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Determination of nickel-molybdenum surface alloy structures using LEED
SURFACE
SCIENCE 18 (1969) 350-356 0 North-Holland
DETERMINATION ALLOY
Publishing
OF NICKEL-MOLYBDENUM STRUCTURES
USING
Co., Amsterdam
SURFACE
LEED”
L. G. FEINSTEIN NASA/Electronics
Research
Center t, Cambridge,
Massachusetts
02139,
U.S.A.
and Laboratoire
d’Electrostatique
et de Physique
du M&al,
3%Grenoble,
France
du M&al,
3&Grenoble,
France
and E. BLANCt Laboratoire
d’Electrostatique
et de Physique
Received 5 June 1969 Four well-ordered surface alloys in the Ni-Mo system were investigated by LEED. The alloys were obtained by surface diffusion of MO onto a Ni(l11) face at temperatures between 650 and 950°C. The probable structures of the alloys were determined with the aid of tabulated symmetry and extinction properties of the 2-D space groups, and the phase diagram of the system. A 5 x 5 and a 4 x 4 superstructure possessing the hexagonal symmetry of the Ni(ll1) mesh with 4 and 6 ato% MO, and two rectangular structures containing 15 and 20 at % MO were found. No surface structures corresponding to the bulk alloys Ni4Mo or NiaMo were detected.
1. Introduction Low energy electron diffraction (LEED) and Field Ion Microscopy (FIM)l) appear to be the only tools which may be useful for the determination of the two-dimensional surface structure of ordered alloys. Two metal alloys have been characterized by LEED during epitaxy studies233). However, no alloy systems have been specifically studied by LEED. This is due in part to the problem of availability of single crystals and the uncertainty of a structure analysis based upon LEED intensities. A further complication is the possibility that ordering forces and solubilities differ on the surface from those found in the bulk. In this connection, Taylor2) has found an unpredicted surface alloy in the W-Cu system. * Sponsored in part by La Delegation G&n&ale a la Recherche Scientifique et Technique under contract 65FR-250. t Present address. : Present address: Laboratoire Martin d’Heres, France.
de Spectrometrie
350
Physique, Faculte des Sciences, 3%St.
NICKEL-MOLYBDENUM
SURFACE
ALLOY
STRUCTURES
351
For the case of simple alloys it may be possible to completely determine the two-dimensional surface structure as well as the periodicity of the superstructure mesh. In this paper we present LEED diagrams of four surface alloys formed by the diffusion of MO onto an Ni (I 11) face, and show how it is possible to analyze the patterns by utilization of the symmetry and extinction properties of the LEED spots. 2. Experimental procedure A nickel single crystal of 99.999% purity was aligned by X-ray diffraction to within one degree of the (111) plane, and cut by spark erosion into a cylinder of 12 mm diameter and 7 mm length. The (111) face was mechanically polished and electropolished in a perchloric acid solution. The crystal was tightly clamped into a cylinder of high purity molybdenum foil with the Ni( 111) face protruding by 1 mm. A filament placed directly behind the crystal permitted us to heat the sample by radiation. The temperature of the sample was measured by means of an optical pyrometer. A Varian LEED system of the post-acceleration display type was employed, A base pressure of 5 x 10P1* Torr was read on a nude Bayard-Alpert gauge which was inserted directly below the crystal in the chamber. 3. Results An examination of the Ni crystal in the MO foil holder revealed that the two metals had formed a pressure weld when the crystal was heated, with a consequent incorporation of MO into the sides of the Ni cylinder. As a result, MO was able to diffuse to the surface under investigation. At least four superstructures resulting from well-ordered Ni-Mo alloys were detected by LEED, and are shown in figs. I to 4. LEED diagrams of this type were never found for three other Ni(ll1) crystals, mounted in a different configuration without any MO foi14) The non-integral order spots could be removed by an argon ion bombardment of 2yA/cm2 at 400 V for 10 min. Subsequent annealing of the crystal above 800°C would then reestablish a superstructure, presumably by surface diffusion of fresh MO from the sides of the crystal. Despite the fact that we do not know a priori the compositions of the surface structures corresponding to the LEED diagrams, we may solve these structures with some certainty by considering the phase diagrams) for the system, and the properties of the 17 plane groups listed in the International Tables for X-ray Crystallography 6). After the crystal had been heated for a short time at 65O”C, the LEED pattern shown in fig. la was observed. The unit mesh of the structure is
352
L. G. FEINSTEIN
AND E. BLANC
5 x 5 based upon the primitive Ni(ll1) mesh, as indicated in fig. I b*. Below about 150 V the pattern exhibits a six-fold symmetry, indicating that most of the scattering takes place in the first atomic layer. At higher voltages the three-fold symmetry characteristic of the stacking of close packed planes
Fig. la Fig. I.
Fig. lb
(a) Pattern from a 5 x 5 Ni-Mo alloy on a Ni(ll1) (b) Proposed surface structure.
face at 110 V.
in the bulk becomes apparent. The (30) reflections were visible down to an incident beam voltage of 3.5 V with a positive bias on the first grid. At this voltage the spots passed out of the sphere of reflection, i.e. 0 = 90”. Consideration of the symmetry in the intensity of the spots allows us to assign the two-dimensional space group p6m to the 5 x 5 structure. Furthermore, employing the notation of the International Tables, the only special position available to the MO in this surface structure which does not significantly exceed the solubility limit is 1 MO in 1 (a). The only other sets of equivalent positions that are consistent with this mesh require an additional six atoms per unit superstructure cell, or a total of 7/25=28 at% MO. The solid solubility of MO in Ni is only 12 at% at 650°C. However anomalously high alloy concentrations have been detected in surfaces’), so that solubility considerations alone may not be sufficient for positive identification of the present structures. Heating the sample at 800°C for 30 min resulted in the pattern presented in fig. 2. Inspection of the LEED diagram shows that it does not satisfy the requirements for a hexagonal lattice, but is instead the superposition of * Several extra spots in the diagram, not indexed on the 5 x 5 mesh, are due to adsorption of background gases at this early stage of outgassing when the vacuum was not sufficiently good.
NICKEL-MOLYBDENUM
SURFACE
ALLOY
STRUCTURES
353
a number of domains possessing rectangular symmetry. There are three orientations at 120” to each other, and individual domains may be partially resolved by moving the beam. The rectangular superlattice mesh may be defined in terms of the Ni mesh as illustrated in fig. 2b: a’ = 2a,
b’=5(a+Lb).
The plane group may be identified as pmm from symmetries in the intensities of the spots. However assignment of the MO positions is not unambiguous as in the previous case. Nonetheless it is suggested that in addition to 1 MO in I (a) we have 2 MO in 2(f) at $, 3; z, +. This choice would result in a
Fig. 2b
Fig. 2a Fig. 2.
(a) Pattern from three superposed domains of a rectangular Ni-Mo Ni (111) face at 110 V. (b) Proposed surface structure.
alloy on a
composition of 15 at% MO, compared to the maximum allowed bulk solubility of 16 at% at 800°C. The reason for this assignment will be apparent in discussing the following surface alloy structure. Further heating of the crystal at 950°C for 5 hr led to a structure with the LEED diagram of fig. 3a. Here one of the domains has grown to a size larger than the beam diameter. The two related domains at 120” to this one were found in small regions of the crystal surface. The superlattice mesh corresponding to this LEED diagram is, a’=a,
b’ = 5 (a + 2b)
as illustrated in fig. 3b. The observation of systematic abscences in the LEED diagram may be used to further determine the plane group. In this case the condition limiting possible reflections is, hk: h+ k=2n, if we exclude the weaker, streaked rows whose presence is explained below. This information
354
L. G. FEINSTEIN
AND E. BLANC
allows us to unambiguously assign the centered rectangular plane group cmm with 2 MO in 2(a) to the surface alloy structure. Inspection of the unit mesh outlined in fig. 3b, yields an alloy composition of 20 at% MO, which is approximately the bulk solubility at 950°C. The introduction of further
Fig. 3a
Fig. 3b
Fig. 3. (a) Pattern from a centered rectangular Ni-Mo alloy on a Ni(ll1)
face at 1lOV.
(b) Proposed surface structure.
MO atoms into this net would require a solid solubility of at least 40 at%. Comparison of the structures illustrated in figs. 2b and 3b indicates the reason for the seemingly arbitrary choice of special positions in the former case. It seems a reasonable assumption that the transition to the alloy of higher concentration proceeds by the filling in of the less dense alternate rows by additional MO atoms. The inset in fig. 3a has been greatly overexposed to show streaked alternate rows of reflections: remnants of the previous pattern, whose presence indicates the lack of complete infilling of the less dense rows of the antecedent structure. A fourth alloy structure developed after many cycles of argon ion bombardment and heating to 950°C. The unit mesh of the surface structure is 4 x 4 based upon the primitive Ni(l11) mesh, as indicated in fig. 4. The extra set of six spots, just inside the principal reflections of the Ni mesh, results from the subsequent epitaxy of Ag on this surface. The epitaxy experiment is reported more fully elsewhere4). As in the case of the 5 x 5 structure, consideration of the symmetry of the spots and of the phase diagram allows us to assign the two-dimensional space group p6m with 1 MO in I (a) to the 4 x 4 structure. The Ni-No system contains two bulk alloys in the concentration range
NICKEL-MOLYBDENUM
of interest.
Saito
and
SURFACE
Becks)
have
ALLOY
described
355
STRUCTURES
the close-packed
plane
of
Ni,Mo, and the corresponding plane of Ni,Mo was constructed by us from structural information given by Newman and Hrenl). However no LEED patterns were observed which could be ascribed to the bulk structure
Fig. 4b
Fig. 4a Fig. 4.
(a) Pattern from a 4 x 4 Ni-Mo alloy on a Ni(lll) (b) Proposed surface structure.
TABLE
face at llOV,
1
Proposed surface alloy structures in the Ni-Mo system Illustration ______~ Fig. 1 Fig. 2 Fig. 3 Fig. 4
Surface alloy mesh
Plane group
At% MO
p6m
l/25 = 4%
mm
3120 = 15%
cmm
2/10=20x
p6m
l/16=6”/,
a’=5a b’ = 56 a’=2a b’=5(a+2b) a’=a b’=5(a+2b) a’=4a b’=4b
of the known alloys. A summary study is presented in table 1.
of surface
structures
determined
in this
4. Summary LEED has been successfully employed in the structure determination surface alloys in the system Ni-Mo, formed by diffusion of MO onto
of an
L. G. FEINSTEIN
356
Ni (111)
surface.
Assignment
AND E. BLANC
of the positions
of the MO atoms
in
the
superstructure unit meshes was possible based upon the symmetry and extinction properties of the seventeen two-dimeensional space groups. An attempt at a detailed analysis of the intensities of the reflections was not necessary. Assignments of the number of MO atoms per unit cell were based partially upon solubility characteristics of the bulk Ni-Mo system, although the possibility of an anomolously high concentration of MO at the suface cannot be completely ruled out. However the choices seem reasonable based upon the sequence of the structures observed, particularly the transition pmm- cmm. In addition, with higher concentrations one would expect a multiplicity of structures with smaller unit meshes. Two hexagonal patterns were observed with unit meshes of 5 x 5 and 4 x 4 based upon the primitive Ni (111) mesh, and containing 4 and 6 at% MO respectively. Two rectangular structures, one primitive and one centered, were found with 15 and 20 at% MO respectively. A reasonable explanation for the transition between these two alloys has been proposed. Below 150 V, most of the scattering takes place in the first atomic layer. No surface structures corresponding to the bulk alloys Ni,Mo or Ni,Mo were detected. However, one should not necessarily expect the same ordering forces in the two-dimensional case considered here.
Acknowledgements Thanks are due to R. to D. Shoemaker of MIT J-L. Georges of C.E.N.G. des Sciences for orienting
Montmory for support and encouragement, and for helpful discussions. We are also grateful to for spark cutting and to P. Charbit of the Faculte the crystal. References
1) 2) 3) 4) 5) 6)
R. W. Newman and J. J. Hren, Surface Sci 8 (1967) 373. N. J. Taylor, Surface Sci. 4 (1966) 161. P. W. Palmberg and T. N. Rhodin, J. Chem. Phys. 49 (1968) 134. L. G. Feinstein, E. Blanc, and D. Dufayard to be published. Constitution ofBinary Alloys, Ed. M. Hansen (McGraw-Hill, New York, 1958). International Tables for X-Ray Crystallography, Vol. 1, Eds. N. F. M. Henry and K. Lonsdale (Kynock Press, Birmingham, England, 1965). 7) C. Gonzalez, Acta Met. 15 (1967) 1373. 8) S. Saito and P. A. Beck, Trans. ALME 215 (1959) 938.
SCIENCE 18 (1969) 350-356 0 North-Holland
DETERMINATION ALLOY
Publishing
OF NICKEL-MOLYBDENUM STRUCTURES
USING
Co., Amsterdam
SURFACE
LEED”
L. G. FEINSTEIN NASA/Electronics
Research
Center t, Cambridge,
Massachusetts
02139,
U.S.A.
and Laboratoire
d’Electrostatique
et de Physique
du M&al,
3%Grenoble,
France
du M&al,
3&Grenoble,
France
and E. BLANCt Laboratoire
d’Electrostatique
et de Physique
Received 5 June 1969 Four well-ordered surface alloys in the Ni-Mo system were investigated by LEED. The alloys were obtained by surface diffusion of MO onto a Ni(l11) face at temperatures between 650 and 950°C. The probable structures of the alloys were determined with the aid of tabulated symmetry and extinction properties of the 2-D space groups, and the phase diagram of the system. A 5 x 5 and a 4 x 4 superstructure possessing the hexagonal symmetry of the Ni(ll1) mesh with 4 and 6 ato% MO, and two rectangular structures containing 15 and 20 at % MO were found. No surface structures corresponding to the bulk alloys Ni4Mo or NiaMo were detected.
1. Introduction Low energy electron diffraction (LEED) and Field Ion Microscopy (FIM)l) appear to be the only tools which may be useful for the determination of the two-dimensional surface structure of ordered alloys. Two metal alloys have been characterized by LEED during epitaxy studies233). However, no alloy systems have been specifically studied by LEED. This is due in part to the problem of availability of single crystals and the uncertainty of a structure analysis based upon LEED intensities. A further complication is the possibility that ordering forces and solubilities differ on the surface from those found in the bulk. In this connection, Taylor2) has found an unpredicted surface alloy in the W-Cu system. * Sponsored in part by La Delegation G&n&ale a la Recherche Scientifique et Technique under contract 65FR-250. t Present address. : Present address: Laboratoire Martin d’Heres, France.
de Spectrometrie
350
Physique, Faculte des Sciences, 3%St.
NICKEL-MOLYBDENUM
SURFACE
ALLOY
STRUCTURES
351
For the case of simple alloys it may be possible to completely determine the two-dimensional surface structure as well as the periodicity of the superstructure mesh. In this paper we present LEED diagrams of four surface alloys formed by the diffusion of MO onto an Ni (I 11) face, and show how it is possible to analyze the patterns by utilization of the symmetry and extinction properties of the LEED spots. 2. Experimental procedure A nickel single crystal of 99.999% purity was aligned by X-ray diffraction to within one degree of the (111) plane, and cut by spark erosion into a cylinder of 12 mm diameter and 7 mm length. The (111) face was mechanically polished and electropolished in a perchloric acid solution. The crystal was tightly clamped into a cylinder of high purity molybdenum foil with the Ni( 111) face protruding by 1 mm. A filament placed directly behind the crystal permitted us to heat the sample by radiation. The temperature of the sample was measured by means of an optical pyrometer. A Varian LEED system of the post-acceleration display type was employed, A base pressure of 5 x 10P1* Torr was read on a nude Bayard-Alpert gauge which was inserted directly below the crystal in the chamber. 3. Results An examination of the Ni crystal in the MO foil holder revealed that the two metals had formed a pressure weld when the crystal was heated, with a consequent incorporation of MO into the sides of the Ni cylinder. As a result, MO was able to diffuse to the surface under investigation. At least four superstructures resulting from well-ordered Ni-Mo alloys were detected by LEED, and are shown in figs. I to 4. LEED diagrams of this type were never found for three other Ni(ll1) crystals, mounted in a different configuration without any MO foi14) The non-integral order spots could be removed by an argon ion bombardment of 2yA/cm2 at 400 V for 10 min. Subsequent annealing of the crystal above 800°C would then reestablish a superstructure, presumably by surface diffusion of fresh MO from the sides of the crystal. Despite the fact that we do not know a priori the compositions of the surface structures corresponding to the LEED diagrams, we may solve these structures with some certainty by considering the phase diagrams) for the system, and the properties of the 17 plane groups listed in the International Tables for X-ray Crystallography 6). After the crystal had been heated for a short time at 65O”C, the LEED pattern shown in fig. la was observed. The unit mesh of the structure is
352
L. G. FEINSTEIN
AND E. BLANC
5 x 5 based upon the primitive Ni(ll1) mesh, as indicated in fig. I b*. Below about 150 V the pattern exhibits a six-fold symmetry, indicating that most of the scattering takes place in the first atomic layer. At higher voltages the three-fold symmetry characteristic of the stacking of close packed planes
Fig. la Fig. I.
Fig. lb
(a) Pattern from a 5 x 5 Ni-Mo alloy on a Ni(ll1) (b) Proposed surface structure.
face at 110 V.
in the bulk becomes apparent. The (30) reflections were visible down to an incident beam voltage of 3.5 V with a positive bias on the first grid. At this voltage the spots passed out of the sphere of reflection, i.e. 0 = 90”. Consideration of the symmetry in the intensity of the spots allows us to assign the two-dimensional space group p6m to the 5 x 5 structure. Furthermore, employing the notation of the International Tables, the only special position available to the MO in this surface structure which does not significantly exceed the solubility limit is 1 MO in 1 (a). The only other sets of equivalent positions that are consistent with this mesh require an additional six atoms per unit superstructure cell, or a total of 7/25=28 at% MO. The solid solubility of MO in Ni is only 12 at% at 650°C. However anomalously high alloy concentrations have been detected in surfaces’), so that solubility considerations alone may not be sufficient for positive identification of the present structures. Heating the sample at 800°C for 30 min resulted in the pattern presented in fig. 2. Inspection of the LEED diagram shows that it does not satisfy the requirements for a hexagonal lattice, but is instead the superposition of * Several extra spots in the diagram, not indexed on the 5 x 5 mesh, are due to adsorption of background gases at this early stage of outgassing when the vacuum was not sufficiently good.
NICKEL-MOLYBDENUM
SURFACE
ALLOY
STRUCTURES
353
a number of domains possessing rectangular symmetry. There are three orientations at 120” to each other, and individual domains may be partially resolved by moving the beam. The rectangular superlattice mesh may be defined in terms of the Ni mesh as illustrated in fig. 2b: a’ = 2a,
b’=5(a+Lb).
The plane group may be identified as pmm from symmetries in the intensities of the spots. However assignment of the MO positions is not unambiguous as in the previous case. Nonetheless it is suggested that in addition to 1 MO in I (a) we have 2 MO in 2(f) at $, 3; z, +. This choice would result in a
Fig. 2b
Fig. 2a Fig. 2.
(a) Pattern from three superposed domains of a rectangular Ni-Mo Ni (111) face at 110 V. (b) Proposed surface structure.
alloy on a
composition of 15 at% MO, compared to the maximum allowed bulk solubility of 16 at% at 800°C. The reason for this assignment will be apparent in discussing the following surface alloy structure. Further heating of the crystal at 950°C for 5 hr led to a structure with the LEED diagram of fig. 3a. Here one of the domains has grown to a size larger than the beam diameter. The two related domains at 120” to this one were found in small regions of the crystal surface. The superlattice mesh corresponding to this LEED diagram is, a’=a,
b’ = 5 (a + 2b)
as illustrated in fig. 3b. The observation of systematic abscences in the LEED diagram may be used to further determine the plane group. In this case the condition limiting possible reflections is, hk: h+ k=2n, if we exclude the weaker, streaked rows whose presence is explained below. This information
354
L. G. FEINSTEIN
AND E. BLANC
allows us to unambiguously assign the centered rectangular plane group cmm with 2 MO in 2(a) to the surface alloy structure. Inspection of the unit mesh outlined in fig. 3b, yields an alloy composition of 20 at% MO, which is approximately the bulk solubility at 950°C. The introduction of further
Fig. 3a
Fig. 3b
Fig. 3. (a) Pattern from a centered rectangular Ni-Mo alloy on a Ni(ll1)
face at 1lOV.
(b) Proposed surface structure.
MO atoms into this net would require a solid solubility of at least 40 at%. Comparison of the structures illustrated in figs. 2b and 3b indicates the reason for the seemingly arbitrary choice of special positions in the former case. It seems a reasonable assumption that the transition to the alloy of higher concentration proceeds by the filling in of the less dense alternate rows by additional MO atoms. The inset in fig. 3a has been greatly overexposed to show streaked alternate rows of reflections: remnants of the previous pattern, whose presence indicates the lack of complete infilling of the less dense rows of the antecedent structure. A fourth alloy structure developed after many cycles of argon ion bombardment and heating to 950°C. The unit mesh of the surface structure is 4 x 4 based upon the primitive Ni(l11) mesh, as indicated in fig. 4. The extra set of six spots, just inside the principal reflections of the Ni mesh, results from the subsequent epitaxy of Ag on this surface. The epitaxy experiment is reported more fully elsewhere4). As in the case of the 5 x 5 structure, consideration of the symmetry of the spots and of the phase diagram allows us to assign the two-dimensional space group p6m with 1 MO in I (a) to the 4 x 4 structure. The Ni-No system contains two bulk alloys in the concentration range
NICKEL-MOLYBDENUM
of interest.
Saito
and
SURFACE
Becks)
have
ALLOY
described
355
STRUCTURES
the close-packed
plane
of
Ni,Mo, and the corresponding plane of Ni,Mo was constructed by us from structural information given by Newman and Hrenl). However no LEED patterns were observed which could be ascribed to the bulk structure
Fig. 4b
Fig. 4a Fig. 4.
(a) Pattern from a 4 x 4 Ni-Mo alloy on a Ni(lll) (b) Proposed surface structure.
TABLE
face at llOV,
1
Proposed surface alloy structures in the Ni-Mo system Illustration ______~ Fig. 1 Fig. 2 Fig. 3 Fig. 4
Surface alloy mesh
Plane group
At% MO
p6m
l/25 = 4%
mm
3120 = 15%
cmm
2/10=20x
p6m
l/16=6”/,
a’=5a b’ = 56 a’=2a b’=5(a+2b) a’=a b’=5(a+2b) a’=4a b’=4b
of the known alloys. A summary study is presented in table 1.
of surface
structures
determined
in this
4. Summary LEED has been successfully employed in the structure determination surface alloys in the system Ni-Mo, formed by diffusion of MO onto
of an
L. G. FEINSTEIN
356
Ni (111)
surface.
Assignment
AND E. BLANC
of the positions
of the MO atoms
in
the
superstructure unit meshes was possible based upon the symmetry and extinction properties of the seventeen two-dimeensional space groups. An attempt at a detailed analysis of the intensities of the reflections was not necessary. Assignments of the number of MO atoms per unit cell were based partially upon solubility characteristics of the bulk Ni-Mo system, although the possibility of an anomolously high concentration of MO at the suface cannot be completely ruled out. However the choices seem reasonable based upon the sequence of the structures observed, particularly the transition pmm- cmm. In addition, with higher concentrations one would expect a multiplicity of structures with smaller unit meshes. Two hexagonal patterns were observed with unit meshes of 5 x 5 and 4 x 4 based upon the primitive Ni (111) mesh, and containing 4 and 6 at% MO respectively. Two rectangular structures, one primitive and one centered, were found with 15 and 20 at% MO respectively. A reasonable explanation for the transition between these two alloys has been proposed. Below 150 V, most of the scattering takes place in the first atomic layer. No surface structures corresponding to the bulk alloys Ni,Mo or Ni,Mo were detected. However, one should not necessarily expect the same ordering forces in the two-dimensional case considered here.
Acknowledgements Thanks are due to R. to D. Shoemaker of MIT J-L. Georges of C.E.N.G. des Sciences for orienting
Montmory for support and encouragement, and for helpful discussions. We are also grateful to for spark cutting and to P. Charbit of the Faculte the crystal. References
1) 2) 3) 4) 5) 6)
R. W. Newman and J. J. Hren, Surface Sci 8 (1967) 373. N. J. Taylor, Surface Sci. 4 (1966) 161. P. W. Palmberg and T. N. Rhodin, J. Chem. Phys. 49 (1968) 134. L. G. Feinstein, E. Blanc, and D. Dufayard to be published. Constitution ofBinary Alloys, Ed. M. Hansen (McGraw-Hill, New York, 1958). International Tables for X-Ray Crystallography, Vol. 1, Eds. N. F. M. Henry and K. Lonsdale (Kynock Press, Birmingham, England, 1965). 7) C. Gonzalez, Acta Met. 15 (1967) 1373. 8) S. Saito and P. A. Beck, Trans. ALME 215 (1959) 938.