Effect of magnetism on kinetics of γ–α transformation and pattern formation in iron

Abstract

Abstract. Kinetics of polymorphous  - transformation in Fe is studied numerically within a model taking into account both lattice and magnetic degrees of freedom, based on first-principle calculations of the total energy for different magnetic states. It is shown that magnetoelastic phenomena, namely, a strong sensitivity of the potential relief along the Bain deformation path to the magnetic state, are crucial for the picture of the transformation. With the temperature increase, a scenario of the phase transformation evolves from a homogeneous lattice instability at T < M S (M S is the temperature of the beginning of the martensitic transformation) to the growth and nucleation of embryos of the new phase at T > M S . In the latter case, a stage of formation of a tweed-like structure occurs, with a strong short-range order and slow interphase fluctuations.MSC: 74N10, 74N15, 82B26, 82B80, 82C26, 37K60

Role of magnetic degrees of freedom in a scenario of phase transformations in steel

“…One should stress that this agreement is reached for the model where main temperature dependence enters via the degree of short-range magnetic order. Thus, the closeness of the Curie temperature in bcc iron to the temperature of structural transformation is not accidental but is related with the essence of phase transformations both in elemental iron [5] and steel.…”

“…Other relevant degrees of freedom are volume per atom and magnitude of magnetic moment but we assume (following Ref. [5]) that they are fast and can therefore be taken into account just by optimization of the total energy along the Bain transformation path. The parameter of short-range magnetic order is introduced as for the case of pure iron [5].…”

“…We exploit the equations of motion used by us earlier for elemental iron [5] plus the equation of carbon diffusion:…”

“…Indeed, it was shown in Ref. [5] that above M S a broad temperature range exists where the transformation is martensite-like but includes nucleation and growth processes. We follow the concept of isothermal martensitic transformation [31][32][33][34] The results presented in Figure 4 are purely thermodynamic for the lines A 3 ,T 0 ,T F and do not take into account the internal strain produced by transformation which plays a crucial role in phase morphology and transformation kinetics.…”

Стабилизация Роста Перлитной Колонии В Результате Взаимодействия Углерода С Дилатациями Решетки

“…Энер-гии этих фаз на промежуточных температурах полу-чены в согласии с моделью Огучи для температур-ной зависимости спинового коррелятора [28]. Магнит-ная энтропия учитывается с привлечением теоремы Гельмана−Фейнмана [29]. Конфигурационная энтропия углерода учитывает, что атомы углерода в α-фазе рас-пределяются по трем подрешеткам октаэдрических меж-доузлий, а в γ-фазе могут занимать только четвертую часть октаэдрических междоузлий [30].…”