Quantum Mechanical Tunneling of Dislocations: Quantization and Depinning from Peierls Barrier

Abstract

Theories of Mott and Weertmann pertaining to quantum mechanical tunneling of dislocations from Peierls barrier in cubic crystals are revisited. Their mathematical calculations about logarithmic creep rate and lattice vibrations as a manifestation of Debye temperature for quantized thermal energy are found correct but they can not ascertain to choose the mass of phonon or “quanta” of lattice vibrations. The quantum mechanical yielding in metals at relatively low temperatures, where Debye temperatures operate, is resolved and the mathematical formulas are presented. The crystal plasticity is studied with stress relaxation curves instead of logarithmic creep rate. With creep rate formulas of Mott and Weertmann, a new formula based on logarithmic profile of stress relaxation curves is proposed which suggests simultaneous quantization of dislocations with their stress, i.e., and depinning of dislocations, i.e., , where is quantum action, σ is the stress, N is the number of dislocations, A is the area and t is the time. The two different interpretations of “quantum length of Peierls barrier”, one based on curvature of space, i.e., yields quantization of Burgers vector and the other based on the curvature of time, i.e., yields depinning of dislocations from Peierls barrier in cubic crystals, are presented. , i.e., the unitary operator on shear modulus yields the variations in the curvature of time due to which simultaneous quantization, and depinning of dislocations occur from Peierls barrier in cubic crystals.