Non-cubic Metals Research Articles

Electric field-gradients at gallium in noncubic metals: Role of the impurity valence

Electric field-gradients at gallium in noncubic metals: Role of the impurity valence

Electric quadrupole interactions measured by nuclear orientation and NMR on oriented nuclei

A review is given of the situations in which low temperature nuclear orientation and NMR of oriented nuclei have been applied in recent years to the measurement of electric quadrupole interactions in metals and in dielectric crystals. The review is concerned with the variety of methods by which quadrupole interactions have been measured. Illustrative examples are given for each technique, but no attempt is made to give a full bibliography of work. As regards nuclear orientation, pure quadrupole algnment is discussed (although in non-cubic metals rather than in dielectric crystals), followed by outlines of work on mixed magnetic dipole and electric quadrupole hfi when these interactions are (a) co-axial and (b) mutually perpendicular. The sensitivity of nuclear orientation to small quadrupole interactions is shown to be improved in the second case.

The Electric Field Gradient in Noncubic Metals and Alloys

ABSTRACTThe electric field gradient (efg) present in noncubic solids causes an energy–splitting of the nuclear levels via the quadrupole hyperfine interaction. During the last few years the perturbed angular correlation method has proved a unique experimental tool for investigating this interaction especially in metals. The basic principles of the method are discussed. Recent experimental results are given for pure metals and highly diluted systems as well as for alloys and intermetallics. The last section deals with theoretical aspects of the temperature dependence of the efg in pure metals.

On the temperature dependence and magnitude of the electric field gradient in noncubic metals

Optimised model potential theory, including orthogonalisation of the conduction states to the core states, has been used to calculate the temperature dependence and magnitude of the electric field gradient in the metals Be, Zn, Cd and In. Good agreement with measured temperature dependences is obtained, with improved values for magnitudes compared to previous model potential theory calculations. Anisotropy in the thermal vibration of the atoms is found to affect noticeably the calculated temperature dependences, and correlation and exchange interactions among conduction electrons are found to affect the magnitudes substantially. Problems in obtaining a simple explanation for the empirical 3/2 power law for the temperature dependence are discussed.

Linear temperature dependence of the electric quadrupole interaction of111Cd impurities in holmium

The electric quadrupole interaction of111Cd impurities in metallic holmium has been investigated between 140 K and 655 K by time differential perturbed angular correlation measurements. The quadrupole frequency decreases with increasing temperature. This decrease is a linear function of temperature, in contrast to theT3/2 dependence usually observed in non-cubic metals. Possible reasons for the deviation from theT3/2 relation are discussed.

The quadrupole interaction of100Rh in various intermetallic compounds of palladium

The nuclear quadrupole interaction of the 75 keV excited state of100Rh in the ordered intermetallic compounds PdHg, PdPb2 PdSb and PdTe was measured. Using an estimate for the nuclear quadrupole moment of the 75 keV state in100Rh and point ion lattice sums for the lattice electric field gradient (EFG) at the Rh site, the electronic contributionV zz el to the total EFG was derived.V zz el was found to be correlated with the average valence electron concentration in the compounds studied. In the case of PdPb2, the temperature dependence of the quadrupole interaction was also studied and found not to follow theT 3/2 rule which is observed in virtually all pure noncubic metals.

Systematically weak temperature dependence of electric field gradients in distorted cubic metals

The temperature dependence of the electric field gradient for radiation-damaged copper and for the dilute alloy Zn Ag has been measured using the perturbed angular correlation technique. A systematically weak temperature dependence is found for distorted cubic metals compared to non-cubic metals. The strong temperature dependence for the Zn Ag , In Ag and Sn Ag alloys as reported in literature has not been confirmed in the present experiment.

Search for an isotopic mass effect on the quadrupole coupling constants in non-cubic metals

Search for an isotopic mass effect on the quadrupole coupling constants in non-cubic metals

Effects of probe valence on the conduction-electron electric-field gradient in the non-cubic metals

A study is reported of the magnitudes of the local electric-field gradient contribution eqce due to conduction electrons at sp-valent impurities in six sp-band non-cubic metals. Available data show a strong correlation of eqce with the valence of the probe ion and show little dependence on impurity size.

The effect of orthogonalization on the conduction electron electric field gradient in noncubic metals

By orthogonalizing the conduction electron states of model potential theory to the core electron states, the local conduction electron electric field gradient (EFG) is expressed by a model wave function EFG enhanced by a factor correlated with the Sternheimer antishielding factor.

Vacancy concentrations in noncubic metals. Lattice constants of zinc

Measurements of the thermal expansion of the lattice parameters of Zn are combined with earlier measurements of the bulk expansion of oriented single-crystal bars to give a measure of the fraction of vacant lattice sites at temperatures near the melting point. The vacancy fraction at the melting point, $\ensuremath{\eta}({T}_{m})$, is (3.0 \ifmmode\pm\else\textpm\fi{} 1.0) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$, and the single-vacancy formation parameters are energy of formation ${E}^{f}=0.52\ifmmode\pm\else\textpm\fi{}0.05$ eV, and entropy of formation ${S}^{f}=(0.5\ifmmode\pm\else\textpm\fi{}0.3)k$. The strains associated with dislocation climb in response to changing vacancy concentrations favor dilation perpendicular to the $c$ axis. A comparison is made of the principal-axis strains in noncubic metals as measured by thermal expansion and vacancy-flux electromigration methods.

Electric field gradient in pure hexagonal transition metals

Using a general calculation of the nuclear quadrupole interaction in non-cubic metals which was presented in a previous paper, this article gives an interpretation of experimental data dealing with signs and temperature dependence of the electric field gradient in 3d(Sc, Ti), 4d(Y, Zr, Tc, Ru) and 5d (Hf, Re, Os) transition hexagonal close-packed metals.

The fraction of ions in unique sites after implantation into cubic and non-cubic metals derived from hyperfine interaction studies

A survey of experimental data of implantations of 111In, 119mSn, 181Hf, 197Hg, 197mHg (EMIS Bonn) and 100Pd (EMIS Karlsruhe) into different metals has been made. TDPAC, ME and NMR/ON investigations of the magnetic dipole and electric quadrupole interaction gave information on the efficiency of the implantation process in providing dilute alloy systems with fractions of impurity atoms at unique lattice sites. For some thirty host-guest combinations unique site fractions have been reported. They are discussed in terms of atomic size, electronegativity, solid solubility, concentration and temperature. Additionally, results of TDPAC methods applied to the study of radiation damage effects after implantation of radioactive probes into cubic lattices are included.

Temperature Dependence of the Electric Field Gradient in a Quasi-Two-Dimensional Metal: NbSe2

The /sup 93/Nb nuclear-quadrupole-resonance frequencies have been measured as a function of temperature in 2H-NbSe/sub 2/ between 38 and 376 K. A nearly linear behavior ..nu../sub Q/=a-bT is observed between 77 and 376 K in contrast to an approximate ..nu../sub Q/(0)(1-..cap alpha..T/sup 3///sup 2/) dependence found in most noncubic metals over the same temperature range. Using a variation of Jena's theoretical treatment of the temperature dependence of ..nu../sub Q/ in noncubic metals, with the consideration that NbSe/sub 2/ is a quasi-two-dimensional structure, we present an explanation of the nearly linear dependence of ..nu../sub Q/ on T in NbSe/sub 2/. (AIP)

Theory of the Temperature Dependence of the Electric Field Gradient in Noncubic Metals

The temperature dependence of the electric field gradient $\mathrm{eq}(T)$ in noncubic metals is calculated within a pseudopotential approach including the influence of lattice vibrations. The resulting $\mathrm{eq}(T)$ factorizes into a Debye-Waller factor and a lattice sum over screened ions. The accurately measured $\frac{\mathrm{eq}(T)}{\mathrm{eq}(0)}$ values for In, Cd, Zn, Sb, and Sn are quantitatively reproduced using known data for the lattice constants and for the mean-square atomic displacements.

Recent developments in the study of quadrupolar gradients in non-cubic metals

This paper surveys the existing experimental data on quadrupolar coupling constants in metals emphasizing the principal trends emerging from these data and their significance to theoretical models on electric field-gradients in non-cubic metals.

The pressure and temperature dependence of the electric field gradient in non-cubic metals

The pressure and temperature dependence of the electric field gradient in non-cubic metals

Low temperature nuclear orientation and NMR of oriented nuclei

Recent developments in nuclear orientation (NO) and radiative detection of NMR (NMR/ON) are reviewed. Details of the hyperfine interaction hamiltonian in cubic ferromagnets and the principles of measurement by these techniques of both magnetic dipole and electric quadrupole terms are outlined. In the experimental survey a full account is given of measurements of the electric quadrupole interaction by frequency modulated and fast passage NMR/ON, with briefer coverage of applications of both techniques to implanted systems, of linewidths, concentration dependent line structure, and Knight shifts in NMR/ON and of NO measurements of electric quadrupole interactions in non-cubic non-magnetic metals. The review incorporates a tabulation of NMR/ON measurements to date.

Explanation of the pressure and concentration dependence of the EFG in noncubic metals and alloys

The pressure and concentration dependence of the electric field gradient (EFG) in noncubic metals and alloys is calculated within a pseudopotential approach. The results agree well with experiment. Far-reaching consequences about the Debye-Waller-factor and about the origin of the EFG are discussed.

Sign and magnitude of the quadrupole interaction ofCd111in noncubic metals: Universal correlation of ionic and electronic field gradients

The magnitude and sign of the nuclear quadrupole interaction of the 247-keV excited state of $^{111}\mathrm{Cd}$ has been measured in a number of noncubic metals by means of the technique of $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ time-differential perturbed angular correlations. The state was populated by the unique first-forbidden $\ensuremath{\beta}$ decay of 7.5-day $^{111}\mathrm{Ag}$ which was implanted by an an isotope separator into single crystals of Be, Mg, Ti, Zn, Sn, Re, Hf, and Bi. Well-defined precession patterns indicating unique lattice location of the $^{111}\mathrm{Cd}$ impurity have been observed in all these cases except Hf and Bi. The sign and magnitude of the quadrupole coupling constants ${e}^{2}\mathrm{qQ}$ have thus been derived. Using lattice-sum calculations for the lattice electric field-gradient (EFG) $e{q}_{\mathrm{latt}}$, $Q=+0.77$ b for the quadrupole moment of the 247-keV level of $^{111}\mathrm{Cd}$ and a Sternheimer antishielding factor ${\ensuremath{\gamma}}_{\ensuremath{\infty}}=\ensuremath{-}29.3$ for Cd, the EFG presumably due to the conduction electrons $e{q}_{\mathrm{el}}$, has been derived for each of these cases. These results strongly indicate that $e{q}_{\mathrm{el}}$ is linearly related to $e{q}_{\mathrm{latt}}(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}})$. In an attempt to examine whether such a simple relation is effective in metallic systems in general, a survey of all ${e}^{2}\mathrm{qQ}$ values (with signs) measured in noncubic metals has been made. This survey reveals, for the first time, that in most cases, the values of $e{q}_{\mathrm{el}}$ and $e{q}_{\mathrm{latt}}(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}})$ could be connected by a universal correlation according to which $e{q}_{\mathrm{el}}=\ensuremath{-}Ke{q}_{\mathrm{latt}}(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}})$, $|K|\ensuremath{\approx}3$ for moderate values of $e{q}_{\mathrm{latt}}(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}})$. Based on this universal correlation curve, a number of ${e}^{2}\mathrm{qQ}$ values, whose signs are yet undetermined, have been phenomenologically examined and their signs predicted. These general systematics, especially the universality of the correlation of the electronic gradient with the ionic gradient $e{q}_{\mathrm{latt}}(1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}})$, and its dependence on the ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ of the impurity, is unexpected in the framework of current theoretical models of the EFG in noncubic metals.