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Electron paramagnetic resonance of Mn2+ in Sm2Zn3(NO3)12·24H2O single crystals
Specrrochimica Acto. Vol. 46A. Printed in Great Britain
No.
10. pp.
1535-1539.
19W 0
0584-8539/9a 13.00+0.00 1990 Pergamon Press plc
RESEARCH NOTE
Electron paramagnetic resonance of Mn2+ in Sm2Zn,(N0,),, single crystals (Received
l
24H20
15 March 1990, accepted 22 April 1990)
Abstract-The X-band electron paramagnetic resonance of Mn’+ doped in Sm,Zn,(NO,),z - 24H,O single crystals has been studied. MnZ+ substitutes at two inequivalent Zn*+ sites. The spin-Hamiltonian analysis of the EPR spectra is presented at 298 and 77 K.
Electron paramagnetic resonance (EPR) studies require the presence of unpaired electrons in the sample. In general, these are not present in the pure materials but can be introduced by doping with paramagnetic substances such as transition elements, or by radiation damage. Among all the ions which exhibit EPR spectra, the d5 and f’ ions (S-state ions) are particulaly interesting when one is concerned with the local symmetry of the environment of the ion. In fact, all sublevels of the S-state are generally observed in low magnetic fields for two reasons; (a) the zero field splitting is zero to first order, and (b) only higher-order effects permit lifting of the degeneracy of the fundamental states (!S and xS). Therefore, a detailed study of the angular variation of paramagnetic resonance absorption lines permits one to establish the point symmetry around the magnetic ion. The hydrated double nitrates of the rare earth elements form an interesting series of salts for EPR studies of S-state ions. Their general formula is M:” Mq (N03),2 - 24H20, where Mu’ is a trivalent cation (Bi or an ion of the 4f group) and Ml’ is a divalent cation (Zn, Mg or an ion of the 3d group). Although the trivalent lanthanide ions are generally paramagnetic, their spin-lattice relaxation times are so much shorter than those of the S-state ions (at sufficiently high temperature) that the magnetic interaction between the paramagnetic ions and the S-state ions are averaged essentially to zero with the consequence that magnetic resonance absorption by the S-state ion can be observed without extensive broadening. In this paper we describe the EPR of Mn2+ in Sm, Zn3(NOJ),z - 24HzO(SZN) single crystals from 298 down to 77 K.
CRYSTAL STRUCTURE The crystal structure of Ce2Mg,(N03),2 - 24H20 has been determined by ZALKIN etal.[l]. The other hydrated double nitrates can be expected to have similar structures. The primitive cell containing one formula unit is rhombohedral with dimensions II= 13.165 A and a=49.37”. The space group is R3. The rhombohedral unit cell contains three divalent ions situated at two different lattice sites. One of them occupies the site with point symmetry Csi (site I or Y site) and the other two divalent ions occupy lattice sites with point symmetry C, (site II or X site). The trivalent ion is found at a site of C,i point symmetry and the positions of the rest of the atoms are consistent with the space group.
EXPERIMENTAL Single crystals of SZN doped with MnZ+ were grown by slow evaporation of an aqueous solution of Sm(NO& - 6H2O and Zn(N0,)2 +6H20, mixed in stoichiometric ratios, at room temperature. The Mn2+ impurities were introduced into the host lattices by adding a small amount (0.1 wt%) of manganese nitrate. The double nitrate grows in flat hexagonal plates, the plane of which is perpendicular to the trigonal axis. 1535
Research Note
1536
The experiments were performed on a JEOL JES-FE3X homodyne spectrometer operating at -9.45 GHz, equipped with a TE”,,-cylindrical cavity and 100 KHz field modulation. As a reference for magnetic field strength, the resonance line of DPPH with g=2.0036 was used. The crystals were mounted on quartz rods. The angular variation studies were peformed using a TES-UCR-2X sample angular rotating device. Liquid nitrogen temperature measurements were made by using an ES-UCD-2X insertion type dewar.
RESULTS AND DISCUSSION
Mn2+ has 3d5 electronic configuration and according to Hund’s rule the ground state is 6S5,,. In a crystalline field of low symmetry the ground state is split into three Kramers doublets. In a magnetic field, the degeneracy is completely removed and five fine structure transitions are possible. Due to the interaction with the nucleus of spin 5/2, each electronic transition gives rise to six hyperfine transitions. For an arbitrary orientation of the magnetic field, the EPR spectrum consists of a number of lines corresponding to allowed and forbidden transitions. Angular variation studies of Mn2+ spectra reveal the presence of two inequivalent Mn2+ centres of unequal intensity. The Mn2+ substitutes for Zn2+ and shows the spectrum of two Mn2+ complexes. The spectrum having large intensity is due to Mn2+ substituting for Zn2+ at site II while that having low intensity is due to Mn2+ at site I (Fig. 1). The Mn” centre occupying site II is more intense because there are twice as many X sites as Y sites. The principal axes of the spectra were located by searching the directions of extrema in the spread of the spectrum. It was found that the principal z-axis of two Mn2+ complexes are along the trigonal axis (c-axis) and the x-axis is perpendicular to the trigonal axis. For a field applied along the trigonal axis, each type of Mn2+ complex produces an EPR spectrum consisting of five nearly equally spaced sets of six nearly equally spaced hyperfine components. The spectra of Mn 2+ showing large zero-field splitting (site I) were measured for various angles of the magnetic field relative to the c-axis. Figure 2 shows the angular variation of the allowed fine structure transitions (AM = + 1) in the 2.x plane for site I at 298 K. It is seen from the angular variation plot in the zx plane that fine structure transition lines move rapidly as 0 changes from the z-axis. The lines collapse to a very small spread at an orientation 8 = 54.5” away from the z-axis. As 8 increases further, the lines spread out to a second maximum at 8 = 90” (x-axis). A n/3 rotational symmetry of the spectrum was observed when the crystal was rotated about the trigonal axis. The g value, however, shows no angular variation in this plane. The observed behaviour of the spectrum is consistent with original symmetry of the Zn2+ sites.
H-
Fig. 1. EPR spectrum of Mn’+ in Sm2Zn3(N03),2 - 24H,O single crystals at 298 K. The positions of the extreme hyperfine lines of Mn*+ complexes for two sites are designated by I and 11, respectively.
1537
Research Note The EPR spectrum of Mn2+ for both sites can be described by the spin-Hamiltonian
given by
GESCHWIND [2];
>+ + AZ,&
alh
+ ,,{S,[S:
exp(-3i#)
+ [S: exp(-3i$)
B (SxZx+ S,Z,)
+ S3_exp(3i@)]
+ Sl exp(3i@)]S,}
(1)
where the z-axis is parallel to the trigonal symmetry axis of the crystal. The symbols have their usual meaning and S = I = 512 for Mn2+. Using the above spin-Hamiltonian, the Mn 2+ EPR spectra were analysed and the best fit parameters thus obtained are listed in Table 1 for both sites at 298 and 77 K. The signs of the parameters given in the table are relative. Since the hyperfine splitting constant is always found to be negative for a manganese ion [3,4], this sign is taken for A in this case as well. Examination of the magnitude of the splitting of hyperfine sextets appearing at high fields and low fields when the magnetic field is parallel to the z-axis attributes a sign to the axial parameter D [5]. The values of g and A, for both the sites, are independent of temperature. The work of VAN WIERINGEN [6] shows that the magnitude of the hyperfine coupling constant depends on the amount of covalent bonding in the crystal. That is, the greater the covalent bonding the smaller will be the hyperfme splitting. Plots of the hyperfine parameter A (average hypertine coupling constant) for Mn2+ as a function of colvalency or ionicity parameters have been given for simple crystal systems by MATUMURA, HENNING, SIMANEKand MUELLER[7-91. It is well established that Mn2+ in tutton salts, fluosilicate, struvite, GASH and perchlorate, where it is surrounded by six water molecules, the average value of the hyperfine splitting constant is observed at -90.0~ 10-4cm-’ which corresponds to a covalency of 7% from the curve (hyperfine parameter vs
2500 Z-axis
I la
20
I 30
I 1 40 Q Angle (13I in deg.
Fig. 2. Angular dependence of allowed fine structke
I 60
I 70
I 80
93
X-axis
transitions (AM = f 1) of Mn’+ for site I in
the zx plane at 298 K.
1538
Research Note
Table 1. Spin-Hamiltonian parameters for Mn *+ in Sm2Zn~(N0~)i2 * 24H20 single crystals at 98 and 77 K. All the crystal field and h.f. parameters are in units of 10e4 cm-‘. Spin Hamiltonian parameters D a-F
gll 81 A B
Site I
Site II
298 K
77 K
-192.93 + 1 7.38&l 2.0020~0.001 2.0035 +0.002 -89.56+ 1 -87.81 f. 1
-222.54 It: 1 6.53 + 1 2.0002 f 0.001 2.0013 kO.002 -90.09+1 -87.44 f 1
298 K
77 K
9.35 + 1 3.02+ 1 2.0024+0.001 2.0091~0.002 -88.89f 1 -87.2+ 1
-64.38f 1 9.812 1 2.0013 f0.001 2.0070+0.002 -89.04+ 1 -88.16kl
covalency) given by SIMANCK and MUELLER[9]. The observed value of hypertine splitting in SZN: Mn2+ indicates that Mn2+ at both sites is surrounded by six water molecules since the value of A corresponds to a covalency parameter of 7% which is characteristic of the Mn2+-6HrO complex. Moreover, the linewidth of Mn2+ in SZN is of the order of 11 gauss. In hydrated crystals, an appreciable degree of line broadening of the order of 10 gauss can originate due to the local magnetic fields of the proton nuclear moments in the water molecules [lo]. From Table 1 it can be seen that the value of zero-field splitting parameter D is very different for two sites and is sensitive to temperature. The value of D increases as temperature decreases. An increase in the value of D at low temperature can probably be explained as due to thermal contraction and vibrational mechanism of the lattice [ll, 121. The differing values of D for Mn*+ at two sites indicates that the two sites differ greatly in static crystal field seen by the ions. The crystal field is presumed to be due to an octahedron of water molecules oriented with the (111) axis along the trigonal axis of the crystal, and it appears that the octahedron is nearly perfect for site II and has appreciable trigonal distortion for site I. The large difference in the D value is also observed for Ni2+ doped in LMN, LZN by GEIFMANetal. [13] and Mn2+ in CMN, CCoN, PZN, PMN by JAIN el al. [14-161. In theoretical analysis of the ground state splitting of the S-state ion it is generally recognized that more than one mechanism is required to account for the magnitude of the parameter D. A theoretical interpretation of the latter for site I was given by CHATERJEE el al. [17]. They concluded that the relativistic second-order effect of WYBOURNE [18] yields the major contribution to the value of the zero-field splitting parameter D. Their calculated values are in agreement with the observed values for site I. Acknowledgements-The
author is thankful to M. D. University, Rohtak for financial support.
JITENDER SINGHPHOR
Department of Physics M.D. Unioersity Rohtak-I24 001 India
REFERENCES
[l] A. Zalkin, J. D. Forrester and D. H. Templeton, J. Chem. Phys. 39, 2881 (1963). [2] S. Geschwind, Phys. Reo. 121, 363 (1961). [3] R. E. Watson and A. J. Freeman, Phys. Reu. 123, 2027 (1961). [4] R. J. Richardson, S. Lee and T. J. Menne, Phys. Reo. B2, 2295 (1970). [S] W. Low, ParamagneticResonance in Solids (Solid State Phys. Suppl. 2). Academic Press, New York. (61 J. S. van Wieringen, Disc. Faraday Sot. 19, 118 (19.55). [7] 0. Matumura, J. Phys. Sot. Jpn 14, 108 (1959). [8] J. C. M. Henning, Phys. Left. A24. 40 (1967). [9] E. Simanek and K. A. Mtiller, J. Phys. Chem. So/id. 31. 1027 (1970). [lo] A. Abragam and B. Bleaney, Electron Paramagmeric Resonance of Transition Ions, p. 217. Clarendon Press, Oxford. [ll] W. M. Walsh, Phys. Rev. 114, 1473 (1959). [12] I. N. Geifman and M. D. Glinchuk, Sooief Phys. Solid State 13, 872 (1971).
Research Note [13] [14] [15] [16] [17] [18]
R. V. V. V. R. B.
T. Dixon and J. W. Culvahouse, Whys. Reo. B3, 2279 (1971). P. Seth, V. K. Jain and R. S. Bansal, Phys. S&r. Solid B 129, 375 (1985). K. Jain and T. M. Sirinivasan, Parumuna 10, No. 2, 155 (1978). K. Jain and T. M. Sirinivasan, Z. Naturforsch. 32a, 665 (1977). Chatterjee, M. R. Smith and H. A. Buckmaster, Can. J. Phys. 54, 1224 (1976). G. Wybourne, Phys. Rev. 148,317 (1966).
1539
No.
10. pp.
1535-1539.
19W 0
0584-8539/9a 13.00+0.00 1990 Pergamon Press plc
RESEARCH NOTE
Electron paramagnetic resonance of Mn2+ in Sm2Zn,(N0,),, single crystals (Received
l
24H20
15 March 1990, accepted 22 April 1990)
Abstract-The X-band electron paramagnetic resonance of Mn’+ doped in Sm,Zn,(NO,),z - 24H,O single crystals has been studied. MnZ+ substitutes at two inequivalent Zn*+ sites. The spin-Hamiltonian analysis of the EPR spectra is presented at 298 and 77 K.
Electron paramagnetic resonance (EPR) studies require the presence of unpaired electrons in the sample. In general, these are not present in the pure materials but can be introduced by doping with paramagnetic substances such as transition elements, or by radiation damage. Among all the ions which exhibit EPR spectra, the d5 and f’ ions (S-state ions) are particulaly interesting when one is concerned with the local symmetry of the environment of the ion. In fact, all sublevels of the S-state are generally observed in low magnetic fields for two reasons; (a) the zero field splitting is zero to first order, and (b) only higher-order effects permit lifting of the degeneracy of the fundamental states (!S and xS). Therefore, a detailed study of the angular variation of paramagnetic resonance absorption lines permits one to establish the point symmetry around the magnetic ion. The hydrated double nitrates of the rare earth elements form an interesting series of salts for EPR studies of S-state ions. Their general formula is M:” Mq (N03),2 - 24H20, where Mu’ is a trivalent cation (Bi or an ion of the 4f group) and Ml’ is a divalent cation (Zn, Mg or an ion of the 3d group). Although the trivalent lanthanide ions are generally paramagnetic, their spin-lattice relaxation times are so much shorter than those of the S-state ions (at sufficiently high temperature) that the magnetic interaction between the paramagnetic ions and the S-state ions are averaged essentially to zero with the consequence that magnetic resonance absorption by the S-state ion can be observed without extensive broadening. In this paper we describe the EPR of Mn2+ in Sm, Zn3(NOJ),z - 24HzO(SZN) single crystals from 298 down to 77 K.
CRYSTAL STRUCTURE The crystal structure of Ce2Mg,(N03),2 - 24H20 has been determined by ZALKIN etal.[l]. The other hydrated double nitrates can be expected to have similar structures. The primitive cell containing one formula unit is rhombohedral with dimensions II= 13.165 A and a=49.37”. The space group is R3. The rhombohedral unit cell contains three divalent ions situated at two different lattice sites. One of them occupies the site with point symmetry Csi (site I or Y site) and the other two divalent ions occupy lattice sites with point symmetry C, (site II or X site). The trivalent ion is found at a site of C,i point symmetry and the positions of the rest of the atoms are consistent with the space group.
EXPERIMENTAL Single crystals of SZN doped with MnZ+ were grown by slow evaporation of an aqueous solution of Sm(NO& - 6H2O and Zn(N0,)2 +6H20, mixed in stoichiometric ratios, at room temperature. The Mn2+ impurities were introduced into the host lattices by adding a small amount (0.1 wt%) of manganese nitrate. The double nitrate grows in flat hexagonal plates, the plane of which is perpendicular to the trigonal axis. 1535
Research Note
1536
The experiments were performed on a JEOL JES-FE3X homodyne spectrometer operating at -9.45 GHz, equipped with a TE”,,-cylindrical cavity and 100 KHz field modulation. As a reference for magnetic field strength, the resonance line of DPPH with g=2.0036 was used. The crystals were mounted on quartz rods. The angular variation studies were peformed using a TES-UCR-2X sample angular rotating device. Liquid nitrogen temperature measurements were made by using an ES-UCD-2X insertion type dewar.
RESULTS AND DISCUSSION
Mn2+ has 3d5 electronic configuration and according to Hund’s rule the ground state is 6S5,,. In a crystalline field of low symmetry the ground state is split into three Kramers doublets. In a magnetic field, the degeneracy is completely removed and five fine structure transitions are possible. Due to the interaction with the nucleus of spin 5/2, each electronic transition gives rise to six hyperfine transitions. For an arbitrary orientation of the magnetic field, the EPR spectrum consists of a number of lines corresponding to allowed and forbidden transitions. Angular variation studies of Mn2+ spectra reveal the presence of two inequivalent Mn2+ centres of unequal intensity. The Mn2+ substitutes for Zn2+ and shows the spectrum of two Mn2+ complexes. The spectrum having large intensity is due to Mn2+ substituting for Zn2+ at site II while that having low intensity is due to Mn2+ at site I (Fig. 1). The Mn” centre occupying site II is more intense because there are twice as many X sites as Y sites. The principal axes of the spectra were located by searching the directions of extrema in the spread of the spectrum. It was found that the principal z-axis of two Mn2+ complexes are along the trigonal axis (c-axis) and the x-axis is perpendicular to the trigonal axis. For a field applied along the trigonal axis, each type of Mn2+ complex produces an EPR spectrum consisting of five nearly equally spaced sets of six nearly equally spaced hyperfine components. The spectra of Mn 2+ showing large zero-field splitting (site I) were measured for various angles of the magnetic field relative to the c-axis. Figure 2 shows the angular variation of the allowed fine structure transitions (AM = + 1) in the 2.x plane for site I at 298 K. It is seen from the angular variation plot in the zx plane that fine structure transition lines move rapidly as 0 changes from the z-axis. The lines collapse to a very small spread at an orientation 8 = 54.5” away from the z-axis. As 8 increases further, the lines spread out to a second maximum at 8 = 90” (x-axis). A n/3 rotational symmetry of the spectrum was observed when the crystal was rotated about the trigonal axis. The g value, however, shows no angular variation in this plane. The observed behaviour of the spectrum is consistent with original symmetry of the Zn2+ sites.
H-
Fig. 1. EPR spectrum of Mn’+ in Sm2Zn3(N03),2 - 24H,O single crystals at 298 K. The positions of the extreme hyperfine lines of Mn*+ complexes for two sites are designated by I and 11, respectively.
1537
Research Note The EPR spectrum of Mn2+ for both sites can be described by the spin-Hamiltonian
given by
GESCHWIND [2];
>+ + AZ,&
alh
+ ,,{S,[S:
exp(-3i#)
+ [S: exp(-3i$)
B (SxZx+ S,Z,)
+ S3_exp(3i@)]
+ Sl exp(3i@)]S,}
(1)
where the z-axis is parallel to the trigonal symmetry axis of the crystal. The symbols have their usual meaning and S = I = 512 for Mn2+. Using the above spin-Hamiltonian, the Mn 2+ EPR spectra were analysed and the best fit parameters thus obtained are listed in Table 1 for both sites at 298 and 77 K. The signs of the parameters given in the table are relative. Since the hyperfine splitting constant is always found to be negative for a manganese ion [3,4], this sign is taken for A in this case as well. Examination of the magnitude of the splitting of hyperfine sextets appearing at high fields and low fields when the magnetic field is parallel to the z-axis attributes a sign to the axial parameter D [5]. The values of g and A, for both the sites, are independent of temperature. The work of VAN WIERINGEN [6] shows that the magnitude of the hyperfine coupling constant depends on the amount of covalent bonding in the crystal. That is, the greater the covalent bonding the smaller will be the hyperfme splitting. Plots of the hyperfine parameter A (average hypertine coupling constant) for Mn2+ as a function of colvalency or ionicity parameters have been given for simple crystal systems by MATUMURA, HENNING, SIMANEKand MUELLER[7-91. It is well established that Mn2+ in tutton salts, fluosilicate, struvite, GASH and perchlorate, where it is surrounded by six water molecules, the average value of the hyperfine splitting constant is observed at -90.0~ 10-4cm-’ which corresponds to a covalency of 7% from the curve (hyperfine parameter vs
2500 Z-axis
I la
20
I 30
I 1 40 Q Angle (13I in deg.
Fig. 2. Angular dependence of allowed fine structke
I 60
I 70
I 80
93
X-axis
transitions (AM = f 1) of Mn’+ for site I in
the zx plane at 298 K.
1538
Research Note
Table 1. Spin-Hamiltonian parameters for Mn *+ in Sm2Zn~(N0~)i2 * 24H20 single crystals at 98 and 77 K. All the crystal field and h.f. parameters are in units of 10e4 cm-‘. Spin Hamiltonian parameters D a-F
gll 81 A B
Site I
Site II
298 K
77 K
-192.93 + 1 7.38&l 2.0020~0.001 2.0035 +0.002 -89.56+ 1 -87.81 f. 1
-222.54 It: 1 6.53 + 1 2.0002 f 0.001 2.0013 kO.002 -90.09+1 -87.44 f 1
298 K
77 K
9.35 + 1 3.02+ 1 2.0024+0.001 2.0091~0.002 -88.89f 1 -87.2+ 1
-64.38f 1 9.812 1 2.0013 f0.001 2.0070+0.002 -89.04+ 1 -88.16kl
covalency) given by SIMANCK and MUELLER[9]. The observed value of hypertine splitting in SZN: Mn2+ indicates that Mn2+ at both sites is surrounded by six water molecules since the value of A corresponds to a covalency parameter of 7% which is characteristic of the Mn2+-6HrO complex. Moreover, the linewidth of Mn2+ in SZN is of the order of 11 gauss. In hydrated crystals, an appreciable degree of line broadening of the order of 10 gauss can originate due to the local magnetic fields of the proton nuclear moments in the water molecules [lo]. From Table 1 it can be seen that the value of zero-field splitting parameter D is very different for two sites and is sensitive to temperature. The value of D increases as temperature decreases. An increase in the value of D at low temperature can probably be explained as due to thermal contraction and vibrational mechanism of the lattice [ll, 121. The differing values of D for Mn*+ at two sites indicates that the two sites differ greatly in static crystal field seen by the ions. The crystal field is presumed to be due to an octahedron of water molecules oriented with the (111) axis along the trigonal axis of the crystal, and it appears that the octahedron is nearly perfect for site II and has appreciable trigonal distortion for site I. The large difference in the D value is also observed for Ni2+ doped in LMN, LZN by GEIFMANetal. [13] and Mn2+ in CMN, CCoN, PZN, PMN by JAIN el al. [14-161. In theoretical analysis of the ground state splitting of the S-state ion it is generally recognized that more than one mechanism is required to account for the magnitude of the parameter D. A theoretical interpretation of the latter for site I was given by CHATERJEE el al. [17]. They concluded that the relativistic second-order effect of WYBOURNE [18] yields the major contribution to the value of the zero-field splitting parameter D. Their calculated values are in agreement with the observed values for site I. Acknowledgements-The
author is thankful to M. D. University, Rohtak for financial support.
JITENDER SINGHPHOR
Department of Physics M.D. Unioersity Rohtak-I24 001 India
REFERENCES
[l] A. Zalkin, J. D. Forrester and D. H. Templeton, J. Chem. Phys. 39, 2881 (1963). [2] S. Geschwind, Phys. Reo. 121, 363 (1961). [3] R. E. Watson and A. J. Freeman, Phys. Reu. 123, 2027 (1961). [4] R. J. Richardson, S. Lee and T. J. Menne, Phys. Reo. B2, 2295 (1970). [S] W. Low, ParamagneticResonance in Solids (Solid State Phys. Suppl. 2). Academic Press, New York. (61 J. S. van Wieringen, Disc. Faraday Sot. 19, 118 (19.55). [7] 0. Matumura, J. Phys. Sot. Jpn 14, 108 (1959). [8] J. C. M. Henning, Phys. Left. A24. 40 (1967). [9] E. Simanek and K. A. Mtiller, J. Phys. Chem. So/id. 31. 1027 (1970). [lo] A. Abragam and B. Bleaney, Electron Paramagmeric Resonance of Transition Ions, p. 217. Clarendon Press, Oxford. [ll] W. M. Walsh, Phys. Rev. 114, 1473 (1959). [12] I. N. Geifman and M. D. Glinchuk, Sooief Phys. Solid State 13, 872 (1971).
Research Note [13] [14] [15] [16] [17] [18]
R. V. V. V. R. B.
T. Dixon and J. W. Culvahouse, Whys. Reo. B3, 2279 (1971). P. Seth, V. K. Jain and R. S. Bansal, Phys. S&r. Solid B 129, 375 (1985). K. Jain and T. M. Sirinivasan, Parumuna 10, No. 2, 155 (1978). K. Jain and T. M. Sirinivasan, Z. Naturforsch. 32a, 665 (1977). Chatterjee, M. R. Smith and H. A. Buckmaster, Can. J. Phys. 54, 1224 (1976). G. Wybourne, Phys. Rev. 148,317 (1966).
1539