The Phonon-Dislocation Interaction and its Rôle in Dislocation Dragging and Thermal Resistivity

Analytic model of the remobilization of pinned glide dislocations: Including dislocation drag from phonon wind

“…The energy dissipated per unit length of a moving dislocation is D = F v = Bv 2 [44,52]. In the first principles calculations of Refs.…”

“…Temperature dependence: The drag coefficient depends on temperature via the phonon spectrum and the second (SOEC) and third-order (TOEC) elastic constants; the SOECs also affect the sound speeds. At temperatures (on the order of or) higher than the Debye temperature, the isotropic phonon spectrum can be Taylor expanded, exhibiting a linear temperature dependence to leading order [44,45]. In fact, at constant density this is the dominating effect since the elastic constants are more sensitive to density and pressure than to temperature [57,59].…”

“…Density dependence: In Ref. [44,45] it was shown that the drag coefficient at low velocity, being dominated by transverse phonons, takes the form TOECs), where the Burgers vector is proportional to the lattice constant a in a cubic lattice, the edge of the Brillouin zone scales as q BZ ∼ 1/a, the transverse sound speed is determined from G/ρ, and the function f () represents a ratio of polynomials of SOEC and TOEC whose behavior under density changes is still unknown. If all elastic constants scaled similarly with density, f would hardly change.…”

“…Whenever temperature dependence is considered, it is assumed to be linear, sometimes including a small quadratic correction [34]. The latter assumption has its roots in the linear temperature dependence of the Debye phonon spectrum in its high temperature expansion [44,45]. However, none of the velocity dependencies mentioned above are well motivated from first principles, but are rather assumptions proposed ad hoc.…”

“…Although the model framework is valid for a velocity-, density-, and temperature-dependent drag coefficient, B(v, ρ, T ), the focus in [40] was dislocation intersection node dissociation, hence for simplicity B was taken to be a constant. In addition to the development of the kinetic equation, Blaschke et al developed a new functional form for B based on first principles calculations of elastic scattering of phonons by a moving dislocation via linear response theory [45,47,51,52], thereby generalizing earlier work [44]. This model for the drag coefficient focuses primarily on the dependence of B on the dislocation velocity, and shows that the asymptotic behavior of B in the isotropic limit indeed exhibits a "relativistic" form with m = 1/2 and v crit = c t (the transverse sound speed) [45,52].…”