In this work, we study the effect of relaxation of the atomic positions and lattice parameter of mixed ${\mathrm{Ga}}_{1-x}{\mathrm{In}}_x\mathrm{As}$ systems on the 002 electron atomic scattering amplitudes (ASA). The ASAs are shown to vary strongly with lattice parameter but to be indistinguishable for different In concentrations when the lattice parameter is held fixed. The resulting relationship between ASA and lattice parameter is then used in a finite temperature, zero pressure Monte Carlo relaxation of the mixed crystal. The consequence of the use of this atomic scattering amplitude is a reduction of the structure factor, leading to an increase of the In concentration at which the 002 structure factor vanishes. This method directly includes the effect of temperature on the ASA and on the structure factors and therefore does not require an explicit knowledge of the Debye-Waller factor.

• Received 7 May 2007

DOI:https://doi.org/10.1103/PhysRevB.76.073303