Nuclear-acoustic-resonance determination of the strain electric-field-gradient tensorSand its temperature dependence in Ta single crystals

Abstract

The first quantitative nuclear-acoustic-resonance study of the temperature dependence of the tensor $\mathit{S}$ is presented for a cubic metal. The fourth-rank tensor $\mathit{S}$ relates the electric field gradient (EFG) at a nuclear site to the elastic strain field. For cubic metals, its temperature dependence allows a conclusive test of actual theoretical EFG models. A comprehensive discussion of the tensor $\mathit{S}$ is given and, by applying the screened potential approach of Nishiyama et al. [Phys. Rev. Lett. 37, 357 (1976)] to a lattice with both thermal and ultrasonic vibrations, simple expressions are derived for $\mathit{S}$ and its temperature dependence. In addition, the rotational contribution to the ultrasound-induced EFG is discussed in an appendix. With an internal calibration by the Alpher-Rubin effect the following experimental results were obtained for Ta at 300 K: $|{S}_{44}|=(6.33\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}{10}^{22}$ V/${\mathrm{m}}^{2}$ and $\frac{({S}_{11}\ensuremath{-}{S}_{12})}{2{S}_{44}}=\ensuremath{-}0.65\ifmmode\pm\else\textpm\fi{}0.03$. For both components of $\mathit{S}$ a decrease with temperature is observed. With regard to the empirical ${T}^{1.5}$ law of the static EFG the decrease can be described by $S(T)=S(0)(1\ensuremath{-}B{T}^{1.5})$ with $B=(7\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{K}}^{\ensuremath{-}1.5}$. This result strongly supports the "phonon model" of Nishiyama et al. which attributes the temperature dependence of the nuclear electric quadrupole interaction in metals to the effect of lattice vibrations.