Many-body effects in the mobility and diffusivity of interstitial solute in a crystalline solid: The case of helium in BCC tungsten

The many-body dynamics of a crystalline solid containing an interstitial solute atom (ISA) is usually interpreted within the one-particle approximation as a random walker hopping among trapping centers at periodic lattice sites. The corresponding mobility and diffusivity can be formulated based on the transition-state theory in the form of the Arrhenius law. Possible issues arising from the many-body nature of the dynamics may need to be understood and resolved both scientifically and technologically. Noting the congruence between the dynamics of the many-body and stochastic systems within the Mori-Zwanzig theory, we analyzed the dynamics of a model particle subjected to a saw-tooth potential in a noisy medium. The ISA mobility is found to be governed by two sources of dissipative friction: that which is produced by the scattering of lattice waves by the moving ISA (phonon wind), and that which is derived from the energy dissipation associated with overcoming the migration barrier screened by lattice waves (i.e., phonon screened). The many-body effect in both cases increases with temperature, so that the first component of the friction is important at high temperatures and the second component is important at low temperatures. A formulation built on this mechanistic structure of the dissipative friction requires the mobility and diffusivity to be expressed not only in terms of the migration enthalpy and entropy, but also of the phonon drag coefficient. As a test, the complex temperature dependence of the mobility and diffusivity of interstitial helium in BCC W obtained from molecular-dynamics simulation is very well reproduced.