Does Altaite Exhibit Emphanitic Behavior? A High Resolution Neutron Powder Diffraction Investigation of the Crystallographic and Thermoelastic Properties of PbTe Between 10 and 500 K

Abstract

Abstract The recent claim, based on an analysis of the pair distribution function (pdf), that altaite, PbTe, exhibits emphanitic behavior above room temperature has been re-investigated using high resolution, neutron time-of-flight powder diffraction between 10 and 500 K. The results of this study refute the two supporting assertions of emphanisis, namely that the temperature dependence of the unit-cell parameter and the atomic displacement parameter of the lead cation in altaite behave in a non-Debye-like manner. Within the temperature interval 10 to 500 K, the thermoelastic properties of altaite can be treated in a simple, self-consistent phenomenological model in which the cation and anion vibrate independently of one another in a Debye-like manner, with fitted vibrational Debye temperatures of 99.6(2) K for the lead cation and 156.0(5) K for the tellurium anion. Simultaneous fitting of the unit-cell volume and isochoric heat capacity in a self-consistent, two-term Debye internal energy model yields characteristic temperatures of 91(3) and 175(5) K, in good agreement with those values determined from fitting the atomic-displacement parameters. Taking into account the limitations of the Debye model for lattice vibrations, the calculated vibrational density of states derived from the two-term Debye model is found to be in fair agreement with that calculated by density functional theory. Both vibrational Debye temperatures closely match the mean predicted frequency cut-offs calculated from the partial phonon densities of states for the two constituent atomic species. The differences in conclusions drawn from this current investigation and the earlier pdf measurements are attributable to a linear temperature-dependent offset (decrease) from the published temperatures in the total scattering study. The offset is found to become significant around room temperature, with a magnitude that increases with increasing temperature. The supporting evidence for emphanitic behavior in altaite in the pdf study, such as discontinuities in the thermal expansion coefficient and the temperature variation of the atomic displacement parameters, are therefore most probably artefacts that arise from the sample temperature being substantially cooler than the claimed set-point temperature for temperatures greater that ∼300 K.