This review presents the recent progress in computational materials design, experimental realization, and control methods of spinodal nanodecomposition under three- and two-dimensional crystal-growth conditions in spintronic materials, such as magnetically doped semiconductors. The computational description of nanodecomposition, performed by combining first-principles calculations with kinetic Monte Carlo simulations, is discussed together with extensive electron microscopy, synchrotron radiation, scanning probe, and ion beam methods that have been employed to visualize binodal and spinodal nanodecomposition (chemical phase separation) as well as nanoprecipitation (crystallographic phase separation) in a range of semiconductor compounds with a concentration of transition metal (TM) impurities beyond the solubility limit. The role of growth conditions, codoping by shallow impurities, kinetic barriers, and surface reactions in controlling the aggregation of magnetic cations is highlighted. According to theoretical simulations and experimental results the TM-rich regions appear in the form of either nanodots (the dairiseki phase) or nanocolumns (the konbu phase) buried in the host semiconductor. Particular attention is paid to Mn-doped group III arsenides and antimonides, TM-doped group III nitrides, Mn- and Fe-doped Ge, and Cr-doped group II chalcogenides, in which ferromagnetic features persisting up to above room temperature correlate with the presence of nanodecomposition and account for the application-relevant magneto-optical and magnetotransport properties of these compounds. Finally, it is pointed out that spinodal nanodecomposition can be viewed as a new class of bottom-up approach to nanofabrication.

Carbon segregation is known to have an extreme influence on the cohesive energies and mechanical properties of grain boundaries (GBs) in steel. In this paper, the stability of a series of α-Fe〈110〉 symmetrical tilt grain boundaries (STGBs) with C was systematically investigated based on first-principles calculations. We used the newly-developed Tersoff/ZBL potential of Fe–C interaction constructed from the forces and disolution energies of various defect complexes with C in Fe calculated from first-principles. This potential shows a great effectiveness in considering large complex systems of STGB and determining the segregation sites of various STGB configurations. The stable location of C was analyzed from the view point of free volume formed by the GB systems. We found that the compact GBs were less attractive to C than the open ones. The GBs exhibited a strong attractive interaction with C compared to vacancies, therefore, a higher solubility of C can be expected in GB systems. The present simulation results are consistent with the experimental observations by TEM and APT method, and qualitatively explains the behaviour of C in Fe.

By combining first-principles electronic structure calculations and machine learning techniques, prediction models of elastic constants are constructed for BCC high-entropy alloys (HEA) containing 5 different elements chosen from 3d, 4d and 5d transition metals with equal concentration. Three independent elastic constants of randomly selected 2555 HEAs are calculated by using the full potential Korringa–Kohn–Rostoker (FPKKR) method with taking configurational disorder into account within the coherent potential approximation (CPA). From the obtained database of the elastic constants, prediction models are constructed by the linear regression using the descriptors generated by the linearly independent descriptor generation (LIDG) method. By optimizing the selection of descriptors based on the genetic algorithm (GA), prediction errors of 10.2 GPa, 4.5 GPa, 2.4 GPa and 7.7 GPa are achieved for bulk modulus $B$, shear moduli $c{ }^{\mathrm{\prime }}$, $c_{44}$ and Young’s modulus $E$, respectively. By using the generated model we propose some HEAs with low $E$. It is well known that the magnitude of $E$ is closely related to the shape of the calculated density of states (DOS). This statement is reconfirmed within the BCC HEAs, i.e., HEAs with larger DOS at the Fermi level shows smaller Young’s modulus and vice versa. Graphical abstract

An effective combination of the KKR-CPA method and the Kubo–Greenwood formula allows quantitative reproduction of electrical resistivity of CoSi and its alloys with 3d transition metals.

In this paper, the interaction of C with edge dislocations in α-Fe with Burgers vectors of 1/2⟨111⟩, ⟨100⟩, and ⟨110⟩ has been investigated using the classical force-field method in conjunction with the newly-developed Tersoff/ZBL interatomic potential of Fe–C. Here, the potential was constructed from the first-principles database containing force and energy information of various defect complexes with C in body centered cubic (BCC) Fe. The interaction of C and dislocations has been analyzed from the viewpoint of Voronoi volume formed by C and surrounding Fe atoms. It is found that the interaction between dislocations and C is more attractive when the Voronoi volume around C becomes larger. This tendency is similar to the case of grain boundaries reported previously. It is also found that the grain boundaries and dislocations trap C strongly compared to a single vacancy in BCC Fe, and among them more unstable defect structures attract C more strongly. The obtained tendency might offer a useful guideline to analyse the atomistic distribution of C in Fe with extended defects.

This review presents the recent progress in computational materials design, experimental realization, and control methods of spinodal nanodecomposition under three- and two-dimensional crystal-growth conditions in spintronic materials, such as magnetically doped semiconductors. The computational description of nanodecomposition, performed by combining first-principles calculations with kinetic Monte Carlo simulations, is discussed together with extensive electron microscopy, synchrotron radiation, scanning probe, and ion beam methods that have been employed to visualize binodal and spinodal nanodecomposition (chemical phase separation) as well as nanoprecipitation (crystallographic phase separation) in a range of semiconductor compounds with a concentration of transition metal (TM) impurities beyond the solubility limit. The role of growth conditions, co-doping by shallow impurities, kinetic barriers, and surface reactions in controlling the aggregation of magnetic cations is highlighted. According to theoretical simulations and experimental results the TM-rich regions appear either in the form of nanodots (the {\em dairiseki} phase) or nanocolumns (the {\em konbu} phase) buried in the host semiconductor. Particular attention is paid to Mn-doped group III arsenides and antimonides, TM-doped group III nitrides, Mn- and Fe-doped Ge, and Cr-doped group II chalcogenides, in which ferromagnetic features persisting up to above room temperature correlate with the presence of nanodecomposition and account for the application-relevant magneto-optical and magnetotransport properties of these compounds. Finally, it is pointed out that spinodal nanodecomposition can be viewed as a new class of bottom-up approach to nanofabrication.