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Crystal growth by chemical transport reactions—I
J. Phys. Chm. Solids
Pergamon
CRYSTAL
Press 1961. Vol. 21, Nos. 314, pp. 199-205.
GROWTH
Printed in Great Britain.
BY CHEMICAL
TRANSPORT
REACTIONS-I BINARY,
TERNARY, R. NITSCI-IR, Laboratories
AND
MIXED-CRYSTAL
H. U. B&STRRLI
R.C.A.
Ltd.,
CHALCOGENIDES
and M. LICHTENSTRIGER
Hardturmstrasse
169, Zurich,
5, Switzerland
(I&&wed 15 May 1961)
Abstract-The concept of chemical transport reactions (volatilization of a material via a low-volatile chemical intermediate at a temperature Tl and back-reaction of the mixture at a temperature Ta, using the temperature dependence of the chemical equilibrium involved) is a valuable tool for growing single crystals of many materials which cannot be easily obtained from the melt. The main advantage is the use of growth temperatures well below the melting or sublimation point. The method was used to grow crystals of the binary chalcogenides: ZnS, ZnSe, CdS, CdSe, MnS, SnS, SnSs, In&, Gas&, GaS and GaSe. Ternary chalcogenides of the type ABaX4 (A = Zn, Cd, Hg; B = Ga, In; X = S, Se) were obtained for the first time as single crystals. Mixed crystals of ZnS*MnS were prepared over a wide range of composition.
INTRODUCTION
CRYSTALgrowth from the melt by the classical methods of Kyropoulos and Bridgman becomes exceedingly difficult if applied to materials having high melting points. Additional difficulties arise if compounds are to be grown which show appreciable dissociation at the melting point or which melt only under elevated pressure. To obtain single crystals of such materials usually vapor phase methods are used. The polycrystalline starting material is sublimed either in wucuoor in a stream of a carrier gas or the vapors of its constituents are reacted in a crystallization chamber. The temperatures required for these processes are high-in the vicinity of the sublimation pointand they have to be closely controlled in order to avoid polynucleation by surpassing the usually small supersaturation range. If the process is carried out in a closed system because oxygen has to be excluded, the limiting temperature is usually given by the softening point of quartz. If inert carrier gases are used the control of their flow and the geometry of the arrangement pose additional problems. It therefore is highly desirable to devise methods for growing crystals from the vapor phase which
will work well below the sublimation point of the material involved without increasing the difference in free energy between vapor and growing seeds to a degree which would lead to nucleation. This can be achieved by utilizing the concept of chemical transport reactions, a term first introduced by SCHXFER (1). Instead of vaporizing a solid directly at high temperatures it may be vaporized at much lower temperatures by forming highly volatile chemical intermediates and reacting back the resulting gas mixture at a different temperature utilizing the temperature dependence of the chemical equilibrium involved. By properly adjusting the two temperatures the departure from chemical equilibrium in the vicinity of the growing seeds can be made small enough to avoid nucleation but large enough to make the seeds grow, i.e. the proper supersaturation can be maintained. In a recent note(s) a brief description was given on the growth of a few chalcogenides by this method. This paper discusses the method in detail and gives a survey of the growth conditions of a large number of chalcogenides. Part I will deal with the physical chemistry of transport reactions in general, in Part II the requirements for growing crystals by chemical
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transport reactions will be discussed, and in Part III the binary and ternary chalcogenides will be described of which crystals have been grown by the outlined principles. 1. PHYSICAL CHEMISTRY OF CHEMICAL TRANSPORT REACTIONS Consider a closed system containing n + 1 components all of which are in chemical equilibrium with each other. The temperature is chosen such that only one component is solid, the other n components gaseous. If there were a local perturbation of the equilibrium such that the solid component would have a smaller free energy at the perturbed area, it would migrate via the gas phase to this area until equilibrium is established again. The simplest way to bring about such a perturbation is a local change in temperature; that is, imposing a temperature gradient on the system. For n = 1 the trivial case of sublimation of a solid via its gaseous atoms or molecules results. In the following, the case n = 3 is considered which applies to the transport of metal chalcogenides by halogens. The equilibria involved are: MeCh+Hal + MeHal+Ch; a specific example is ZnS +Is + ZnIs + 4 Ss. The simplest experimental arrangement for a transport experiment is a closed horizontal tube. One end, the vaporization chamber, contains some polycrystalline feed material, e.g. ZnS and a small amount of iodine, the transporter. If the vaporization chamber is held at 1000°C and the other end, the crystallization chamber, at 750°C ZnS will be transported via the vapor phase and deposit in crystals in the crystallization chamber because of the temperature dependence of the above equilibrium. The elegant feature of the method is that already tiny amounts of the transporter are sufficient to transport practically unlimited amounts of the solid, because the transporter set free during crystallization diffuses back to pick up more solid, etc. Now the question arises which parameters govern such a transport reaction, and is it possible to make predictions of what kind of transporter would yield optimal transport in a given system? The yield of a transport reaction can be characterized by the quantity fi, i.e. the amount of material transported per unit time from the vaporization to the crystallization chamber. In a similar way as the current flowing through a resistor is
and M. LICHTENSTEIGER given by the product of the potential difference Ap at its ends and its conductance L, tir can be written as the product of two functions, Ap and L. The function Ap characterizes the “chemical potential difference” between vaporization and crystallization chamber and is proportional to the difference in vapor pressure of the transporter in the two chambers. Ap is a function of the “chemical parameters” of the system: the temperature Tl of the vaporization chamber, the temperature Ts of the crystallization chamber, the change in free energy AG for the reaction involved and the concentration of the transporter CT. Ap = Ap(T1, T2 . AG, CT’)- L, on the other hand, characterizing the “conductance” of the system in respect to the vapor transport between the two chambers, is a function of the “geometrical parameters” of the system; the length I of the tube, its cross-section q and a “specific conductance” (T which characterizes the physical nature of the transport mechanism: diffusion, convection or laminar flow. Thus fi 2 Ap(Tl, T2, AG, CT) . q&q,24 To predict +z for a chosen system it thus is necessary to derive the functions Ap and L explicitly. For Ap this is possible if the types of reaction taking part in the transport and their free energy changes in the operating temperature range, i.e. the specific heats of the reaction components, are known. By forming the expression AG = AH- TAS = - RT - In K at the two temperatures Tl and Ts and observing the conditions imposed by CT on the partial pressures of the components occuring in the explicit expression for K, one can solve for Ap of the transporter. Important information can already be gained, however, if only the sign of the heat of reaction AH is known, because the expression d In K/dT = AH/RTz indicates whether transport is to be expected from hot to cold, or vice versa. Unlike ordinary sublimation not all reactions transport from hot to cold. Only if AH r 0, i.e. for endothermic reactions where K increases with temperature, will transport occur from hot to cold. If AH < 0 the reaction will transport from cold to hot. Examples are known for both cases. Transport of metal chalcogenides with iodine as transporter, however, occurs always from hot to cold. A good qualitative insight on the connection between Ap and AG is gained by the method of SCH~FER'~)who plots Ap vs. AH curves
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with the entropy change As as parameter. Such curves are particularly useful for estimating the relative magnitude of ni for various substances transported by the same mechanism. The essential conclusion is that transport can only occur if X is of the order of unity, i.e. if the equilibrium is not extreme. It is much more difficult to derive an explicit expression for L because transport of the vapor can be effected in three ways. 1. By diffusion between the two chambers, if narrow tubes are used, and if the total pressure in the system is small, Several cases have been treated theoretically by SCHXFERand are in good agreement with experimental data. Transport by diffusion only, however, is slow and all the experiments described below were well in the pressure range (of the order of I atm) above pure diffusion. 2. By convection. This takes over at higher pressures, in wider tubes, and in tubes inclined against the horizontal. 3. By laminar flow, if the reaction involves a change in mole numbers, and if the reaction velocity on both sides is high enough to maintain a constant pressure difference. Which mechanism prevails depends largely on the transporter concentration cyt determining the total pressure, and on the geometry of the system, Since there is usually an overlap between several of these mechanisms and the exact temperature distribution along the tube plays a role also, it is difficult to arrive at an analytical expression for L. Qualitative estimates of & however, can usually be obtained by estimating AP, especially since L will not vary very much if related reactions are compared. 2. CRYSTAL GROWTH BY T~SPORT REACTIONS
In general, transport reactions yield polycrystaline material consisting of intergrown crystallites. Attempts were made to investigate the influence the forementioned parameters have on the growth of well developed single crystals and to arrive at reproducible experimental conditions. Basically one can say that if transport reactions are to be used for crystal growth, ni, the amount of material arriving in the growing chamber per unit time has to be carefully controlled. & should N
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not exceed a certain maximum value because otherwise the growing seeds cannot digest the arriving materials and supersaturation will increase until additional nucleation takes place. fh can be controlled by Ap (variation of AT= TJ- Tz) as well as by L (variation of geometry). To obtain optimal velocity of growth rri should be raised during the experiment since a growing crystal can increase its intake as its surface increases. ZnS was chosen as a model substance to study the influence of the various parameters on its growth but the results apply to the other chalcogenides mentioned below as well. It was tried to vary only one parameter at a time. First the role of the chemical parameters wiil be considered. Having found a strong transport effect with iodine, bromine and chlorine also were studied as transporters. Br gave much smaller & values and CI showed practicalfy no transport at all. This is in qualitative agreement with an estimate of the AG values at room temperatures from literature data. They showed that the iodine reaction had the lowest AG value and thus the least extreme equilibrium position as required for a reasonabfe transport effect. Iodine was used as transporter in all other systems, although this may not necessarily mean optimal transport. The experimental technique was as follows. Approximately 3 g of pure, polycrystalline ZnS was placed into one end of a quartz ampule (length 15 cm, internal diameter 8 mm). It was degassed in high vacuum at 8OO”C, iodine condensed in with liquid air and the ampule drawn OR. The ampule was then placed horizontally into a tubular two-zone furnace. The usual reaction time was 16 hr. Since SGN.&ER~~)had previously described the transport of iron oxide with HCl gas according to: FesOa + 6HCl + ZFeCls+HsQ one bad to think about the analogous reaction: ZnS+ZHI + ZnIs + HsS. However, by adding various amounts of hydrogen up to the equivalent to HI, no differences in riz or in crystal habit were found as compared to pure iodine. The role of CT: 7it increased stronger than linear with CT up to a value of CT = 1.5 mg Tjcms which could not be exceeded for safety reasons. A strong dependence of the size and the quality of the resulting crystals on CT however was noted. At c~ = 1 mg I/cm3 growth was very stow although
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well developed individual crystals resulted. Best results CT = 5 mg I/cm3 were obtained at (7it = 20mg ZnS/hr). Clear crystals witk well developed faces formed which after 40 kr had sizes up to 5 x 5 mm. At kigher iodine concentrations, e.g. CT = 15 mg I/cm3, lit was so large (80 mg ZnS/hr) that polynucleation occured and layers of intergrown crystallites resulted. The role of Tl and Tz. The absolute values of tkese temperatures can be varied over a relatively wide range if one considers only Gz and not the quality of the crystals. For a CT of 5 mg I/cm3 not too different ti values were obtained for 13001100°C as well as for 900-600°C. The range of permissible supersaturation, however, decreases with temperature. At Tz = 600°C only a microcrystalline cake is formed because of polynucleation. A minimum Tz of 700°C was required to obtain individual, well developed crystals. The difference AT between Tl and Tz was found to be of minor importance since at the geometry employed the ‘Lconductance” L rather than the partial pressure difference Ap appeared to be the rate determining step in the growth process. The optimal growth temperature Ts has to be evaluated empirically for a given substance. The proper choice of Tz depends also on the physical properties required from tke crystal such as the amount of transporter dissolved in the crystal, the number of imperfections etc. If pol~orp~sm exists, Tz has to be chosen according to the stability range of the modification desired. Now the influence of the geometrical parameters will be discussed. rit decreases approximately linearly with the tube length I because of the increasing flow resistance. The obvious conclusion to use very short tubes, however, is not quite correct since one has to consider that if several seeds are to form and grow in one experiment the crystallization chamber should not be too small in order to avoid intergrowth between the crystals. A good compromise between these requirements is to heat the tube not symmetrically but asymmetrically in such a way that the vaporization chamber is small but the crystallization chamber is large. The temperature distribution in the crystallization chamber skould be as uniform as possible in order to avoid re-evaporation of crystals from warmer parts in the course of an experiment. For
and
M.
LICHTENSTEIGER
orientating experiments, on the other hand, it is quite useful to kave a sloping temperature distribution along the crystallization chamber in order to find tke temperature of optimal crystal growth. The temperature drop between the two chambers should not be too abrupt in order to avoid a clogging up of the tube in this region. The most important geometrical parameter is the tube cross section 4 which influences tfr decisively. For CT I= 5 mg I/m-r? and Tl = lOOO”C, Tz = 75O”C, & was 20 mg ZnS/hr for a tube with 8 mm diameter but 300 mg/hr for a tube with 20 mm diameter. This large influence of q on m is probably due to the relative decrease of the friction of tke moving gases along the walls of the tube and to a partial transition from diffusion to convection with increasing q. The latter is also substantiated by the fact that in large diameter tubes the crystals are always found at the bottom of the tube (according to the direction of the gas flow) whereas in smaller tubes they are found all around the circumference of the tube. Concluding, the following requirements have to be observed if transport reactions are to be used for the growth of single crystals. 1. The rate of transport ni is not to exceed the rate of growth of the seeds. 2. The optimal c~stallization temperature has to be evaluated empirically for each system taking into account the possibility of polymorpkism. 3. The crystallization chamber should be large in order to prevent intergrowth between adjacent seeds. Asymmetric heating is useful. 4. The temperature distribution in the crystallization chamber should be as uniform as possible to avoid partial re-evaporation of already grown crystals. 5. Well developed crystals form easier in large diameter tubes where convection determines the rate of transport. 6. The temperature difference between the MO chambers can be made smaller if wider tubes are used (thus facilitating an even temperature distribution along the crystallization chamber) since the gas flow is here the rate determining step. 3. CI-iALCOGENIDE CRYSTALS GROWN TH[E T~SPORT %XETHOD
If a simple binary ckalcogenide
BY
is transported,
CRYSTAL
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CHEMICAL
the structure of the crystals formed corresponds to the phase stable at the growing temperature. If the chalcogenide exists in various valency states, the resulting crystals are not necessarily identical with the valency state of the starting material. Depending on temperature, the transported crystals can have a different com~sition, e.g. if SnS is transported at 650-500°C pure SnS is obtained. At 950400°C however, SnSs is formed in the crystallization chamber. If a mixture of two binary chalcogenides is transported the following cases are possible. (a) Formation binaries. (b) Formation
of mixed
crystals
of the
two
of a ternary chalcogenide.
(c) Separate transport of the two binaries if complete immiscibility exists. In most cases it is not necessary to start with well defined binary chalcogenides or mixtures thereof. Often it is sufficient to react a stoichiometric mixture of the elements at high temperatures and subject this resulting product to the transport reaction.
The binary chalcogenides prepared are listed in Table 1. An interesting case is ZnS because it exhibits polymorphism. Crystals grown previously by reacting zinc vapor with hydrogen sulfide are always mixtures of the cubic and the hexagonal phase, the boundaries of which are visible as “striations”. The transport method allows a separation of the phases by varying the growth temperature. At temperatures below 1000°C the pure cubic modification-as checked by X-rays and optical inspection-is obtained. Around 1150” mainIy hexagonal crystals form containing only very few striations. By admixing small amounts of silver or copper these crystals can be made to luminesce blue or green respectively. In the case of CdS the amount of iodine incorporated in the crystals was determined quantitatively by using radioactive I131 as a tracer in the transporting iodine. The iodine content was found to be 10-a weight per cent. It is evenly distributed throughout the crystals, as found by partial etching.
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B. Mixed crystals of binary chalcogenides The system ZnS-MnS was found to be a good example of mixed crystal formation by chemical transport reactions. If a mixture of polycrystalline ZnS and MnS is transported in a sloping temperature gradient (7’1 = lOSO”C, Ta = 950-750°C) and one collects the crystals formed at various temperatures, one finds crystals grown at 750°C are slightly orange colored, have the cubic sphalerite structure and contain 2 per cent by weight of Mn. With increasing T2 the manganese content increases and the crystals remain cubic up to 850°C. Between 860” and 880°C a mixture between the cubic and the hexagonal wurtzite phase forms and above 900°C the crystals are purely hexagonal and contain around 10 per cent of Mn. This is very surprising since both pure ZnS and pure MnS (NaCl structure) grow in the cubic form at 900°C the mixture however prefers the hexagonal structure. The phenomenon was used to “construct” crystals with built-in phase changes. A mixture of ZnS and MnS was transported and the temperature T2 of the growing chamber oscillated periodically during the growth process between 750” and 950°C. The crystals obtained showed indeed striations corresponding to the number of temperature cycles during the growth period. C. Ternary chalcogenides The transport method proved to be capable of yielding a large variety of ternary chalcogenide crystals of the general formula ABaX4, where A = Zn, Cd, Hg; B = In, Ga and X = S, Se. They are listed in Table 2. These materials, known so far only in the microcrystalline state, show interesting photoelectric properties which have been reported elsewhere.(s) HAHN@) and coworkers obtained polycrystalline samples of these ternaries by sintering together the binary constituents at high temperatures. Our X-ray data obtained so far are in agreement with the structures these authors propose. 4. CONCLUSIONS
The concept of chemical transport reactions isif properly modified-a useful tool for growing single crystals of metal chalcogenides having high
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o~m~ooo*omo r.bwwwowmobr.
d
e
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melting or sublimation points. Not only simple binary, but also ternary and probably quaternary compounds as well as mixed crystals can be prepared. The method will certainly be useful for other chemical systems. If means are found to control nucleation at will over wide ranges of temperature and composition it should be possible to prepare large single crystals as well as thin microcrystalline layers. A disadvantage is the possibility of incorporation of the transporter in the crystals formed.
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On the other hand, being a complicated distillation a transport reaction might also prove to be a means of purification for certain compounds. REFERENCES
1. SCHAFERH., 2. anorg. Chem. 286, 27, 42 (1956);
290,279 (1957); 291, 221, 254 (1957). 2. NITSCHER., J. Phys. Chem. Solids 17, 163 (1960). 3. BEUN J. A., NITSCHER. and LICHTENSTEIGER M., Physica 26, 647 (1960); Physica, to be published. 4. HAHN H. et al., Z. morg. Chem. 279, 241 (1955).
Pergamon
CRYSTAL
Press 1961. Vol. 21, Nos. 314, pp. 199-205.
GROWTH
Printed in Great Britain.
BY CHEMICAL
TRANSPORT
REACTIONS-I BINARY,
TERNARY, R. NITSCI-IR, Laboratories
AND
MIXED-CRYSTAL
H. U. B&STRRLI
R.C.A.
Ltd.,
CHALCOGENIDES
and M. LICHTENSTRIGER
Hardturmstrasse
169, Zurich,
5, Switzerland
(I&&wed 15 May 1961)
Abstract-The concept of chemical transport reactions (volatilization of a material via a low-volatile chemical intermediate at a temperature Tl and back-reaction of the mixture at a temperature Ta, using the temperature dependence of the chemical equilibrium involved) is a valuable tool for growing single crystals of many materials which cannot be easily obtained from the melt. The main advantage is the use of growth temperatures well below the melting or sublimation point. The method was used to grow crystals of the binary chalcogenides: ZnS, ZnSe, CdS, CdSe, MnS, SnS, SnSs, In&, Gas&, GaS and GaSe. Ternary chalcogenides of the type ABaX4 (A = Zn, Cd, Hg; B = Ga, In; X = S, Se) were obtained for the first time as single crystals. Mixed crystals of ZnS*MnS were prepared over a wide range of composition.
INTRODUCTION
CRYSTALgrowth from the melt by the classical methods of Kyropoulos and Bridgman becomes exceedingly difficult if applied to materials having high melting points. Additional difficulties arise if compounds are to be grown which show appreciable dissociation at the melting point or which melt only under elevated pressure. To obtain single crystals of such materials usually vapor phase methods are used. The polycrystalline starting material is sublimed either in wucuoor in a stream of a carrier gas or the vapors of its constituents are reacted in a crystallization chamber. The temperatures required for these processes are high-in the vicinity of the sublimation pointand they have to be closely controlled in order to avoid polynucleation by surpassing the usually small supersaturation range. If the process is carried out in a closed system because oxygen has to be excluded, the limiting temperature is usually given by the softening point of quartz. If inert carrier gases are used the control of their flow and the geometry of the arrangement pose additional problems. It therefore is highly desirable to devise methods for growing crystals from the vapor phase which
will work well below the sublimation point of the material involved without increasing the difference in free energy between vapor and growing seeds to a degree which would lead to nucleation. This can be achieved by utilizing the concept of chemical transport reactions, a term first introduced by SCHXFER (1). Instead of vaporizing a solid directly at high temperatures it may be vaporized at much lower temperatures by forming highly volatile chemical intermediates and reacting back the resulting gas mixture at a different temperature utilizing the temperature dependence of the chemical equilibrium involved. By properly adjusting the two temperatures the departure from chemical equilibrium in the vicinity of the growing seeds can be made small enough to avoid nucleation but large enough to make the seeds grow, i.e. the proper supersaturation can be maintained. In a recent note(s) a brief description was given on the growth of a few chalcogenides by this method. This paper discusses the method in detail and gives a survey of the growth conditions of a large number of chalcogenides. Part I will deal with the physical chemistry of transport reactions in general, in Part II the requirements for growing crystals by chemical
199
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BdLSTERLI
transport reactions will be discussed, and in Part III the binary and ternary chalcogenides will be described of which crystals have been grown by the outlined principles. 1. PHYSICAL CHEMISTRY OF CHEMICAL TRANSPORT REACTIONS Consider a closed system containing n + 1 components all of which are in chemical equilibrium with each other. The temperature is chosen such that only one component is solid, the other n components gaseous. If there were a local perturbation of the equilibrium such that the solid component would have a smaller free energy at the perturbed area, it would migrate via the gas phase to this area until equilibrium is established again. The simplest way to bring about such a perturbation is a local change in temperature; that is, imposing a temperature gradient on the system. For n = 1 the trivial case of sublimation of a solid via its gaseous atoms or molecules results. In the following, the case n = 3 is considered which applies to the transport of metal chalcogenides by halogens. The equilibria involved are: MeCh+Hal + MeHal+Ch; a specific example is ZnS +Is + ZnIs + 4 Ss. The simplest experimental arrangement for a transport experiment is a closed horizontal tube. One end, the vaporization chamber, contains some polycrystalline feed material, e.g. ZnS and a small amount of iodine, the transporter. If the vaporization chamber is held at 1000°C and the other end, the crystallization chamber, at 750°C ZnS will be transported via the vapor phase and deposit in crystals in the crystallization chamber because of the temperature dependence of the above equilibrium. The elegant feature of the method is that already tiny amounts of the transporter are sufficient to transport practically unlimited amounts of the solid, because the transporter set free during crystallization diffuses back to pick up more solid, etc. Now the question arises which parameters govern such a transport reaction, and is it possible to make predictions of what kind of transporter would yield optimal transport in a given system? The yield of a transport reaction can be characterized by the quantity fi, i.e. the amount of material transported per unit time from the vaporization to the crystallization chamber. In a similar way as the current flowing through a resistor is
and M. LICHTENSTEIGER given by the product of the potential difference Ap at its ends and its conductance L, tir can be written as the product of two functions, Ap and L. The function Ap characterizes the “chemical potential difference” between vaporization and crystallization chamber and is proportional to the difference in vapor pressure of the transporter in the two chambers. Ap is a function of the “chemical parameters” of the system: the temperature Tl of the vaporization chamber, the temperature Ts of the crystallization chamber, the change in free energy AG for the reaction involved and the concentration of the transporter CT. Ap = Ap(T1, T2 . AG, CT’)- L, on the other hand, characterizing the “conductance” of the system in respect to the vapor transport between the two chambers, is a function of the “geometrical parameters” of the system; the length I of the tube, its cross-section q and a “specific conductance” (T which characterizes the physical nature of the transport mechanism: diffusion, convection or laminar flow. Thus fi 2 Ap(Tl, T2, AG, CT) . q&q,24 To predict +z for a chosen system it thus is necessary to derive the functions Ap and L explicitly. For Ap this is possible if the types of reaction taking part in the transport and their free energy changes in the operating temperature range, i.e. the specific heats of the reaction components, are known. By forming the expression AG = AH- TAS = - RT - In K at the two temperatures Tl and Ts and observing the conditions imposed by CT on the partial pressures of the components occuring in the explicit expression for K, one can solve for Ap of the transporter. Important information can already be gained, however, if only the sign of the heat of reaction AH is known, because the expression d In K/dT = AH/RTz indicates whether transport is to be expected from hot to cold, or vice versa. Unlike ordinary sublimation not all reactions transport from hot to cold. Only if AH r 0, i.e. for endothermic reactions where K increases with temperature, will transport occur from hot to cold. If AH < 0 the reaction will transport from cold to hot. Examples are known for both cases. Transport of metal chalcogenides with iodine as transporter, however, occurs always from hot to cold. A good qualitative insight on the connection between Ap and AG is gained by the method of SCH~FER'~)who plots Ap vs. AH curves
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with the entropy change As as parameter. Such curves are particularly useful for estimating the relative magnitude of ni for various substances transported by the same mechanism. The essential conclusion is that transport can only occur if X is of the order of unity, i.e. if the equilibrium is not extreme. It is much more difficult to derive an explicit expression for L because transport of the vapor can be effected in three ways. 1. By diffusion between the two chambers, if narrow tubes are used, and if the total pressure in the system is small, Several cases have been treated theoretically by SCHXFERand are in good agreement with experimental data. Transport by diffusion only, however, is slow and all the experiments described below were well in the pressure range (of the order of I atm) above pure diffusion. 2. By convection. This takes over at higher pressures, in wider tubes, and in tubes inclined against the horizontal. 3. By laminar flow, if the reaction involves a change in mole numbers, and if the reaction velocity on both sides is high enough to maintain a constant pressure difference. Which mechanism prevails depends largely on the transporter concentration cyt determining the total pressure, and on the geometry of the system, Since there is usually an overlap between several of these mechanisms and the exact temperature distribution along the tube plays a role also, it is difficult to arrive at an analytical expression for L. Qualitative estimates of & however, can usually be obtained by estimating AP, especially since L will not vary very much if related reactions are compared. 2. CRYSTAL GROWTH BY T~SPORT REACTIONS
In general, transport reactions yield polycrystaline material consisting of intergrown crystallites. Attempts were made to investigate the influence the forementioned parameters have on the growth of well developed single crystals and to arrive at reproducible experimental conditions. Basically one can say that if transport reactions are to be used for crystal growth, ni, the amount of material arriving in the growing chamber per unit time has to be carefully controlled. & should N
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not exceed a certain maximum value because otherwise the growing seeds cannot digest the arriving materials and supersaturation will increase until additional nucleation takes place. fh can be controlled by Ap (variation of AT= TJ- Tz) as well as by L (variation of geometry). To obtain optimal velocity of growth rri should be raised during the experiment since a growing crystal can increase its intake as its surface increases. ZnS was chosen as a model substance to study the influence of the various parameters on its growth but the results apply to the other chalcogenides mentioned below as well. It was tried to vary only one parameter at a time. First the role of the chemical parameters wiil be considered. Having found a strong transport effect with iodine, bromine and chlorine also were studied as transporters. Br gave much smaller & values and CI showed practicalfy no transport at all. This is in qualitative agreement with an estimate of the AG values at room temperatures from literature data. They showed that the iodine reaction had the lowest AG value and thus the least extreme equilibrium position as required for a reasonabfe transport effect. Iodine was used as transporter in all other systems, although this may not necessarily mean optimal transport. The experimental technique was as follows. Approximately 3 g of pure, polycrystalline ZnS was placed into one end of a quartz ampule (length 15 cm, internal diameter 8 mm). It was degassed in high vacuum at 8OO”C, iodine condensed in with liquid air and the ampule drawn OR. The ampule was then placed horizontally into a tubular two-zone furnace. The usual reaction time was 16 hr. Since SGN.&ER~~)had previously described the transport of iron oxide with HCl gas according to: FesOa + 6HCl + ZFeCls+HsQ one bad to think about the analogous reaction: ZnS+ZHI + ZnIs + HsS. However, by adding various amounts of hydrogen up to the equivalent to HI, no differences in riz or in crystal habit were found as compared to pure iodine. The role of CT: 7it increased stronger than linear with CT up to a value of CT = 1.5 mg Tjcms which could not be exceeded for safety reasons. A strong dependence of the size and the quality of the resulting crystals on CT however was noted. At c~ = 1 mg I/cm3 growth was very stow although
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well developed individual crystals resulted. Best results CT = 5 mg I/cm3 were obtained at (7it = 20mg ZnS/hr). Clear crystals witk well developed faces formed which after 40 kr had sizes up to 5 x 5 mm. At kigher iodine concentrations, e.g. CT = 15 mg I/cm3, lit was so large (80 mg ZnS/hr) that polynucleation occured and layers of intergrown crystallites resulted. The role of Tl and Tz. The absolute values of tkese temperatures can be varied over a relatively wide range if one considers only Gz and not the quality of the crystals. For a CT of 5 mg I/cm3 not too different ti values were obtained for 13001100°C as well as for 900-600°C. The range of permissible supersaturation, however, decreases with temperature. At Tz = 600°C only a microcrystalline cake is formed because of polynucleation. A minimum Tz of 700°C was required to obtain individual, well developed crystals. The difference AT between Tl and Tz was found to be of minor importance since at the geometry employed the ‘Lconductance” L rather than the partial pressure difference Ap appeared to be the rate determining step in the growth process. The optimal growth temperature Ts has to be evaluated empirically for a given substance. The proper choice of Tz depends also on the physical properties required from tke crystal such as the amount of transporter dissolved in the crystal, the number of imperfections etc. If pol~orp~sm exists, Tz has to be chosen according to the stability range of the modification desired. Now the influence of the geometrical parameters will be discussed. rit decreases approximately linearly with the tube length I because of the increasing flow resistance. The obvious conclusion to use very short tubes, however, is not quite correct since one has to consider that if several seeds are to form and grow in one experiment the crystallization chamber should not be too small in order to avoid intergrowth between the crystals. A good compromise between these requirements is to heat the tube not symmetrically but asymmetrically in such a way that the vaporization chamber is small but the crystallization chamber is large. The temperature distribution in the crystallization chamber skould be as uniform as possible in order to avoid re-evaporation of crystals from warmer parts in the course of an experiment. For
and
M.
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orientating experiments, on the other hand, it is quite useful to kave a sloping temperature distribution along the crystallization chamber in order to find tke temperature of optimal crystal growth. The temperature drop between the two chambers should not be too abrupt in order to avoid a clogging up of the tube in this region. The most important geometrical parameter is the tube cross section 4 which influences tfr decisively. For CT I= 5 mg I/m-r? and Tl = lOOO”C, Tz = 75O”C, & was 20 mg ZnS/hr for a tube with 8 mm diameter but 300 mg/hr for a tube with 20 mm diameter. This large influence of q on m is probably due to the relative decrease of the friction of tke moving gases along the walls of the tube and to a partial transition from diffusion to convection with increasing q. The latter is also substantiated by the fact that in large diameter tubes the crystals are always found at the bottom of the tube (according to the direction of the gas flow) whereas in smaller tubes they are found all around the circumference of the tube. Concluding, the following requirements have to be observed if transport reactions are to be used for the growth of single crystals. 1. The rate of transport ni is not to exceed the rate of growth of the seeds. 2. The optimal c~stallization temperature has to be evaluated empirically for each system taking into account the possibility of polymorpkism. 3. The crystallization chamber should be large in order to prevent intergrowth between adjacent seeds. Asymmetric heating is useful. 4. The temperature distribution in the crystallization chamber should be as uniform as possible to avoid partial re-evaporation of already grown crystals. 5. Well developed crystals form easier in large diameter tubes where convection determines the rate of transport. 6. The temperature difference between the MO chambers can be made smaller if wider tubes are used (thus facilitating an even temperature distribution along the crystallization chamber) since the gas flow is here the rate determining step. 3. CI-iALCOGENIDE CRYSTALS GROWN TH[E T~SPORT %XETHOD
If a simple binary ckalcogenide
BY
is transported,
CRYSTAL
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the structure of the crystals formed corresponds to the phase stable at the growing temperature. If the chalcogenide exists in various valency states, the resulting crystals are not necessarily identical with the valency state of the starting material. Depending on temperature, the transported crystals can have a different com~sition, e.g. if SnS is transported at 650-500°C pure SnS is obtained. At 950400°C however, SnSs is formed in the crystallization chamber. If a mixture of two binary chalcogenides is transported the following cases are possible. (a) Formation binaries. (b) Formation
of mixed
crystals
of the
two
of a ternary chalcogenide.
(c) Separate transport of the two binaries if complete immiscibility exists. In most cases it is not necessary to start with well defined binary chalcogenides or mixtures thereof. Often it is sufficient to react a stoichiometric mixture of the elements at high temperatures and subject this resulting product to the transport reaction.
The binary chalcogenides prepared are listed in Table 1. An interesting case is ZnS because it exhibits polymorphism. Crystals grown previously by reacting zinc vapor with hydrogen sulfide are always mixtures of the cubic and the hexagonal phase, the boundaries of which are visible as “striations”. The transport method allows a separation of the phases by varying the growth temperature. At temperatures below 1000°C the pure cubic modification-as checked by X-rays and optical inspection-is obtained. Around 1150” mainIy hexagonal crystals form containing only very few striations. By admixing small amounts of silver or copper these crystals can be made to luminesce blue or green respectively. In the case of CdS the amount of iodine incorporated in the crystals was determined quantitatively by using radioactive I131 as a tracer in the transporting iodine. The iodine content was found to be 10-a weight per cent. It is evenly distributed throughout the crystals, as found by partial etching.
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204
R.
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H.
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B. Mixed crystals of binary chalcogenides The system ZnS-MnS was found to be a good example of mixed crystal formation by chemical transport reactions. If a mixture of polycrystalline ZnS and MnS is transported in a sloping temperature gradient (7’1 = lOSO”C, Ta = 950-750°C) and one collects the crystals formed at various temperatures, one finds crystals grown at 750°C are slightly orange colored, have the cubic sphalerite structure and contain 2 per cent by weight of Mn. With increasing T2 the manganese content increases and the crystals remain cubic up to 850°C. Between 860” and 880°C a mixture between the cubic and the hexagonal wurtzite phase forms and above 900°C the crystals are purely hexagonal and contain around 10 per cent of Mn. This is very surprising since both pure ZnS and pure MnS (NaCl structure) grow in the cubic form at 900°C the mixture however prefers the hexagonal structure. The phenomenon was used to “construct” crystals with built-in phase changes. A mixture of ZnS and MnS was transported and the temperature T2 of the growing chamber oscillated periodically during the growth process between 750” and 950°C. The crystals obtained showed indeed striations corresponding to the number of temperature cycles during the growth period. C. Ternary chalcogenides The transport method proved to be capable of yielding a large variety of ternary chalcogenide crystals of the general formula ABaX4, where A = Zn, Cd, Hg; B = In, Ga and X = S, Se. They are listed in Table 2. These materials, known so far only in the microcrystalline state, show interesting photoelectric properties which have been reported elsewhere.(s) HAHN@) and coworkers obtained polycrystalline samples of these ternaries by sintering together the binary constituents at high temperatures. Our X-ray data obtained so far are in agreement with the structures these authors propose. 4. CONCLUSIONS
The concept of chemical transport reactions isif properly modified-a useful tool for growing single crystals of metal chalcogenides having high
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d
e
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melting or sublimation points. Not only simple binary, but also ternary and probably quaternary compounds as well as mixed crystals can be prepared. The method will certainly be useful for other chemical systems. If means are found to control nucleation at will over wide ranges of temperature and composition it should be possible to prepare large single crystals as well as thin microcrystalline layers. A disadvantage is the possibility of incorporation of the transporter in the crystals formed.
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On the other hand, being a complicated distillation a transport reaction might also prove to be a means of purification for certain compounds. REFERENCES
1. SCHAFERH., 2. anorg. Chem. 286, 27, 42 (1956);
290,279 (1957); 291, 221, 254 (1957). 2. NITSCHER., J. Phys. Chem. Solids 17, 163 (1960). 3. BEUN J. A., NITSCHER. and LICHTENSTEIGER M., Physica 26, 647 (1960); Physica, to be published. 4. HAHN H. et al., Z. morg. Chem. 279, 241 (1955).