Phason-Dominated Thermal Transport in Fresnoite

Fast-propagating waves in the phase of incommensurate structures, called phasons, have long been argued to enhance thermal transport. Although supersonic phason velocities have been observed, the lifetimes, from which mean free paths can be determined, have not been resolved. Using inelastic neutron scattering and thermal conductivity measurements, we establish that phasons in piezoelectric fresnoite make a major contribution to thermal conductivity by propagating with higher group velocities and longer mean free paths than phonons. The phason contribution to thermal conductivity is maximum near room temperature, where it is the single largest contributing degree of freedom.

Figure 1

Thermal conductivity of fresnoite measured along the tetragonal $a$ axis (with phasons) and $c$ axis (without phasons). (a) Low temperature thermal conductivity measured using a four-point method (this work). (b) High temperature thermal conductivity measured using the laser flash technique along with heat capacity measurements both by Shen et al. [16].

Figure 2

Phason and low-energy phonon dispersion and linewidths measured in the basal plane of fresnoite using the HYSPEC time-of-flight cold neutron instrument at the SNS. (a) Intensity map of the elastic scattering for data collected with $E_i=15\mathrm{meV}$. (b) Slice in energy of the same data along $\mathit{Q}=[4,\mathrm{K},0]$ through a commensurate reflection, revealing transverse acoustic (TA) and optic (${\mathrm{TO}}_1$) phonons. (c) Slice in energy along $\mathit{Q}=[4.61,\mathrm{K},0]$ through an incommensurate reflection, revealing the phason. The out-of-plane directions were integrated $\pm 0.05$ r.l.u. for the slices displayed in (a) and (c). (d) Measurement of lower energy part of phason along $\mathit{Q}=[\mathrm{H},3.61,0]$ using $E_i=7.5\mathrm{meV}$ and 20’ Soller collimation for significantly improved energy and momentum resolution. Constant energy cuts in top panels show the resolution limited elastic peak at $E=0$ and the broader phason at $E=2\mathrm{meV}$. The out-of-plane directions were integrated $\pm 0.025$ r.l.u. for the slices and cuts displayed in (d). (e) Summary of the phason and low-energy phonon dispersion with linewidths along the [100] and [110] directions. Shading indicates the intrinsic full width at half maximum (FWHM) found by fitting with Lorentzian convoluted with a small Gaussian instrument resolution width; example fits shown in right panel. All phonons are fit in energy at fixed $\mathit{Q}$, while the phason widths are fit in $\mathit{Q}$ at fixed $E$.

Figure 3

Full neutron-weighted density of states and powder averaged dynamical structure factor at 5 K for fresnoite measured using the ARCS time-of-flight instrument at the SNS. (a) Extracted neutron-weighted density of states for the lattice dynamics that includes mainly phonons, but also phasons and amplitudons. (b) Intensity map of the powder averaged dynamical structure factor, $S(|Q|,E)$, from which the density of states was determined.