Incommensurate Direction of the Modulated Structure in Iron-Carbon Martensite

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Mura-Mori’s linear elasticity theory for continuum body has been applied to interpret the incommensurate direction of the modulated structure in iron-carbon martensite. Based on the assumption that the strain caused by the invasion of carbon atoms is proportional to the carbon concentration, an equation for the strain energy is derived as a function of the modulation direction on the (010) plane. A numerical calculation is made for the limiting case of zero carbon content by the use of the elastic constant of α-iron, since any elastic constant data for the bet martensite are absent. The theoretical modulation angle given by the minimum strain energy is 19.1°, and this is close to the observed angle 22° determined by the extrapolation to zero carbon content. It is concluded that the incommensurate direction comes from such an anisotropic lattice distortion that the lattice parameter c increases with carbon content while a decreases simultaneously.

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