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On quadrupolar effects in alloys
170
LETTERS
TO
field will be expelled by the Meissner effect and the conditions for resonance at least partially restored. The degree of restoration will provide information related to the Matthias-Suhl model of ferromagnetic superconductors. (14) While the experiment may be marginally possible in an ordinary superconductor using a suitably chosen isotope, (e.g. 237) the effect will be largest in a ferromagnetic superconductor. In ordinary superconductors the magnetic field required to affect nuclear resonance will exceed the superconducting critical field. We are presently attempting to increase the sensitivity of nuclear resonance as a probe through the use of resonance scattering of narrow gamma rays. It appears likely that a probe for superconductors may be made with a sensitivity approaching that which the Knight shift provides in ordinary materials. Acknowledgements-We wish to thank B. MATTHIASfor several discussions and for suggesting various compounds and J. G. DASH for a number of discussions. The aid of the Omega West reactor group in source activation is acknowledged.
University of California Las Alamos Scienti$c Laboratory Los Alamos New Mexico
P. P. CRAIG D. E. NAGLE R. D. REISWIG
References 1. M~SSBAUER R. L., 2. Phys. 151, 124 (1958); Nuturwissenschaften 45, 538 (1958); 2 Naturf. 14a, 211 (1959). 2. CRAIGP. P., DASH J. G., MCGUIRE A. D., NACLE D. E. and REISWIGR. D., Phys. Rev. Letters 3, 221 (1959). 3. LEE L. L., Jr., MEYER-SCHUTZMEISTER L., SCHIFFER J. P. and VINCENTD., Phys. Rev. Letters 3, 223 (1959). 4. NACLE D. E., CRAIG P. P. and KELLER W. E., Nature, Lond. 186, 707 (1960); CRAIG P. P., NAGLED. E. and COCHFUND. R. F., Phys. Rev. Letters 4, 561 (1960). 5. POUNDR. V. and REBKAG. A., Phys. Rev. Letters 4, 274 (1960). 6. COOPERL. N., Amer. J. Phys. 28, 91 (1960). 7. NAGLED. E., CRAIGP. P., DASHJ. G. and REISWIG R. D., Phys. Rew. Letters 4, 237 (1960). 8. LIPKIN H., Ann. Phys. 9, 332 (1960). 9. SHOENBERC D., Nature, Lond. 142, 874 (1938). 10. MATTH~AS B. T., Progress in Low Temperature Physics (edited by GORTERC. J.) Vol. II. North Holland Publishing Company, Amsterdam (1957).
THE
EDITOR
11. POUND R. V. and REBKA G. A., Jr., Phys. Rev. Letters 3, 439 (1959). 12. PERLOW G. J., HANNA S. S., HAMERMESHM., LITTLEJOHN C., VINCENTD. H., PRF~TONR. S. and HEBERLB J., Phys. Rev. Letters 4, 74 (1960). 13. MATTHIASB. T., SUHL H. and CORENZWIT E., Phys. Rev. Letters 1, 449 (1958). 14. MATTHIASB. T. and SUHL A., Phys. Rev. Letters 3, 51 (1960).
On quadrupolar (Received
effects 15 Match
in alloys 1960)
IN A paper to appear shortly KOHN and VOSKO(~) explain the field gradients produced at the copper nuclei in the copper base alloys as due to the oscillating fluctuations of electronic density around the solute atoms. Their conclusions are in agreement with ROWLAND’S experimental workti) on a series of copper base alloysI We wish to point out that we reached independently the same conclusions. Our work will be published in J. Phys. Radium.@) It was initiated by the study of N.M.R. in cold worked copper done by AVERBUCH et al.@, who found a /\factor of enhancement for elastic strain of the order of unity, against the value of 60 proposed by BLOEMBERGEN. This result shows that the size effects cannot predominate in producing field gradients in alloys; it is in agreement with ROWLAND’S measurements(s) which were not known to us. We
have analysed the previous
measurements
on Al base alloys: around each solute atom there are variations of electronic density decreasing in y-3 from the
by
BLOEMBERGEN and
ROWLAND(~)
solute atom, as was pointed out by FRIEDEL(~). To compute
the field gradients we take into account
the periodic
structure
the Wigner-Seitz
by a simple
extension
of
method(T) in the presence of a
solute atom; the free electron results for the field gradient,
a
cos
(2kF + 4) Y3
’
(where a and + depend only on the scattering at the Fermi surface) are then simply multiplied by a factor p which depends only on the matrix. The value of pit obtained with orthogonalized plane waves is 5, while a value of 15 is needed to explain
LETTERS
TO
THE
171
EDITOR
him to give what I believe to be the correct disposition of the Fermi surface within the Brillouin zone. It does, on the other hand, give another rather striking example of the insight that can be obtained by this very simple approach, and an illustration of the procedure for a case in which the lattice potential is quite important. What KOHN’S. follows is a brief summary of this treatment. The single-OPW Fermi surface has been conThe main result of this study is to emphasize the importance of the long-range oscillations of structed according to the procedures discussed electronic density., which can perturb the elecpreviously. (G-J)The single-OPW sphere contains tronic density at large distances from the solute 10 electrons, since there are two pentavalent atoms per cell; this gives rise to segments of surface atom. This confirms the results already obtained in the Knight shift of dilute alloys.@) in bands 2-8. We expect that under the combined influence of the potential and of spin-orbit Service de Physique des Solides coupling this will be reduced to segments surA. BLANDIN B.P. 11 rounding electrons in the sixth band and holes in J. FRIEDEL Facultk d’ Orsay the fifth, so we are interested only in the surface (S. et 0.) in these two bands. A section of these surfaces is France shown in Fig. 1. The electron Fermi surface is expected to arise from either the surface B or the surface C. Experimentally it is known that the References electron surface is elongated and is tipped slightly 1. KOHN W. and VOSKO S. H., Phys. Rev. 119, 912 out of a plane perpendicular to the c-axis. It is (1960). clear from the symmetry of the point B that the 2. ROWLANDT. J., Phys. Rev. 119, 900 (1960). 3. BLANDINA. and FRIEDEL J., to be published. addition of a potential and spin-orbit coupling 4. A~ERB~CH P., DE BEREGEVIN F. and MUELLERcould not give rise to such segments there, while
the experimental results. In view of the approximations made this result can be considered to be satisfactory. Our paper analyses the underlying assumptions in the use of the Wigner-Seitz approximation and in the computation of the field gradients. Our final method and results are essentially the same as
5. 6. 7. 8.
WARMUTH W., C.R. Acad. Sci., Paris 249, 2315 (1959). BLOEMBERCENN. and ROWLAND T. J., Acta Met. 1, 731 (1953). FRIEDEL J., Phil. Mug. 43, 153 (1952). ROTH L. M., Thesis, Harvard University (1957). BLANDIN A. and DANIEL E., J. Phys. Chem. Solids 10, 126 (1959).
Bismuth (Received
Fermi 22 March
1C-AXIS
surface 1960)
As AN ADDENDUM to the work on the single-OPW approximation in polyvalent metals,(l) a preliminary study of bismuth has been made. This does not add any striking new information on bismuth, partly because of the very extensive experimental work@-@ which has given a great deal of information on the subject, partly because failure to include spin-orbit coupling explicitly leads to appreciable uncertainties, and partly because recent band calculations on bismuth by MASE(‘) have allowed
FIG. 1. Sections of the Fermi surface in the fifth and sixth bands according to the single-OPW approximation. The dashed lines give the outline of the Brillouin zone. The segments of surface are continued out of the reduced zone in order to give a better picture of their shape and connectivity. The section shown contains the c-axis and a principal reciprocal lattice vector.
LETTERS
TO
field will be expelled by the Meissner effect and the conditions for resonance at least partially restored. The degree of restoration will provide information related to the Matthias-Suhl model of ferromagnetic superconductors. (14) While the experiment may be marginally possible in an ordinary superconductor using a suitably chosen isotope, (e.g. 237) the effect will be largest in a ferromagnetic superconductor. In ordinary superconductors the magnetic field required to affect nuclear resonance will exceed the superconducting critical field. We are presently attempting to increase the sensitivity of nuclear resonance as a probe through the use of resonance scattering of narrow gamma rays. It appears likely that a probe for superconductors may be made with a sensitivity approaching that which the Knight shift provides in ordinary materials. Acknowledgements-We wish to thank B. MATTHIASfor several discussions and for suggesting various compounds and J. G. DASH for a number of discussions. The aid of the Omega West reactor group in source activation is acknowledged.
University of California Las Alamos Scienti$c Laboratory Los Alamos New Mexico
P. P. CRAIG D. E. NAGLE R. D. REISWIG
References 1. M~SSBAUER R. L., 2. Phys. 151, 124 (1958); Nuturwissenschaften 45, 538 (1958); 2 Naturf. 14a, 211 (1959). 2. CRAIGP. P., DASH J. G., MCGUIRE A. D., NACLE D. E. and REISWIGR. D., Phys. Rev. Letters 3, 221 (1959). 3. LEE L. L., Jr., MEYER-SCHUTZMEISTER L., SCHIFFER J. P. and VINCENTD., Phys. Rev. Letters 3, 223 (1959). 4. NACLE D. E., CRAIG P. P. and KELLER W. E., Nature, Lond. 186, 707 (1960); CRAIG P. P., NAGLED. E. and COCHFUND. R. F., Phys. Rev. Letters 4, 561 (1960). 5. POUNDR. V. and REBKAG. A., Phys. Rev. Letters 4, 274 (1960). 6. COOPERL. N., Amer. J. Phys. 28, 91 (1960). 7. NAGLED. E., CRAIGP. P., DASHJ. G. and REISWIG R. D., Phys. Rew. Letters 4, 237 (1960). 8. LIPKIN H., Ann. Phys. 9, 332 (1960). 9. SHOENBERC D., Nature, Lond. 142, 874 (1938). 10. MATTH~AS B. T., Progress in Low Temperature Physics (edited by GORTERC. J.) Vol. II. North Holland Publishing Company, Amsterdam (1957).
THE
EDITOR
11. POUND R. V. and REBKA G. A., Jr., Phys. Rev. Letters 3, 439 (1959). 12. PERLOW G. J., HANNA S. S., HAMERMESHM., LITTLEJOHN C., VINCENTD. H., PRF~TONR. S. and HEBERLB J., Phys. Rev. Letters 4, 74 (1960). 13. MATTHIASB. T., SUHL H. and CORENZWIT E., Phys. Rev. Letters 1, 449 (1958). 14. MATTHIASB. T. and SUHL A., Phys. Rev. Letters 3, 51 (1960).
On quadrupolar (Received
effects 15 Match
in alloys 1960)
IN A paper to appear shortly KOHN and VOSKO(~) explain the field gradients produced at the copper nuclei in the copper base alloys as due to the oscillating fluctuations of electronic density around the solute atoms. Their conclusions are in agreement with ROWLAND’S experimental workti) on a series of copper base alloysI We wish to point out that we reached independently the same conclusions. Our work will be published in J. Phys. Radium.@) It was initiated by the study of N.M.R. in cold worked copper done by AVERBUCH et al.@, who found a /\factor of enhancement for elastic strain of the order of unity, against the value of 60 proposed by BLOEMBERGEN. This result shows that the size effects cannot predominate in producing field gradients in alloys; it is in agreement with ROWLAND’S measurements(s) which were not known to us. We
have analysed the previous
measurements
on Al base alloys: around each solute atom there are variations of electronic density decreasing in y-3 from the
by
BLOEMBERGEN and
ROWLAND(~)
solute atom, as was pointed out by FRIEDEL(~). To compute
the field gradients we take into account
the periodic
structure
the Wigner-Seitz
by a simple
extension
of
method(T) in the presence of a
solute atom; the free electron results for the field gradient,
a
cos
(2kF + 4) Y3
’
(where a and + depend only on the scattering at the Fermi surface) are then simply multiplied by a factor p which depends only on the matrix. The value of pit obtained with orthogonalized plane waves is 5, while a value of 15 is needed to explain
LETTERS
TO
THE
171
EDITOR
him to give what I believe to be the correct disposition of the Fermi surface within the Brillouin zone. It does, on the other hand, give another rather striking example of the insight that can be obtained by this very simple approach, and an illustration of the procedure for a case in which the lattice potential is quite important. What KOHN’S. follows is a brief summary of this treatment. The single-OPW Fermi surface has been conThe main result of this study is to emphasize the importance of the long-range oscillations of structed according to the procedures discussed electronic density., which can perturb the elecpreviously. (G-J)The single-OPW sphere contains tronic density at large distances from the solute 10 electrons, since there are two pentavalent atoms per cell; this gives rise to segments of surface atom. This confirms the results already obtained in the Knight shift of dilute alloys.@) in bands 2-8. We expect that under the combined influence of the potential and of spin-orbit Service de Physique des Solides coupling this will be reduced to segments surA. BLANDIN B.P. 11 rounding electrons in the sixth band and holes in J. FRIEDEL Facultk d’ Orsay the fifth, so we are interested only in the surface (S. et 0.) in these two bands. A section of these surfaces is France shown in Fig. 1. The electron Fermi surface is expected to arise from either the surface B or the surface C. Experimentally it is known that the References electron surface is elongated and is tipped slightly 1. KOHN W. and VOSKO S. H., Phys. Rev. 119, 912 out of a plane perpendicular to the c-axis. It is (1960). clear from the symmetry of the point B that the 2. ROWLANDT. J., Phys. Rev. 119, 900 (1960). 3. BLANDINA. and FRIEDEL J., to be published. addition of a potential and spin-orbit coupling 4. A~ERB~CH P., DE BEREGEVIN F. and MUELLERcould not give rise to such segments there, while
the experimental results. In view of the approximations made this result can be considered to be satisfactory. Our paper analyses the underlying assumptions in the use of the Wigner-Seitz approximation and in the computation of the field gradients. Our final method and results are essentially the same as
5. 6. 7. 8.
WARMUTH W., C.R. Acad. Sci., Paris 249, 2315 (1959). BLOEMBERCENN. and ROWLAND T. J., Acta Met. 1, 731 (1953). FRIEDEL J., Phil. Mug. 43, 153 (1952). ROTH L. M., Thesis, Harvard University (1957). BLANDIN A. and DANIEL E., J. Phys. Chem. Solids 10, 126 (1959).
Bismuth (Received
Fermi 22 March
1C-AXIS
surface 1960)
As AN ADDENDUM to the work on the single-OPW approximation in polyvalent metals,(l) a preliminary study of bismuth has been made. This does not add any striking new information on bismuth, partly because of the very extensive experimental work@-@ which has given a great deal of information on the subject, partly because failure to include spin-orbit coupling explicitly leads to appreciable uncertainties, and partly because recent band calculations on bismuth by MASE(‘) have allowed
FIG. 1. Sections of the Fermi surface in the fifth and sixth bands according to the single-OPW approximation. The dashed lines give the outline of the Brillouin zone. The segments of surface are continued out of the reduced zone in order to give a better picture of their shape and connectivity. The section shown contains the c-axis and a principal reciprocal lattice vector.