  Single crystal elastic constants of bcc iron and bct FeC and FeN alloys,
martensites, have been evaluated by ab initio calculations based on the density
functional theory. The energy of a strained crystal has been computed using the
supercell method at several values of the strain intensity, and the stiffness
coefficient has been determined from the slope of the energy versus square of
strain relation. Some of the third order elastic constants have also been
evaluated. The absolute magnitudes of the calculated values for bcc iron are in
fair agreement with experiment, including the third order constants, although
the computed elastic anisotropy is much weaker than measured. The tetragonally
distorted dilute FeC and FeN alloys exhibit lower stiffness than bcc iron,
particularly in the tensor component C33, while the elastic anisotropy is
virtually the same. Average values of elastic moduli for polycrystalline
aggregates are also computed. Youngs modulus and the rigidity modulus, as well
as the bulk modulus, are decreased by about 10 per cent by the addition of C or
N to 3.7 atomic per cent, which agrees with the experimental data for FeC
martensite.
