- Email: [email protected]
The electric field gradient at Ta in HfB2
J. Phys. Chem. Solids, 1973, Vol. 34. pp. 2025-2028. Pergamon Press. Printed in Great Britain
THE ELECTRIC FIELD GRADIENT AT Ta IN HfB2 E. N. KAUFMANN Bell Laboratories, M u r r a y Hill, N.J. 07974, U.S.A. (Received 26 February 1973)
Abstract--Using the time-differential perturbed-angular correlation technique, we have o b s e r v e d the nuclear electric quadrupole interaction at 18'Ta (482 keV) as an impurity in the refractory c o m p o u n d HfB:. T h e m e a s u r e d interaction f r e q u e n c y is vo =730-+ 5 M H z which c o r r e s p o n d s to an electric field gradient of leql = (1.19-+0-05) x 10 ~8V / c m 2 at r o o m temperature. By considering a second m e a s u r e m e n t at 4.2~ which yields the s a m e result as above, and by comparison with available results for H f in HfB2, we conclude that t h e d-electron density of states at the Fermi level is quite sr0all in a g r e e m e n t with trends o b s e r v e d by others. 1. I N T R O D U C T I O N
THE TRANSmON-metal diborides form an isostructural series displaying the hexagonal C32 structure (typified by A1B2)[1]. Measurements of electrical and thermal conductivities and of Hall coefficients[2] have shown that these materials are metallic. Several other properties, however, including high melting points and brittleness resemble those of ceramic materials [3]. Because of this interesting combination of macroscopic properties, the diborides have been the subject of several studies intended to reveal their underlying electronic structure. Systematic trends have been observed in the bulk transport properties as well as in the electronic specific heats, magnetic susceptibilities and nuclear electric quadrupole interactions and Knight shifts at ttB[2,4-6]. The several interpretations of these results are at variance regarding the role played by the boron valence electrons. Some proposals favor the transfer of an electron to the boron to form a B- ion with appropriately hybridized wave functions for the resulting four valence electrons [5] while others suggest that the boron donates three valence electrons to metallic bands[2]. One obser:cation common to all investigation is the progressive addition of electrons to a conduction band as the group number of the transition-metal atom
rises from IV to V and from V to VI. Although an early suggestion[2] proposed s-orbital character for the main conduction band, more recent work[5,6] favors a d-like conduction band. The group IV transition-metal diborides are thought to have a nearly empty conduction band while still being of metallic character. During the course of a study[7], using the time-differential perturbed-angular-correlation (TDPAC) technique[8], to measure the electric quadrupole interaction at lg'Ta [482 keV, I = 5/2 level] in the group IVB metals, we took the opportunity to do the same in the diboride of hafnium. Our results support the notion that in HfB2 no significant occupation of a d-like conduction band is present. 2. EXPERIMENT AND RESULTS prepared by heating a mixture of Hf and B, in the appropriate stoichiometric ratio, with an A1 metal flux to 1550~ for 10 rain followed by rapid cooling. The Hf compound was then extracted by leaching out the A1 with hot NaOH. X-ray powder diffraction analysis indicated that over 90 per cent of the sample was the desired compound, the remainder being unidentified. The samples were irradiated with pile neutrons to form the ~8~Hf radioisotope needed for the TDPAC experiment. The details of the experimental system
2025
HfB2 was
2026
E.N. KAUFMANN
and of the method of data analysis h a v e been presented elsewhere[7]. Data was acquired for sample t e m p e r a t u r e s of 296 and 4.2~ A typical data set showing the experimental T D P A C anisotropy vs time is s h o w n in Fig. 1 along with a theoretical curve which resulted f r o m a least-squares fit to the data. In the
1
T
T
~
The least-squares fits showed some evidence of a small axial a s y m m e t r y in the interaction as well as a n a r r o w ( - 8 % ) distribution of frequencies a b o u t the fitted value. T h e s e effects were m o s t evident in the low t e m p e r a t u r e data. T h e y h a v e been attributed to strain in the sample, the p r e s e n c e of a small amount of a second phase, and possibly to a slight b o r o n deficiency in the phase of interest.
n"--'-
3. DISCUSSION One interesting f e a t u r e of our results is the absence of a significant t e m p e r a t u r e dependence in vQ. Since the thermal expansion coefficients of the diborides are e x p e c t e d to be smaller and more isotopic than those of the -0A corresponding metals [2], this result might be expected so far as the contribution of the lattice ionic charges to e q is concerned. It also indicates, however, that the electrons at the Fermi level, which can redistribute them-0.2 selves a m o n g states of different spatial symm e t r y as the t e m p e r a t u r e changes, are very f e w (i.e. low density of states at the Fermi level) and/or are in states of spherical (s) orbi20 30 4 0 50 0 I0 TIME (nsec) tal character. F o r the analogous case of Ta in Fig. 1. Experimental time spectrum for the TDPAC H f metal, there is a significant t e m p e r a t u r e deanisotropy with the nuclear decay factor removed. The pendence in eq b e y o n d that ascribed to lattice solid curve resulted from a least-squares fit to the data. constant changes [7]. This is consistent with the well-known electronic characteristics of figure, the nuclear d e c a y factor has b e e n re- transition metals which include a high density m o v e d f r o m both the data and the theoretical of states at the Fermi level and a d-type concurve. The quadrupole interaction frequencies duction band. vo = e 2 q Q / h extracted f r o m the data w e r e vo = Additional evidence in support of the a b o v e 730-+5 M H z and v0=719--- 10 M H z f o r sam- interpretation arises f r o m a c o m p a r i s o n of our ple t e m p e r a t u r e s of 296 and 4.2~ respec- result for T a in HfB2 with one reported for H f tively. Thus, within the statistical errors, no in HfB2 b y Boolchand et al. [10] w h o have apt e m p e r a t u r e d e p e n d e n c e of vo was observed. plied the M 6 s s b a u e r effect to ~7SHf. Their B y inserting the k n o w n value of the nuclear value of e 2 q Q = - 2.25-+0.03/zeV, which quadrupole m o m e n t [9] of Q(482 keV) = corresponds to v Q = - 5 4 7 _+13 M H z , trans2.53• and using the weighted average lates into a value for eq of +(1.17-+0.04)• of the results quoted above, we find leq(Ta 10 TM V]cm 2 w h e n the quadrupole moment[11], in H f B 2 ) [ = ( 1 - 1 9 - 0 . 0 5 ) • 10 ~s V / c m 2. As an Q = - l . 9 3 + - 0 . 0 5 b , of the 9 3 - 2 k e V state of additional check on our analysis, the time- t78Hf is used. We note that this value of eq for domain data was Fourier transformed. Only H f equals the value quoted a b o v e for the T a the fundamental interaction f r e q u e n c y quoted impurity, within the stated errors, and m a y be a b o v e and its harmonics were evident. contrasted with the analogous case of metal
1
THE ELECTRIC FIELD GRADIENT AT Ta IN HfB2 hosts where the field gradient at H f in H f metal [ 11, 12] is nearly twice that found for Ta in H f metal[9, 13]. The effect in the metal can be attributed to charge screening[14, 15] of a Ta 5+ ion which represents an impurity charge of AZ = +1. Since the screening is accomplished by d-electrons at the Fermi level, the density of non-spherical electron charge about the Ta impurity would be significantly different f r o m that about a host H f ion. As mentioned earlier, it is known that the substitution of group V transition metals into the group IV diborides adds electrons to the conduction band. Thus it is reasonable to assume that Ta in HfB2 represents an impurity charge of AZ = +1 and that charge screening should occur. The equality of eq(Ta) to eq(Hf) in the diboride then again suggests a dearth of electrons at the Fermi level and/or that only selectrons are available for charge screening. This conclusion is in qualitative agreement with recent theoretical work on the diborides [ 16]. In order to have some r e f e r e n c e with which to compare the measured magnitudes of uo, a point-ion lattice sum calculation is useful. The appropriate sums have been evaluated for the C32 structure-type b y K a u f m a n n and McWhan[7] who based their calculations on the work of de Wette and Schacher[17]. The basis of such a calculation lies in the assignment of specific ionic charges to each occupied lattice site in the unit cell and the assumption of a uniform background of electronic charge with density chosen to render the unit cell electrically neutral. Lacking knowledge of the appropriate effective ionic charges to be associated with the H f and B sites in HfB2, we will simply denote these as Z ( H f ) and Z(B), respectively, and assume they represent the net charge contained within spherical volumes centered at the lattice points. The resulting relations for the "ionic" electric field gradients at the H f and B sites are eqi~176 = [ - 0-94Z(Hf) +3-53Z(B)] • 1016V/cm 2
(la)
2027
and eqi~
= [1.76Z(Hf) - 7 . 6 6 Z ( B ) ] • 10 ~ V/cm 2 (lb)
respectively, where lattice constants of a = 3.141A and c / a = 1.10 were used[18]. It is reasonable to assume that the charge parameters lie in the ranges 0--Z(Hf)--<4 and -1--< Z(B) ~ 3. Once the experimental field gradients quoted earlier are divided by the Sternheimer antishielding factors [19] of (1 - ~ ) ~ 6 2 for Ta or (1 - ~ ) ~ 6 9 for Hf, it can be seen that they yield field gradients external to the ion core in question of comparable size to that indicated in equation (la). In fact, since the sign of eq at H f in HfB2 is known to be positive [10], we see that the values of Z ( H f ) - ~ + 2 and Z ( B ) ~ + I would be necessary in equation (la) to explain the observation entirely in terms of the pointion lattice contribution. T o our knowledge, the quadrupole interaction at "B in HfB~ has not been measured. Equation (lb) does however agree in order of magnitude with measurements [5] on X~B in ZrB2 once the Sternheimer factor[19] (which is a shielding factor for boron) is accounted for. Some support for the value Z ( B ) ~ + 1 has in fact been provided by the low temperature specific heat study of Tyan et al. [20]. The rather nai've picture presented above can account, at least in a phenomenological way, for the effects of electronic and ionic charges at points distant from the nucleus under study. It completely ignores however the distribution of electronic charge in the Wigner-Seitz cell containing the nucleus in question. The bonding in the diborides is most likely of highly covalent and directional nature. It is therefore probable that the local electronic configuration about the constituent atoms is not spherically symmetric and does contribute to the observed electric quadrupole interactions. Nevertheless, comparison with the point-ion lattice sum result may be a convenient artifice for revealing systematic trends among the diborides. Unfortunately, aside
2028
E.N. KAUFMANN
from the case of HfB2 presented here, the metal site quadrupole interaction has only b e e n o b s e r v e d i n S c B 2 [6] a n d V B 2 [5]. F u r t h e r measurements in these compounds would be of considerable value toward understanding their electronic structure.
Note added in proof: In a recent report by Hass and Shirley (J. chem. Phys. 58, 3339 (1973)) a value of 7 2 0+19 MHz is given for the quadrupole interaction frequency of '~'Ta (482 keV) in HfB2 in excellent agreement with the value quoted here. Acknowledgements--We would like to thank P. H. Schmidt and R. N. Castellano for help with sample preparation and A. S. Cooper for X-ray diffraction analysis. M. L. Thomson provided~assistance in the analysis of the data. We are also grateful to Dr. A. C. Gossard, Dr. P. Boolchand and Dr. G. C. Carter for helpful discussions regarding the diborides.
8.
9.
10. 11. 12. 13.
REFERENCES
1. W E R N I C K J. H. In: lntermetallic Compounds (Edited by J. H. Westbrook), p. 212. Wiley, New York (1967); GOLDSCHMIDT H. J., Interstitial Alloys, p. 254. Plenum Press, New York (1967). 2. JURETSCHKE H. J. and STEINITZ R., J. Phys. Chem. Solids 4, 118 (1958). 3. STEINITZ R. In: Fundamentals of Refradtory Compounds (Edited by H. H. Hausner and M. G. Bowman), p. 155. Plenum Press, New York (1968); POST B., GLASER F. W. and MOSKOWITZ D., Acta Met. 2, 20 (1954). 4. MALYUCHKOV O. T. and POVITSKII V. A., Fiz. Met. i Metalloved 13, 676 (1962) [translated in Phys. Metals Metallogr. 13, 38 (1962)]. 5. SILVER A. H. and BRAY P. J., J. chem. Phys. 32, 288 (1960); SILVER A. H. and KUSHIDA T., J. chem. Phys. 38, 865 (1963). 6. CARTER G. C. and SWARTZ J. C., J. Phys. Chem. Solids 32, 2415 (1971). 7. K A U F M A N N E. N., Phys. Rev. B 8 (Aug. 1973); and
14. 15.
16.
17. 18. 19. 20.
KAUFMANN E. N. and McWHAN D. B., Phys. Rev. B 8 (Aug. 1973). FRAUENFELDER H. and STEFFEN R. M. In: Alpha-, Beta- and Gamma-Ray Spectroscopy (Edited by K. Siegbahn), Vol. II, p. 997. North Holland, Amsterdam (1965). SOMMERFELDT R. W., CANNON T. W., COLEMAN L. W. and SCHECTER L., Phys. Rev. 138, B763 (1965); STELSON P. H. and McGOWAN F. K., Phys. Rev. 105, 1346 (1957). BOOLCHAND P., LIN C. L., JHA S. and KOUCKY F. L., International Conf. on Applications of the Mfssbauer Effect, Israel (1972). BOOLCHAND P., ROBINSON B. L. and JHA S., Phys. Rev. 187, 475 (1969). BOOLCHAND P., LANGHAMMER D., LIN C. L. and JHA S., Phys. Rev. C6, 1093 (1972). See for example: KAINDL G. and SALOMON D., Phys. Lett. 40A, 179 (1972); GERDAU E., WOLF J., WINKLER H. and BRAUNSFURTH J., Proc. Roy. Soc. A311, 197 (1969); and LIEDER R. N., BUTTLER N., KILLIG K., BECK K. and BODENSTEDT E. In: Hyperline Interactions in Excited Nuclei (Edited by G. Goldring and R. Kalish), Vol. lI, p. 449. Gordon and Breach, London (1971). FRIEDEL J., Adv. Phys. 3, 446 (1954); Nuovo Cim. 7, 287 (1958); J. Phys. Rad. 23, 692 (1962). DANIEL E. In: HyperIine Interactions (Edited by A. J. Freeman and R. B. Frankel), p. 712. Academic Press, New York (1967). (Also see in the same volume the chapter by WATSON R. E. on p. 413). CARTER F. L., NBS special publication 364, Solid State Chemistry, Proc. 5th Materials Research Symposium (July 1972) pp. 515-559; and McALISTER A. J., CUTHILL J. R., WILLIAMS M. L. and DOBBYN R. C., preprint. DE WETTE F. W. and SCHACHER G. E., Phys. Rev. 137, A78 and A92 (1965). ARONSSON B. In: Modern Materials (Edited by H. H. Hausner), Vol. 2, p. 143. Academic Press, New York (1960). FEIOCK F. D. and JOHNSON W. R., Phys. Rev. 187, 39 (1969) and references therein. TYAN Y. S., TOTH L. E. and CHANG Y. A., J. Phys. Chem. Solids 30, 785 (1969).
THE ELECTRIC FIELD GRADIENT AT Ta IN HfB2 E. N. KAUFMANN Bell Laboratories, M u r r a y Hill, N.J. 07974, U.S.A. (Received 26 February 1973)
Abstract--Using the time-differential perturbed-angular correlation technique, we have o b s e r v e d the nuclear electric quadrupole interaction at 18'Ta (482 keV) as an impurity in the refractory c o m p o u n d HfB:. T h e m e a s u r e d interaction f r e q u e n c y is vo =730-+ 5 M H z which c o r r e s p o n d s to an electric field gradient of leql = (1.19-+0-05) x 10 ~8V / c m 2 at r o o m temperature. By considering a second m e a s u r e m e n t at 4.2~ which yields the s a m e result as above, and by comparison with available results for H f in HfB2, we conclude that t h e d-electron density of states at the Fermi level is quite sr0all in a g r e e m e n t with trends o b s e r v e d by others. 1. I N T R O D U C T I O N
THE TRANSmON-metal diborides form an isostructural series displaying the hexagonal C32 structure (typified by A1B2)[1]. Measurements of electrical and thermal conductivities and of Hall coefficients[2] have shown that these materials are metallic. Several other properties, however, including high melting points and brittleness resemble those of ceramic materials [3]. Because of this interesting combination of macroscopic properties, the diborides have been the subject of several studies intended to reveal their underlying electronic structure. Systematic trends have been observed in the bulk transport properties as well as in the electronic specific heats, magnetic susceptibilities and nuclear electric quadrupole interactions and Knight shifts at ttB[2,4-6]. The several interpretations of these results are at variance regarding the role played by the boron valence electrons. Some proposals favor the transfer of an electron to the boron to form a B- ion with appropriately hybridized wave functions for the resulting four valence electrons [5] while others suggest that the boron donates three valence electrons to metallic bands[2]. One obser:cation common to all investigation is the progressive addition of electrons to a conduction band as the group number of the transition-metal atom
rises from IV to V and from V to VI. Although an early suggestion[2] proposed s-orbital character for the main conduction band, more recent work[5,6] favors a d-like conduction band. The group IV transition-metal diborides are thought to have a nearly empty conduction band while still being of metallic character. During the course of a study[7], using the time-differential perturbed-angular-correlation (TDPAC) technique[8], to measure the electric quadrupole interaction at lg'Ta [482 keV, I = 5/2 level] in the group IVB metals, we took the opportunity to do the same in the diboride of hafnium. Our results support the notion that in HfB2 no significant occupation of a d-like conduction band is present. 2. EXPERIMENT AND RESULTS prepared by heating a mixture of Hf and B, in the appropriate stoichiometric ratio, with an A1 metal flux to 1550~ for 10 rain followed by rapid cooling. The Hf compound was then extracted by leaching out the A1 with hot NaOH. X-ray powder diffraction analysis indicated that over 90 per cent of the sample was the desired compound, the remainder being unidentified. The samples were irradiated with pile neutrons to form the ~8~Hf radioisotope needed for the TDPAC experiment. The details of the experimental system
2025
HfB2 was
2026
E.N. KAUFMANN
and of the method of data analysis h a v e been presented elsewhere[7]. Data was acquired for sample t e m p e r a t u r e s of 296 and 4.2~ A typical data set showing the experimental T D P A C anisotropy vs time is s h o w n in Fig. 1 along with a theoretical curve which resulted f r o m a least-squares fit to the data. In the
1
T
T
~
The least-squares fits showed some evidence of a small axial a s y m m e t r y in the interaction as well as a n a r r o w ( - 8 % ) distribution of frequencies a b o u t the fitted value. T h e s e effects were m o s t evident in the low t e m p e r a t u r e data. T h e y h a v e been attributed to strain in the sample, the p r e s e n c e of a small amount of a second phase, and possibly to a slight b o r o n deficiency in the phase of interest.
n"--'-
3. DISCUSSION One interesting f e a t u r e of our results is the absence of a significant t e m p e r a t u r e dependence in vQ. Since the thermal expansion coefficients of the diborides are e x p e c t e d to be smaller and more isotopic than those of the -0A corresponding metals [2], this result might be expected so far as the contribution of the lattice ionic charges to e q is concerned. It also indicates, however, that the electrons at the Fermi level, which can redistribute them-0.2 selves a m o n g states of different spatial symm e t r y as the t e m p e r a t u r e changes, are very f e w (i.e. low density of states at the Fermi level) and/or are in states of spherical (s) orbi20 30 4 0 50 0 I0 TIME (nsec) tal character. F o r the analogous case of Ta in Fig. 1. Experimental time spectrum for the TDPAC H f metal, there is a significant t e m p e r a t u r e deanisotropy with the nuclear decay factor removed. The pendence in eq b e y o n d that ascribed to lattice solid curve resulted from a least-squares fit to the data. constant changes [7]. This is consistent with the well-known electronic characteristics of figure, the nuclear d e c a y factor has b e e n re- transition metals which include a high density m o v e d f r o m both the data and the theoretical of states at the Fermi level and a d-type concurve. The quadrupole interaction frequencies duction band. vo = e 2 q Q / h extracted f r o m the data w e r e vo = Additional evidence in support of the a b o v e 730-+5 M H z and v0=719--- 10 M H z f o r sam- interpretation arises f r o m a c o m p a r i s o n of our ple t e m p e r a t u r e s of 296 and 4.2~ respec- result for T a in HfB2 with one reported for H f tively. Thus, within the statistical errors, no in HfB2 b y Boolchand et al. [10] w h o have apt e m p e r a t u r e d e p e n d e n c e of vo was observed. plied the M 6 s s b a u e r effect to ~7SHf. Their B y inserting the k n o w n value of the nuclear value of e 2 q Q = - 2.25-+0.03/zeV, which quadrupole m o m e n t [9] of Q(482 keV) = corresponds to v Q = - 5 4 7 _+13 M H z , trans2.53• and using the weighted average lates into a value for eq of +(1.17-+0.04)• of the results quoted above, we find leq(Ta 10 TM V]cm 2 w h e n the quadrupole moment[11], in H f B 2 ) [ = ( 1 - 1 9 - 0 . 0 5 ) • 10 ~s V / c m 2. As an Q = - l . 9 3 + - 0 . 0 5 b , of the 9 3 - 2 k e V state of additional check on our analysis, the time- t78Hf is used. We note that this value of eq for domain data was Fourier transformed. Only H f equals the value quoted a b o v e for the T a the fundamental interaction f r e q u e n c y quoted impurity, within the stated errors, and m a y be a b o v e and its harmonics were evident. contrasted with the analogous case of metal
1
THE ELECTRIC FIELD GRADIENT AT Ta IN HfB2 hosts where the field gradient at H f in H f metal [ 11, 12] is nearly twice that found for Ta in H f metal[9, 13]. The effect in the metal can be attributed to charge screening[14, 15] of a Ta 5+ ion which represents an impurity charge of AZ = +1. Since the screening is accomplished by d-electrons at the Fermi level, the density of non-spherical electron charge about the Ta impurity would be significantly different f r o m that about a host H f ion. As mentioned earlier, it is known that the substitution of group V transition metals into the group IV diborides adds electrons to the conduction band. Thus it is reasonable to assume that Ta in HfB2 represents an impurity charge of AZ = +1 and that charge screening should occur. The equality of eq(Ta) to eq(Hf) in the diboride then again suggests a dearth of electrons at the Fermi level and/or that only selectrons are available for charge screening. This conclusion is in qualitative agreement with recent theoretical work on the diborides [ 16]. In order to have some r e f e r e n c e with which to compare the measured magnitudes of uo, a point-ion lattice sum calculation is useful. The appropriate sums have been evaluated for the C32 structure-type b y K a u f m a n n and McWhan[7] who based their calculations on the work of de Wette and Schacher[17]. The basis of such a calculation lies in the assignment of specific ionic charges to each occupied lattice site in the unit cell and the assumption of a uniform background of electronic charge with density chosen to render the unit cell electrically neutral. Lacking knowledge of the appropriate effective ionic charges to be associated with the H f and B sites in HfB2, we will simply denote these as Z ( H f ) and Z(B), respectively, and assume they represent the net charge contained within spherical volumes centered at the lattice points. The resulting relations for the "ionic" electric field gradients at the H f and B sites are eqi~176 = [ - 0-94Z(Hf) +3-53Z(B)] • 1016V/cm 2
(la)
2027
and eqi~
= [1.76Z(Hf) - 7 . 6 6 Z ( B ) ] • 10 ~ V/cm 2 (lb)
respectively, where lattice constants of a = 3.141A and c / a = 1.10 were used[18]. It is reasonable to assume that the charge parameters lie in the ranges 0--Z(Hf)--<4 and -1--< Z(B) ~ 3. Once the experimental field gradients quoted earlier are divided by the Sternheimer antishielding factors [19] of (1 - ~ ) ~ 6 2 for Ta or (1 - ~ ) ~ 6 9 for Hf, it can be seen that they yield field gradients external to the ion core in question of comparable size to that indicated in equation (la). In fact, since the sign of eq at H f in HfB2 is known to be positive [10], we see that the values of Z ( H f ) - ~ + 2 and Z ( B ) ~ + I would be necessary in equation (la) to explain the observation entirely in terms of the pointion lattice contribution. T o our knowledge, the quadrupole interaction at "B in HfB~ has not been measured. Equation (lb) does however agree in order of magnitude with measurements [5] on X~B in ZrB2 once the Sternheimer factor[19] (which is a shielding factor for boron) is accounted for. Some support for the value Z ( B ) ~ + 1 has in fact been provided by the low temperature specific heat study of Tyan et al. [20]. The rather nai've picture presented above can account, at least in a phenomenological way, for the effects of electronic and ionic charges at points distant from the nucleus under study. It completely ignores however the distribution of electronic charge in the Wigner-Seitz cell containing the nucleus in question. The bonding in the diborides is most likely of highly covalent and directional nature. It is therefore probable that the local electronic configuration about the constituent atoms is not spherically symmetric and does contribute to the observed electric quadrupole interactions. Nevertheless, comparison with the point-ion lattice sum result may be a convenient artifice for revealing systematic trends among the diborides. Unfortunately, aside
2028
E.N. KAUFMANN
from the case of HfB2 presented here, the metal site quadrupole interaction has only b e e n o b s e r v e d i n S c B 2 [6] a n d V B 2 [5]. F u r t h e r measurements in these compounds would be of considerable value toward understanding their electronic structure.
Note added in proof: In a recent report by Hass and Shirley (J. chem. Phys. 58, 3339 (1973)) a value of 7 2 0+19 MHz is given for the quadrupole interaction frequency of '~'Ta (482 keV) in HfB2 in excellent agreement with the value quoted here. Acknowledgements--We would like to thank P. H. Schmidt and R. N. Castellano for help with sample preparation and A. S. Cooper for X-ray diffraction analysis. M. L. Thomson provided~assistance in the analysis of the data. We are also grateful to Dr. A. C. Gossard, Dr. P. Boolchand and Dr. G. C. Carter for helpful discussions regarding the diborides.
8.
9.
10. 11. 12. 13.
REFERENCES
1. W E R N I C K J. H. In: lntermetallic Compounds (Edited by J. H. Westbrook), p. 212. Wiley, New York (1967); GOLDSCHMIDT H. J., Interstitial Alloys, p. 254. Plenum Press, New York (1967). 2. JURETSCHKE H. J. and STEINITZ R., J. Phys. Chem. Solids 4, 118 (1958). 3. STEINITZ R. In: Fundamentals of Refradtory Compounds (Edited by H. H. Hausner and M. G. Bowman), p. 155. Plenum Press, New York (1968); POST B., GLASER F. W. and MOSKOWITZ D., Acta Met. 2, 20 (1954). 4. MALYUCHKOV O. T. and POVITSKII V. A., Fiz. Met. i Metalloved 13, 676 (1962) [translated in Phys. Metals Metallogr. 13, 38 (1962)]. 5. SILVER A. H. and BRAY P. J., J. chem. Phys. 32, 288 (1960); SILVER A. H. and KUSHIDA T., J. chem. Phys. 38, 865 (1963). 6. CARTER G. C. and SWARTZ J. C., J. Phys. Chem. Solids 32, 2415 (1971). 7. K A U F M A N N E. N., Phys. Rev. B 8 (Aug. 1973); and
14. 15.
16.
17. 18. 19. 20.
KAUFMANN E. N. and McWHAN D. B., Phys. Rev. B 8 (Aug. 1973). FRAUENFELDER H. and STEFFEN R. M. In: Alpha-, Beta- and Gamma-Ray Spectroscopy (Edited by K. Siegbahn), Vol. II, p. 997. North Holland, Amsterdam (1965). SOMMERFELDT R. W., CANNON T. W., COLEMAN L. W. and SCHECTER L., Phys. Rev. 138, B763 (1965); STELSON P. H. and McGOWAN F. K., Phys. Rev. 105, 1346 (1957). BOOLCHAND P., LIN C. L., JHA S. and KOUCKY F. L., International Conf. on Applications of the Mfssbauer Effect, Israel (1972). BOOLCHAND P., ROBINSON B. L. and JHA S., Phys. Rev. 187, 475 (1969). BOOLCHAND P., LANGHAMMER D., LIN C. L. and JHA S., Phys. Rev. C6, 1093 (1972). See for example: KAINDL G. and SALOMON D., Phys. Lett. 40A, 179 (1972); GERDAU E., WOLF J., WINKLER H. and BRAUNSFURTH J., Proc. Roy. Soc. A311, 197 (1969); and LIEDER R. N., BUTTLER N., KILLIG K., BECK K. and BODENSTEDT E. In: Hyperline Interactions in Excited Nuclei (Edited by G. Goldring and R. Kalish), Vol. lI, p. 449. Gordon and Breach, London (1971). FRIEDEL J., Adv. Phys. 3, 446 (1954); Nuovo Cim. 7, 287 (1958); J. Phys. Rad. 23, 692 (1962). DANIEL E. In: HyperIine Interactions (Edited by A. J. Freeman and R. B. Frankel), p. 712. Academic Press, New York (1967). (Also see in the same volume the chapter by WATSON R. E. on p. 413). CARTER F. L., NBS special publication 364, Solid State Chemistry, Proc. 5th Materials Research Symposium (July 1972) pp. 515-559; and McALISTER A. J., CUTHILL J. R., WILLIAMS M. L. and DOBBYN R. C., preprint. DE WETTE F. W. and SCHACHER G. E., Phys. Rev. 137, A78 and A92 (1965). ARONSSON B. In: Modern Materials (Edited by H. H. Hausner), Vol. 2, p. 143. Academic Press, New York (1960). FEIOCK F. D. and JOHNSON W. R., Phys. Rev. 187, 39 (1969) and references therein. TYAN Y. S., TOTH L. E. and CHANG Y. A., J. Phys. Chem. Solids 30, 785 (1969).