Thermal conductivity of minerals at high pressure: The effect of phase transitions

Abstract

Theory predicts and measurements confirm that anharmonic properties such as the lattice thermal resistivity, the Grüneisen parameter, and the coefficient of thermal expansion generally decrease as a function of increasing density upon compression of solids. The Debye‐Grüneisen continuum model further predicts a discontinuous decrease of anharmonic properties during a phase transition with a density increase, in contradiction with available experimental data on alkali halides. We present results calculated from a model based on interatomic potentials. This model correctly predicts an increase in anharmonic properties for simple compounds transforming from a six‐ to an eight‐coordinated structure. These results stress the importance of interatomic spacing as well as density in determining changes in thermodynamic properties due to polymorphism. The change in crystal structure across a phase transition also affects the thermal conductivity via Brillouin zone summations over the interacting phonon modes. We have used in the calculations either the bulk sound speed, or the Debye average velocity calculated from the longitudinal and transverse velocities (in both cases, theoretically derived from the interatomic potentials). We have found that the pressure dependence of thermal conductivity determined from the bulk sound speed agrees much better with experimental data for each phase than that determined from the average velocity. Apparently, shear modes contribute less to the change of thermal conductivity with compression than has been thought.

Thermal and mechanical response of [0001]-oriented GaN nanowires during tensile loading and unloading

“…The thermal conductivity is known to be related to the phonon group velocity and the relaxation time of phonons. 34 At the strain of 0.01, the elastic modulus of the nanowires in the intermediate state is 206 GPa, which is 37% lower than that of the WZ-structured nanowires and causes the group velocity to be approximately 20% lower. However, the average relaxation time of phonons in the intermediate state is very similar to that for the WZ-structured nanowires.…”

“…The difference in conductivities between the wires with different structures results from the stiffness, which is related to the phonon group velocity. 34 This velocity is estimated simply by calculating a harmonic average over the longitudinal and transverse sound velocities, 45,46 …”

Shock temperatures and the melting point of iron

“…3, are some 12 to 32% greater than that calculated using the Weidemann-Franz law for ~(n, (11) and Debye theou for K, (12)(13)(14). Revised values of Tu for Fe ( Fig.…”

Thermal conductivity of hcp iron at high pressure and temperature

“…Moreover, the mobility of free electrons is also affected by a magnetic state, and/or coordination number, which further complicates the predictions [9]. This is readily observed in ambient-pressure data on certain metals such as nickel or iron where the magnetic/structural transitions manifest themselves with change in slope and magnitude of the thermal conductivity [10].…”