Abstract
Local strain is introduced into the lattice around solute atom due to the size mismatch between solute and solvent atoms in alloy. In this study, local lattice strains are calculated for the first time in titanium alloys, using the plane-wave pseudopotential method. As an extreme case, the local lattice strain around a vacancy is also calculated in various bcc, fcc and hcp metals. It is found that the local strain energy is very high in both bcc Ti and bcc Fe, where the martensitic transformation takes place. From a series of calculations, it is shown that the magnitude of the strain energy stored in the local lattice is comparable to the thermal energy, kBT, where kB is the Boltzmann constant and T is the absolute temperature. Therefore, the presence of local lattice strains in alloy could influence the phase stability that varies largely depending on temperatures. For example, the local lattice strain correlates with the martensitic transformation start temperature, Ms, in binary titanium alloys.
Highlights
IntroductionAs illustrated in Fig. (a) and (b), it is well known that local strains are introduced into the lattice around solute atom due to the size difference between solute and solvent atoms in alloy
The calculated results of the local strain energy around a vacancy are shown in Fig.3 (a) bcc, (b) fcc and (c) hcp metals
Local strain energy around martensite start temperature (Ms) atom is compared between bcc Ti and hcp Ti in Fig.8 for typical elements
Summary
As illustrated in Fig. (a) and (b), it is well known that local strains are introduced into the lattice around solute atom due to the size difference between solute and solvent atoms in alloy. As shown in Fig. (c), a vacancy introduces the local strain into the crystal lattice, but the information is very limited, too. Local lattice strains are calculated for various alloying elements, M, in both hcp Ti and bcc Ti, using the plane-wave pseudopotential method. Such local lattice strains are evaluated around a vacancy in typical bcc, fcc and hcp metals
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