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Growth of zinc sulfide by iodine transport
Journal of Crystal Growth 19 (1973) 1—4 © North-Holland Publishing Co.
GROWTH OF ZINC SULFIDE BY IODINE TRANSPORT PHILIP N. DANGEL and B. J. WUENSCH Ceramics Division, Department of Metallurgy and Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. Received 7 August 1972; revised manuscript received 2 February 1973 Rates of chemical transport ofZnS by iodine at 800 °Cwere determined for closed tubes as a function oftube geometry, temperature gradient (3 to 35 °C) and concentration of the transporting agent (0 to 7>< I0~ 3 Ii). At high iodine concentrations the transport was found to be a linear function of reciprocal tube g cm length, tube cross sectional area, and the partial pressure difference ofZn1 2, and was essentially independent of the concentration of transporting agent. These relations, as well as the magnitude of the observed rate, are 3 gwith cm3the(0.6 atm) transport ratesfor decreased markedly and asymptotically the rate of in accord predictions of models diffusion-controlled kinetics. At iodineapproached concentrations below sublimation-condensation. Although the sphalerite modification of ZnS was the stable phase at all growth 2x10 conditions, the transport product was predominantly the wurtzite form of the seed material in the surfacereaction limited region of iodine concentrations. At high concentrations of the transporting agent, as in previous studies, the product was entirely sphalerite. Intermediate iodine concentrations produced crystals with severe stacking disorder.
1. Infroduction Synthesis of zinc sulfide crystals in closed tubes has been achieved with the use of transport agents such as 12), HC18’°) NH 7) and H 11”2). In the 4C1 and viscous 2S effects, and if absence of free convection surface reactions are negligible, transport rates will be controlled by the diffusion of the gaseous species. If one assumes that the flux of the component of highest molecular weight constitutes the rate-limiting step, the transport rate, r, for a reaction such as ZnS+1 2
~—
ZnI~+~~‘2
should be given by’ 3) D(P2 P1)A r R IL —
—
(2)
where P2 and P1 are the equilibrium vapor pressures of Zn12 at T2 and T1, the temperatures of the source and growth zones, respectively; D is the diffusion coefficient of Zn12 (g); R is the gas constant, T the average ternperature; and A is the cross-sectional area ofa transport tube of length L. Most experimental tests of (2) with ZnS have employed HC1 as the transport agent. The rate8), of transport A 9), and has been found to be proportional 1 /L independent of time9). After initial to dependence on the
square root of HC1 pressure at low pressures9), the transport rate was found to become essentially independent of the concentration of the transporting agent9” 0) These observations, combined with the result that porous plugs had no effect on transport rates, confirm diffusion-controlled kinetics. In contrast, the kinetics of transport with 12 appeared to be controlled by thermal convection4). Similar kinetics have been observed in the transport of MnS—MnSe by 1214). These results were obtained, however, for fairly high 12 pressures (1 to 10 atm) and high temperature gradients (75 to 100 °C).The objectives of the present study were to examine ZnS transport with ‘2 at lower temperature gradients and transporting agent concentrations, compare the dependence of transport rates on system parameters with the predictions of diffusion-controlled kinetics, and to determine the conditions at which surface reactions became a rate-limiting step. 2. Experimental procedure Vycor capsules ranging from 0.40 to 2.20 cm in diameter and 5.0 to 14.0 cm in length were sealed at one end and loaded with an appropriate amount of ZnS and iodine. Thefrom iodine whichpowder were employed ranged 0 toconcentrations 0.007 g cm (0 to 2.12 atm at 800 °C).The loaded capsules were
2
PHILIP N. DANGEL AND B. J. WUENSCH I
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3) Fig. I. Transport rate as a function of cross sectional area of tube (0.007 g cm3 12, source temperature 800 °C,AT = 60 °C, tube length = 14 cm; rate normalized to unit AT, unit tube length).
Fig. 2. Transport rate as a function of AT, linearly related to AP for the range of temperatures examined (0.007 g cm3 12, source temperature 800 °C, 14 cm tube length, 4.04 mm tube diameter; rate normalized to unit tube length, unit tube area).
flushed with helium several times and sealed with an
where P
TUBE CROSS SECTIONAL AREA (cm
atmosphere approximately mmofHe at room ternperature. Theofhelium inhibited10loss iodine through volatilization and slowed diffusion of other gaseous species during runs by negligible amounts. A fine dusting of ZnS powder was allowed to adhere to the growth end of the capsule to provide sites for nudeation. The tubes were carefully placed in a gradient furnace, the source end of which was maintained at 800 °C. The growth region was at 800 °C—AT,where AT ranged from 3° to 75° in various runs. Upon completion of transport, the capsule was water quenched, broken open, and, after the condensed iodine sublimed, the mass of material transported to the had growth zone was determined, 3. Observed fransport rates At carrier concentrations of 0.007 g cm3 the transport rate was found to be a linear function of time, tube area, and reciprocal length as predicted by (2). Fig. 1 presents the variation of transport rate with tube area. The partial-pressure differences were calculated on the assumption of diatomic sulfur gas and, for reaction (I) 15~16), AF = 8000—1.5 T cal/mole. The Zn1 2 partial pressure, X, was then obtained from the cubic equation X(~X~~ = K(T) = exp AF/RT), (3) (PQ_X) (—
0 is the pressure of 12 ideal gas generated byand the 3 of iodine iodine*. For example, at 0.0005 g cm AT = 54 °C, AX was 5.5 x i0~ atm. Because the maximum temperature difference in any run was only 75 °C, the partial pressure difference of Zn1 2 was essentially a linear function of AT. The transport rate in a tube of fixed geometry was thus found to be a linear function of AT as shown in fig. 2. The measured dependence oftransport rate on iodine concentration is given in fig. 3. At the highest iodine concentrations which were examined the transport rate appears to become independent of the concentration of the transporting agent as predicted 3byiodine diffusion-con(0.6 atm) trolled kinetics. Below 2 x l0~g cm the rate of transport decreased sharply as surface reaction slowed the rate and, at very low carrier concentrations, asymptotically approached the rate of sublimation—condensation. Fig. 3 also includes the transport rate predicted by the simplified model for diffusion-controlled kinetics. For these computations, using (2), Zn1 2 partial pressure differences were evaluated from (3) and 4) the for diffusion Zn1 coefficient was attaken that 2—12 2/sec 1268 as°K andreported 1 atm total pressure) (0.19 cm normalized to the temperature and pressures of the Dissociation to 1(g) is neglected. This assumption becomes atm 12. increasingly invalid 2with decreasing 12 partial pressures, especially below ca. 5x10 *
3
GROWTH OF ZINC SULFIDE BY IODINE TRANSPORT IODINE I
function of the transporting agent concentration which would have been equivalent to the partial pressure differences at the conditions of the present work. The
PRESSURE (ATM AT 800 ~C(
IO~
52 I
-
I
I
I
I
5 COMPONENT 3 REACTION DIFFUSION MODEL (ADAPTED FROM JONA & MANDEL~1964)
2
0
result is also included in fig. 3. The rates are larger than those predicted by (2) and those observed experimentally, but it should be noted that different thermochemical data had been employed18) and, further, that no attempt has been made to reduce the ten binary
~
-
~
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ONE REACTION
-
APPROXIMATE
/
DIFFUSION MODEL
~
0
-(PRESENT WORK)
I 55 _L~ C /
.
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102
IODINE CONCENTRATION IN GAS PHASE(gms/cm3I
Fig. 3. Transport rate as a function of iodine concentration. Experimental data: 14 cm tube length, 1.50 cm tube diameter, source temperature 800 °C,AT = 48°to 75 °C.Rate normalized to unit tube length, unit tube area and unit AT. Predicted curves: diffusion of component of highest molecular weight as ratecontrolling step, present work. Three-reaction, five-component model adapted from Jona and Mandel4) by plotting predicted rates at carrier concentrations which correspond to the same Zn1 2 partial-pressure differences at the conditions of the present
present work. [An independent estimate using classical kinetic theory’ 7) yielded essentially the same value.] The rates predicted by a more elaborate three-reaction, five-component diffusion-controlled model 4) for T = have 1268 been °K, reported by Jona and Mandel AT = 107 °K,L = 20 cm, and A = 0.502 cm2. These results are not readily converted to the conditions of the present study but, for purposes of rough comparison, we have normalized these computed rates to unit AT, A, and L, according to (2), and plotted them as a
diffusion coefficients involved to the temperature and pressure conditions of the present study. The salient feature, however, despite the uncertainty in thermochemical data and diffusion coefficients, is that both the three-reaction, five-component diffusion model, and the simplified diffusion model (2) predict a transport rate which is essentially independent oftransporting agent concentration and, at concentrations of ca. l0_2 g cm3, a rate which is qualitatively in agreement with experiment. 4. Characterization of crystals The crystals synthesized through the chemical transport process were transparent and colorless to pale yellow-green in color. They frequently assumed the form of hexagonal plates, fig. 4. Crystals grown under the full range of growth conditions were subjected to examination by powder and single-crystal diffraction techniques. The starting powder (and that used in seeding) was found to be entirely wurtzite. Although the cubic sphalerite form of ZnS was the stable phase ofall growth temperatures of that this study, (T
~1.
___
,~°
Fig. 4.
Hexagona1~pIatesof ZnS produced by iodine transport (ca. 15
x).
4
PHILIP N. DANGEL AND B. J. WUENSCH
sphalerite. Crystals grown at intermediate carrier concentrations produced single crystal diffraction patterns which displayed sharp maxima for reflections hk 1 with —h+k = 3n and diffuse rods along c in reciprocal space for reflections with —h+k s’~3n. Weak diffuse maxima occurred along these loci at positions corresponding to both the two-layer c of wurtzite and the ‘
three-layer c of sphalerite. This diffraction effect implies a one-dimensionally disordered crystal with ubiquitous stacking errors of ±*ai ±~a2 in successive tetrahedral layers. Nearly all previous workers (ref. 1—4, 7, 9, 10) have reported formation of cubic ZnS in its stability4’5’9’10). range, although “faulting” was Samelson8), however, frequently observed has described highly disordered crystals produced at temperatures well into the stability field of sphalerite. Acknowledgements This study was supported under Contract AT(30-l)— 3773 with the U.S. Atomic Energy Commission.
References I) R. Nitsche, Phys. Chem. Solids 17 (1960) 163. 2) R. Nitsche, H. U. Bdlsterli and M. Lichtensteiger, J. Phys. Chem. Solids 21 (1961) 199. 3) R. Nitsche, in: Crystal Growth, Ed. H. S. Peiser (Pergamon, Oxford, 1967) p.215. 4) F. Jona and G. Mandel, J. Phys. Chem. Solids 25 (1964) 187. 5) Y. M. Rumyantsev, F. A. Kuzetsov and S. A. Stroitlev, Soviet Phys.-Cryst. 10 (1965) 212. 6) H. Schafer and H. Odenbach, Z. Anorg. AUg. Chem. 346 (1966) 127. 7) E. Lendvay, J. Crystal Growth 10 (1971) 77. 8) H. Samelson, J. Appl. Phys. 33 (1962) 1779. 9) F. Jona, J. Phys. Chem. Solids 23 (1962) 1719. 10) S. Ujiie and Y. Kotera, J. Crystal Growth 10 (1971) 320. 11) Patek, Czech. J. Phys. B 11 (1961) 686. 12) K. K. Phtek, (1962) 313.M. Skála and L. Sou~ková, Czech. J. Phys. B 12 13) G. Mandel, J. Phys. Chem. Solids 23(1962) 587. 14) H. Wiedemeier and A. G. Sigai, J. Crystal Growth 6(1969)67. 15) H. R. Larson and J. F. Elliott, Trans. AIME 239 (1967) 1713. 16) C. E. Wicks and F. E. Block, Thermodynamic Properties of 65 Elements, Bull. U.S. Bureau of Mines 605 (1963). 17) R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1968). 18) 0. Kubaschewski and E. L. Evans, Metallurgical Thermochemistry (Pergamon, New York, 1958).
GROWTH OF ZINC SULFIDE BY IODINE TRANSPORT PHILIP N. DANGEL and B. J. WUENSCH Ceramics Division, Department of Metallurgy and Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. Received 7 August 1972; revised manuscript received 2 February 1973 Rates of chemical transport ofZnS by iodine at 800 °Cwere determined for closed tubes as a function oftube geometry, temperature gradient (3 to 35 °C) and concentration of the transporting agent (0 to 7>< I0~ 3 Ii). At high iodine concentrations the transport was found to be a linear function of reciprocal tube g cm length, tube cross sectional area, and the partial pressure difference ofZn1 2, and was essentially independent of the concentration of transporting agent. These relations, as well as the magnitude of the observed rate, are 3 gwith cm3the(0.6 atm) transport ratesfor decreased markedly and asymptotically the rate of in accord predictions of models diffusion-controlled kinetics. At iodineapproached concentrations below sublimation-condensation. Although the sphalerite modification of ZnS was the stable phase at all growth 2x10 conditions, the transport product was predominantly the wurtzite form of the seed material in the surfacereaction limited region of iodine concentrations. At high concentrations of the transporting agent, as in previous studies, the product was entirely sphalerite. Intermediate iodine concentrations produced crystals with severe stacking disorder.
1. Infroduction Synthesis of zinc sulfide crystals in closed tubes has been achieved with the use of transport agents such as 12), HC18’°) NH 7) and H 11”2). In the 4C1 and viscous 2S effects, and if absence of free convection surface reactions are negligible, transport rates will be controlled by the diffusion of the gaseous species. If one assumes that the flux of the component of highest molecular weight constitutes the rate-limiting step, the transport rate, r, for a reaction such as ZnS+1 2
~—
ZnI~+~~‘2
should be given by’ 3) D(P2 P1)A r R IL —
—
(2)
where P2 and P1 are the equilibrium vapor pressures of Zn12 at T2 and T1, the temperatures of the source and growth zones, respectively; D is the diffusion coefficient of Zn12 (g); R is the gas constant, T the average ternperature; and A is the cross-sectional area ofa transport tube of length L. Most experimental tests of (2) with ZnS have employed HC1 as the transport agent. The rate8), of transport A 9), and has been found to be proportional 1 /L independent of time9). After initial to dependence on the
square root of HC1 pressure at low pressures9), the transport rate was found to become essentially independent of the concentration of the transporting agent9” 0) These observations, combined with the result that porous plugs had no effect on transport rates, confirm diffusion-controlled kinetics. In contrast, the kinetics of transport with 12 appeared to be controlled by thermal convection4). Similar kinetics have been observed in the transport of MnS—MnSe by 1214). These results were obtained, however, for fairly high 12 pressures (1 to 10 atm) and high temperature gradients (75 to 100 °C).The objectives of the present study were to examine ZnS transport with ‘2 at lower temperature gradients and transporting agent concentrations, compare the dependence of transport rates on system parameters with the predictions of diffusion-controlled kinetics, and to determine the conditions at which surface reactions became a rate-limiting step. 2. Experimental procedure Vycor capsules ranging from 0.40 to 2.20 cm in diameter and 5.0 to 14.0 cm in length were sealed at one end and loaded with an appropriate amount of ZnS and iodine. Thefrom iodine whichpowder were employed ranged 0 toconcentrations 0.007 g cm (0 to 2.12 atm at 800 °C).The loaded capsules were
2
PHILIP N. DANGEL AND B. J. WUENSCH I
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3) Fig. I. Transport rate as a function of cross sectional area of tube (0.007 g cm3 12, source temperature 800 °C,AT = 60 °C, tube length = 14 cm; rate normalized to unit AT, unit tube length).
Fig. 2. Transport rate as a function of AT, linearly related to AP for the range of temperatures examined (0.007 g cm3 12, source temperature 800 °C, 14 cm tube length, 4.04 mm tube diameter; rate normalized to unit tube length, unit tube area).
flushed with helium several times and sealed with an
where P
TUBE CROSS SECTIONAL AREA (cm
atmosphere approximately mmofHe at room ternperature. Theofhelium inhibited10loss iodine through volatilization and slowed diffusion of other gaseous species during runs by negligible amounts. A fine dusting of ZnS powder was allowed to adhere to the growth end of the capsule to provide sites for nudeation. The tubes were carefully placed in a gradient furnace, the source end of which was maintained at 800 °C. The growth region was at 800 °C—AT,where AT ranged from 3° to 75° in various runs. Upon completion of transport, the capsule was water quenched, broken open, and, after the condensed iodine sublimed, the mass of material transported to the had growth zone was determined, 3. Observed fransport rates At carrier concentrations of 0.007 g cm3 the transport rate was found to be a linear function of time, tube area, and reciprocal length as predicted by (2). Fig. 1 presents the variation of transport rate with tube area. The partial-pressure differences were calculated on the assumption of diatomic sulfur gas and, for reaction (I) 15~16), AF = 8000—1.5 T cal/mole. The Zn1 2 partial pressure, X, was then obtained from the cubic equation X(~X~~ = K(T) = exp AF/RT), (3) (PQ_X) (—
0 is the pressure of 12 ideal gas generated byand the 3 of iodine iodine*. For example, at 0.0005 g cm AT = 54 °C, AX was 5.5 x i0~ atm. Because the maximum temperature difference in any run was only 75 °C, the partial pressure difference of Zn1 2 was essentially a linear function of AT. The transport rate in a tube of fixed geometry was thus found to be a linear function of AT as shown in fig. 2. The measured dependence oftransport rate on iodine concentration is given in fig. 3. At the highest iodine concentrations which were examined the transport rate appears to become independent of the concentration of the transporting agent as predicted 3byiodine diffusion-con(0.6 atm) trolled kinetics. Below 2 x l0~g cm the rate of transport decreased sharply as surface reaction slowed the rate and, at very low carrier concentrations, asymptotically approached the rate of sublimation—condensation. Fig. 3 also includes the transport rate predicted by the simplified model for diffusion-controlled kinetics. For these computations, using (2), Zn1 2 partial pressure differences were evaluated from (3) and 4) the for diffusion Zn1 coefficient was attaken that 2—12 2/sec 1268 as°K andreported 1 atm total pressure) (0.19 cm normalized to the temperature and pressures of the Dissociation to 1(g) is neglected. This assumption becomes atm 12. increasingly invalid 2with decreasing 12 partial pressures, especially below ca. 5x10 *
3
GROWTH OF ZINC SULFIDE BY IODINE TRANSPORT IODINE I
function of the transporting agent concentration which would have been equivalent to the partial pressure differences at the conditions of the present work. The
PRESSURE (ATM AT 800 ~C(
IO~
52 I
-
I
I
I
I
5 COMPONENT 3 REACTION DIFFUSION MODEL (ADAPTED FROM JONA & MANDEL~1964)
2
0
result is also included in fig. 3. The rates are larger than those predicted by (2) and those observed experimentally, but it should be noted that different thermochemical data had been employed18) and, further, that no attempt has been made to reduce the ten binary
~
-
~
E
ONE REACTION
-
APPROXIMATE
/
DIFFUSION MODEL
~
0
-(PRESENT WORK)
I 55 _L~ C /
.
I Ic~5
I
I IO~
102
IODINE CONCENTRATION IN GAS PHASE(gms/cm3I
Fig. 3. Transport rate as a function of iodine concentration. Experimental data: 14 cm tube length, 1.50 cm tube diameter, source temperature 800 °C,AT = 48°to 75 °C.Rate normalized to unit tube length, unit tube area and unit AT. Predicted curves: diffusion of component of highest molecular weight as ratecontrolling step, present work. Three-reaction, five-component model adapted from Jona and Mandel4) by plotting predicted rates at carrier concentrations which correspond to the same Zn1 2 partial-pressure differences at the conditions of the present
present work. [An independent estimate using classical kinetic theory’ 7) yielded essentially the same value.] The rates predicted by a more elaborate three-reaction, five-component diffusion-controlled model 4) for T = have 1268 been °K, reported by Jona and Mandel AT = 107 °K,L = 20 cm, and A = 0.502 cm2. These results are not readily converted to the conditions of the present study but, for purposes of rough comparison, we have normalized these computed rates to unit AT, A, and L, according to (2), and plotted them as a
diffusion coefficients involved to the temperature and pressure conditions of the present study. The salient feature, however, despite the uncertainty in thermochemical data and diffusion coefficients, is that both the three-reaction, five-component diffusion model, and the simplified diffusion model (2) predict a transport rate which is essentially independent oftransporting agent concentration and, at concentrations of ca. l0_2 g cm3, a rate which is qualitatively in agreement with experiment. 4. Characterization of crystals The crystals synthesized through the chemical transport process were transparent and colorless to pale yellow-green in color. They frequently assumed the form of hexagonal plates, fig. 4. Crystals grown under the full range of growth conditions were subjected to examination by powder and single-crystal diffraction techniques. The starting powder (and that used in seeding) was found to be entirely wurtzite. Although the cubic sphalerite form of ZnS was the stable phase ofall growth temperatures of that this study, (T
~1.
___
,~°
Fig. 4.
Hexagona1~pIatesof ZnS produced by iodine transport (ca. 15
x).
4
PHILIP N. DANGEL AND B. J. WUENSCH
sphalerite. Crystals grown at intermediate carrier concentrations produced single crystal diffraction patterns which displayed sharp maxima for reflections hk 1 with —h+k = 3n and diffuse rods along c in reciprocal space for reflections with —h+k s’~3n. Weak diffuse maxima occurred along these loci at positions corresponding to both the two-layer c of wurtzite and the ‘
three-layer c of sphalerite. This diffraction effect implies a one-dimensionally disordered crystal with ubiquitous stacking errors of ±*ai ±~a2 in successive tetrahedral layers. Nearly all previous workers (ref. 1—4, 7, 9, 10) have reported formation of cubic ZnS in its stability4’5’9’10). range, although “faulting” was Samelson8), however, frequently observed has described highly disordered crystals produced at temperatures well into the stability field of sphalerite. Acknowledgements This study was supported under Contract AT(30-l)— 3773 with the U.S. Atomic Energy Commission.
References I) R. Nitsche, Phys. Chem. Solids 17 (1960) 163. 2) R. Nitsche, H. U. Bdlsterli and M. Lichtensteiger, J. Phys. Chem. Solids 21 (1961) 199. 3) R. Nitsche, in: Crystal Growth, Ed. H. S. Peiser (Pergamon, Oxford, 1967) p.215. 4) F. Jona and G. Mandel, J. Phys. Chem. Solids 25 (1964) 187. 5) Y. M. Rumyantsev, F. A. Kuzetsov and S. A. Stroitlev, Soviet Phys.-Cryst. 10 (1965) 212. 6) H. Schafer and H. Odenbach, Z. Anorg. AUg. Chem. 346 (1966) 127. 7) E. Lendvay, J. Crystal Growth 10 (1971) 77. 8) H. Samelson, J. Appl. Phys. 33 (1962) 1779. 9) F. Jona, J. Phys. Chem. Solids 23 (1962) 1719. 10) S. Ujiie and Y. Kotera, J. Crystal Growth 10 (1971) 320. 11) Patek, Czech. J. Phys. B 11 (1961) 686. 12) K. K. Phtek, (1962) 313.M. Skála and L. Sou~ková, Czech. J. Phys. B 12 13) G. Mandel, J. Phys. Chem. Solids 23(1962) 587. 14) H. Wiedemeier and A. G. Sigai, J. Crystal Growth 6(1969)67. 15) H. R. Larson and J. F. Elliott, Trans. AIME 239 (1967) 1713. 16) C. E. Wicks and F. E. Block, Thermodynamic Properties of 65 Elements, Bull. U.S. Bureau of Mines 605 (1963). 17) R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1968). 18) 0. Kubaschewski and E. L. Evans, Metallurgical Thermochemistry (Pergamon, New York, 1958).