Lattice distortion and volume change in a dilute heterovalent alloy:AlLi

A theoretical and experimental study of the lattice strain and volume change in the dilute solid solution $\mathrm{Al}\mathrm{Li}$ is presented. The experimental data were obtained by diffuse elastic neutron scattering in Al single crystals containing 0.26 and 0.88 at.% ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, respectively. The isotope ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ was used because of the small absorption and the known incoherent cross section of this nucleus. The theoretical method to calculate the volume change, the lattice distortion, and the heat of solution for a heterovalent substitutional impurity is developed within the framework of the perturbed electron-liquid pseudopotential formalism. It is shown that in determining the long-range part of the lattice displacement in a heterovalent dilute alloy such as $\mathrm{Al}\mathrm{Li}$, third- and fourth-order nonlinear screening contributions to the distorting force are equally significant in addition to the traditional linear screening term. This is in contrast to the case of a homovalent solution, where fourth-order nonlinear screening can be ignored. The numerical calculation is based on the ion-electron potentials for pure Al and Li that have been determined by using lattice-constant and elastic or phonon data for each of the pure constituents. The agreement is reasonably good with both the observed anomalous, negative volume change and with the measured lattice strain. The inadequacy of Vegard's rule to predict even the sign of the volume change in this alloy is discussed.