Self-organization of charged particles on a 2D lattice, subject to an anisotropic Jahn-Teller-type interaction and 3D Coulomb repulsion is investigated. In the mean-field approximation without Coulomb interaction, the system displays a phase transition of first order. In the presence of the Coulomb repulsion the global phase separation becomes unfavorable and the system shows a mesoscopic phase separation, where the size of the charged regions is determined by the competition between the ordering energy and the Coulomb energy.The phase diagram of the system as a function of particle density and temperature is obtained by systematic Monte Carlo simulations. With decreasing temperature a crossover from a disordered state to a state composed from mesoscopic charged clusters is observed. In the phase separated state charged clusters with even number of particles are more stable than those with odd number of particles in a large range of particle densities. With increasing particle density at low temperatures a series of crossovers between states with different cluster sizes is observed. Above half filling in addition to the low temperature clustering another higher temperature scale, which corresponds to orbital ordering of particles, appears.We suggest that the diverse functional behaviour -including superconductivity -observed in transition metal oxides can be thought to arise from the self-organization of this type.PACS numbers:
If cooled down from high temperatures, some half‐Heusler alloys based on CoTiSb show a spontaneous phase separation into coexisting domains. In thermoelectric applications, this domain structure is beneficial for the efficiency because it reduces the lattice thermal conductivity, which increases the figure of merit. For this reason, it is of great relevance to understand the details of the demixing phenomenon. We combine density functional theory, Monte Carlo simulations, and mean field calculations in order to investigate the demixing behavior of CoTi1−xZxSb with Z= Sc, V, Cr, Mn, Fe, Cu. Based on the calculations we present phase diagrams, which provide the coexistence region of the materials. Density functional theory results show that for low temperatures, demixed states are more stable than mixed ones. With the help of an ab initio‐based cluster expansion of the configurational energy, we can perform mean field calculations and Monte Carlo simulations to study half‐Heusler alloys at higher temperature on a larger scale. With the mean field calculations, the coexistence region and the spinodal can be determined for regions far from the critical point. The Monte Carlo simulations help to improve the coexistence lines and provide insights into structures formed in alloys that are quenched into the coexistence region.
The half-Heusler system CoTi 1Àx Y x Sb (Y = Sc, V, Mn, Fe) has been investigated by means of an ab initio-based mean-field model which provides phase diagrams of alloys. Co(Ti,Y)Sb materials show a miscibility gap, which leads to spontaneous demixing within a spinodal region. The results are compared with experimental investigations of microstructure and transport properties of the alloys. The thermoelectric properties of the solid solution were investigated comprehensively by measuring the temperature dependence of the Seebeck coefficient as well as electrical and thermal conductivity. Compared with pure CoTiSb, the thermal conductivity of substituted CoTi 0:9 Y 0:1 Sb was significantly reduced by approximately 53% for Y = V. Here, we report on the effect of phase separation in the Co(Ti,Y)Sb system and its consequences for the thermoelectric figure or merit.
The effects of the vacancy concentration at the cation site of three half-Heuslers, VCoSb, NbCoSb, and TaCoSb, were studied with a combination of two computational methods: density functional theory and Monte Carlo simulations, both linked by a cluster expansion method. Our density functional method allows us to follow a gap opening in the electronic density of states in NbCoSb and TaCoSb as a function of vacancy concentration, starting from a metallic state with the Fermi-level crossing the valence states in the pristine crystal, passing throughout a p-type doped behavior, down to a semiconducting state at 20% of vacancies. In the case of VCoSb, the transition starts from the half-metallic ferromagnetic state, where VCoSb remains half-metallic until it achieves a semiconductor state at V$$_{0.8}$$ 0.8 CoSb composition, the transition leading to a magnetic–nonmagnetic crossover. Further increase of vacancies leads to non-polarized in-gap states in V$$_{0.75}$$ 0.75 CoSb, and polarized in-gaps in Nb$$_{0.77}$$ 0.77 CoSb, while Ta$$_{0.75}$$ 0.75 CoSb recovers a metallic behavior but with an n-character. Based on our cluster expansion, we can assert that Ta$$_{0.8}$$ 0.8 CoSb is slightly more stable than Nb$$_{0.8}$$ 0.8 CoSb, while both are much more stable than V$$_{0.8}$$ 0.8 CoSb. Temperature effects were studied through Monte Carlo simulations. The simulations show that, upon cooling, the ground states are hard to recover, and instead metastable states are formed. The vacancy arrangements were scrutinized with the help of suitable order parameters for the lattice vacancy occupation.
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