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Glass transition and specific heats in the systems PS, PSe, AsS and AsSe
Journal of Non-Crystalline Solids 34 (1979) 191-201 © North-Holland Publishing Company
GLASS TRANSITION AND SPECIFIC HEATS IN THE SYSTEMS P - S , P-Se, A s - S AND A s - S e R. BLACHNIK and A. HOPPE Laboratorium fiir A norganische Chemie der Gesamthochschule/Universiez't Siegen, A dolfReichwein-Strasse, D 5900 Siegen 21, W. Germany Received 26 March 1979
The glass transition temperatures were measured in the systems As-S, As0.5Po.5-S, P-Se, As-Se and P-As-Se. Heat capacities of the glasses in the selenium systems were obtained by differential scanning calorimetry. As shown by the residual entropies departures from ideality are high in the chalcogenglasses. The results are discussed in terms of the structure of glasses in these systems. The thermodynamic data of glasses and liquids in these systems indicate a balance of intra- and intermolecular saturation of bonds. The amount of polymerizationincreases with increasing average molecular weight in the glass and with increasing temperature in some of the investigated liquids.
1. Introduction In recent investigations of the transport properties of amorphous V b-VI b systems the variation of these properties with compbsition revealed extreme values related to the structure of compounds in these systems. Kasatkin [1] found a minimum between 12 and 15 at.% P for the activation energy of the electrical conductivity in the P-Se system. In As-S glasses Tsuchihashi [2] and Novoselova [3] observed minima in the concentration dependence of the linear coefficient of thermal expansion and Vinogradova [4] found a maximum of the speed of ultrasound at 40 at.% As. Similar points were reported in glassy A s Se mixtures. Minima in the concentration dependence of the optical gap, the activation energy of electrical conductivity and thermopower were measured by Hurst [5], resp. minima of the coefficient of thermal expansion by Felty [6], Maxima in the electrical conductivity, in the density, and in the thermal conductivity were obtained by Hurst, Arai [7], Renninger [8] and Kuriyama [9]. All extreme values of the properties appeared near the composition of 40 at.% As, which corresponds to the solid compounds As2Se3 and As2S a, resp. The purpose of our experiments was to prove whether a similar behaviour can be observed in the thermodynamic properties. 191
192
R. Blachnik, A. Hoppe / Glass transition and specific heats
2. Experimental The materials used in the preparation were As (99.9999% Preussag), Se (99.999% Norddeutsche Affinerie), P (99.9999% Knapsack-Hoechst) and S (99.99% Fluka). For the synthesis of the glasses proper amounts of the components were placed in quartz ampoules, which were evacuated to 10 -3 Torr, sealed, and heated in a rotating furnace to ensure thorough mixing of the elements. The temperature of the furnace was raised to the melting point of the lowest melting component and held constant for 12 h, in the next 24 h the temperature was increased slowly to the reaction temperature (As-Se 923 K; As-S and P-Se 773 K; P - S 723 K) and kept constant for 12 h. The samples were then quenched in ice/water mixtures. For the measurements of the specific heats the samples were reheated in the DSC-2 (Perkin-Elmer) above the liquidus temperature, then cooled to 300 K at a rate of 80 K min-l to ensure similar thermal histories for all glasses. After thermal equilibrium was reached, the measurements of the specific heats and glass transition temperatures as indicated by the change of Cp were started. All specific heat experiments were carried out with the DSC-2 using the specific heat mode [10]. A detailed description of the technique has been reported previously by Mills [ 11 ]. All data are mean values of at least three sometimes ten experiments in the same temperature interval. The error of the specific heat measurements is +1-1.5% between 130-300 K and +3-4% between 300 and 700 K. The heating rate in all experiments was 10 K rain -1.
3. Results
The glass transition temperatures (TG) of the systems Po.sAs0.s-S and As-S are shown in fig. 1. The data of the P - S system obtained by Heyder [12] are included for comparison. In all systems T~ increases monotonically with the amount of V b-element. A sharp maximum of TG appears in the As-S system at "--40 at.% As. The Tc values of the latter system are in good agreement with those reported by Tobolsky [13], Vinogradova [4], Myers [14], Tsuchihashi [2], Hattori [15] and Maruno [16]. Beyond the glass forming region of the P - S and P0.sAso.s-S systems rapid cooling of the melts produces products similar in physical behaviour to rubber (elastic products) in some cases with freezing temperatures below 240 K. In the system Po.sAso.s-S the compound P2As2Ss crystallizes from these products, the crystallization rate being increased on addition of some iodidecrystallites.Fig. 1 contains the polymerization temperatures (Tx) of sulphur. Tx is 432 K for the pure element and decreases on addition of a few at.% V b-element to a constant value depending on the system under consideration. The dependence of Tc on concentration is given in fig. 2 for the systems P-Se, P0.sAso.s-Se and As-Se. To-values for the P-Se system, previously reported by Heyder [12] agree well with our data. However, we observed a first maximum at 71
193
R. Blachnik, A. Hoppe / Glass transition and specific heats
450
~_(:~
+ P-s
35O ~./+j 250
o As- 5e
I
10
20
30
40
10
50
atomic % ~ b
A
20
I
30
i
I
40
50
atomic% !Tb
Fig. 1. Glass transition temperatures and polymerization temperatures in the sulphur systems (data of the P - S system from ref. [ 12]).
Fig. 2. Glass transition temperatures in the selenium systems. at.% Se (P4Selo). For the As-Se system TG-values have been published by Dembovskii [17], Myers [14], Kralova [18] and Skulska [19]. Those of Myers and Dembovskii agree well, though Dembovskii reported two maxima instead of one. TG-values found by Kralova and Skulska are higher and the latter authors did not observe the maximum at 40 at.% As. A considerable amount of structure is apparent in the P - S e and As-Se curves. The formation of glasses in the P-Se system is independent of the cooling rate. Amorphous samples were produced in all preparations. Attempts to crystallize samples of the composition PaSen (n = 10, 7, 6, 5) by annealing, sublimation or crystallization in organic" solvents failed. In the ternary Se
P
As
Fig. 3. Glass forming region in the P-As-Se system (o glassy, ~ partially crystallized, o crystalline).
194
R. Blachnik, A. Hoppe / Glass transition and specific heats
Table 1 Glass transition temperatures in the system P-As-Se. Mole fraction of As2Se3 P4Se3-As2 Se3 P4 Se4-As2 Se3
0.1 459
0.2 457
0.3 442 455
0.4 444 452
0.5 445 448
Mole fraction of As2Se3 P4Se3-As2Se3 P4Se4-As2Se3
0.6 446 447
0.7 448 451
0.8 452 456
0.9 456 459
TG (K) TG (K)
system P - A s - S e the glass forming region for cooling in air was determined (fig. 3). Table 1 gives the glass transition temperature in this system for the sections P4Se3-As2Se3 and P4Sea-As2Se 3. In table 2 the relevant data of all systems are collected. The specific heats of crystalline, glassy and liquid As2S 3 as functions of temperature are given in fig. 4. The values fit the low temperature Cp-curve of Tarasov [20] resp. Hattori [ 15] well. The agreement between data reported by Haggerty [21 ] and Schnaus [22] for high-temperature Cp of solid glasses is very good. However, our Cp-values for the liquid are about 6% lower. Data reported by Kuriyama [23] disagree considerably. Figure 5 shows a graph of the experimental values of Cp of amorphous and liquid samples in the P-Se system between 250 and 700 K. The experimental Cp of the As-Se glasses between 100 and 700 K are given in fig. 6, the high temperature data fit smoothly the low temperature values of Zigel [24]. The low temperature Cp of the samples Aso.aSeo. 7 and Aso.s7Seo.43 were measured in the course of this investigation. The agreement between high-temperature data of As2Se 3 by Schnaus [25] and Eastal [26] is very good, data of Thornburg
Table 2 Characteristic data of the glasses in the investigated systems.
P-S P-Se As-S As-Se P0.sAs0.s-S P0.sAso.5-Se
Glass formation at. % Vb
TG (max) (K)
Colour
T h between at. % Vb
0-25 0-52 0-42.5 0-57.1 0-36 0-57
382 460 466 462 464 457
Yellow Black-dark red Yellow-red Black-dark red Yellow-red Black-dark red
0-15
Occurrenceof elastic products at. % Vb 36-57
0-32 0-25
>36
R. Blachnik, A. Hoppe
KXJ
/
Glass transition and specific heats
200
300
400
195
500 600 700 T/K
/
40
30 "T
20
2.,20
2bO
2,60
0
IogT/K Fig. 4. Specific heats of glassy (o), crystalline (+) and liquid (+) As2S 3. The shaded area represents the entropy of melting, values below 250 K are from ref. [20].
36
4O
38
34 37 3C 28 26
AsASe3
22 20
~
"40 38 36
Set0 3E
58 36 34
3C ',,~ 25 P
~ 20, O. u
J J
36 34
LI~)/S2se3"~i ~s%
34 32 30 28
~ 2 0 T /~s3Se7 30
22 ~
26 25
2 0 ~ 300
400
i
i
500
600
20 T/K
24 22 20
1' ./f_ 100
Fig. 5. Specifics heats of glassy and liquid P - S e mixtures.
200
300
400
500
600
~K
Fig. 6. Specific heats of mixtures in the system As-Se. Values below 250 K for As 0.1, 0.2, 0.4, 0.5 from ref. [24].
196
R. Blachnik, A. Hoppe / Glass transition and specific heats
[27] are about 8% higher. The curve overlaps nicely with the low temperature curve of Tarasov and Zhdanov [28]. Again the data of Kuriyama disagree considerably.
4. Discussion X-ray and neutron diffraction studies for the systems As-S (Se) by several authors [2], [7] and [29-35] have shown that in these glasses As and S (Se) have three and two nearest neighbours. Spectroscopic resuks by other groups [2] [36-40] provided the additional information that the glasses contain pyramidal ASS3/2 and S-S-units. The glass forming ability and glass transition temperatures are related to these structures, the occurrence of which is required by the 8-N rule. At present the best interpretation of the structure of As2S(Se)a-glasses is established by the molecular model of Lucovsky [41], in which the three chalcogen atoms of the AsX3/2-unit are bound either to two or to three other As atoms in a two-dimensional network polymer. This arrangement is related to the structure of the liquid state, for which we proposed a similar structure from an analysis of the entropies of fusion [42]. Deviations from the composition As2X3 with an excess of As lead to the formation of As-As bonds, which due to the preference of intramolecular bond saturation produce a phase separation by the formation of As4S4 molecules, as observed by Maruno [16] and Bertoluzza [40]. These molecules are thermally stable and crystallize readily so that the glass forming ability is limited by an excess of As4S4. On the contrary, a broad maximum in TG is obtained in the As-Se system between As2Se 3 and As4Se4, because As4Se4 melts peritectic. We assume that in these meks the 8-N rule can be fulfilled either by intramolecular (cage molecules) or by intermolecular bond saturation (polymeric networks). In the As-Se system the latter structural type dominates. Deviations from As2X 3 by excess S (Se) introduces - X - X - linkages, which with increasing X content, lower T G by the decreasing number of branching As atoms. In the As-S system at temperatures lower than Tx S8-rings can be formed. Differing concentrations of S8-rings and S-chains, resp. in samples with different thermal histories may be responsible for the scatter in T6.values found in the literature. Double-bounded chalcogen atoms exist in the P - S (Se) system and lead to a new structural unit X = P-X3/2 with tetrahedral geometry besides the - X - X - and P-X3/2 units. In the P - S systems the glass forming region is limited by the appearance of P481omolecules, due to the intramolecular saturation of the X = P-X3/2 units. In the P-Se system addition of P leads initially to branching of selenium chains and increase of TG. Contrary to the observations in the P - S system the P4Selo-units are polymeric and determine the first maximum in T G. Further added P atoms destroy the P = Se double bonds; this view is supported by the vanishing P = Se band in the IR spectra of P-rich glasses [43]. A second P-Se polymer, consisting of P-Sea/2-pyramids, is formed and raises TG steadily. At the composition
R. Blachnik, A. Hoppe / Glass transition and specific heats
197
of 40 at.% P the glass consists o f P-Se3/2 polymeric sheets. A further increase in the P-concentration leads to P - P bridges which link the P-Se3/2-sheets to a threedimensional network. This process is finished at 50 at. % P. The glass is now built from P4Se4-cages in which on the average two P - S e - P bridges are opened and linked to other P4Se4-cages. Again an equilibrium between isolated P4Se4-molecules and polymers is possible which can be shifted to the molecular side by annealing or further addition o f P - in both cases the P4Se4 glass recrystallizes easily. Haggerty [21] has demonstrated that for a number o f glasses Cp reaches the limiting value of 3R at Tc. The chalcogenide glasses confirm this observation (table 3), except for As4Se3 and P4Se4 which exceed 3R at Tc outside the experimental error. Formally it would be necessary to calculate the heat capacities at constant pressure equivalent to 3R from the Griineisen-relation, however, the quotient Cp/Cv is 1.002 for As2S3 and 1.003 for As2Se3. This negligible difference made it possible to calculate Debye temperatures from our Cp-data, which are summarized in table 3. The agreement with data obtained by the expression 0D =
hcvo/K
(1)
with frequencies for the harmonic oscillators given by Hilton [44] is reasonable. The Debye temperatures decrease with increasing average molecular weight o f the glasses. Angel [45] has stated that at the glass transition a dynamic equilibrium between vibrational and configurational states becomes possible. In this case the glass tern-
Table 3 Deviation of the investigated glasses from the Dulong-Petit value of 3R at TG, Debye temperatures, ideal glass temperatures and residual entropies.
AslSe9 As2Se8 AsaSe7 As2Sea As4Se4 AsaSe3 P4 Se4 P4Ses P4Se6 P4Selo As2S3 P2 As2 Sea
Cp/3R
®D (K)
1.02 1.02 1.02 1.03 1.04 1.11 1.13 0.99 1.0 1.0 1.0 0.99
250 250 280 300 350a 310 b 300 250 400 400 400 400 400 450 a 42()b 400
TO (K)
TG/T0
AS (res) J g at -1 . K-l
309
1.49
5.8
362
1.27
2.8
246
1.89
6.9
a) From ref. [25]. b) Calculated from formula (1) with OAs_s = 291 cm-1 and UAs_Se = 217 cm -1 .
198
R. Blachnik, A. Hoppe / Glass transition and specific heats
perature would lie near the Debye temperature for the disordered solid. The observed glass temperatures (350-450 K) fall somewhat above the Debye temperatures (250-400 K), however, the ideal glass temperatures (To) for As2Se a and P4Se4 are lying close to the resp. Debye temperatures. In fig. 4 the heat capacities are plotted versus log T/K, such that the entropy of the phases at a given temperature can be obtained directly from the area under the Cp-curve. The ideal thermodynamic glass temperature, To, where the area between Cp (liquid) and Cp (crystal) matches the area representing the entropy of fusion and the residual entropies obtained in this manner are listed in table 3. The ratio TG/To decreases as To increases, contrary to organic glasses, in which it is approximately constant. The latter correlation indicates that in organic glasses the configurational entropy of the melt determines the temperature dependence of cooperative relaxation processes in the glass transition region [46]. The variations in TG/To in the chalcogenide glasses confirm the anticipation of Angell that besides the excess entropy as important factor in the glass transitions a configurational enthalpic term is possible. TG/To and AS (res) for As2S 3 and As2Se 3 are unusually high and comparable to the resp. values of silica glasses. This indicates that these network glasses strongly deviate from the state of an ideal glass - e.g. simple ionic glasses. The deviation from ideality of the P4Se4 glass is much lower, as one would expect for this glass, which easily recrystallizes by the formation of isolated cage molecules. The concentration dependence of Cp in the glasses of the systems As-Se and P-Se, together with literature data of As-S by Hattori, is given in fig. 7. In view of the aim of our investigation, the graph seems to exhibit similar minima as the transport properties. For two reasons this conclusion may be incorrect. Firstly the sharp minimum of the As-S system is due to the very low Co-value of As2S 3 glass by Hattori, which is about 10% lower than the average literature value. Sec-
"T
30
a As-S
313K
* As-Se o P-Se
320K 320K
& &
2'.
2o
~"'--. ÷ ~ ÷ l~J " \ - ° ~ ° L - .....
'
8'o
'
6'o
'
4'o
atomic °/o ~ b
Fig. 7. Composition dependence of Cp in the system As-Se, P - S e and As-S at 313 and 150 K.
R. Blachnik, A. Hoppe / Glass transition and specific heats
199
Table 4 Values of Cp calculated by Neumann-Kopp rule at Tr = 0.9 TG. Mole fraction of As Co(As-Se) J g at -1 . K-1 Mole fraction of P Cp(P -Se) J g at -1. K-1
0 25.8 0 25.8
0.1 25.6 0.29 23.9
0.2 25.7 0.4 24.6
0.3 25.7 0.44 24.0
0.4 25.7 0.5 26.4
0.5 26.3
at 0.9 TG at 0.9 TG
ondly the Co-values were taken in the temperature interval between TO and Tc and thus in different vibrational and configurational states of excitation. To avoid misinterpretation we have taken Co-values at a reduced temperature of Tr = 0.9 TG, now constant Co-values in the As-Se system were obtained whereas the values in the P-Se system reveal a minimum (table 4). Additionally, the heat capacities of the As-S and As-Se systems were calculated in good agreement with the experiment from the heat capacities of pure S(Se) and pure AszS 3 (As2Se3) by the Neumann-Kopp rule. In the P-Se system, however, the calculated data showed severe deviations again. The independence of C o on concentration and the fact that these data could be calculated using the Neumann-Kopp rule supports the view that glasses in the As-S and As-Se system are based only on - X - X - and As-X3/2 molecular units. In the P-Se system different bond types (single and double bonds) and changing coordination numbers of P (4 and 3), lead to the concentration dependence of Cp and to wrong results in the simple calculation by the Neumann-Kopp rule. Haggerty pointed out that for a glass which is vibrationally fully excited (C o = 3R) the heat capacity of the liquid should be constant over a wide range of temperature. From fig. 5 and 6 it is evident that this is true for most of the compositions considered. For As4Se4 and As4Se 3 the observation that despite a C o value of 3R in the solid state Co keeps rising in the liquid can be explained by the assumption of an increasing amount of polymerized molecules in the melt. The equilibrium between molecular and polymeric forms or intra- respectively intermolecular saturation of the coordination is thus temperature dependent. More polymeric species are produced as the temperature rises. The similar increase of Co in the P4Selo, P4Se6 and P4Se s compositions may be due to reactions of the double bonds in these melts. Thus the behaviour of the specific heats in the melts confirms the picture gained by the interpretation of T c.
5. Conclusion (1) The extrema observed in the transport properties of V b-Vl b glasses do not occur in the concentration dependence of Cp. Thus the specific heat is rather insensitive to gradual structural changes. (2) The interpretation of TG and C o of the glasses leads to the assumption of an
200
R. Blachnik, A. Hoppe / Glass transition and specific heats
equilibrium between inter- and intramolecular connections of the basic structural units. (3) The thermodynamic data indicate that arsenic-chalcogen glasses are nonideal glasses.
Acknowledgements The authors wish to thank the "Fonds der ChemiC' and the Minister ftir Forschung des Landes NRW for financial support.
References [1] B.E. Kasatkin and Z.U. Borisova, Inorg. Mat. 10 (1974) 1237. [2] S. Tsuehihashi and J. Kawamoto, J. Non-Crystalline Solids 5 (1971) 286. [3] N.A. Novoselova, S.K. Novoselov and L.A. Baidakov, Russ. J. Appl. Chem. 44 (1971) 2615. [4] G.Z. Vinogradova, S.A. Dembovskii, T.N. Kuz'mina and A.P. Chernov, Russ. J. Inorg. Chem. 12 (1967) 1715. [5] C.H. Hurst and E.A. Davis, J. Non-Crystalline Solids 16 (1974) 343. [6] E.J. Felty and M.B. Myers, J. Am. Ceram. Soe. 50 (1967) 335. [7] K. Arai, T. Kuwahata, H. Namikawa and S. Saito, Jap. J. Appl. Phys. l I (1972) 1080. [8] A.L. Renninger and B.L. Averbach, Phys. Rev. B8 (1973) 1507. [9] U. Kuriyama, J. Am. Ceram. Soc. 58 (1975) 302. [10] B. Wunderlich, J. Phys. Chem. 69 (1965) 2078. [11] K.C. Mills and M.J. Richardson, Thermochimica Acta 6 (1973) 427. [12] F. Heyder and D. Linke, Z. Chem. 12 (1973) 480. [13] A.V. Tobolsky, G.D.T. Owen and A. Eisenberg, J. Colloid. Sci. 17 (1962) 717. [14] M.B. Myers and E.J. Felty, Mat. Res. Bull. 2 (1967) 535. [15] M. Hattori, K. Nagaya, S. Umubachi and M. Tanaka, J. Non-Crystalline Solids 3 (1970) 195. [ 16] S. Maruno and M. Noda, J. Non-Crystalline Solids 7 (1972) 1. [17] S.A. Dembovskii, Russ. J. Inorg. Chem. 7 (1962) 1454. [18] B. Kr~lowl, Czech. J. Phys. B22 (1972) 704. [19] E. Skulska, E. Augusciuk, W. Jablonski and J. Jagiello, Bull. Acad. Pol. Sci. Set. Math. Astr. Phys. 23 (1975) 99. [20] V.V. Tarasov and V.M. Zhdanov, Russ. J. Phys. Chem. 44 (1970) 1349. [21] J.S. Haggerty, A.R. Cooper and J.H. Heasley, Phys. Chem. Glasses 9 (1968) 47. [22] U.E. Schnaus, C.T. Moynihan, R.W. Gammon and P.B. Macedo, Phys. Chem. Glasses 11 (1970) 213. [23] M. Kuriyama, Yogyo-Kyokai-Shi 82 (1974) 16. [24] V.V. Zigel and G.M. Orlova, Russ. J. Appl. Chem. 46 (1973) 771. [25] U.E. Schnaus, C.T. Moynihan, R.W. Gammon and P.B. Macedo, Techn. Rep. AD No. 6 698842 (1970) 1. [26] A.J. Eastal, J.A. Wilder, R.K. Mohr and C.T. Moynihan, J. Am. Ceram. Soc. 60 (1977) 134. [27] D.D. Thornburg and R.I. Johnson, J. Non-Crystalline Solids 17 (1975) 2.
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[28] V.V. Tarasov, V.M. Zhdanov, A.K. Maltsev and S.A. Dembovskii, Russ. J. Phys. Chem. 43 (1969) 249. [29] Yu.G. Poltavtsev, V.P. Zakharov, V.M. Pozdnyakova and T.V. Remizovich, Inorg. Mat. 8 (1972) 813. [30] Yu.G. Poltavtsev, Russ. J. Phys. Chem. 49 (1975) 840. [31] D.B. Dove and J. Chang, Trans. Am. Cryst. Assoc. 10 (1974) 61. [32] J. Sagara, O. Uemura, S. Okuyama andT. Satow, Phys. Stat. Sol. 31a (1975) K33. [33] J. Chang and D.B. Dove, J. Non-Crystalline Solids 16 (1974) 72. [34] K.S. Liang, J. Non-Crystalline Solids 18 (1975) 197. [35] A.J. Leadbetter and A.J. Apling, J. Non-Crystalline Solids 15 (1974) 250. [36] T. Arai, S. Komiya and K. Kudo, J. Non-Crystalline Solids 18 (1975) 289. [37] T. Ohsaka, J. Non-Crystalline Solids 15 (1974) 149. [38] A.T. Ward, J. Phys. Chem. 72 (1968) 4133. [39] R.J. Kobliska and S.A. Solin, J. Non-Crystalline Solids 8-10 (1972) 191. [40] A. Bertoluzza C. Fagnano, P. Monti and G. Semerano, J. Non-Crystalline Solids 26 (1978) 49. [41] G. Lucovsky and R.M. Martin, J. Non-Crystalline Solids 8-10 (1972) 185. [42] R. Blachnik and A. Schneider, Z. Anorg. AUg. Chem. 372 (1970) 314. [43] A. Hoppe, Thesis Siegen 1978. [44] A.R. Hilton, C.E. Jones and M. Bran, Phys. Chem. Glasses 7 (1966) 116. [451 C.A. AngeU, J. Am. Ceram. Soc. 51 (1968) 117. [46] G. Adams and J.H. Gibbs, J. Chem. Phys. 43 (1965) 139.
GLASS TRANSITION AND SPECIFIC HEATS IN THE SYSTEMS P - S , P-Se, A s - S AND A s - S e R. BLACHNIK and A. HOPPE Laboratorium fiir A norganische Chemie der Gesamthochschule/Universiez't Siegen, A dolfReichwein-Strasse, D 5900 Siegen 21, W. Germany Received 26 March 1979
The glass transition temperatures were measured in the systems As-S, As0.5Po.5-S, P-Se, As-Se and P-As-Se. Heat capacities of the glasses in the selenium systems were obtained by differential scanning calorimetry. As shown by the residual entropies departures from ideality are high in the chalcogenglasses. The results are discussed in terms of the structure of glasses in these systems. The thermodynamic data of glasses and liquids in these systems indicate a balance of intra- and intermolecular saturation of bonds. The amount of polymerizationincreases with increasing average molecular weight in the glass and with increasing temperature in some of the investigated liquids.
1. Introduction In recent investigations of the transport properties of amorphous V b-VI b systems the variation of these properties with compbsition revealed extreme values related to the structure of compounds in these systems. Kasatkin [1] found a minimum between 12 and 15 at.% P for the activation energy of the electrical conductivity in the P-Se system. In As-S glasses Tsuchihashi [2] and Novoselova [3] observed minima in the concentration dependence of the linear coefficient of thermal expansion and Vinogradova [4] found a maximum of the speed of ultrasound at 40 at.% As. Similar points were reported in glassy A s Se mixtures. Minima in the concentration dependence of the optical gap, the activation energy of electrical conductivity and thermopower were measured by Hurst [5], resp. minima of the coefficient of thermal expansion by Felty [6], Maxima in the electrical conductivity, in the density, and in the thermal conductivity were obtained by Hurst, Arai [7], Renninger [8] and Kuriyama [9]. All extreme values of the properties appeared near the composition of 40 at.% As, which corresponds to the solid compounds As2Se3 and As2S a, resp. The purpose of our experiments was to prove whether a similar behaviour can be observed in the thermodynamic properties. 191
192
R. Blachnik, A. Hoppe / Glass transition and specific heats
2. Experimental The materials used in the preparation were As (99.9999% Preussag), Se (99.999% Norddeutsche Affinerie), P (99.9999% Knapsack-Hoechst) and S (99.99% Fluka). For the synthesis of the glasses proper amounts of the components were placed in quartz ampoules, which were evacuated to 10 -3 Torr, sealed, and heated in a rotating furnace to ensure thorough mixing of the elements. The temperature of the furnace was raised to the melting point of the lowest melting component and held constant for 12 h, in the next 24 h the temperature was increased slowly to the reaction temperature (As-Se 923 K; As-S and P-Se 773 K; P - S 723 K) and kept constant for 12 h. The samples were then quenched in ice/water mixtures. For the measurements of the specific heats the samples were reheated in the DSC-2 (Perkin-Elmer) above the liquidus temperature, then cooled to 300 K at a rate of 80 K min-l to ensure similar thermal histories for all glasses. After thermal equilibrium was reached, the measurements of the specific heats and glass transition temperatures as indicated by the change of Cp were started. All specific heat experiments were carried out with the DSC-2 using the specific heat mode [10]. A detailed description of the technique has been reported previously by Mills [ 11 ]. All data are mean values of at least three sometimes ten experiments in the same temperature interval. The error of the specific heat measurements is +1-1.5% between 130-300 K and +3-4% between 300 and 700 K. The heating rate in all experiments was 10 K rain -1.
3. Results
The glass transition temperatures (TG) of the systems Po.sAs0.s-S and As-S are shown in fig. 1. The data of the P - S system obtained by Heyder [12] are included for comparison. In all systems T~ increases monotonically with the amount of V b-element. A sharp maximum of TG appears in the As-S system at "--40 at.% As. The Tc values of the latter system are in good agreement with those reported by Tobolsky [13], Vinogradova [4], Myers [14], Tsuchihashi [2], Hattori [15] and Maruno [16]. Beyond the glass forming region of the P - S and P0.sAso.s-S systems rapid cooling of the melts produces products similar in physical behaviour to rubber (elastic products) in some cases with freezing temperatures below 240 K. In the system Po.sAso.s-S the compound P2As2Ss crystallizes from these products, the crystallization rate being increased on addition of some iodidecrystallites.Fig. 1 contains the polymerization temperatures (Tx) of sulphur. Tx is 432 K for the pure element and decreases on addition of a few at.% V b-element to a constant value depending on the system under consideration. The dependence of Tc on concentration is given in fig. 2 for the systems P-Se, P0.sAso.s-Se and As-Se. To-values for the P-Se system, previously reported by Heyder [12] agree well with our data. However, we observed a first maximum at 71
193
R. Blachnik, A. Hoppe / Glass transition and specific heats
450
~_(:~
+ P-s
35O ~./+j 250
o As- 5e
I
10
20
30
40
10
50
atomic % ~ b
A
20
I
30
i
I
40
50
atomic% !Tb
Fig. 1. Glass transition temperatures and polymerization temperatures in the sulphur systems (data of the P - S system from ref. [ 12]).
Fig. 2. Glass transition temperatures in the selenium systems. at.% Se (P4Selo). For the As-Se system TG-values have been published by Dembovskii [17], Myers [14], Kralova [18] and Skulska [19]. Those of Myers and Dembovskii agree well, though Dembovskii reported two maxima instead of one. TG-values found by Kralova and Skulska are higher and the latter authors did not observe the maximum at 40 at.% As. A considerable amount of structure is apparent in the P - S e and As-Se curves. The formation of glasses in the P-Se system is independent of the cooling rate. Amorphous samples were produced in all preparations. Attempts to crystallize samples of the composition PaSen (n = 10, 7, 6, 5) by annealing, sublimation or crystallization in organic" solvents failed. In the ternary Se
P
As
Fig. 3. Glass forming region in the P-As-Se system (o glassy, ~ partially crystallized, o crystalline).
194
R. Blachnik, A. Hoppe / Glass transition and specific heats
Table 1 Glass transition temperatures in the system P-As-Se. Mole fraction of As2Se3 P4Se3-As2 Se3 P4 Se4-As2 Se3
0.1 459
0.2 457
0.3 442 455
0.4 444 452
0.5 445 448
Mole fraction of As2Se3 P4Se3-As2Se3 P4Se4-As2Se3
0.6 446 447
0.7 448 451
0.8 452 456
0.9 456 459
TG (K) TG (K)
system P - A s - S e the glass forming region for cooling in air was determined (fig. 3). Table 1 gives the glass transition temperature in this system for the sections P4Se3-As2Se3 and P4Sea-As2Se 3. In table 2 the relevant data of all systems are collected. The specific heats of crystalline, glassy and liquid As2S 3 as functions of temperature are given in fig. 4. The values fit the low temperature Cp-curve of Tarasov [20] resp. Hattori [ 15] well. The agreement between data reported by Haggerty [21 ] and Schnaus [22] for high-temperature Cp of solid glasses is very good. However, our Cp-values for the liquid are about 6% lower. Data reported by Kuriyama [23] disagree considerably. Figure 5 shows a graph of the experimental values of Cp of amorphous and liquid samples in the P-Se system between 250 and 700 K. The experimental Cp of the As-Se glasses between 100 and 700 K are given in fig. 6, the high temperature data fit smoothly the low temperature values of Zigel [24]. The low temperature Cp of the samples Aso.aSeo. 7 and Aso.s7Seo.43 were measured in the course of this investigation. The agreement between high-temperature data of As2Se 3 by Schnaus [25] and Eastal [26] is very good, data of Thornburg
Table 2 Characteristic data of the glasses in the investigated systems.
P-S P-Se As-S As-Se P0.sAs0.s-S P0.sAso.5-Se
Glass formation at. % Vb
TG (max) (K)
Colour
T h between at. % Vb
0-25 0-52 0-42.5 0-57.1 0-36 0-57
382 460 466 462 464 457
Yellow Black-dark red Yellow-red Black-dark red Yellow-red Black-dark red
0-15
Occurrenceof elastic products at. % Vb 36-57
0-32 0-25
>36
R. Blachnik, A. Hoppe
KXJ
/
Glass transition and specific heats
200
300
400
195
500 600 700 T/K
/
40
30 "T
20
2.,20
2bO
2,60
0
IogT/K Fig. 4. Specific heats of glassy (o), crystalline (+) and liquid (+) As2S 3. The shaded area represents the entropy of melting, values below 250 K are from ref. [20].
36
4O
38
34 37 3C 28 26
AsASe3
22 20
~
"40 38 36
Set0 3E
58 36 34
3C ',,~ 25 P
~ 20, O. u
J J
36 34
LI~)/S2se3"~i ~s%
34 32 30 28
~ 2 0 T /~s3Se7 30
22 ~
26 25
2 0 ~ 300
400
i
i
500
600
20 T/K
24 22 20
1' ./f_ 100
Fig. 5. Specifics heats of glassy and liquid P - S e mixtures.
200
300
400
500
600
~K
Fig. 6. Specific heats of mixtures in the system As-Se. Values below 250 K for As 0.1, 0.2, 0.4, 0.5 from ref. [24].
196
R. Blachnik, A. Hoppe / Glass transition and specific heats
[27] are about 8% higher. The curve overlaps nicely with the low temperature curve of Tarasov and Zhdanov [28]. Again the data of Kuriyama disagree considerably.
4. Discussion X-ray and neutron diffraction studies for the systems As-S (Se) by several authors [2], [7] and [29-35] have shown that in these glasses As and S (Se) have three and two nearest neighbours. Spectroscopic resuks by other groups [2] [36-40] provided the additional information that the glasses contain pyramidal ASS3/2 and S-S-units. The glass forming ability and glass transition temperatures are related to these structures, the occurrence of which is required by the 8-N rule. At present the best interpretation of the structure of As2S(Se)a-glasses is established by the molecular model of Lucovsky [41], in which the three chalcogen atoms of the AsX3/2-unit are bound either to two or to three other As atoms in a two-dimensional network polymer. This arrangement is related to the structure of the liquid state, for which we proposed a similar structure from an analysis of the entropies of fusion [42]. Deviations from the composition As2X3 with an excess of As lead to the formation of As-As bonds, which due to the preference of intramolecular bond saturation produce a phase separation by the formation of As4S4 molecules, as observed by Maruno [16] and Bertoluzza [40]. These molecules are thermally stable and crystallize readily so that the glass forming ability is limited by an excess of As4S4. On the contrary, a broad maximum in TG is obtained in the As-Se system between As2Se 3 and As4Se4, because As4Se4 melts peritectic. We assume that in these meks the 8-N rule can be fulfilled either by intramolecular (cage molecules) or by intermolecular bond saturation (polymeric networks). In the As-Se system the latter structural type dominates. Deviations from As2X 3 by excess S (Se) introduces - X - X - linkages, which with increasing X content, lower T G by the decreasing number of branching As atoms. In the As-S system at temperatures lower than Tx S8-rings can be formed. Differing concentrations of S8-rings and S-chains, resp. in samples with different thermal histories may be responsible for the scatter in T6.values found in the literature. Double-bounded chalcogen atoms exist in the P - S (Se) system and lead to a new structural unit X = P-X3/2 with tetrahedral geometry besides the - X - X - and P-X3/2 units. In the P - S systems the glass forming region is limited by the appearance of P481omolecules, due to the intramolecular saturation of the X = P-X3/2 units. In the P-Se system addition of P leads initially to branching of selenium chains and increase of TG. Contrary to the observations in the P - S system the P4Selo-units are polymeric and determine the first maximum in T G. Further added P atoms destroy the P = Se double bonds; this view is supported by the vanishing P = Se band in the IR spectra of P-rich glasses [43]. A second P-Se polymer, consisting of P-Sea/2-pyramids, is formed and raises TG steadily. At the composition
R. Blachnik, A. Hoppe / Glass transition and specific heats
197
of 40 at.% P the glass consists o f P-Se3/2 polymeric sheets. A further increase in the P-concentration leads to P - P bridges which link the P-Se3/2-sheets to a threedimensional network. This process is finished at 50 at. % P. The glass is now built from P4Se4-cages in which on the average two P - S e - P bridges are opened and linked to other P4Se4-cages. Again an equilibrium between isolated P4Se4-molecules and polymers is possible which can be shifted to the molecular side by annealing or further addition o f P - in both cases the P4Se4 glass recrystallizes easily. Haggerty [21] has demonstrated that for a number o f glasses Cp reaches the limiting value of 3R at Tc. The chalcogenide glasses confirm this observation (table 3), except for As4Se3 and P4Se4 which exceed 3R at Tc outside the experimental error. Formally it would be necessary to calculate the heat capacities at constant pressure equivalent to 3R from the Griineisen-relation, however, the quotient Cp/Cv is 1.002 for As2S3 and 1.003 for As2Se3. This negligible difference made it possible to calculate Debye temperatures from our Cp-data, which are summarized in table 3. The agreement with data obtained by the expression 0D =
hcvo/K
(1)
with frequencies for the harmonic oscillators given by Hilton [44] is reasonable. The Debye temperatures decrease with increasing average molecular weight o f the glasses. Angel [45] has stated that at the glass transition a dynamic equilibrium between vibrational and configurational states becomes possible. In this case the glass tern-
Table 3 Deviation of the investigated glasses from the Dulong-Petit value of 3R at TG, Debye temperatures, ideal glass temperatures and residual entropies.
AslSe9 As2Se8 AsaSe7 As2Sea As4Se4 AsaSe3 P4 Se4 P4Ses P4Se6 P4Selo As2S3 P2 As2 Sea
Cp/3R
®D (K)
1.02 1.02 1.02 1.03 1.04 1.11 1.13 0.99 1.0 1.0 1.0 0.99
250 250 280 300 350a 310 b 300 250 400 400 400 400 400 450 a 42()b 400
TO (K)
TG/T0
AS (res) J g at -1 . K-l
309
1.49
5.8
362
1.27
2.8
246
1.89
6.9
a) From ref. [25]. b) Calculated from formula (1) with OAs_s = 291 cm-1 and UAs_Se = 217 cm -1 .
198
R. Blachnik, A. Hoppe / Glass transition and specific heats
perature would lie near the Debye temperature for the disordered solid. The observed glass temperatures (350-450 K) fall somewhat above the Debye temperatures (250-400 K), however, the ideal glass temperatures (To) for As2Se a and P4Se4 are lying close to the resp. Debye temperatures. In fig. 4 the heat capacities are plotted versus log T/K, such that the entropy of the phases at a given temperature can be obtained directly from the area under the Cp-curve. The ideal thermodynamic glass temperature, To, where the area between Cp (liquid) and Cp (crystal) matches the area representing the entropy of fusion and the residual entropies obtained in this manner are listed in table 3. The ratio TG/To decreases as To increases, contrary to organic glasses, in which it is approximately constant. The latter correlation indicates that in organic glasses the configurational entropy of the melt determines the temperature dependence of cooperative relaxation processes in the glass transition region [46]. The variations in TG/To in the chalcogenide glasses confirm the anticipation of Angell that besides the excess entropy as important factor in the glass transitions a configurational enthalpic term is possible. TG/To and AS (res) for As2S 3 and As2Se 3 are unusually high and comparable to the resp. values of silica glasses. This indicates that these network glasses strongly deviate from the state of an ideal glass - e.g. simple ionic glasses. The deviation from ideality of the P4Se4 glass is much lower, as one would expect for this glass, which easily recrystallizes by the formation of isolated cage molecules. The concentration dependence of Cp in the glasses of the systems As-Se and P-Se, together with literature data of As-S by Hattori, is given in fig. 7. In view of the aim of our investigation, the graph seems to exhibit similar minima as the transport properties. For two reasons this conclusion may be incorrect. Firstly the sharp minimum of the As-S system is due to the very low Co-value of As2S 3 glass by Hattori, which is about 10% lower than the average literature value. Sec-
"T
30
a As-S
313K
* As-Se o P-Se
320K 320K
& &
2'.
2o
~"'--. ÷ ~ ÷ l~J " \ - ° ~ ° L - .....
'
8'o
'
6'o
'
4'o
atomic °/o ~ b
Fig. 7. Composition dependence of Cp in the system As-Se, P - S e and As-S at 313 and 150 K.
R. Blachnik, A. Hoppe / Glass transition and specific heats
199
Table 4 Values of Cp calculated by Neumann-Kopp rule at Tr = 0.9 TG. Mole fraction of As Co(As-Se) J g at -1 . K-1 Mole fraction of P Cp(P -Se) J g at -1. K-1
0 25.8 0 25.8
0.1 25.6 0.29 23.9
0.2 25.7 0.4 24.6
0.3 25.7 0.44 24.0
0.4 25.7 0.5 26.4
0.5 26.3
at 0.9 TG at 0.9 TG
ondly the Co-values were taken in the temperature interval between TO and Tc and thus in different vibrational and configurational states of excitation. To avoid misinterpretation we have taken Co-values at a reduced temperature of Tr = 0.9 TG, now constant Co-values in the As-Se system were obtained whereas the values in the P-Se system reveal a minimum (table 4). Additionally, the heat capacities of the As-S and As-Se systems were calculated in good agreement with the experiment from the heat capacities of pure S(Se) and pure AszS 3 (As2Se3) by the Neumann-Kopp rule. In the P-Se system, however, the calculated data showed severe deviations again. The independence of C o on concentration and the fact that these data could be calculated using the Neumann-Kopp rule supports the view that glasses in the As-S and As-Se system are based only on - X - X - and As-X3/2 molecular units. In the P-Se system different bond types (single and double bonds) and changing coordination numbers of P (4 and 3), lead to the concentration dependence of Cp and to wrong results in the simple calculation by the Neumann-Kopp rule. Haggerty pointed out that for a glass which is vibrationally fully excited (C o = 3R) the heat capacity of the liquid should be constant over a wide range of temperature. From fig. 5 and 6 it is evident that this is true for most of the compositions considered. For As4Se4 and As4Se 3 the observation that despite a C o value of 3R in the solid state Co keeps rising in the liquid can be explained by the assumption of an increasing amount of polymerized molecules in the melt. The equilibrium between molecular and polymeric forms or intra- respectively intermolecular saturation of the coordination is thus temperature dependent. More polymeric species are produced as the temperature rises. The similar increase of Co in the P4Selo, P4Se6 and P4Se s compositions may be due to reactions of the double bonds in these melts. Thus the behaviour of the specific heats in the melts confirms the picture gained by the interpretation of T c.
5. Conclusion (1) The extrema observed in the transport properties of V b-Vl b glasses do not occur in the concentration dependence of Cp. Thus the specific heat is rather insensitive to gradual structural changes. (2) The interpretation of TG and C o of the glasses leads to the assumption of an
200
R. Blachnik, A. Hoppe / Glass transition and specific heats
equilibrium between inter- and intramolecular connections of the basic structural units. (3) The thermodynamic data indicate that arsenic-chalcogen glasses are nonideal glasses.
Acknowledgements The authors wish to thank the "Fonds der ChemiC' and the Minister ftir Forschung des Landes NRW for financial support.
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[28] V.V. Tarasov, V.M. Zhdanov, A.K. Maltsev and S.A. Dembovskii, Russ. J. Phys. Chem. 43 (1969) 249. [29] Yu.G. Poltavtsev, V.P. Zakharov, V.M. Pozdnyakova and T.V. Remizovich, Inorg. Mat. 8 (1972) 813. [30] Yu.G. Poltavtsev, Russ. J. Phys. Chem. 49 (1975) 840. [31] D.B. Dove and J. Chang, Trans. Am. Cryst. Assoc. 10 (1974) 61. [32] J. Sagara, O. Uemura, S. Okuyama andT. Satow, Phys. Stat. Sol. 31a (1975) K33. [33] J. Chang and D.B. Dove, J. Non-Crystalline Solids 16 (1974) 72. [34] K.S. Liang, J. Non-Crystalline Solids 18 (1975) 197. [35] A.J. Leadbetter and A.J. Apling, J. Non-Crystalline Solids 15 (1974) 250. [36] T. Arai, S. Komiya and K. Kudo, J. Non-Crystalline Solids 18 (1975) 289. [37] T. Ohsaka, J. Non-Crystalline Solids 15 (1974) 149. [38] A.T. Ward, J. Phys. Chem. 72 (1968) 4133. [39] R.J. Kobliska and S.A. Solin, J. Non-Crystalline Solids 8-10 (1972) 191. [40] A. Bertoluzza C. Fagnano, P. Monti and G. Semerano, J. Non-Crystalline Solids 26 (1978) 49. [41] G. Lucovsky and R.M. Martin, J. Non-Crystalline Solids 8-10 (1972) 185. [42] R. Blachnik and A. Schneider, Z. Anorg. AUg. Chem. 372 (1970) 314. [43] A. Hoppe, Thesis Siegen 1978. [44] A.R. Hilton, C.E. Jones and M. Bran, Phys. Chem. Glasses 7 (1966) 116. [451 C.A. AngeU, J. Am. Ceram. Soc. 51 (1968) 117. [46] G. Adams and J.H. Gibbs, J. Chem. Phys. 43 (1965) 139.