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Transport properties of the systems SnS2-SnI4 and SnS2-I2
Journal of Crystal Growth 46 (1979) 189—197 © North-Holland Publishing Company
TRANSPORT PROPERTIES OF THE SYSTEMS SnS2—Sn14 AND SnS2—12
*
Heribert WIEDEMEIER and Frank J. CSILLAG Department of Chemistry, Rensselaer Polytechnic Institute, Troy, New York 12181, USA Received 5 May 1978; manuscript received in final form 26 June 1978
Mass transport rate studies on SnS2 in the temperature gradient 648—723 K using Sn14 as initial transport agent revealed the existence of forward (high -+ low temperature) and reverse (low -. high temperature) transport. The net transport direction was found to be pressure dependent. At higher temperatures, only forward transport was observed for the SnS2—Sn14 system. When elemental iodine is employed as initial transport agent in the above gradient, SnS2 is transported from low to high temperature for pressures between about 0.3 and 150 kPa. Thermodynamic calculations for these systems yielded partial pressures of the major gaseous species Sn14, Sn12, 12, I, S2, S3, S4, S5, S6, S7 and Ss, which led to the formulation of the dominant transport reactions consistent with the observed net transport direction. Based on the hypothetical pressure P~’of SnS2, defined as the “solubility” of SnS2 in the gas phase, the quantity ~.P* is given by the equation b.P* =P*(SnS2)T2 _P*(SflS2)Tl, where T2 > Ti. The solubility of SnS2 can be expressed in terms of the gaseous sulfur or Sn—iodide species. In the absence of kinetic limitations, for positive values of ~ forward transport (T2 — Ti) is dominant. When ,5.P* is negative, net reverse transport will occur. The presence of both forward and reverse transport implies the existence of an inversion temperature at which the solubility of the solid is a minimum. Calculations of ~P* as a function of pressure reveal that the inversion pressure (change in transport direction) occurs at higher total pressures with increasing temperature. The results of these calculations are consistent with present investigations and previous studies on the SOS2—Sn14 and SnS2—12 systems.
1. Introduction
and dominant reaction of a given transport system [8]. The possible interaction of several heterogeneous solid—gas phase reactions and mass transport in a temperature gradient create a complex situation for predictive purposes. The SnS2—Sn14 and SnS2—12 systems are good examples to elucidate the transport properties of multi-component, multi-reaction systems. In previous transport studies of SnS2, different temperature gradients between 1220 andvolume) 870 K and 3 tube werea fixed amount of iodine (5 mg/cm employed [9—13]. In all of these earlier investigations crystal growth and forward transport, i.e., from high to low temperature, were observed. The present studies revealed the existence of both forward and reverse (from low to high temperature) transport. Based on the enthalpies of the two simple transport reactions when Sn1 4 and elemental iodine, respectively, are added initially SnS2(s) + Sn14(g) = 2 Sn12(g) + S2(g) (1)
The vapor transport technique has been widely employed for the growth of single crystals of various materials. The basic principles and experimental details of this method have been discussed earlier by Schafer [1]. Subsequent applications and further theoretical developments have been reviewed by Kaldis [21 and by Faktor and Garrett [3]. However, relatively few systematic studies of the transport mode and its effect crystalyears morphology been reported [4,5]. on In recent increasinghave attention has been devoted to the elucidation of transport phenomena in closed ampoules including conditions of reduced gravity [6,7]. The combination of chemical transport and continuous mass-loss measurements appears to be promising to investigate the suitability
*
. Based on part of a thesis. to be submitted by Frank J. Csillag to the Graduate School of Rensselaer Polytechnic Institute in partial fulfillment of the requirements for a Ph.D. degree.
SnS2(s) + 2 12(g) = Sn14(g) + S2(g); 189
(2)
190
H. Wiedemeier, F.J. Csillag
/ Transport properties of systems SnS2-Sn14 and SnS2-12
the endothermic nature of both reactions suggests only transport in a forward direction. When higher molecular sulfur species important under the conditions of reaction (2) are considered, this reaction can be rewritten to yield SnS2(s)
+
2 12(g)
— —
.
Sn14(g) + (2/i) S1(g),
(2
,
)
where i = 3, 4, 5, 6, 7 or 8. The exothermic nature of reaction (2’) is consistent with reverse transport. The simultaneous occurrence of the above reactions and possible kinetic limitations make the selection of the dominant transport reaction difficult, The present work is concerned with the systematic investigation of the mass transport rate and mode of SnS2 employing 5n14 and elemental iodine as initial transport agents. Thermodynamic predictions of the net transport direction for various pressure and ternperature conditions are compared with experimental data and with previous observations,
2. Experimental procedures 2.1. Apparatus The mass transport rate studies were performed in closed ampoules of fused silica of 15 mm inner diameter and about 15 cm in length. The pretreatment, loading and sealing of the ampoules have been described previously [14]. For the transport experiments a horizontal, two-zone, tubular resistance furnace was used. The furnace core consisted of a fused silica tube which was surrounded by a pyrex jacket. Various radiation shields were used to obtain the desired, nearly linear temperature profile which was maintained to within ±1K employing proportional temperature controllers, 2.2. Materials The starting materials were elemental tin (99.999%), sulfur (99.999%) and triply sublimed iodine (initially 99.99%). The direct synthesis of SnS2 from stoichiometric ratios of the elements yielded a mixture of SnS, Sn2S3 and SnS2, in particular at lower temperatures. Employing an excess of about 2 at% sulfur and prolonged annealing (300 h) of the elements in evacuated closed ampoules at
about 870 K produced SnS2. During the above annealing, the intermediate products were repeatedly ground and mixed. The excess sulfur was removed by heating the end product under vacuum at about 470 K for several hours. Under these conditions, the decomposition pressure of SnS2(s) is less than 108 Pa [15]. Similarly, Sn14(s) was prepared from the elements using an excess of about 2 at% iodine by annealing at 520 K for about 25 h. The unreacted iodine was removed by vacuum sublimation. Since the vapor pressure of Sn14 at room temperature is less than 1 Pa, it can be directly weighed and transferred into the ampoule. Elemental iodine was added to the loaded transport ampoule by subliming iodine from a pyrex bulb under vacuum into the tube and condensing it at the source region using liquid nitrogen before sealing the ampoule. The identification of the starting materials and transport products was established by X-ray diffraction techniques. All reflections of Debye—Scherrer photographs (114.59 mm diameter camera, Ni-filtered Cu Ka radiation) could be indexed on the basis of the hexagonal structure of Sn52 and the cubic structure of Sn14, respectively. Calculated lattice parameters of SnS2 (ao = 0.3653 ±0.0004 nrn, c0 = 0.5891 ±0.0007 nm) and of Sn14 (ao = 1.2257 ± 0.0012 nm) were in close agreement with literature values [16,17] in all cases. .
-
2.3. Calculation of partial pressures and mass fluxes From the amount of transport agent (Sn14 or iodine) initially added, the pressure of Sn14 or 12 is calculated for the mean temperature of the gradient assuming the exclusive presence of Sn14 or ‘2 and ideal gas conditions. (This initial pressure is used in the graphical representation of flux versus pressure.) Based on the above calculated initial pressure and thermochemical data for the transport reactions (1) and (2), for the dissociation reaction of iodine and for the association reactions of sulfur, partial pressures at the mean temperature are calculated for the gaseous species Sn14, SnI2, ‘2, S2, S3, S4, S5, S6, S7 and S8. The presence of other species in this system is negligible for these computations. Assuming that the resulting total pressure calculated at the mean teniperature is uniform throughout the ampoule, equiib. rium partial pressures of the above species are corn~,
H. Wiedemeier, F..!.
Csillag I Transport properties of systems SnS2-SnI4
puted for the temperatures of the source and con’densation region. This yields the desired partial pressure gradients. The calculational procedures applied in this work are very similar to those of Arizumi and Nishinaga [18,19] and inherently imply minimization of the free energy of the system as employed by other authors [20—23]. mass calculated transport from rates in flux 2The s) were theterms total of mass of (mol/ SnS m 2 transported away from the source per unit crosssectional area of the ampoule and per unit time of the experiment. The amount of source material (Sn52) used in all experiments was close to 500 mg. The total amount of transport agent added varied from 0.01 mg to 1 g for Sn14 and from 0.4 to 190 mg for iodine. Based on the wide range of transport times (3—115 h) used in these studies, any initial time dependent variations in the flux were found to be insignificant. The uncertainties associated with the transport rates due to errors in temperature, transport time and weight measurements are estimated to be about 15%.
and 5n52-12
191
5
~,i E ‘
,
,
0 __________________
(/cc w IS
-
r
20
_________________
20
100
25 0
5
200
I
I
10
IS
Pressure Sn14 (kPa)
Fig. 1. The mass transport rate in terms of flux versus pressure for the SnS2—Sn14 system in the temperature gradient 723—648 K. (.) Forward transport, source material at 723 K. (0) Reverse transport, source material at 648 K. Inset is extension of flux curve.
concerning the transport direction changes with pressure when Sn14 is added initially to the system. In order to further explain the above observed transport phenomena at low pressures, the deposition range and the change in the maximum and minimum
3. Results and discussion (cm)
3.1. Mass transport rate studies 0
The mass transport rates of SnS2 were studied as a function initial pressure of transport agent employing three of different temperature gradients. A graphical representation of the flux of Sn5 2 versus pressure of Sn1 4 for the ampoule end temperatures ~‘1 = 648 K and T2 = 723 K is thown in fig. 1. Both forward reverse transport are 0.1 observed various pressureand ranges. Between about and 8 over kPa the forward flux is not measurable under these conditions. In the same pressure range, the rate of reverse transport decreases with increasing pressure and approaches zero at about 15 kPa. (Fig. 1 illustrates that the sublimation flux (PSnI4 = 0) is small compared to the total transport rates at low pressures and becomes insignificant at higher pressures.) This region is followed by a continuous increase in forward flux up to about 150 kPa at which pressure precipitation
5 io
3
6
9
12
I
I
I
IS
__________
_______
C
4
___________ -
io 3
‘~
CI)
_______
-
io
____________
ID
U,
I
_____________ _________________
0
I
_______________
648
678
I
Temperature
I
708
(K)
Fig. 2. SnS2 deposition profile in the 648—723 K temperature gradient using Sn14 as transport agent. Arrows from low
of SnI 4 is observed in the ampoule. The results in fig. 1 suggest strongly, that reactions (1) and (2’) occur simultaneously and that their relative importance
to high and from high to low temperature indicate the source material at 648 and 723 K, respectively. Length of arrows indicates deposition range.
192
H. Wiedemeier, F.J. Csilag / Transport properties of systems SnS
deposition temperature are shown in fig. 2 for different initial pressures of Sn14 when the ampoule is in the forward and reverse position. For a given pressure an inversion temperature can be defined from which neither forward nor reverse transport thould occur, The presence of a deposition range can be attributed to the limited duration of the transport experiments (<115 h). The observation that the inversion temperatures appear to be independent of pressure in the ranges from about 0.1 to 2 kPa and from 10 to 250 kPa is due to the constraints imposed by ampoule lengths. The true inversion temperatures are most likely above and below 723 and 648 K, respectively, in the above pressure ranges. This would yield the expected smooth curve for the pressure dependence of the inversion temperature rather than a “step-like” behavior as indicated by fig. 2. This would also explain the observation that there is no measurable forward transport in the pressure range 0.1 to about 8 kPa (fig. 1). Since the forward and reverse transports are based on the same initial pressure but different source temperatures, the relative magnitude of the transport rates (fig. 1) cannot be compared directly. The observed flux in a given direction is the net result of both transport modes. A further interpretation of the flux data will be presented later in connection with detailed thermodynamic calculations for this system. In order to examine the effect of reaction (2’) on the overall transport of the above system, the mass
~:Tii0:0i00i
Pressure 12(kPa) Fig. 3. The mass transport rate in terms of flux versus pressure for the SnS2—iodine system in the temperature gradient 648—723 K. (.) Sublimation. (o) Reverse transport, source material at 648 K.
2-Sn14 and SnS2-12
transport rates of SnS2 were investigated in the same temperature interval (648 to 723 K) using elemental iodine as initial transport agent. The results in fig. 3 show that under present temperature and pressure conditions reverse transport (648 723 K) is observed exclusively. In all cases, the transported matena! is condensed at the extreme hot end of the anipoule. The flux curve in fig. 3 appears to be the “mirror image” of that of typical forward transport systems. The multispecies nature of this system makes it difficult to unambiguously assign dominant transport reactions and modes to the low pressure regions (below about 30 kPa). The considerable increase in flux at higher pressures is most likely due to convective flow under these conditions. Precipitation of Sn14 at about 150 kPa causes a leveling of the flux curve. The results in figs. 1 and 3 demonstrate a considerable difference when Sn14 or elemental iodine is added initially as a transport agent. Using elemental iodine in this temperature range, transport reaction (2’) is predominant at all pressures. When Sn14 is added initially (fig. 1), reaction (2’) dominates only at low pressures. The transport properties of the SnS2—5n14 system in the temperature range 798 to 723 K are represented in fig. 4. Although there is some similarity between the flux curve in fig. 4 and the forward portion of the flux in fig. 1, there is no measurable reverse transport in the higher temperature range (fig. 4). However, the steep decrease in flux with increas-~
i~~I~OI2:O
Pressure Sn14(kPa) Fig. 4. The mass transport rate in terms of flux versus pressure for the SnS2—Sn14 system in the temperature gradient 798 —÷ 723 K, showing forward transport. Inset is extension of flux curve.
H. Wiedemeier, F.J. Csillag / Transport properties of systems SnS
2-SnI4 and SnS2-12
12
(figs. 1 and 4). This and the absence of reverse transport demonstrate, that the effect of reaction (2’) is
~
•,.o
reduced at higher temperatures. Transport under these conditions is accomplithed predominantly by reaction (1). For this reaction, the change in the number of gaseous moles is 2. This suggests a definite contribution to the total mass flux by Stephan-type [24] bulk flow which predominates at lower pressures (up to about 10 kPa). The transition from Stephan flow (streaming) to convective motion could explain the continuous increase in flux and the absence of the so-called diffusion-controlled regime.
•A
8
—
o 4
~ 7 c
I
0
I
I
50
100
193
I
150
Pressure Sn14(kPa)
3.2. Thermodynamic calculations
Fig. 5. The mass transport rate in terms of flux versus pressure for the SnS2—Sn14 system in the temperature gradient 923 — 823 K, showing forward transport.
In order to generalize the transport phenomena of the above systems observed in this work and by previous authors [9—13], the hypothetical pressure P~of SnS2 is a useful concept [1]. The quantity P* is a measure of the “solubility” of the solid SnS2 in the gas phase as a result of transport reactions. Based on the transport reactions (1) and (2), on the dissociation reaction of iodine and the association reactions of sulfur, the total amount of SnS2 “dissolved” in the gas phase (P*(SnS2)) is represented by the total amount of sulfur in the vapor expressed in terms of S2 molecules. This is given by the appropriate summa-
ing pressure of Sn14 (fig. 4) could be attributed to the influence of reaction (2’) as discussed above for fig. 1. The failure to observe reverse transport could be due to an inversion temperature close to 723 K. The increase in flux between about 20 and 250 kPa is caused by convective gas flow. The contribution of sublimation to the total flux is small. The thape of the flux curve of the SnS2—Sn14 system for the 923 823 K gradient (fig. 5) is considerably different from that for lower temperature ranges —~
Table 1 Thermochemical values of species in the SnS2-Sn14-12 system used for partial pressure calculations Species
SnS2(s) Sn14(g) Sn12(g) SS2(g) S3(g) S4(g) S5(g) S6(g) S7(g) 1 8(g) 1(g) 2(g)
0
‘~~‘298 (kJ/mol) —148.2 [151 —126.4 a) —8.0 b) 130.6 [28] 141.6 [28] 145.9 [28] 109.4 [28] 102.2 [28] 113.8 [28] 101.1 [28] 106.7 62.30 [29] [29]
a) Computed from ref. [25]. b) Computed from refs. [26,27]. c) Estimated.
0
0
S298 (J/K ‘ mol)
Cp (J/K ‘ mol)
95.9 446.3 343 227.8 269.6 310.8 308.7 354.2 407.9 430.3 260.8 180.8
64.94 108.4 63 c) 35.8 53.82 79.94 107.01 132.23 155.08 178.66 37.4 20.1
[151 [271 [30] [28] [28] [28] [28] [31] [28] [32] [29] [29]
+ —
+ + + + + + + +
17.6 2.34 1.17 4.35 3.28 1.06 0.502 2.57 3.60 0.59 0.67
X l0~T x io~j’—2
x
l0~ T— X i0~T — X i0~ T— x i0”~T — X lO~T— x i0~ T— X 10~ T — X i0~ T T— +
3.31 6.507 11.81 15.79 18.42 19.78 21.40 0.71 0.46
2 lO~T2 X io~T2 X 10~ T 5 T2 x i05 T2 X i0 2 X lO~T2 X l0~T2 X i05 lO~T2 T
x
[33] [34] [28] [28] [281 [28] [28] [28] [28] 135] [35]
H. Wiedemeier, F.J.
194
Csillag / Transport properties of systems 5n52-5n14 and
tion of the equilibrium partial pressures of sulfur species 3m’S “+ 2 I8~5~ + ~ ~4~5 \ p*(5 ~ n 5 2)\ Th’5 ‘. 2) + ~ 3) 41 2 k
5n52-12
(4)
port (T2 —* T5) thould occur. This is contrary to observations in fig. shows at low pressures. It 1is which apparent fromreverse figs. 6 transport and 7, that the ratio P(1 2)/P(5n14) is highest at low pressures and decreases with increasing pressure. The combined results (figs. 1, 6 and 7) suggest, that transport reaction (1) is lanetically lanited at low pressures and that the system transports as if iodine were added mtially. With increasing concentration of SnI4 kinetic
Values for F*(5n52) are calculated according to eq. (3) at T5 and T2. The sign of AP* determines the direction of net mass transport. If AP* is positive, forward transport (T2 -÷ T5) will occur. If AF* is negative, reverse transport (T5 —~ T2) will predominate. The thermodynamic calculations are based on the data listed in table 1. The procedures for the computation of partial pressures have been discussed above, Values for the partial pressures of the above species at the low and high temperature of the 648—723 K gradient are graphically represented as a function of total pressure in figs. 6 and 7, respectively, when 5n14 is added initially. Based on these data, At calculated according to eq. (4) is positive in the applied pressure range 1 to io~ Pa, implying that only forward trans-
limitations are reduced and the predicted transport properties based on thermodynamic considerations (figs. 6 and 7) are observed from about 8 kPa onward (fig. 1). The results of analogous partial pressure calculations for the temperature gradient 648—723 K when elemental iodine is added initially are given in figs. 8 and 9. These results thow that the magnitude and pressure dependence of the ratio F(I2)/F(5n14) are similar to those when 5n14 is added initially (figs. 6 and 7). However, figs. 8 and 9 demonstrate that the absolute partial pressures of the sulfur species are considerably greater when elemental iodine instead of 5n14 is added. More importantly, computed values of AP* (eq. (4)) for this system thown in fig. 10, curve A are negative above 30 Pa. This is consistent
— —
+3
‘~
‘.
~-
~-‘
F(S~)+ ~ F(S7) + 4 F(S8).
(3)
A quantity LiP * can now be defined by the equation .
* =
AP
r(SnS2)T 2
*
—
F (Sn52)T i
.
.
.
.
efli: Total Pressure (Pa) Fig. 6. Equilibrium partial pressures of gaseous species computed at 648 K as a function of total pressure when 5n14 is used as initial transport agent in the temperature gradient 648—723 K. The partial pressures of Ss, S6, S7 and 58 are less than io~Pa under these conditions,
4 Total io~ Pressure 1o (Pa) Fig. 7. Equilibrium partial pressures of gaseous species computed at 723 K as a function of total pressure when Sn14 is used as initial transport agent in the temperature gradient 648—723 K. The partial pressure of S8 is less than iO’5 Pa under these conditions.
H. Wiedemeier, F..!. Csillag
/ Transport properties of systems SnS2-Sn14 and SnS2-12
195
C
io
Sni
-10
10
I
I0~ Total Pressure
4
snl4
io~ S4
Sn
2
12
0_
~ io’ Se
: io-~
0 I
102
Total
Pressure
lo~
io~
Fig. 10. The hypothetical pressure difference 1..P” of SnS2 (defmed by eq. (4)) as a function of total pressure for the temperature gradients 648—723 K (curve A), 723—798 K (curve B) and 798—873 K (curve C).
with the observation of net reverse transport (fig. 3) demonstrating the predominance of reaction (2’). Verification of the forward portion of curve A below 30 Pa (z~P*>0) was experimentally not feasible. The results of similar partial pressure calculations for the SnS2—iodine system for the temperature ranges
?
S
B
Total Pressure (Pa)
10 (Pa)
Fig. 8. Equilibrium partial pressures of gaseous species cornputed at 648 K as a function of total pressure when elemental iodine is used as initial transport agent in the temperature gradient 648—723 K.
10
T2—T1
io~ (Pa)
Fig. 9. Equthbrium partial pressures of gaseous species cornputed at 723 K as a function of total pressure when elemental iodine is used as initial transport agent in the temperature gradient 648—723 K.
723—798 K and 798—873 K in terms of ~.P* are thown in fig. 10, curves B and C, respectively. The general trend of curves A, B and C reveals, that for the same temperature difference the change in sign of ~p* (change in transport direction)is pressure dependent and occurs at higher total pressures with increasing temperature. The thapes of these curves reflect that with decreasing iodine concentration (decreasing total pressure) ~P* approaches zero. Transport experiments selected in the forward 4> 0) andforreverse (AP*pressures <0) regions of curves B (~.PC confirmed these calculations. and Based on quantitative Knudsen effusion measurements [15], SnS 2(s) decomposes to Sn2S3(s) and S2 (g). However, under the conditions of curves A, B and C in fig. 10 this does not occur, because the transport reactions yield greater sulfur pressures than those which would result from the decomposition. Thus, the thermodynamic calculations of i~.F*values for a given temperature gradient (fig. 10) are terminated at
.
196
H. Wiedemeier, F.J. Csillag / Transport properties of systems SnS
the total pressure corresponding to the onset of decomposition. For the transport conditions of figs. 1 and 3, the decomposition is suppressed at all pressures; for those of figs. 4 and 5 the onset of decomposition is below 30 Pa and 2.5 kPa, respectively, 3.3. Correlations with the literature The combined thermodynamic results indicate that forward and reverse transport should exist in all temperature gradients for which the above reactions are valid. The observation of reverse transport in this work and the pressure and temperature dependence of AP* (fig. 10) are consistent with the results of previous transport studies [9—13]on SnS2. For the temperature and pressure conditions employed earlier [9—13] and based on fig. 10, forward transport is expected and was reported [9—13]. Reverse transport has also been observed for various metals [1], for GeSe2 [4], Sn02 [21], niobium arsenides and antimonides [36] and niobium oxide [36,37]. Preliminary results on SnSe2 are similar to those of the present work on SnS2.
4. Summary and conclusions Systematic mass transport rate studies on SnS2 using Sn!4 and elemental iodine as initial transport agents revealed the existence of forward and reverse transport. The net transport direction is temperature and, pressure dependent. The results of thermodynamic calculations in terms of AP* versus total pressure are in general agreement with experimental observations. The calculations also reveal the importance of higher molecular sulfur species for the net transport direction. The trends predicted by the calculations are consistent with earlier transport studies on SnS2. This work demonstrates that an accurate knowledge of the gas phase composition is required to define the dominant transport reactions and the net transport direction of a system. For further applica. tions, “solubiity” minima and maxima of solids to be transported and the deposition temperatures could be. calculated from known thermochemical data. This information is useful for the optimization of transport conditions. In the absence of thermodynamic data,
2-Sn14 and SnS2-12
thermochemical properties of the system could be estimated from the observed inversion temperature. In addition, the existence of reverse transport can be used for possible phase separation. The results of quantitative thermodynamic computations similar to those obtained in this work are of importance for fluid dynamic characterizations of such systems. The present studies demonstrate, that closed tube vapor transport is a useful technique to elucidate even complex transport reactions.
Acknowledgments The authors are pleased to acknowledge the support of this work by the National Aeronautics and Space Administration and in part by the National Science Foundation.
References [1] H. Schafer, Chemical Transport Reactions (Academic Press, New York, 1964). [2] E. Kaldis, in: Crystal Growth Theory and Techniques, Vol. 1, Ed. C.H.L. Goodman (Plenum Press, London 1974). [3] M.M. Faktor and I. Garrett, Growth of Crystals from the Vapour (Chapman and Hall, London, 1974). [4] H. Wiedemeier, E.A. Irene and A.K. Chaudhuri, J. Crystal Growth 13/14 (1972) 393. [5] H. Wiedemeier and E.A. Irene, Z. Anorg. Allg. Chem. 400 (1973) 59 [6] H. Wiedemeier, F.C. Klaessig, E.A. Irene and S.J. Wey, J. Crystal Growth 31(1975) 36. [7] H. Wiedemeier, H. Sadeek, F.C. Klaessig, M. Norek and Santandrea, J. Electrochem. 124 (1977) 1095.38 [8] R. M.M. Faktor and I. Garrett, Soc. J. Crystal Growth (1977) 213 [9] R. Nitsche; H.U. Bölsterli and M. Lichtensteiger, J. Phys. Chem. Solids 21(1961)199. [10] D.L. Greenway and R. Nitsche, J. Phys. Chem. Solids 26 (1965)1445. [11] H.P.B. Rimmmgton and A.A. Balchm Phys. Status Solidi (a) 6 (1971) K47. [12] H.P.B. Rimmington, A.A. Balchin and B.K. Tanner, J. Crystal Growth 15 (1972) 51. [13] F.A.S. AL-Alamy and A.A. Balchin, J. Crystal Growth 221. and A.G. Sigai, J. Crystal Growth 6 [14] 38 H. (1977) Wiedemeier (1969) 67 [15] H. Wiederneier and F.J. Csiilag, to be published. [16] I. Oftedal, Z. Physik. Chern. 134 (1928) 301.
H. Wiedemeier, F.J. Csillag / Transport properties of systems SnS
2-Sn14 and SnS2-12
[17] E. Swanson and E. Tage,US Dept. Commerce,Natl. Bur. Stand., Circ. 539 (1953). [181 T. Arizumi and T. Nishinaga, Japan. J. Appl. Phys. 4 (1965) 165. [19] T. Arizumi and T. Nishinaga, Japan. J. Appl. Phys. 5 (1966) 21. [20] B.I. Nolàng and M.W. Richardson, J. Crystal Growth 34 (1976) 198. [211 B.l. Nolang and M.W. Richardson, J. Crystal Growth 34 (1976) 205. [22] C. Bernard, Y. Deniel, A. Jacquot, P. Vay and M. Ducarroir, J. Less Common Metals 40 (1975) 165. [23] C. Bernard, G. Fourcaudot and J. Mercier, J. Crystal Growth 35 (1976) 192. [24] J. Stephan, Ann. Physik. Chem. 17 (1890) 550. [251J. Mikier, Monatsh. Chem. 104 (1973) 376. [26] R.G. Feber, Heats of Dissociation of Gaseous Halides, USEAC Report No. LA-3164 (1964). [27] D.D. Wagman, W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey and R.H. Schumm, Selected Values of Thermodynamic Properties, NBS Technical Note 27 0-3 (Washington, DC, 1968).
197
[28] H. Rau, T.R.N. Kutty and J.R.F. Guedes de Carvalho, J. Chem. Thermodynamics 5 (1973) 833. [29] D.R. Stull and G.C. Sinke, Advan. Chem. 5cr. 18 (1956) 108, 109. [30] L. Brewer, G.R. Somayajulu and E. Brackett, Chem. Rev. 63 (1963) 111. [31] J. Berkowitz, W.A. Chupka, E. Bromels and R.L.J. Belford, J. Chem. Phys. 47 (1967) 4320. [321 G.B. Guthrie Jr., D.W. Scott and G.J. Waddington, J. Am. Chem. Soc. 76 (1954) 1488. [33] R.L. Orr and AU. Christensen, J. Phys. Chem. 62 (1958) 124. [34] K.K. Keiley, US Dept. Interior, But. Mines, Bull. 584 (1960) 193. [35] K.K. Kelley, US Dept. Interior, Bur. Mines, Bull. 584 (1960) 91. [36] H. Schafer and W. Fuhr, J. Less Common Metals 8 (1965) 375. [37] H. Kodama and H. Komatsu, J. Crystal Growth 36 (1976) 121.
TRANSPORT PROPERTIES OF THE SYSTEMS SnS2—Sn14 AND SnS2—12
*
Heribert WIEDEMEIER and Frank J. CSILLAG Department of Chemistry, Rensselaer Polytechnic Institute, Troy, New York 12181, USA Received 5 May 1978; manuscript received in final form 26 June 1978
Mass transport rate studies on SnS2 in the temperature gradient 648—723 K using Sn14 as initial transport agent revealed the existence of forward (high -+ low temperature) and reverse (low -. high temperature) transport. The net transport direction was found to be pressure dependent. At higher temperatures, only forward transport was observed for the SnS2—Sn14 system. When elemental iodine is employed as initial transport agent in the above gradient, SnS2 is transported from low to high temperature for pressures between about 0.3 and 150 kPa. Thermodynamic calculations for these systems yielded partial pressures of the major gaseous species Sn14, Sn12, 12, I, S2, S3, S4, S5, S6, S7 and Ss, which led to the formulation of the dominant transport reactions consistent with the observed net transport direction. Based on the hypothetical pressure P~’of SnS2, defined as the “solubility” of SnS2 in the gas phase, the quantity ~.P* is given by the equation b.P* =P*(SnS2)T2 _P*(SflS2)Tl, where T2 > Ti. The solubility of SnS2 can be expressed in terms of the gaseous sulfur or Sn—iodide species. In the absence of kinetic limitations, for positive values of ~ forward transport (T2 — Ti) is dominant. When ,5.P* is negative, net reverse transport will occur. The presence of both forward and reverse transport implies the existence of an inversion temperature at which the solubility of the solid is a minimum. Calculations of ~P* as a function of pressure reveal that the inversion pressure (change in transport direction) occurs at higher total pressures with increasing temperature. The results of these calculations are consistent with present investigations and previous studies on the SOS2—Sn14 and SnS2—12 systems.
1. Introduction
and dominant reaction of a given transport system [8]. The possible interaction of several heterogeneous solid—gas phase reactions and mass transport in a temperature gradient create a complex situation for predictive purposes. The SnS2—Sn14 and SnS2—12 systems are good examples to elucidate the transport properties of multi-component, multi-reaction systems. In previous transport studies of SnS2, different temperature gradients between 1220 andvolume) 870 K and 3 tube werea fixed amount of iodine (5 mg/cm employed [9—13]. In all of these earlier investigations crystal growth and forward transport, i.e., from high to low temperature, were observed. The present studies revealed the existence of both forward and reverse (from low to high temperature) transport. Based on the enthalpies of the two simple transport reactions when Sn1 4 and elemental iodine, respectively, are added initially SnS2(s) + Sn14(g) = 2 Sn12(g) + S2(g) (1)
The vapor transport technique has been widely employed for the growth of single crystals of various materials. The basic principles and experimental details of this method have been discussed earlier by Schafer [1]. Subsequent applications and further theoretical developments have been reviewed by Kaldis [21 and by Faktor and Garrett [3]. However, relatively few systematic studies of the transport mode and its effect crystalyears morphology been reported [4,5]. on In recent increasinghave attention has been devoted to the elucidation of transport phenomena in closed ampoules including conditions of reduced gravity [6,7]. The combination of chemical transport and continuous mass-loss measurements appears to be promising to investigate the suitability
*
. Based on part of a thesis. to be submitted by Frank J. Csillag to the Graduate School of Rensselaer Polytechnic Institute in partial fulfillment of the requirements for a Ph.D. degree.
SnS2(s) + 2 12(g) = Sn14(g) + S2(g); 189
(2)
190
H. Wiedemeier, F.J. Csillag
/ Transport properties of systems SnS2-Sn14 and SnS2-12
the endothermic nature of both reactions suggests only transport in a forward direction. When higher molecular sulfur species important under the conditions of reaction (2) are considered, this reaction can be rewritten to yield SnS2(s)
+
2 12(g)
— —
.
Sn14(g) + (2/i) S1(g),
(2
,
)
where i = 3, 4, 5, 6, 7 or 8. The exothermic nature of reaction (2’) is consistent with reverse transport. The simultaneous occurrence of the above reactions and possible kinetic limitations make the selection of the dominant transport reaction difficult, The present work is concerned with the systematic investigation of the mass transport rate and mode of SnS2 employing 5n14 and elemental iodine as initial transport agents. Thermodynamic predictions of the net transport direction for various pressure and ternperature conditions are compared with experimental data and with previous observations,
2. Experimental procedures 2.1. Apparatus The mass transport rate studies were performed in closed ampoules of fused silica of 15 mm inner diameter and about 15 cm in length. The pretreatment, loading and sealing of the ampoules have been described previously [14]. For the transport experiments a horizontal, two-zone, tubular resistance furnace was used. The furnace core consisted of a fused silica tube which was surrounded by a pyrex jacket. Various radiation shields were used to obtain the desired, nearly linear temperature profile which was maintained to within ±1K employing proportional temperature controllers, 2.2. Materials The starting materials were elemental tin (99.999%), sulfur (99.999%) and triply sublimed iodine (initially 99.99%). The direct synthesis of SnS2 from stoichiometric ratios of the elements yielded a mixture of SnS, Sn2S3 and SnS2, in particular at lower temperatures. Employing an excess of about 2 at% sulfur and prolonged annealing (300 h) of the elements in evacuated closed ampoules at
about 870 K produced SnS2. During the above annealing, the intermediate products were repeatedly ground and mixed. The excess sulfur was removed by heating the end product under vacuum at about 470 K for several hours. Under these conditions, the decomposition pressure of SnS2(s) is less than 108 Pa [15]. Similarly, Sn14(s) was prepared from the elements using an excess of about 2 at% iodine by annealing at 520 K for about 25 h. The unreacted iodine was removed by vacuum sublimation. Since the vapor pressure of Sn14 at room temperature is less than 1 Pa, it can be directly weighed and transferred into the ampoule. Elemental iodine was added to the loaded transport ampoule by subliming iodine from a pyrex bulb under vacuum into the tube and condensing it at the source region using liquid nitrogen before sealing the ampoule. The identification of the starting materials and transport products was established by X-ray diffraction techniques. All reflections of Debye—Scherrer photographs (114.59 mm diameter camera, Ni-filtered Cu Ka radiation) could be indexed on the basis of the hexagonal structure of Sn52 and the cubic structure of Sn14, respectively. Calculated lattice parameters of SnS2 (ao = 0.3653 ±0.0004 nrn, c0 = 0.5891 ±0.0007 nm) and of Sn14 (ao = 1.2257 ± 0.0012 nm) were in close agreement with literature values [16,17] in all cases. .
-
2.3. Calculation of partial pressures and mass fluxes From the amount of transport agent (Sn14 or iodine) initially added, the pressure of Sn14 or 12 is calculated for the mean temperature of the gradient assuming the exclusive presence of Sn14 or ‘2 and ideal gas conditions. (This initial pressure is used in the graphical representation of flux versus pressure.) Based on the above calculated initial pressure and thermochemical data for the transport reactions (1) and (2), for the dissociation reaction of iodine and for the association reactions of sulfur, partial pressures at the mean temperature are calculated for the gaseous species Sn14, SnI2, ‘2, S2, S3, S4, S5, S6, S7 and S8. The presence of other species in this system is negligible for these computations. Assuming that the resulting total pressure calculated at the mean teniperature is uniform throughout the ampoule, equiib. rium partial pressures of the above species are corn~,
H. Wiedemeier, F..!.
Csillag I Transport properties of systems SnS2-SnI4
puted for the temperatures of the source and con’densation region. This yields the desired partial pressure gradients. The calculational procedures applied in this work are very similar to those of Arizumi and Nishinaga [18,19] and inherently imply minimization of the free energy of the system as employed by other authors [20—23]. mass calculated transport from rates in flux 2The s) were theterms total of mass of (mol/ SnS m 2 transported away from the source per unit crosssectional area of the ampoule and per unit time of the experiment. The amount of source material (Sn52) used in all experiments was close to 500 mg. The total amount of transport agent added varied from 0.01 mg to 1 g for Sn14 and from 0.4 to 190 mg for iodine. Based on the wide range of transport times (3—115 h) used in these studies, any initial time dependent variations in the flux were found to be insignificant. The uncertainties associated with the transport rates due to errors in temperature, transport time and weight measurements are estimated to be about 15%.
and 5n52-12
191
5
~,i E ‘
,
,
0 __________________
(/cc w IS
-
r
20
_________________
20
100
25 0
5
200
I
I
10
IS
Pressure Sn14 (kPa)
Fig. 1. The mass transport rate in terms of flux versus pressure for the SnS2—Sn14 system in the temperature gradient 723—648 K. (.) Forward transport, source material at 723 K. (0) Reverse transport, source material at 648 K. Inset is extension of flux curve.
concerning the transport direction changes with pressure when Sn14 is added initially to the system. In order to further explain the above observed transport phenomena at low pressures, the deposition range and the change in the maximum and minimum
3. Results and discussion (cm)
3.1. Mass transport rate studies 0
The mass transport rates of SnS2 were studied as a function initial pressure of transport agent employing three of different temperature gradients. A graphical representation of the flux of Sn5 2 versus pressure of Sn1 4 for the ampoule end temperatures ~‘1 = 648 K and T2 = 723 K is thown in fig. 1. Both forward reverse transport are 0.1 observed various pressureand ranges. Between about and 8 over kPa the forward flux is not measurable under these conditions. In the same pressure range, the rate of reverse transport decreases with increasing pressure and approaches zero at about 15 kPa. (Fig. 1 illustrates that the sublimation flux (PSnI4 = 0) is small compared to the total transport rates at low pressures and becomes insignificant at higher pressures.) This region is followed by a continuous increase in forward flux up to about 150 kPa at which pressure precipitation
5 io
3
6
9
12
I
I
I
IS
__________
_______
C
4
___________ -
io 3
‘~
CI)
_______
-
io
____________
ID
U,
I
_____________ _________________
0
I
_______________
648
678
I
Temperature
I
708
(K)
Fig. 2. SnS2 deposition profile in the 648—723 K temperature gradient using Sn14 as transport agent. Arrows from low
of SnI 4 is observed in the ampoule. The results in fig. 1 suggest strongly, that reactions (1) and (2’) occur simultaneously and that their relative importance
to high and from high to low temperature indicate the source material at 648 and 723 K, respectively. Length of arrows indicates deposition range.
192
H. Wiedemeier, F.J. Csilag / Transport properties of systems SnS
deposition temperature are shown in fig. 2 for different initial pressures of Sn14 when the ampoule is in the forward and reverse position. For a given pressure an inversion temperature can be defined from which neither forward nor reverse transport thould occur, The presence of a deposition range can be attributed to the limited duration of the transport experiments (<115 h). The observation that the inversion temperatures appear to be independent of pressure in the ranges from about 0.1 to 2 kPa and from 10 to 250 kPa is due to the constraints imposed by ampoule lengths. The true inversion temperatures are most likely above and below 723 and 648 K, respectively, in the above pressure ranges. This would yield the expected smooth curve for the pressure dependence of the inversion temperature rather than a “step-like” behavior as indicated by fig. 2. This would also explain the observation that there is no measurable forward transport in the pressure range 0.1 to about 8 kPa (fig. 1). Since the forward and reverse transports are based on the same initial pressure but different source temperatures, the relative magnitude of the transport rates (fig. 1) cannot be compared directly. The observed flux in a given direction is the net result of both transport modes. A further interpretation of the flux data will be presented later in connection with detailed thermodynamic calculations for this system. In order to examine the effect of reaction (2’) on the overall transport of the above system, the mass
~:Tii0:0i00i
Pressure 12(kPa) Fig. 3. The mass transport rate in terms of flux versus pressure for the SnS2—iodine system in the temperature gradient 648—723 K. (.) Sublimation. (o) Reverse transport, source material at 648 K.
2-Sn14 and SnS2-12
transport rates of SnS2 were investigated in the same temperature interval (648 to 723 K) using elemental iodine as initial transport agent. The results in fig. 3 show that under present temperature and pressure conditions reverse transport (648 723 K) is observed exclusively. In all cases, the transported matena! is condensed at the extreme hot end of the anipoule. The flux curve in fig. 3 appears to be the “mirror image” of that of typical forward transport systems. The multispecies nature of this system makes it difficult to unambiguously assign dominant transport reactions and modes to the low pressure regions (below about 30 kPa). The considerable increase in flux at higher pressures is most likely due to convective flow under these conditions. Precipitation of Sn14 at about 150 kPa causes a leveling of the flux curve. The results in figs. 1 and 3 demonstrate a considerable difference when Sn14 or elemental iodine is added initially as a transport agent. Using elemental iodine in this temperature range, transport reaction (2’) is predominant at all pressures. When Sn14 is added initially (fig. 1), reaction (2’) dominates only at low pressures. The transport properties of the SnS2—5n14 system in the temperature range 798 to 723 K are represented in fig. 4. Although there is some similarity between the flux curve in fig. 4 and the forward portion of the flux in fig. 1, there is no measurable reverse transport in the higher temperature range (fig. 4). However, the steep decrease in flux with increas-~
i~~I~OI2:O
Pressure Sn14(kPa) Fig. 4. The mass transport rate in terms of flux versus pressure for the SnS2—Sn14 system in the temperature gradient 798 —÷ 723 K, showing forward transport. Inset is extension of flux curve.
H. Wiedemeier, F.J. Csillag / Transport properties of systems SnS
2-SnI4 and SnS2-12
12
(figs. 1 and 4). This and the absence of reverse transport demonstrate, that the effect of reaction (2’) is
~
•,.o
reduced at higher temperatures. Transport under these conditions is accomplithed predominantly by reaction (1). For this reaction, the change in the number of gaseous moles is 2. This suggests a definite contribution to the total mass flux by Stephan-type [24] bulk flow which predominates at lower pressures (up to about 10 kPa). The transition from Stephan flow (streaming) to convective motion could explain the continuous increase in flux and the absence of the so-called diffusion-controlled regime.
•A
8
—
o 4
~ 7 c
I
0
I
I
50
100
193
I
150
Pressure Sn14(kPa)
3.2. Thermodynamic calculations
Fig. 5. The mass transport rate in terms of flux versus pressure for the SnS2—Sn14 system in the temperature gradient 923 — 823 K, showing forward transport.
In order to generalize the transport phenomena of the above systems observed in this work and by previous authors [9—13], the hypothetical pressure P~of SnS2 is a useful concept [1]. The quantity P* is a measure of the “solubility” of the solid SnS2 in the gas phase as a result of transport reactions. Based on the transport reactions (1) and (2), on the dissociation reaction of iodine and the association reactions of sulfur, the total amount of SnS2 “dissolved” in the gas phase (P*(SnS2)) is represented by the total amount of sulfur in the vapor expressed in terms of S2 molecules. This is given by the appropriate summa-
ing pressure of Sn14 (fig. 4) could be attributed to the influence of reaction (2’) as discussed above for fig. 1. The failure to observe reverse transport could be due to an inversion temperature close to 723 K. The increase in flux between about 20 and 250 kPa is caused by convective gas flow. The contribution of sublimation to the total flux is small. The thape of the flux curve of the SnS2—Sn14 system for the 923 823 K gradient (fig. 5) is considerably different from that for lower temperature ranges —~
Table 1 Thermochemical values of species in the SnS2-Sn14-12 system used for partial pressure calculations Species
SnS2(s) Sn14(g) Sn12(g) SS2(g) S3(g) S4(g) S5(g) S6(g) S7(g) 1 8(g) 1(g) 2(g)
0
‘~~‘298 (kJ/mol) —148.2 [151 —126.4 a) —8.0 b) 130.6 [28] 141.6 [28] 145.9 [28] 109.4 [28] 102.2 [28] 113.8 [28] 101.1 [28] 106.7 62.30 [29] [29]
a) Computed from ref. [25]. b) Computed from refs. [26,27]. c) Estimated.
0
0
S298 (J/K ‘ mol)
Cp (J/K ‘ mol)
95.9 446.3 343 227.8 269.6 310.8 308.7 354.2 407.9 430.3 260.8 180.8
64.94 108.4 63 c) 35.8 53.82 79.94 107.01 132.23 155.08 178.66 37.4 20.1
[151 [271 [30] [28] [28] [28] [28] [31] [28] [32] [29] [29]
+ —
+ + + + + + + +
17.6 2.34 1.17 4.35 3.28 1.06 0.502 2.57 3.60 0.59 0.67
X l0~T x io~j’—2
x
l0~ T— X i0~T — X i0~ T— x i0”~T — X lO~T— x i0~ T— X 10~ T — X i0~ T T— +
3.31 6.507 11.81 15.79 18.42 19.78 21.40 0.71 0.46
2 lO~T2 X io~T2 X 10~ T 5 T2 x i05 T2 X i0 2 X lO~T2 X l0~T2 X i05 lO~T2 T
x
[33] [34] [28] [28] [281 [28] [28] [28] [28] 135] [35]
H. Wiedemeier, F.J.
194
Csillag / Transport properties of systems 5n52-5n14 and
tion of the equilibrium partial pressures of sulfur species 3m’S “+ 2 I8~5~ + ~ ~4~5 \ p*(5 ~ n 5 2)\ Th’5 ‘. 2) + ~ 3) 41 2 k
5n52-12
(4)
port (T2 —* T5) thould occur. This is contrary to observations in fig. shows at low pressures. It 1is which apparent fromreverse figs. 6 transport and 7, that the ratio P(1 2)/P(5n14) is highest at low pressures and decreases with increasing pressure. The combined results (figs. 1, 6 and 7) suggest, that transport reaction (1) is lanetically lanited at low pressures and that the system transports as if iodine were added mtially. With increasing concentration of SnI4 kinetic
Values for F*(5n52) are calculated according to eq. (3) at T5 and T2. The sign of AP* determines the direction of net mass transport. If AP* is positive, forward transport (T2 -÷ T5) will occur. If AF* is negative, reverse transport (T5 —~ T2) will predominate. The thermodynamic calculations are based on the data listed in table 1. The procedures for the computation of partial pressures have been discussed above, Values for the partial pressures of the above species at the low and high temperature of the 648—723 K gradient are graphically represented as a function of total pressure in figs. 6 and 7, respectively, when 5n14 is added initially. Based on these data, At calculated according to eq. (4) is positive in the applied pressure range 1 to io~ Pa, implying that only forward trans-
limitations are reduced and the predicted transport properties based on thermodynamic considerations (figs. 6 and 7) are observed from about 8 kPa onward (fig. 1). The results of analogous partial pressure calculations for the temperature gradient 648—723 K when elemental iodine is added initially are given in figs. 8 and 9. These results thow that the magnitude and pressure dependence of the ratio F(I2)/F(5n14) are similar to those when 5n14 is added initially (figs. 6 and 7). However, figs. 8 and 9 demonstrate that the absolute partial pressures of the sulfur species are considerably greater when elemental iodine instead of 5n14 is added. More importantly, computed values of AP* (eq. (4)) for this system thown in fig. 10, curve A are negative above 30 Pa. This is consistent
— —
+3
‘~
‘.
~-
~-‘
F(S~)+ ~ F(S7) + 4 F(S8).
(3)
A quantity LiP * can now be defined by the equation .
* =
AP
r(SnS2)T 2
*
—
F (Sn52)T i
.
.
.
.
efli: Total Pressure (Pa) Fig. 6. Equilibrium partial pressures of gaseous species computed at 648 K as a function of total pressure when 5n14 is used as initial transport agent in the temperature gradient 648—723 K. The partial pressures of Ss, S6, S7 and 58 are less than io~Pa under these conditions,
4 Total io~ Pressure 1o (Pa) Fig. 7. Equilibrium partial pressures of gaseous species computed at 723 K as a function of total pressure when Sn14 is used as initial transport agent in the temperature gradient 648—723 K. The partial pressure of S8 is less than iO’5 Pa under these conditions.
H. Wiedemeier, F..!. Csillag
/ Transport properties of systems SnS2-Sn14 and SnS2-12
195
C
io
Sni
-10
10
I
I0~ Total Pressure
4
snl4
io~ S4
Sn
2
12
0_
~ io’ Se
: io-~
0 I
102
Total
Pressure
lo~
io~
Fig. 10. The hypothetical pressure difference 1..P” of SnS2 (defmed by eq. (4)) as a function of total pressure for the temperature gradients 648—723 K (curve A), 723—798 K (curve B) and 798—873 K (curve C).
with the observation of net reverse transport (fig. 3) demonstrating the predominance of reaction (2’). Verification of the forward portion of curve A below 30 Pa (z~P*>0) was experimentally not feasible. The results of similar partial pressure calculations for the SnS2—iodine system for the temperature ranges
?
S
B
Total Pressure (Pa)
10 (Pa)
Fig. 8. Equilibrium partial pressures of gaseous species cornputed at 648 K as a function of total pressure when elemental iodine is used as initial transport agent in the temperature gradient 648—723 K.
10
T2—T1
io~ (Pa)
Fig. 9. Equthbrium partial pressures of gaseous species cornputed at 723 K as a function of total pressure when elemental iodine is used as initial transport agent in the temperature gradient 648—723 K.
723—798 K and 798—873 K in terms of ~.P* are thown in fig. 10, curves B and C, respectively. The general trend of curves A, B and C reveals, that for the same temperature difference the change in sign of ~p* (change in transport direction)is pressure dependent and occurs at higher total pressures with increasing temperature. The thapes of these curves reflect that with decreasing iodine concentration (decreasing total pressure) ~P* approaches zero. Transport experiments selected in the forward 4> 0) andforreverse (AP*pressures <0) regions of curves B (~.PC confirmed these calculations. and Based on quantitative Knudsen effusion measurements [15], SnS 2(s) decomposes to Sn2S3(s) and S2 (g). However, under the conditions of curves A, B and C in fig. 10 this does not occur, because the transport reactions yield greater sulfur pressures than those which would result from the decomposition. Thus, the thermodynamic calculations of i~.F*values for a given temperature gradient (fig. 10) are terminated at
.
196
H. Wiedemeier, F.J. Csillag / Transport properties of systems SnS
the total pressure corresponding to the onset of decomposition. For the transport conditions of figs. 1 and 3, the decomposition is suppressed at all pressures; for those of figs. 4 and 5 the onset of decomposition is below 30 Pa and 2.5 kPa, respectively, 3.3. Correlations with the literature The combined thermodynamic results indicate that forward and reverse transport should exist in all temperature gradients for which the above reactions are valid. The observation of reverse transport in this work and the pressure and temperature dependence of AP* (fig. 10) are consistent with the results of previous transport studies [9—13]on SnS2. For the temperature and pressure conditions employed earlier [9—13] and based on fig. 10, forward transport is expected and was reported [9—13]. Reverse transport has also been observed for various metals [1], for GeSe2 [4], Sn02 [21], niobium arsenides and antimonides [36] and niobium oxide [36,37]. Preliminary results on SnSe2 are similar to those of the present work on SnS2.
4. Summary and conclusions Systematic mass transport rate studies on SnS2 using Sn!4 and elemental iodine as initial transport agents revealed the existence of forward and reverse transport. The net transport direction is temperature and, pressure dependent. The results of thermodynamic calculations in terms of AP* versus total pressure are in general agreement with experimental observations. The calculations also reveal the importance of higher molecular sulfur species for the net transport direction. The trends predicted by the calculations are consistent with earlier transport studies on SnS2. This work demonstrates that an accurate knowledge of the gas phase composition is required to define the dominant transport reactions and the net transport direction of a system. For further applica. tions, “solubiity” minima and maxima of solids to be transported and the deposition temperatures could be. calculated from known thermochemical data. This information is useful for the optimization of transport conditions. In the absence of thermodynamic data,
2-Sn14 and SnS2-12
thermochemical properties of the system could be estimated from the observed inversion temperature. In addition, the existence of reverse transport can be used for possible phase separation. The results of quantitative thermodynamic computations similar to those obtained in this work are of importance for fluid dynamic characterizations of such systems. The present studies demonstrate, that closed tube vapor transport is a useful technique to elucidate even complex transport reactions.
Acknowledgments The authors are pleased to acknowledge the support of this work by the National Aeronautics and Space Administration and in part by the National Science Foundation.
References [1] H. Schafer, Chemical Transport Reactions (Academic Press, New York, 1964). [2] E. Kaldis, in: Crystal Growth Theory and Techniques, Vol. 1, Ed. C.H.L. Goodman (Plenum Press, London 1974). [3] M.M. Faktor and I. Garrett, Growth of Crystals from the Vapour (Chapman and Hall, London, 1974). [4] H. Wiedemeier, E.A. Irene and A.K. Chaudhuri, J. Crystal Growth 13/14 (1972) 393. [5] H. Wiedemeier and E.A. Irene, Z. Anorg. Allg. Chem. 400 (1973) 59 [6] H. Wiedemeier, F.C. Klaessig, E.A. Irene and S.J. Wey, J. Crystal Growth 31(1975) 36. [7] H. Wiedemeier, H. Sadeek, F.C. Klaessig, M. Norek and Santandrea, J. Electrochem. 124 (1977) 1095.38 [8] R. M.M. Faktor and I. Garrett, Soc. J. Crystal Growth (1977) 213 [9] R. Nitsche; H.U. Bölsterli and M. Lichtensteiger, J. Phys. Chem. Solids 21(1961)199. [10] D.L. Greenway and R. Nitsche, J. Phys. Chem. Solids 26 (1965)1445. [11] H.P.B. Rimmmgton and A.A. Balchm Phys. Status Solidi (a) 6 (1971) K47. [12] H.P.B. Rimmington, A.A. Balchin and B.K. Tanner, J. Crystal Growth 15 (1972) 51. [13] F.A.S. AL-Alamy and A.A. Balchin, J. Crystal Growth 221. and A.G. Sigai, J. Crystal Growth 6 [14] 38 H. (1977) Wiedemeier (1969) 67 [15] H. Wiederneier and F.J. Csiilag, to be published. [16] I. Oftedal, Z. Physik. Chern. 134 (1928) 301.
H. Wiedemeier, F.J. Csillag / Transport properties of systems SnS
2-Sn14 and SnS2-12
[17] E. Swanson and E. Tage,US Dept. Commerce,Natl. Bur. Stand., Circ. 539 (1953). [181 T. Arizumi and T. Nishinaga, Japan. J. Appl. Phys. 4 (1965) 165. [19] T. Arizumi and T. Nishinaga, Japan. J. Appl. Phys. 5 (1966) 21. [20] B.I. Nolàng and M.W. Richardson, J. Crystal Growth 34 (1976) 198. [211 B.l. Nolang and M.W. Richardson, J. Crystal Growth 34 (1976) 205. [22] C. Bernard, Y. Deniel, A. Jacquot, P. Vay and M. Ducarroir, J. Less Common Metals 40 (1975) 165. [23] C. Bernard, G. Fourcaudot and J. Mercier, J. Crystal Growth 35 (1976) 192. [24] J. Stephan, Ann. Physik. Chem. 17 (1890) 550. [251J. Mikier, Monatsh. Chem. 104 (1973) 376. [26] R.G. Feber, Heats of Dissociation of Gaseous Halides, USEAC Report No. LA-3164 (1964). [27] D.D. Wagman, W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey and R.H. Schumm, Selected Values of Thermodynamic Properties, NBS Technical Note 27 0-3 (Washington, DC, 1968).
197
[28] H. Rau, T.R.N. Kutty and J.R.F. Guedes de Carvalho, J. Chem. Thermodynamics 5 (1973) 833. [29] D.R. Stull and G.C. Sinke, Advan. Chem. 5cr. 18 (1956) 108, 109. [30] L. Brewer, G.R. Somayajulu and E. Brackett, Chem. Rev. 63 (1963) 111. [31] J. Berkowitz, W.A. Chupka, E. Bromels and R.L.J. Belford, J. Chem. Phys. 47 (1967) 4320. [321 G.B. Guthrie Jr., D.W. Scott and G.J. Waddington, J. Am. Chem. Soc. 76 (1954) 1488. [33] R.L. Orr and AU. Christensen, J. Phys. Chem. 62 (1958) 124. [34] K.K. Keiley, US Dept. Interior, But. Mines, Bull. 584 (1960) 193. [35] K.K. Kelley, US Dept. Interior, Bur. Mines, Bull. 584 (1960) 91. [36] H. Schafer and W. Fuhr, J. Less Common Metals 8 (1965) 375. [37] H. Kodama and H. Komatsu, J. Crystal Growth 36 (1976) 121.