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The growth of single crystals of binary and ternary chalcogenides by chemical transport reactions
LETTERS
TO
the surface of the metal this additions drift velocity in general will contain a component parallel to the surface normal which will vitiate the AK effect. As we have seen, however, if in the one-dimensional regions the axis of the cylindrical Fermi surface is normal to the crystal surface or in the two-dimensional regions ~4 is parallel to the crystal surface the drift velocity of allr open orbits will also lie in this plane. This is just the requirement for the AK effect. A well resolved effect will probably be observed only if the motion is nearly periodic; for the two-dimensional regions this requires in addition that the crystal surface be parallel to a mirror plane. With these conditions satisfied, if the open orbit is in the skin depth at time 7’1 and returns to it at time Ts the AK effect will measure the “cyclotron frequency” 64277 = (Ts- T&l directly. Moreover the largest effect will be obtained for &#I, = %-t-V,. The foregoing discussion has assumed that tie(&) will be independent of k~, which in general is not the case. If the open orbits come from a single undulating cylinder (H in a onedimensional region) wc will take on extremal values (say at RH = 0) and this will determine the value of we observed [say we(O)]. For H in the twodimensional regions no extremal is expected in general, but in certain cases wc for the open orbits may be confined to a narrow range so that oscillations may still be observable. We have in mind the open orbits that may be found in Cu, Ag and Au. According to SHOENB~G(~) the Fermi surface in these metals consists of large “bellys” connected by narrow “necks”. The open orbits for H in two dimensional regions differ only by the amount of “neck” included, so that in this case wc may be sensibly constant for open orbits. A similar mechanism may make possible the observation of extended orbits. The situation which obtains when the additional drift velocity vy contains a component parallel to the surface normal has been discussed by BLOUNT@. He observes that by tipping the field H out of the surface it may be possible to find sow orbits with drift velocities VH = vx along H whose normal component cancels the normal component of vy. A similar explanation for “tipped field” resonances has been proposed for closed orbits by CHAMBERS(Q), HEINE(~@ and
THE
163
EDITOR
PHILLIPS( though none of these authors could explain the observation in tin@s) of “isolated resonances” at angles so large as 30”. We agree with BLOUNT that open orbits may account for isolated large angle resonances in general symmetries. Ack~~~~e~ge~~t~~r thoughts on open orbits have benefited greatly from conversations with colleagues in the Mond Laboratory. We wish to express our appreciation particularly to Mr. M. G. PRIESTLY, Dr. D. SHOENBERG and Dr. A. B. PIPPARD for a number of helpful suggestions.
Royal Society Mend Laboratory Cambridge England
J. C. PHILLIPS
References 1. LIFSHITZ I. M. and PE~~HANSKIV. G., Zh. exsp. tear. fiz. 35, 875 (1959). 2. BLOUNT E. I., Phys. Rev. Letters 4, 114 (1960). 3. This case and the discussion of it were suggested by Dr. L. M. FALICOV. 4. ONSACERIL., Phil. Mug. 43, 1006 (1952). 5. Pr~~~~~A.B.,Rep.lOthSolvayCong.,p. 123 (1955) (unpublished). 6. ZIL’BERM~, G. E., Zh. exsp. teor. jiz. 6, 299 (1958); 7, 169 (1958). Note that in the latter the small oscillations stem from the cutoff of closed orbits, the open orbits contributing nothing. 7. AZBEL M. and KANER E. A., Zh. exsp. tear. fix. 5, 730 (1957). 8. SHOENBERGD., Phil. Man., to be published. 9. CHAMBERSR. G., Canad. J. Phys. 34, 1395 (1956). 10. HEINE V.. Pkvs. Rev. 107, 431 (19573. 11. PHILLIPS j. C!., Phys. Rev: Let&s 3,328 (1959). 12. KIP A. F., LANGENBERGD., ROSENBLUMW. and WAGGONERG. F., Phys. Rev. 108, 494 (1958).
The growth of single crystals of binary and ternary chalcogenides by chemical transport reactions (Received
23 February
1960)
THE method of chemical transport reactions was used to grow single crystals of the following binary and ternary chalcogenides: ZnS, ZnSe, CdS, CdSe, MnS, SnSs,In&& ZnInsS4, CdInsS4, HgIn&, ZnInsSe4 and CdInsSe4. The term chemical transport reactions was first introduced by SCHAFER et al.(l) who studied their
164
LETTERS
TO
thermodynamics. Processes based on the same principle, however, have been known for a long time, e.g. the method of van Arkel-de Boer for preparing certain metals by thermal decomposition of their halides on a hot wire. Transport reactions are based on the fact that a transport of matter can occur in a chemical system consisting of one solid and n gaseous components in equilibrium, if the equilibrium constant K is made to vary locally, e.g. by imposing a temperature gradient on the vessel containing the system. The simplest arrangement is a closed tube with a polycrystalline solid, e.g. ZnS, of temperature Tl in one end, the other end being at Ta (Fig. 1).
ncl, Zone 2
Zone I Tl
/ Thermal insulation
FIG. 1. Schematic
Growing Crystal
h
arrangement for chemical transport reactions.
If nothing else is in the tube we have the trivial case n = 1. At temperatures high enough and for Tl > Ts normal sublimation of ZnS will occur. By introducing a substance forming a volatile compound with ZnS, e.g. iodine, an equilibrium will establish of the form: ZnS+I2
*
ZnIa+*Sa
(n = 3)
The different equilibrium conditions in both halves of the tube can lead to a deposition of ZnS in Zone 2 by transport via the gaseous mixture of ZnIs and Ss. Small amounts of iodine (the “transporter”) are sufficient to transport practically unlimited amounts of ZnS because the Ia liberated in Zone 2 will diffuse back and pick up more ZnS. From the relation: dln K(T)
dT
AH
=- RT2
(K = equilibrium constant, AH = change in enthalpy) follows that the necessary condition for
THE
EDITOR
transport is Tl > Ta for reactions with AH > 0 and Tl < Ta for reactions with AH < 0. Usually ZnS will deposit in polycrystalline form. However, single crystals are also obtainable if the experimental parameters are adjusted in such a way that-once a certain number of seeds are formed in Zone 2 (or introduced previous to the experiment)-the amount of material arriving in Zone 2 per unit time corresponds to the velocity of growth of the seeds. If suitable transporters can be found this method is particularly useful for growing single crystals of materials with high melting or sublimation points because crystal growth can be achieved at much lower temperatures than have to be employed in conventional melting or vapour-phase techniques. In the case of zinc sulphide, e.g. we obtained at a growth temperature of 700°C crystals which were entirely cubic,(z) whereas crystals grown by “normal” sublimation at 1100” are usually mixtures of the cubic and the hexagonal phases. Furthermore, it was found that if mixtures of different chalcogenides are used as feed material the transport method is also suitable for growing single crystals of ternary compounds, e.g. ZnIn&, CdIn& HgInaS4, materials known hitherto only in the polycrystalline state.(s) We have employed the outlined principles to grow crystals of the various binary and ternary chalcogenides listed in Table 1. Iodine was used as a transporter in all experiments. It is, however, possible to use other substances, e.g. HI SnI4, Br etc. Approximately 2 g of polycrystalline feed material were put into a quartz ampoule of 8 mm internal diameter and 200 mm length. After heating in a high vacuum to drive off adsorbed gases, iodine corresponding to a concentration of S-6 mg/cms was condensed in with liquid air and the ampoule drawn off under vacuum. For crystal growth it was placed horizontally into a two-zone furnace, the feed material being in the hot zone. Growing times varied between 12 and 40 hr. For a given temperature gradient the transport rate R is roughly proportional to the cross-section of the tube 4 and to the square of the transporter concentration C. Typical values for ZnS are: AT = 1050” -750”, C = 5 mg I/ems, Q = 0.5 cma and R = 20 mg/hr. Work on the optical and electrical properties of these crystals is in progress.
LETTERS
TO
THE
165
EDITOR
Table 1
_
Maximal size (mm)
Crystal shape
Compound
ZnS
White
ZnSe CdS
Yellow Orange
CdSe MnS SnSz In&s ZnInzS4 CdInzS4 HgInzS4 ZnInzSer CdInsSep
Black Dark green Orange Red Yellow Red Black Dark red Black I
Plates, rods, polyhedra hex. columns. polyhedra needles plates plates octahedra thin plates octahedra octahedra polyhedra
Ltd.
I’emperature Tl
gradient TZ
__
5
1050”-750”
4X4X3 5X1X1
6 5
1050”-800” 1000”-400”
5X1X1 4 x 4 x 0.1 4 x 4 x 0.1 4X4X4 4 x 4 x 0.1 4X4X4 3X3X3 3X3X3 3X3X3
6 5 5 6 6 6 6 6 6
lOOO”-500” 1000”-550” 950”-600” 950”-+50” 1000”-700” 1000”-600” 950”-650” 1000”-700” 1000”-700”
are due to Messrs. H. U. B&STERLI and M. LICHTENSTEICERfor their help in building equipment and carrying out many experiments.
R.C.A.
Transporter concentration (mg I/ cm3)
6x6x2
Acknowledgements-Thanks
Laboratories Zurich Switzerland
_-
-
R. NITSCHE
References 1. SCHAEFERH. et al., 2. anorg. Chem. 286, 27, 42 (1956); 290, 279 (1957); 291, 221, 294 (1957). 2. WHITE J. C., R.C.A. Laboratories, Princeton, N.J., private communication. 3. HAHN H., Z. anorg. Chem. 263, 177 (1950).
Generation of vacancies during plastic deformation of KC1 crystals (Received 17 February 1960; revised 4 April 1960) PLASTIC deformation is known to produce detectable changes of conductivity in many types of solids. Following the interpretation of SEIT~ these changes are generally ascribed to point defects which are created during the movement of dislocations. In ionic crystals the generated defects are charged, and take part directly to the conduction processes, thus increasing considerably the conductivity. This enhancement of conductivity is known as the Gyulai-Hartly effect and has already been observed by several workers in alkali
halides.@) However, a systematic study of its temperature dependence and of its annealing properties has yet been lacking. An investigation of the effect at low temperatures, where the point defects are not mobile, should also allow us to separate the two possible contributions (ionic and electronic) to the extra-conductivity. As is known, TYLER suggested that electrons are liberated during plastic flow and that the Gyulai-Hartly effect could be partially due to them.(s) In the present experiments, the effect of plastic strain on the conductivity of KC1 crystals was studied in the range of temperature from - 170°C to + 70°C. The crystals were mounted in a vacuum cryostat, and given a constant amount of strain (of the order of 5 per cent) by squeezing them uniaxially and homogeneously between two massive, insulated electrodes. The external current under a fixed applied field was measured during and after deformation by means of a vibrating-reed electrometer, whose output was fed into a pen recorder. The response time of the apparatus was kept as low as possible, in order to follow the conductivity decay soon after deformation. With a load resistor of 1010 s2 the time constant was O-3 set and the sensitivity lo-14 A/division. The deformation was imparted to the crystal in a time of the order of the time constant of the apparatus. In Fig. 1 the external current recorded during and after deformation is shown for three KC1
TO
the surface of the metal this additions drift velocity in general will contain a component parallel to the surface normal which will vitiate the AK effect. As we have seen, however, if in the one-dimensional regions the axis of the cylindrical Fermi surface is normal to the crystal surface or in the two-dimensional regions ~4 is parallel to the crystal surface the drift velocity of allr open orbits will also lie in this plane. This is just the requirement for the AK effect. A well resolved effect will probably be observed only if the motion is nearly periodic; for the two-dimensional regions this requires in addition that the crystal surface be parallel to a mirror plane. With these conditions satisfied, if the open orbit is in the skin depth at time 7’1 and returns to it at time Ts the AK effect will measure the “cyclotron frequency” 64277 = (Ts- T&l directly. Moreover the largest effect will be obtained for &#I, = %-t-V,. The foregoing discussion has assumed that tie(&) will be independent of k~, which in general is not the case. If the open orbits come from a single undulating cylinder (H in a onedimensional region) wc will take on extremal values (say at RH = 0) and this will determine the value of we observed [say we(O)]. For H in the twodimensional regions no extremal is expected in general, but in certain cases wc for the open orbits may be confined to a narrow range so that oscillations may still be observable. We have in mind the open orbits that may be found in Cu, Ag and Au. According to SHOENB~G(~) the Fermi surface in these metals consists of large “bellys” connected by narrow “necks”. The open orbits for H in two dimensional regions differ only by the amount of “neck” included, so that in this case wc may be sensibly constant for open orbits. A similar mechanism may make possible the observation of extended orbits. The situation which obtains when the additional drift velocity vy contains a component parallel to the surface normal has been discussed by BLOUNT@. He observes that by tipping the field H out of the surface it may be possible to find sow orbits with drift velocities VH = vx along H whose normal component cancels the normal component of vy. A similar explanation for “tipped field” resonances has been proposed for closed orbits by CHAMBERS(Q), HEINE(~@ and
THE
163
EDITOR
PHILLIPS( though none of these authors could explain the observation in tin@s) of “isolated resonances” at angles so large as 30”. We agree with BLOUNT that open orbits may account for isolated large angle resonances in general symmetries. Ack~~~~e~ge~~t~~r thoughts on open orbits have benefited greatly from conversations with colleagues in the Mond Laboratory. We wish to express our appreciation particularly to Mr. M. G. PRIESTLY, Dr. D. SHOENBERG and Dr. A. B. PIPPARD for a number of helpful suggestions.
Royal Society Mend Laboratory Cambridge England
J. C. PHILLIPS
References 1. LIFSHITZ I. M. and PE~~HANSKIV. G., Zh. exsp. tear. fiz. 35, 875 (1959). 2. BLOUNT E. I., Phys. Rev. Letters 4, 114 (1960). 3. This case and the discussion of it were suggested by Dr. L. M. FALICOV. 4. ONSACERIL., Phil. Mug. 43, 1006 (1952). 5. Pr~~~~~A.B.,Rep.lOthSolvayCong.,p. 123 (1955) (unpublished). 6. ZIL’BERM~, G. E., Zh. exsp. teor. jiz. 6, 299 (1958); 7, 169 (1958). Note that in the latter the small oscillations stem from the cutoff of closed orbits, the open orbits contributing nothing. 7. AZBEL M. and KANER E. A., Zh. exsp. tear. fix. 5, 730 (1957). 8. SHOENBERGD., Phil. Man., to be published. 9. CHAMBERSR. G., Canad. J. Phys. 34, 1395 (1956). 10. HEINE V.. Pkvs. Rev. 107, 431 (19573. 11. PHILLIPS j. C!., Phys. Rev: Let&s 3,328 (1959). 12. KIP A. F., LANGENBERGD., ROSENBLUMW. and WAGGONERG. F., Phys. Rev. 108, 494 (1958).
The growth of single crystals of binary and ternary chalcogenides by chemical transport reactions (Received
23 February
1960)
THE method of chemical transport reactions was used to grow single crystals of the following binary and ternary chalcogenides: ZnS, ZnSe, CdS, CdSe, MnS, SnSs,In&& ZnInsS4, CdInsS4, HgIn&, ZnInsSe4 and CdInsSe4. The term chemical transport reactions was first introduced by SCHAFER et al.(l) who studied their
164
LETTERS
TO
thermodynamics. Processes based on the same principle, however, have been known for a long time, e.g. the method of van Arkel-de Boer for preparing certain metals by thermal decomposition of their halides on a hot wire. Transport reactions are based on the fact that a transport of matter can occur in a chemical system consisting of one solid and n gaseous components in equilibrium, if the equilibrium constant K is made to vary locally, e.g. by imposing a temperature gradient on the vessel containing the system. The simplest arrangement is a closed tube with a polycrystalline solid, e.g. ZnS, of temperature Tl in one end, the other end being at Ta (Fig. 1).
ncl, Zone 2
Zone I Tl
/ Thermal insulation
FIG. 1. Schematic
Growing Crystal
h
arrangement for chemical transport reactions.
If nothing else is in the tube we have the trivial case n = 1. At temperatures high enough and for Tl > Ts normal sublimation of ZnS will occur. By introducing a substance forming a volatile compound with ZnS, e.g. iodine, an equilibrium will establish of the form: ZnS+I2
*
ZnIa+*Sa
(n = 3)
The different equilibrium conditions in both halves of the tube can lead to a deposition of ZnS in Zone 2 by transport via the gaseous mixture of ZnIs and Ss. Small amounts of iodine (the “transporter”) are sufficient to transport practically unlimited amounts of ZnS because the Ia liberated in Zone 2 will diffuse back and pick up more ZnS. From the relation: dln K(T)
dT
AH
=- RT2
(K = equilibrium constant, AH = change in enthalpy) follows that the necessary condition for
THE
EDITOR
transport is Tl > Ta for reactions with AH > 0 and Tl < Ta for reactions with AH < 0. Usually ZnS will deposit in polycrystalline form. However, single crystals are also obtainable if the experimental parameters are adjusted in such a way that-once a certain number of seeds are formed in Zone 2 (or introduced previous to the experiment)-the amount of material arriving in Zone 2 per unit time corresponds to the velocity of growth of the seeds. If suitable transporters can be found this method is particularly useful for growing single crystals of materials with high melting or sublimation points because crystal growth can be achieved at much lower temperatures than have to be employed in conventional melting or vapour-phase techniques. In the case of zinc sulphide, e.g. we obtained at a growth temperature of 700°C crystals which were entirely cubic,(z) whereas crystals grown by “normal” sublimation at 1100” are usually mixtures of the cubic and the hexagonal phases. Furthermore, it was found that if mixtures of different chalcogenides are used as feed material the transport method is also suitable for growing single crystals of ternary compounds, e.g. ZnIn&, CdIn& HgInaS4, materials known hitherto only in the polycrystalline state.(s) We have employed the outlined principles to grow crystals of the various binary and ternary chalcogenides listed in Table 1. Iodine was used as a transporter in all experiments. It is, however, possible to use other substances, e.g. HI SnI4, Br etc. Approximately 2 g of polycrystalline feed material were put into a quartz ampoule of 8 mm internal diameter and 200 mm length. After heating in a high vacuum to drive off adsorbed gases, iodine corresponding to a concentration of S-6 mg/cms was condensed in with liquid air and the ampoule drawn off under vacuum. For crystal growth it was placed horizontally into a two-zone furnace, the feed material being in the hot zone. Growing times varied between 12 and 40 hr. For a given temperature gradient the transport rate R is roughly proportional to the cross-section of the tube 4 and to the square of the transporter concentration C. Typical values for ZnS are: AT = 1050” -750”, C = 5 mg I/ems, Q = 0.5 cma and R = 20 mg/hr. Work on the optical and electrical properties of these crystals is in progress.
LETTERS
TO
THE
165
EDITOR
Table 1
_
Maximal size (mm)
Crystal shape
Compound
ZnS
White
ZnSe CdS
Yellow Orange
CdSe MnS SnSz In&s ZnInzS4 CdInzS4 HgInzS4 ZnInzSer CdInsSep
Black Dark green Orange Red Yellow Red Black Dark red Black I
Plates, rods, polyhedra hex. columns. polyhedra needles plates plates octahedra thin plates octahedra octahedra polyhedra
Ltd.
I’emperature Tl
gradient TZ
__
5
1050”-750”
4X4X3 5X1X1
6 5
1050”-800” 1000”-400”
5X1X1 4 x 4 x 0.1 4 x 4 x 0.1 4X4X4 4 x 4 x 0.1 4X4X4 3X3X3 3X3X3 3X3X3
6 5 5 6 6 6 6 6 6
lOOO”-500” 1000”-550” 950”-600” 950”-+50” 1000”-700” 1000”-600” 950”-650” 1000”-700” 1000”-700”
are due to Messrs. H. U. B&STERLI and M. LICHTENSTEICERfor their help in building equipment and carrying out many experiments.
R.C.A.
Transporter concentration (mg I/ cm3)
6x6x2
Acknowledgements-Thanks
Laboratories Zurich Switzerland
_-
-
R. NITSCHE
References 1. SCHAEFERH. et al., 2. anorg. Chem. 286, 27, 42 (1956); 290, 279 (1957); 291, 221, 294 (1957). 2. WHITE J. C., R.C.A. Laboratories, Princeton, N.J., private communication. 3. HAHN H., Z. anorg. Chem. 263, 177 (1950).
Generation of vacancies during plastic deformation of KC1 crystals (Received 17 February 1960; revised 4 April 1960) PLASTIC deformation is known to produce detectable changes of conductivity in many types of solids. Following the interpretation of SEIT~ these changes are generally ascribed to point defects which are created during the movement of dislocations. In ionic crystals the generated defects are charged, and take part directly to the conduction processes, thus increasing considerably the conductivity. This enhancement of conductivity is known as the Gyulai-Hartly effect and has already been observed by several workers in alkali
halides.@) However, a systematic study of its temperature dependence and of its annealing properties has yet been lacking. An investigation of the effect at low temperatures, where the point defects are not mobile, should also allow us to separate the two possible contributions (ionic and electronic) to the extra-conductivity. As is known, TYLER suggested that electrons are liberated during plastic flow and that the Gyulai-Hartly effect could be partially due to them.(s) In the present experiments, the effect of plastic strain on the conductivity of KC1 crystals was studied in the range of temperature from - 170°C to + 70°C. The crystals were mounted in a vacuum cryostat, and given a constant amount of strain (of the order of 5 per cent) by squeezing them uniaxially and homogeneously between two massive, insulated electrodes. The external current under a fixed applied field was measured during and after deformation by means of a vibrating-reed electrometer, whose output was fed into a pen recorder. The response time of the apparatus was kept as low as possible, in order to follow the conductivity decay soon after deformation. With a load resistor of 1010 s2 the time constant was O-3 set and the sensitivity lo-14 A/division. The deformation was imparted to the crystal in a time of the order of the time constant of the apparatus. In Fig. 1 the external current recorded during and after deformation is shown for three KC1