

~.0

5.0

8,0

7.0

8.0

°°-

Fig. 7(a). Radial electron density distribution curves for amorphous powder and glassy Sb2S3. For their calculation we used an artificial temperature factor exp(-as 2) with a=0.01 and as a sharpening function the square of the scattering power of an electron ]-2. At the bottom of the figure a difference curve of both distributions is shown.

6. Analysis of the radial electron density distribution according to the crystalline structure of Sb2S 3 In order to obtain a deeper insight into relations between atoms which might influence the radial distribution we calculated a crystalline-like radial distribution by s u m m i n g all appropriate pair-functions [see fig. 9 and eq. (3)] in the crystalline structure for interatomic distances smaller than 5 .A. This is the full line ("crystal") in fig. 8. In a similar way we calculated a distribution based only on crystalline intralayer distances (fig. 5). This distribution is shown as a

L. Cervinka, A. Hrubj, / Structure of amorphous and glassy Sb2S ~

243

3000

SbzS3 2000

gloss - omorphous

p o w d e r .....

Z

1000 z o CO

0

8.0

Q D

I~-~ooo -2000

-3000

Fig. 7(b). Reduced electron density distribution curves for amorphous powder and glassy Sb2S3.

dashed line ("layer") in fig. 8. Finally we calculated a distribution using only intraband distances - dotted line ("band") in the same figure; also presented is the experimentally obtained REDD of glassy Sb2S 3. By analysing the curves in fig. 8 important conclusions can be drawn: (a) The position of the first peak of the crystalline-like distribution is shifted to 2.60 A in comparison with the gl,assy one. The first peak of the band-like distribution is still shifted to 2.56 A. We conclude therefore that the nearest neighbour ordering in the glass (characterized by a distance of 2.50A) is different from that in the crystal. The area of the band-like distribution is 1920e 2 and it differs only in the limits of experimental error from the area of the first peak of the experimental distribution, which is 2000e 2. This is not surprizing, because following fig. 5 the coordination numbers of nearest neighbours in the crystalline structure are 3S for Sb and 2Sb for S. We now calculate the area A~ according to the formula (a similar procedure was used in ref. 29)

AI : Nsb ' 'sb + NgP ;,s,

(1)

244

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy SbeSy 8000

F

I

Psb,Sb >,I- -

i

$b-SSYSTEM

PU(dINTHE

z

LIJ Q

~.~.20000

Z

Sb2S3 ~

)-

IaJ

I'-

4 000

z oI.U z

EXPERIMEN

~0 I0000 ,--I

Sb, S

~

/J v

•

~"~".•,2" 3.0

4.0

i\j

" ILAYER

~,j

\

'..BAND

5.o r [~]

1.0

1.5

2.0

2.5

Fig. 8. Comparison of REDD of glassy Sb2S3 (thick line) with crystalline-, layer- and band-like electron distributions calculated by summing all appropriate pair functions situated in the crystalline-, layer- and band-like distance distributions (for distances smaller than 5 ,~). Fig. 9. Pair function analysis for Sb2S3. Variation of pair functions P,j defined by eq. (3), which were calculated for a distance rij = I between atoms. Multiplying the areas of Pu by appropriate concentrations [eq. (2)], we obtain a contribution of an atomic pair to the REDD curve.

where NSb(Ns ) is the number of Sb(S) atoms surrounding a S(Sb) atom and where " : Csbp ' esb,S C Sb,S

Cs p t

and P~',Sb C

Sb.S

(2)

are the concentration dependent pair functions, see table 2; Pi~ are the values of the pair functions Pij when the integral pu(r )

2r s ~ f'~ ='-~- 0 ~ e x p ( - a 2 s 2 ) sin(rijs) sin rs d s

(3)

is calculated for rq ='1, fig. 9. We see that for N s = 3 and for Nssb = 2, i.e. SbS 3 units bound via S atoms; and using values of P " from table 2, we obtain ,4i = 2 × 480 + 3 × 320 : 1920e 2

L. Cervinka, A. Hrut~f~/ Structure of amorphous and glassy Sb2S 3

245

Table 2 Pair function analysis for Sb2S3; values of pair functions P/j and of concentration dependent pair functions Pij in (e2), see eqs. 2 and 3 Material

P~b.S= P~,Sb

P~.s

P~isb

P~b.Sb

Pr'b.Sb

P~,s

Psls

Sb2S 3

800

320

480

2700

1080

235

175

in very good correspondence with the first peak areas in the experimental and band-like distribution. We conclude therefore that a trigonal unit is the basic unit in this structure. (b) A considerable difference between the crystalline-like and the experimental distribution is found in the region between 2.8 and 3.4,~. Diemann pointed out [8] that this difference was caused by the fact that in the amorphous state were absent Sb-S distances which bound in the crystal (Sb4Sr) n layers with one another. This statement, however, is not quite true. As is shown in fig. 8 even for a layer-like distribution we observe in this interval a considerable contribution of Sb-S distances making the first peak asymmetric. This asymmetric course is caused mainly by a significant contribution of interband (intralayer) distances of the type SbnS~ = 2.85 ,~, which join together the (Sb2S3) , bands. We deduce therefore that distances of this type must be absent in the glassy structure. Even for a band-like distribution we observe a peak with a maximum at 3.1 ,~. This is a result of the very important intraband distance Sb ~S~ = 3.11 ,~, see fig. 5, which causes the non-zero values of the R E D D between the first and second peak. We conclude therefore that a distance of this type must be present in the glassy structure. (c) We find that in the region of the second peak the R E D D is controlled completely by Sb-Sb ordering (see also sections 7 and 9). This follows immediately from the relation based on the numerical values of the pair functions tr Pq (table 2), i.e. Ps'.s: PSb,S : PS',Sb: PSb,Sb ----140:320:480:1080 = 1 : 2 : 3 : 8 . The area of the second o peak of the experimental R E D D is "Aexp = 9040e 2, and ill its position R H = 3.85 A corresponds precisely to the value of the b-axis of the crystalline structure, i.e. to the Sb-Sb and S-S intraband (intralayer) ordering distance in crystalline Sb2S3. However, the second peak areas of the crystalline-, layer- and band-like distributions are considerably smaller. We obtained Acryst 7410e 2, alayer ~-~-5910e2, Ab~ n d - - 4730e 2. These numbers indicate that 11 z llll we may expect a higher Sb-Sb coordination in the glassy structure (characterized by an average distance of 3.85 .~) than in the three above mentioned cases. For example in a band a Sb atom is coordinated in the range 3.84 to 4.02 A (medium 3.93 A) to 4 Sb atoms, in a layer there is a highly anisotropic (range 3.84 to 4.54.~, medium 4.04 ,~) Sb-6 Sb coordination and in the crystal

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy Sb2SJ

246

we have again an anisotropic (range 3.84 to 4.54A, but medium already 4.12 ,~) Sb-8 Sb coordination. Now we are able to estimate the Sb-Sb and S-S coordinations necessary for the explanation of the experimental area AII = 9040e 2. For this purpose we use an analogous equation to eq. (1), i.e. Aestim ~__. M S b D , , + II " ' S b " Sb,Sb

N, Sp '' S

S,S~

(4)

in which we are looking for reasonable values of Nsb and Nss. Supposing for a moment that Ns ---0 and subsituting for P~b.Sb the appropriate value from table 2, we obtain Nsb = 9040/1080 = 8.4 -~ 8. On the contrary we may suppose according to fig. 5 that the greatest physically reasonable value of Ns may be 5 or 6; the numerical equation for Nsb is then NsSbb=

9040 - (5 or 6 X 140) 1080 = 7.7 or 7.6 ~ 8.

We conclude therefore that the average Sb-Sb coordination number in the glassy structure for the average distance of 3.85 A is expected to be 8. (d) Our final remark refers to a possible model of the amorphous powder. Let us summarize information concerning this problem: i,t follows from the analysis in section 5 that there is a more perfect ordering in the amorphous powder. Secondly, the band-like distribution follows the course of the REDD in the region from 2.8 to 3.2 A. In the third place there is a striking agreement of positions of the crystalline-, layer- and band-like second peak (3.92 A) with the position of the second peak for amorphous powder (3.90 A). Finally, there is a less pronounced peak at 7.5 A, which is approximately twice the value of the crystalline c-parameter, fig. 7b. A model of the amorphous powder which would obviously suit the above deduction (also taking into consideration the results of DTA, section 3) might consist for example of interconnected and statistically disordered crystalline-like (Sb2S3) n bands. The shortening of the nearest neighbour distance in the amorphous powder (from the crystalline value 2.57 A to 2.50 A) is then explained in the same way as in ref. 8, i.e. that it compensates for the effect of missing coordination partners (with distance between 2.7 to 3.2 A) for two neighbouring bands. These ideas are further supported by an X-ray study of the crystallization of amorphous Sb2S 3 powder as a result of thermal and mechanical treatment. It was observed [8] that the crystallization process is caused by the ordering and linking of bands in the (220) plane and by their growth parallel to c-axis.

7. A working model of the SbzS3 glass On the basis of the conclusions of the preceding sections we tried to construct a simple model of a glassy structure which would combine the

L. Cervinka, A. Hrubf / Structure of amorphous and glassy Sb_,S~

247

constraints of the preceding discussions with necessary additional conditions (concerning bonding angles) deduced from the crystalline structure. We used for our model the following input data: (a) the shortest Sb-S distance is 2.50,~; (b) the bonding angle on the Sb atom is 90 ° (as in the crystal, see also table 6); and (c) the shortest Sb-Sb distance is equal to 3.85 ,~, i.e. the bonding angle on the S atom is therefore 100.7 ° (slightly greater than in the crystal, where it is 98°). The working model is presented in fig. 10. The atoms of a S b 4 S 6 unit are distributed in a brick of which the projection along the c-axis has an area a × b, where a -- 10.91 and b = 4.395 A. The coordinates of the Sb and S atoms are given in table 3. It is interesting that when we started our model with the orpiment-like configurations O 1 (see the Appendix) represented in fig. 10 by combinations of structural units centered on Sb I and Sb 2, we had to combine them - in order to satisfy simultaneously first and second neighbour distances with valence angles on Sb and S - with non-orpiment network-forming configurations of the type N Ocentered on Sb I and Sb 3 or on Sb 2 and Sb4. In this way the decisive role of valence angles which are close to 90 ° during the building of the glassy structure is illustrated. Using translations [10.91; 0; 0], [0; 4.395; -0.525], [10.91; 4.395; -0.525] a 40 atom basic network (layer-like) was constructed. The effective volume of a brick filled by a SbaS6 unit of a Sb2S3 glass (density 4.21 g cm -3) is easily

working model

Sb2S3 network

bl 4.39SJ'

c= 5.5871

"-1

X~/Sb'a--lO.9101~Sb2

Fig. 10. Working model of a Sb2S 3 network. In order to satisfy valence angles on Sb and S and to obtain the right set of distances (2.5; 3.1; 3.5; 3.85; ...) a combination of layer-forming orpiment-like O I configurations with network forming N O configurations had to be used (see Appendix). There are 40 atoms in the basic network and 40 in the shifted one (this shift is characterized by c = 5 . 5 8 7 A in order to have the right density). Shifted atoms enabled the contribution of interlayer distance to be calculated. This model also demonstrates that an interconnection of networks m a y occur in the direction of the b-axis at a distance of about 5b (because 5 x0.525 =2.625), see also section 11.

248

L. Cervinka, A. Hrubj~ / Structure of amorphous and glassy Sb2S3

Table 3 Coordinates of atoms in the working model of a glassy Sb 2 S3 network (see sect. 7 for details) Atom

Coordinates

Atom

Coordinates

Sb~ Sb 2 Sb 3 Sb4 S5

3.53; O; 0 7.38; O; 0 1.925; 2.52; 2.425 8.985; 2.52; 2.425 3.53; 0; 2.50

S6 S7 S8 S9 S~o

7.38; O; 2.50 1.925; 1.92; 0 5.455; 1.595; 0 8.985; 1.92; 0 0; 4.075; 2.05

calculated from the formula V = niAJND, where n, is the number of atoms in the volume, A~ is the atomic weight, N is the Avogadro number and D is the density. Using the values Asb = 121.75, A s = 32.06, N ----6.024 × 10 -23 cm g - 1 and D = 4 . 2 1 g c m -3, we obtain V = 2 6 8 , ~ and therefore the value of the c-parameter of our Sb4S6 unit must be c = 268/(10.91 × 4.395)= 5.589,~. At this moment we imagine that this c-parameter represents the distance between basic networks (layers) in our model. There are many possibilities for a mutual position of the basic and shifted layer. We chose simply that translatio~a which gave a maximum contribution of interlayer Sb-Sb and S-S ordering to the 3.85 and 5.95 ,~ distances. This shift is characterized by a translation [0.52; 1.97; 5.59]. Fig. 11 shows the distance distribution histogram of our 80 atom model and compares it with the R E D D curve. The distribution of all intralayer distances in the basic network is separated from the contribution of the distances between atoms in the basic network and the shifted one (interlayer contribution). For a better comparison the number of distances between pairs of atoms /j is multiplied (weighted) by the appropriate pair function P~j (table 2) and the distribution is then scaled so that the histogram gives in the region of the first coordination sphere (2.50,~) the same area as the R E D D does. A relatively good qualitative agreement between the histogram and the R E D D curve is apparent (bearing in mind the small number of atoms in the working model), e.g. how it reflects the important demand of a non-zero electron density in the region of 3 ,~. This was achieved by a suitable mutual orientation of elementary SbS 3 units in our working model ( N O configuration and distance Sb3-$5, see Appendix and fig. 10). In order to make a further comparison we calculated in a similar way a scaled histogram of the crystalline As2Se 3 structure (80 atoms) according to data presented in ref. 20, see fig. 12. Some general conclusions can now be drawn from both histograms as a result of a closer inspection: (1) In both distributions the intralayer contribution has a discrete character, i.e. forms four separated humps located at positions where we expect' with a certain probability the occurrence of coordination spheres R i (or where the R E D D curve displays its maxima).

L. Cervinka, A. Hrubf~ / Structure of amorphous and glassy Sb,S+

249

F.

Sb2S 3 working mode| 20

~i!~

scaled histogram

~i

>I--

Z O

5

o

n

i

toy,.

~

,--

'

2.0

3.0

4.0

s.0

6.0

r[~,]

Fig. 11. The distance distribution histogram of the working model (80 atoms) in fig. 10. Contributions of interlayer distances are separated from the intralayer ones. All the distances (ranging to 6 A) are scaled by appropriate pair functions using the area of the first coordination sphere in order to obtain a better comparison with the experimental REDD.

>. 3 0

,

,

crystalline As2Se 3

~~Z I.g t-~

scated

histogram I'L

z 20

°

//'

,.=J

.i

10

i'

•"

.!

•

r

,

L

i intertayerint yer :' '

•

L"

o_+ 2.0

3.0

4.0

5.0

60

70

r[~] Fig. 12. A scaled distance distribution historgram of crystalline As2Se3 for distances up to 7 A (80 atoms). There are again 40 atoms in one orpiment layer and 40 in the shifted one. The discrete character of the intralayer contribution (4 humps) and the fact that the contribution of interlayer distances is decisive for distances greater than 5.5 ,~ are of particular interest. The thin line represents the experimental REDD, see fig. 13.

L ~'ervinka, A. Hrubj, / Structure of amorphous and glassy SbeS 3

250

(2) Studying the representation of different atomic pairs in both the crystalline (fig. 12) and the working model (fig. 11) histograms more thoroughly we learn that in the region of the R I sphere the distribution is fully controlled by Sb-S (As-Se) pairs as it must be; in the region of the R~I peak the distribution is fully controlled by Sb-Sb and S-S (As-As and Se-Se) pairs, in the region of the R re.peak Sb-S (As-Se) interactions are decisive for the distribution and finally in the region of the Rlv maximum the distribution is again influenced mainly by Sb-Sb and S-S (As-As and Se-Se) pairs. (3) The contribution of interlayer distances becomes essential only for distances which are greater than R m. These conclusions will help us later to establish a generalized model of the glassy structure.

8. Mutual proportionality of corresponding coordination spheres for Sb2S3 and other As2X 3 arsenic chalcogenides We would like to draw attention to the following interesting observation: in table 4 are summarized the positions of coordination spheres as given by the REDD curves of S b 2 S 3 and A s 2 X 3 arsenic chalcogenides according the measurements made in our laboratory, fig. 13. All REDD curves were calculated in the same way from X-ray data obtained under the same conditions. We consider now for example R i data of As2Se 3 and of ASES3. Calculating the ratios RAs2Se3: R As2s3: 1.066;

RAs2S~:R As~s3= 1.063

"'mpAs2Se3.. "'in~AS~S3---- 1.076;

pAs2S3 : 1.074 RAS2SrS~ : --Iv

it can be seen that these ratios are constant with an average value RA~2Se~: R As~s3= 1.070 --+0.006, where 0.006 is the value of the standard deviation. This observation, however, has a more general character. This is demonstrated in table 5, in which these ratios are calculated for all combinations between Sb2S 3 and As2X 3 com-

Table 4 Positions of coordination spheres R i (~.) in Sb2S 3 and A s 2 X 3 arserlic chalcogenides (compare with fig. 13) Coordination sphere

As 2 S3

As 2 Se3

As 2Te3

Sb 2 S 3

Error

RI Rn Rm R Iv

2.28 3.48 4.20 5.40

2.43 3.70 4.52 5.80

2.65 4.00 4.90 6.35

2.50 3.85 (4.64) 5.95

---0.01 --+0.02 --0.04 -----0.05

251

L. Cervinka, A. Hrubj~ / Structure of amorphous and glassy SbsS s r

/ 45000

,?

40000

/" As2Tea

"~ 35000

/ 30000 Z W O Z O

25000 ! ,

I

.::

i i.

i

20000

sAs

i

4.00

,.A~

J

i.

i !

i. i.

Sb2S3 I

15000

i3.70 )

10000

2.65 2.43] I

5000 t

0

Z50 2.28~

1.0

2.0

3.0

4.0

5.0

6~

7.0

8.0 r[~]

Fig. 13. Radial electron density distribution curves of As 2X3 arsenic chalcogenides. All distributions were calculated in the same way from X-ray data obtained under the same experimental conditions in our laboratory.

p o u n d s a n d are a r r a n g e d a c c o r d i n g to increasing s t a n d a r d deviation. F r o m n o w on we shall consider the c o o r d i n a t i o n spheres which c o m p l y with this "rule o f c o n s t a n t p r o p o r t i o n a l i t y " as generalized c o o r d i n a t i o n spheres in this case o f glasses. T h e physical i n t e r p r e t a t i o n of this rule can o n l y d e p e n d on

L. Cervinka, A. Hrub~, / Structure of amorphous and glassy SbeS~

252

Table 5 Mutual proportionality of corresponding coordination spheres between Sb2S 3 and A s 2 X 3 arsenic chalcogenides, calculated on the basis of data in table 4 (see sect. 8 for details) j, k R{: R k

Sb2S3, As2S 3 1.102 --+0.0045

As2Se 3, As2S 3 1.070 -----0.1)06

As2Te 3, As2Se 3 1.088 ± 0.006

j, k R J: Rik

Sb2S3, As2Se 3 1.030--+0.008

As3Te 3, As2S 3 1.163±0.011

As2Te 3, Sb2S 3 1.0555 -+0.012

the fact that, in this class of glasses, the ordering of trigonal units is a subject of the same regularity. And further, the approach which consists in the calculation of the R E D D only on the basis of generalized coordination spheres, will be designated as the generalized model for this class of glasses. As a consequence, the above mentioned rule enabled us to calculate the unknown position of the generalized coordination sphere Rii I for Sb2S 3. This is illustrated in fig. 14. The value obtained from linear regression values was

.nmexperlv i

6.0

i

I//-~-- -)/

i

i

.......................

t..--..i

,g 5.0 E to._ ae

~R~lc

.

.

.

.

.

.

F

4.0 I n l

.

.

.

.

.

.

.

, )

I i

i

i

,

i

i

,

.

//VT .......

3O 2°2.0si

.

I i

i-/_iZ_if

///

IC/' : i ~0

~l~i~Di"ghL'"igi0l

.... ,,,~,

AslT~e

Fig. 14. The rule of constant proportionality of corresponding generalized coordination spheres in the class of A s 2 X 3 and Sb2S 3 glasses, i.e. the positions of the generalized coordination spheres of Sb2S 3 are a linear function of the positions of generalized coordination spheres in A s 2 X 3 glasses, see section 8 for details. Empty squares - experimental values (table4), full circles - values calculated by linear regression. It is demonstrated how this rule enabled us to calculate the u n k n o w n position of the third generalized coordination sphere in Sb2S 3.

L. Cervinka, A. Hrul~f~/ Structure of amorphous and glassy Sb2S s

253

RC~C= 4.64 + 0.02. this value was then used (table4) when calculating the III ratios R~: R~ between S b 2 S 3 and other arsenic chalcogenides in table 5.

9. The generalized model for glassy Sb2S 3 Only now are we able to set up the generalized model using the following conditions: (a) The first generalized coordination sphere is set in accordance with the position R l of the first peak, i.e. with the nearest neighbour distance S b - S - 2.50A. (b) In order to set the second generalized coordination sphere information on bonding angles is collected from the corresponding crystalline structure a n d / o r combined with information obtained directly from the REDD. Here we use: the bonding angle on the Sb atom (according to the crystalline structure) equal to 90 °, hence S-S = 3.54A. On the other hand, because the second peak is fully controlled only by Sb-Sb pairs [see also section 6. (c)] the Sb-Sb distance must be equal to 3.85 ,~ and thus the bonding angle on the S atom is 100.7 ° . In other words: because of the great difference between the atomic factors of Sb and S, the second peak (generalized coordination sphere) can be considered in fact to be a true second neighbour peak and therefore the average information concerning the bonding angle on S can be obtained directly from the average REDD curve. (c) The position of the third generalized coordination sphere was chosen to be in accordance with the calculation on the basis of the proportionality rule, as shown in section 8; we therefore chose R i l 1 z 4.64 ~,. (d) The discussion and analysis presented in section 7 indicated tha~ the area of each generalized coordination sphere R i was determined only by a certain type of atomic pair (i.e. for the first and the third sphere Sb-S pairs are decisive and for the second and the fourth only Sb-Sb and S-S pairs are important). Therefore only pair functions of these types are used for the calculation of the electron density contribution in the region of the corresponding coordination sphere. (e) Broadening functions Bij(r ) of Gaussian type are introduced for each generalized coordination sphere /j in the following way: the REDD can be represented as a sum of generalized pair functions Po(r, rij)

N,

p(r) = ~ ~ --~Pi~(r, rij), U(!

ij

(5)

tJ

where

Pi*j(r, rij ) = Pij(r, rij ) *Bij (r)

(6)

is the convolution of the primitive pair function P,j(r, 5j) with its broadening function Bo(r). In our case, however, we only used four broadening functions for four generalized coordination spheres k, hence eq. (6) becomes [see also

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy SbaS s

254

eqs. (2) and (3)] Ps*b,s(r, 2.50) P~b.Sb(r, 3.85)

----Psb,s(r, 2.50) ,B,(r) = Psb,Sb(r, 3.85) *Bu(r ),

"s*,s(", 3.85)

= Ps,s(r,

(7)

3.85)*Bii(r),

. . ,

It is clear that the broadening of pair functions which results in their overlap-

l: o

0.30

Y

SbzS3 broadening

0.20

functions

0.10

0

~ /

....

~i~

10

x

{3

II /I

."~.. 20 000 •

z

-

pair functions . . anatysis

>15000

/

r5"24~

FI

[ 5.95 / I ~_ i/

I,

sb-6,8s

Sb-TSb J13851 ,l

S-4.SSb /Z ~.64 & t/// !I

3,', i\', ;\',

?~ //! I~ // I

5-7~ ~L

~I0000

I

¢I

/

z

I

20

3.~AL

;\', i \\

I,LI

Sb-3S

5_ 5o 2.5o

SO00

if'

-v ~'

20

.~

I

~ ~ , 3.0

I

I/\-/i/ //~ ',\ / L/ //! ;\ !A!/ /// 4.0

:

ii ' I ',

i

i

i,~

5.0', /

,

6.0

"~

r[X]

70

Fig. 15. The generalized model for Sb2S3. The thick curve represents the experimental REDD; the thick dashed curve represents the calculated one using eq. (5). The thick dashed curve represents the calculated one using eq. (5). The thin dashed peaks represent the contributions on the basis of primitive (unbroadened) pair functions, eq. (3). The thin full peaks represent contributions of individual types of atomic pairs to generalized coordination spheres. Coordination numbers N,j are given in the notation (I - N,jJ) together with the positions of the generalized coordination spheres (for the second sphere see section 9(b) for details). In the upper part of the figure are given the gaussian broadening functions Bk(r), see eq. (7).

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy Sb2S3

255

ping compensates to a great extent for the simplified assumption of only one type of pair function used for the interpretation of a generalized coordination sphere. This also introduces the minor contribution of atomic pairs in the region of 3 ,~ of the R E D D . F o r this reason we considered as unnecessary the introduction of a generalized coordination sphere for this interval, moreover this sphere would not suit the criterion of the proportionality rule. The result of the analysis is presented in fig. 15 in which coordination n u m b e r s N/j and radii of the generalized coordination spheres are given together with the shape of gaussian broadening functions Bk(r ).

10. The generalized model for glassy AszX 3 arsenic chalcogenides In a similar way as in the preceding section we continue with arsenic chalcogenides. (a) The positions of the first, third and fourth generalized coordination spheres are determined by the positions of the first, third and fourth peaks of the R E D D curve. (b) The input data for the second generalized coordination sphere are determined on the one h a n d by use of the first neighbour distance and on the other h a n d by it/formation on b o n d i n g angles from the corresponding crystalline structure. F o r ASES3 the b o n d i n g angles on S (99.8 °) and As (102.3 °) are calculated according to ref. 19, see table 6. Because there is again a great difference between the atomic factors of As and S, the second peak of the R E D D is influenced mainly by A s - A s pairs and can be considered as a true second neighbour peak, i.e. the average information concerning the b o n d i n g angle on sulphur can be obtained directly from the average R E D D , i.e. from the position of the second maximum. The result is that the b o n d i n g angle on sulphur in the glass is equal to the crystalline value, table6. Using the crystalline value of the b o n d i n g angle on As (102 °) for S - S interactions we

Table 6 Bonding angles on atoms in crystalline and glassy (generalized model) Sb2S 3 and As2X 3 Compound

Refs.

Crystal

As2S3 As2Se3 As2Te3

[19] [20] [21]

As: 102.3° As: 99.7° As: 95.3° a)

Sb2S 3

[17]

Sb: 90.0°

Glass S: 99.8° Se: 94.4° Te: 92.7° a) 95.0° b) S: 98.0° c)

As: 102° As: 100° As: 98°

S: 99.5° Se: 95° Te: 95° to 98°

Sb: 90°

S: 100.7°

a) Value calculated only from the chain of AsTe3 motives. b) Value calculated from the medium of all shortest As-As distances and from the medium length of an As-Te bond (2.77) in a AsTe3 pyramid. c) Value on two-fold coordinated Sn (fig. 5).

L. Cervinka, A. Hrubf / Structure of amorphous and glassy Sb,S3

256

cannot influence the position of the second peak (3.48 ,~) by the distribution of S - S pairs located at 3.54.~, see fig. 16. For As2Se 3 in view of the values of the atomic factors of As and Se the As and Se stoms contribute in equal parts to the second neighbour peak. In order to advance consequently we used for the calculation of As-As (3.58 ,~) and Se-Se (3.72 ,~) distances the crystalline values of bonding angles on As (100 °) and Se (95 °) according to ref. 20. For As2Te 3 the situation is rather complicated. First of all the determination of bonding angles on As and Te in a chain of trigonal msTe 3 units from the crystalline structure is not straightforward because of the complexity of the structure (mutual bonding of trigonal AsTe 3 and octahedral AsTe 6 motives). Considering only AsTe 3 units we can deduce that the value of bonding angle on As is 95 ° and on Te 93 °, thus giving T e - T e - - 3.91 and A s - A s -- 3.84,~, i.e. values smaller than the observed second peak of the R E D D located at 4.00 ,~. On the other hand supposing that the bonding angle on As has the value 100 ° we would obtain Te-Te = 4.06,~ and taking in account the relation of con-

348

As-17As

SJ'-5.5S

10000

As-56AI

S-17S

As-BS

35000

~

5000 ,

~

0

W

V

2.0

,

"",.i

As2Te3 30000

Te-lOTTe

3.0

4.0

5.0

O

II

4 O0

6.0

25000

AS-23As Se- 23 Se

Z

5.80

0

20000

3~0 s,- e s~ 3.721

20000 -sa-e3

As-BAs 358

15000

15000 As-3Te Te-2As 265

10000

10000

As-3Se Se-2As 243

&

5000

5000

0

~

2J0

3.0

4.0

5.0

6,0

- ~

2.0

3.0

4.0

5.0

6.0

0 7.0

Fig. 16. The generalized model for A s 2 X 3 arsenic chalcogenides. The thick line represents the experimental R E D D ; the dashed thick curve represents the calculated one on the basis of the generalized model, eq. (5). The dotted curves represent the R E D D s calculated using for comparison the coordination numbers and broadening functions of Sb2S3, fig. 15. Coordination numbers are given in the notation (I - NqJ).

257

L. Cervinka, A. Hrubp / Structure of amorphous and glassy Sb2S3

centration dependent pair functions in this case P~'~,As: e'r'e,Te = 1 : 4, the contribution of A s - A s pairs at a distance 3.84 fi, (for example) could not compensate for the contribution of T e - T e pairs at 4.06 ,g, and we would again obtain a higher value of the position of the second coordination sphere. We therefore choose the bonding angle on As to be 98 ° in order to obtain T e - T e = 4.00 fi,, following at the same time the trend of bonding angles on arsenic in arsenic chalcogenide glasses, i.e. 102 ° - 100°-98 ° (see table 6). Under this condition it is then possible to choose the valence angle on Te from a rather broad interval of values starting at 95 ° ( A s - A s 3.91 ,~) and ending at 98 ° ( A s - A s = 4.00 ,g,) without a considerable influence on the course of the second maximum. (c) Using now appropriate coordination numbers and gaussian broadening functions we are able to calculate as in the case of Sb2S 3 the R E D D curves. This is demonstrated in figs. 16 and 17. For a better comparison we then calculated for this series the R E D D s again but using the coordination numbers and broadening functions of Sb2S 3 (dotted curves in fig. 16). The predominating influence of the wide broadening functions rather than of the coordination numbers can clearly be recognized. There is, for example, a small difference between ms2Se 3 and Sb2S 3 in the values of coordination numbers (compare figs. 15 and 16) but the R E D D s differ considerably (compare the dashed and dotted curves in fig. 16 for As2Se3-) due to the great difference in the widths of broadening functions (compare figs. 15 and 17). It will be pointed out (See the Appendix) that the increase in the width of broadening functions is caused by the increase of the number of network-forming As2X 5 configurations of the type N, which are favoured when valence angles approach the value of 90 ° .

=

0.40

I - BROADENING

1-00

~1,86

-~

i

FUNCTIONS

AO

--~

~0

-

'

i

Y 0.30

B~

AszS3

AszS%

As2T%

BI

l

],

BI

0.20

; \ Bu

/i,, i B.ql 0.10

,,"/% .,> I \ k~'

z

/ //" r 5

0

,.f~" / ti 5

5

I.IC' 0

5

t 10

i 5

0

5

x

10

Fig. 17. Broadening functions Bk(r ) of generalized coordination spheres in the As2X3 glasses. Note the increase of the widths of the broadening functions in the series As 2$3-As 2Se3-As 2Te3Sb2S3 (fig. 15), e.g. for BI. This increase is produced by an increase of the number of network forming configurations N, forming the structure (see Appendix), which are favoured when valence angles on atoms approach 90° .

258

L. Cervinka, A.. Hrub) / Structure of amorphous and glassy Sb2S3

11. Consequences of the generalized approach First of all we observe that in the series A s 2 S 3 , . . . , Sb2S3, As2Te3 the coordination numbers for individual generalized coordination spheres increase (the first one must be an exception), table 7 *, and secondly that the broadening functions necessary for the modification of the original pair functions get broader, figs. 15 and 17. The only possible explanation of this behaviour is that we have a gradual transition from a glassy layer-like structure in the case of As2S 3 to a continuous random network structure in the case of glassy As2Te3. That this consideration is reasonable may be illustrated by the following examples: the occupation of the second (it increases from 6 to 11 atoms of the same sort) and of the fourth generalized coordination sphere (in As2Se 3 it is about a factor of 1.4 and in As2Te3 approximately a factor of 1.8 denser than in ms2S3) increases in such a way that it can hardly be compatible with a layer-like arrangement. And further, this process is bound not only with increasing distortions of the elementary A s X 3 unit as shown by variations in B I (fluctuations in the length of the first neighbour distances and in the valence angles on As and on the chalcogen atom) but at the same time with greater disorder in coordination spheres of higher order, variations in Bit , BIII, BIV. It can be easily recognized that glassy Sb2S3, in accordance with the values of its generalized coordination numbers and the widths of its broadening functions, fig. 17 and table 7, can be classified in the series of As2X3 arsenic chalcogenides between As2Se 3 and As2Te3. This is understandable bearing in mind the considerations presented by Cornet and Rossier [22] who were interested in the topological characteristics of AsTe3 units. They pointed out that the closer the valence angles are to 90 ° the greater is the probability of the development of As2Te5 configurations, which are not orpiment-type configurations - such configurations are then stabilized by the formation of octahedral arrangements in the crystalline structure of As2Te3. The authors [22], however, give examples of only 3 configurations labelled A, B and C (in our notation see the Appendix - Or, N l and No) and their B configuration (N~) is wrongly designated as an orpiment-type one. We therefore review the problem again in the Appendix. In contrast to Comet and Rossier [22] (they used information only from the position of the first-neighbour peak) supposing that in the disordered phase of As2Te 3 most N0-type configurations seem to be eliminated, our results indicate that generally we must consider all N i network-forming configurations (which play essential role during the transition from As2Se 3 to As2Te3) because only * The relatively low value of the coordination number for the third generalized coordination sphere in As2Te 3 which is an exception to this trend is irrelevant. It is due to the low resolution of our program when calculating coordination numbers for a sphere located between spheres with very high electron density. By slightly increasing, for example, the coordination in the third sphere to (As-8 Te)+(Te-5.2 As) we would obtain only a minor decrease in the values of coordination numbers in the second and fourth spheres.

25q

L. Cervinka, A. Hrub) / Structure of amorphous and glassy Sb_,S3

Table 7 Review of coordination numbers N k and of broadening functions Bk for generalized coordination spheres in As2X3 and glassy Sb2S3 (compare with figs. 15, 16 and 17). Gaussian broadening functions B k are characterized by the values of their maximum Material

Nl

BI

Nn

BII

NIl I

Bm

Niv

Biv

As2S3 As2Se3 Sb2S3 As2Te3

3+2 3+2 3+2 3+2

1.00 0.86 0.30 0.40

6+6 8+8 7+7 11+11

0.20 0.18 0.12 0.09

6+4 7+5 7+5 6+4

0.115 0.115 0.11 0.085

17+17 23+23 24+24 31+31

0.085 0.08 0.057 0.058

they can contribute to chain branching and folding and to the interconnection of layer-type orpiment-like configurations O l and 02. All these processes then lead to a much denser packing of atoms in generalized coordination spheres in comparison with ASES 3. Our conclusions are also consistent with the results of Renninger et al [23,24], who studied arsenic-selenium glasses in films and bulk materials and compared experimental R D F with Monte-Carlo models of atomic arrangements. They found the existence of branched and interconnected chains forming a complex network which was almost continuous throughout their model. They found no evidence of layering as in crystalline As2Se 3 when starting from a random set of atom positions. On the other hand they arrived at the same R D F when their starting position was the crystalline structure. It is clear that these models cannot be considered unique, however, a decision on the validity of one or other model was not possible. We think that in our case of glassy and amorphous Sb2S 3 we have a nice example when it would be possible to decide on the validity of these different approaches. We really have two nearly identical R D F s for two different materials (difference in AS of about 1.22) of a single composition. We are convinced that the R E D D of the a m o r p h o u s powder would then correspond to the model starting from the crystalline structure and the R E D D of the glassy material would correspond to the model based on random starting positions. Our next remark concerns the study of glassy Sb203 as presented in ref. 25. F r o m all that has been said concerning the structure of SbES 3 and arsenic chalcogenides it follows that we are immediately able to find that Sb203 does not belong in this class of glasses. For glassy Sb203 we have (fig. 18) R I = 1.99, RII = 2.8 and R m = 3.6 ,~. Bearing in mind that RIII is the peak influenced by S b - S b ordering and applying the rule of constant proportionality of coordination spheres (section 8) it can easily be recognized that by comparing Sb203 with A s 2 X 3 arsenic chalcogenides this rule is not fulfilled and that the structure of the Sb203 glass must be different from the structure of A s 2 X 3 glasses. The authors found that Sb203 was formed by double chains consisting

L. Cervinka, A. Hrubj~/ Structure of amorphous and glassy Sb2S3

260

[

i

~

i

i

a-Sb253~ 10000 z Q z Q

sooo ¢.) &am.# --I m,J

0

1.0

2.0

3.0

4.0

5.0

r Ix]

Fig. 18. Radial electron density distribution of vitreous Sb203 according to ref. 25. The original distribution was recalculated in order to produce a parabolic curve of the average electron density and thus a better comparison with our distributon in glassy Sb2S 3. The rule of constant proportionality is not valid for Sb203 therefore its structure is different from the structure in the class of As 2 X 3 glasses.

of four membered rings of SbO 3 pyramids, as in the crystalline high-temperature modification of Sb203 - valentinite [28], see the Appendix.

12. C o n c l u s i o n s

Two non-crystalline materials of the composition S b 2 S 3 w e r e prepared, i.e. amorphous powder obtained by precipitating a SbC13 solution in a bath of boiling water and a glassy material in the form of thin platelets obtained by the method of rotating cylinders. The results of DTA showed that both materials differ substantially in their crystallization entropy and therefore they should have different structures. The radial electron density distribution curves were then calculated on the basis of diffracted X-ray intensity data and the results for both materials were almost identical. A comparison of the experimental REDD with a calculated one was made on the basis of a crystalline-like (layer-like and band-like) distribution of atoms in S b 2 S 3. It was found that in both modifications the basic structural unit was a trigonal SbS 3 pyramid and that each S atom was attached to two Sb atoms. The best fit of the REDD curve in the interval 2.8 to 3.1 ,~ was given by the crystalline band-like distribution. It was therefore concluded that a model of the amorphous powder (very low crystallization entropy) might consist of interconnected and statistically disordered crystalline-like (Sb 2S3).-bands (fibre molecules). In order to check whether it is possible to fulfil the demands of the comparative (crystal-glass) analysis and at the same time find a model of the glassy structure, a simple working model of this structure was constructed in

L. Cervinka, A. Hrut~f / Structure of amorphous and glassy Sb_,S¢

261

which orpiment-like Sb2S5 configurations (O1) had to be combined with network forming ones (No) in order to satisfy the valence angle on Sb (which must be 90 ° ) and in order to obtain the right set of distances in the scaled distance distribution histogram. This simple model demonstrated that the basic network had a tendency to interconnect with neighbouring networks (fig. 10). The positions of coordination spheres for As 2 X3 arsenic chalcogenides and Sb2S 3 were compared and a rule was found: there exists a linear dependence between the positions of corresponding coordination spheres of the As 2 X 3 and Sb2S3 glasses. The coordination spheres complying with this rule were designated as generalized ones and the calculation of the R E D D using broadened pair functions assigned to the positions of generalized coordination spheres was called the generalized model in this class of glasses. Using the generalized model for the interpretation of REDDs it was found that there was an increase of the values of the occupation numbers and a gradual broadening of modification (broadening) functions in corresponding coordination spheres in the series As2S3, As2Se3, Sb2S3, ms2Te 3. This behaviour was then explained by proposing that there was a gradual transition from a glassy layer-like structure of As2S 3 to a continuous random network structure of As2Te 3. Glassy Sb2S 3 was then classified between As2Se 3 and As2Te 3. The origin of this transition is as a matter of fact due to the development of the non-orpiment type (network forming) A2X 5 configurations, which are favoured when the valence angle on the A atom approaches 90 °. these configurations then lead to chain branching and folding and to the interconnection of orpiment-type (layer-forming) configurations. The authors wish to thank A. Dobrovodskh and K. Kuderna for technical assistance and M. Sime~kovh for providing the scanning microscope pictures.

Appendix It is worth reviewing the topology of the associated AX 3 units in a more profound way than was done in ref. 22. We start with a basic orpiment-like arrangement, which we designate O l, see fig. 19. Rotating the A2X3 unit counter clockwise around the A2X 3 axis we arrive at the second orpiment-like configuration 02 . Continuing with this rotation we reach the state designated N O(this is the C-configuration in ref. 22), characterized by the plane ¢p in which the AIX3A2X 5 configuration is in the As2Te 3 structure stabilized by the formation of the AIX 5 bond (A -- As, X = Te), because the crystalline valence angles are close to 90 ° , see table 6. We complete the counter clockwise rotation reaching the configuration Nj (in ref. 22 this configuration is wrongly designated as an orpiment-type one). Starting now from the configuration 02 and rotating the AIX3 unit clockwise around the A1X 3 axis we arrive at N 2. This configuration is the building block in the cubic form of Sb203 - senarmonite [26] or in the cubic form of As203 -

L. Cervinka, ,4. Hrub~ / Structure of amorphous and glassy Sb.,S3

262

0~~

TOPOLOGYOF TWO ASSOCIATED AX3 UNITS ORPIMENT-TYPE ~)-=(X I XZX3X~,

ojet ctioo°~~ a~ --

e -=(x'x'x'x~ 2x¶

N•A

projection ( ' ~

o

[

o

n

~

- I 23 ORPIMENT-TYPE ~=(XI XI X.X~2} (X A X'A

U~

pro eotion

SENARMONITE-TYPE

X3A21

(" }

project,on~ o~ooQe, ~ 6±x

N~

(~-= Al

"re'

f~{Xl/~ X3A2X'~

N

VALENTINITE-TYPE. ___,.,IXzXAX ~

i Fig. 19. Schematic figures of basic mutual orientations of two associated trigonal pyramidal A X3 units. These configurations are the basic building blocks in some A 2X3 structures and play at the same time an important role in the determination of the character of the glassy structure. See Appendix for details.

arsenolite [27]; b o t h structures consist of cagelike Sb406 or As406 molecules in w h i c h the cubic axis j o i n s a t o m s X 1 X 4 or X 2 X 5. S t a r t i n g again at 02 b u t r o t a t i n g the A2X3 unit c o u n t e r clockwise a r o u n d the A l x 3 axis we o b t a i n the N 3 configuration, which is f o u n d in the o r t h o r h o m b i c h i g h - t e m p e r a t u r e m o d i f i c a t i o n o f Sb203 - valentinite (stable a b o v e 570°C) [28] a n d in the c l a u d e t i t e f o r m of As203 [35]. O I a n d 02 are layer f o r m i n g c o n f i g u r a t i o n s f a v o u r e d when b o n d i n g angles

L. Cervinka, A. Hrubf, / Structure of amorphous and glas,~v Sb,S¢

263

on A and X atoms are considerably higher than 90 ° (about 100°). Configurations N 1, N 2, N 3 (with the intermediate one N 0) are network-forming (non-layer) configurations and they are favoured for valence angles approaching 90 ° . Valentine is a good example how the effect of a layer forming configuration of the type O 1 (in the real structure, however, one A atom, A 1, is above and the other, A 2, is under the p plane of the X atoms) is compensated by a network forming configuration of the type N 3. As a result a double chain structure is observed with highly deformed pyramids characterized by a medium valence angle on Sb equal to 90 °. Another example is the crystalline structure of Sb2S3, section 4, in which layers are again induced again by O~ configurations. These can be recognized as associated SblIS3 or SblS3 units in the direction of the b-axis, see fig. 5.

References [1] B.T. Kolomijec and N.A. Zacharov, The glassy state (in Russian) (lzd. Akad. Nauk, Moscow, 1960), p. 122. [2] G.G. Gospodinov, B.A. Popovkin, A.S. Paginkin and A.B. Gorjunova, Vest. Moskovskogo Univ., Ser. Chim. 2 (1967) 54. [3] V.P. Zacharov and V.S. Gerasimenko, Structural properties of semiconductors in the amorphous state (in Russian) (Izd. Naukova Dumka, Kijev, 1976), p. 124. [4] L.I. Tatarinova, Electronography of amorphous materials (in Russian) (Izd. Nauka, Moscow, 1972), p. 61. [5] A.M. Re~etnikov, Kristalografia 4 (1959) 926. [6] Ju. G. Poltavcev, B.P. Zacharov, V.S. Gerasimenko and L.P. Ku~zerenko, Izv. Akad. Nauk. SSSR, Neorg. Mat. 10 (1974) 367. [7] Y. Kawamoto and S. Tsuchihashi, J. Ceram. Ass. Japan 77 (1969) 328; citation according to C.A. 72 (1970) No. 5860. [8] E. Diemann, Z. Anorg. Allg. Chem. 433 (1977) 242. [9] L.I. Tatarinova, Kristalografija 4 (1959) 678. [10] Y. Sagara, O. Uemura, Y. Suzuki and T. Satow, Phys. Star. Sol. (a)33 (1976) 691. [I I] A.C. Wright and A.J. Leadbetter, Phys. Chem. Glasses 17 (1976) 122. [12] M. Hansen and K. Anderko, Constitution of binary alloys (McGraw-Hill, New York, 1958). [13] P. Boha~ and P. Kaufmann, Mat. Res. Bull. 10 (1975) 613. [14] A. Hrub¢¢, J. Non-Crystalline Solids 28 (1978) 139. [15] B.T. Melech, Z.V. Maslova, M.S. Ablova, T.B. Zukova and A.A. Andrejev, Fiz. i chimija stekla 2 (1976) 189. [16] Rustum Roy, J. Non-Crystalline Solids 3 (1970) 33. [17] P. Bayliss and W. Nowacki, Z. Kristallogr. 135 (1972) 308. [18] H. Krebs, in: Fundamentals of inorganic crystal chemistry, (McGraw-Hill, London, 1968) p. 246. [19] Structure Reports 12 (1949) 175. [20] A.L. Renninger and B.L. Averbaeh, Acta Cryst. B29 (1973) 1583. [21] G. Carron, Acta Cryst. 16 (1963) 338. [22] J. Cornet and D. Rossier, J. Non-CrystaUine Solids 12 (1973) 85. [23] M.D. Reehtin and B.L. Averbach, Phys. Stat. Sol. (a)28 (1975) 283. [24] A.L. Renninger, M.D. Reehtin and B.L. Averbach, J. Non-Crystalline Solids 16 (1974) 1. [25] H. Hasegawa, M. Sone and M. Imaoka, Phys. Chem. Glasses 19 (1978) 28. [26] R.M. Bozorth, J. Am. Chem. Soc. 45 (1923) 1621. [27] K.E. Almin and A. Westgren, Arkiv Kemi, Mineral., Geol. 15B (1942) 22.

264 [28] [29] [30] [31]

[32] [33] [34] [35]

L. Cervinka, A. Hrub~ / Structure of amorphous and glassy Sb2S3 M.J. Buerger and S.B. Hendricks, Z. Kristailogr. 98 (1938) 1. L (~ervinka and A. Hrub~,, J. Non-Crystalline Solids 34 (1979) 275. U. Steinike, B. Miiller, I. Ebert and H.P. Hennig, Krist. u. Techn. 14 (1979) 1469. G. Herms and H. Steil, Extended Abstracts Conf. Amorphous Solids in the Physical Section of the W. Pieck-University, Rostock, November 1980 (Publ. by the Physical Society of the GDR), p. 100. J.C. Philips, J. Non-Crystalline Solids 43 (1981) 37, J.C. Philips, C.A. Beevers and S.E.B. Gould, Phys. Rev. B21 (1980) 5724. M.F. Daniel and A.J. Leadbetter, J. Non-Crystalline Solids 41 (1980) 127. K.A. Becker, K. Plieth and I.N. Stranski, Z. Anorg. allgem. Chem. 266 (1951) 293.