Abstract
There are some precipitates that undergo transition from a coherent to semi-coherent state during growth. An example of such a precipitate in steel is carbide with a NaCl-type structure, such as TiC and NbC. The interface energy between carbide precipitate and iron is obtained via large-scale first-principles electronic structure calculation. The strain energy is estimated by structure optimization of the iron matrix with virtual carbide precipitate using the empirical potential. The transition of the interface from a coherent to semi-coherent state was examined by comparing the interface and strain energies between the coherent and semi-coherent interfaces. The sizes where both the precipitates undergo this transition are smaller than those of the interfaces with minimum misfit. The estimated transition diameter of TiC is in agreement with the experimentally obtained value.
Highlights
Strengthening of steel is mainly performed through four mechanisms [1]
We focused on the dominant growth plane of the precipitate, namely the broad plane
The conditions of calculating coherent interface energy, which include the shape of the unit cell shown in Figure 1, are followed according to the previous study [21]
Summary
Strengthening of steel is mainly performed through four mechanisms [1]. Increasing the strength of steels by using a solid solution of alloying elements and impurity elements is known as solid solution strengthening. An interface relationship of {001}precipitate //{001}iron and precipitate //iron is reported as a Baker–Nutting orientation relationship for carbide precipitates with an NaCl-type structure [8] One such precipitate, TiC, is considered to exist as a coherent precipitate up to a size of 3 nm [9], and the precipitate transforms to a semi-coherent precipitate due to growth. They showed that the strain energy should be relieved by forming a semi-coherent precipitate for thicker precipitates, since the elastic energy caused by the coherent strain increases with the thickness of the precipitate In their approach, the interface energy was estimated using the extended Peierls–Nabarro framework, in which the chemical interaction energy by the first-principles calculation is combined with the elastic energy by the continuum description. We estimated the transition size of NbC from coherent to semi-coherent precipitate based on the interface and strain energies obtained via the large-scale first-principles calculation and the classical molecular dynamics simulation, respectively. We applied a method to estimate the transition size of TiC and compared it with the previous results of NbC as well as the interface and strain energies, the electronic structure, and the atomic configuration
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