The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni and Cr-Ni alloys, and ternary Fe-Cr-Ni alloys is investigated using a combination of Density Functional Theory (DFT), Cluster Expansion (CE) and Magnetic Cluster Expansion (MCE) approaches. Energies, magnetic moments, and volumes of more than 500 alloy structures have been evaluated using DFT, and the predicted most stable configurations are compared with experimental observations. Deviations from the Vegard law in fcc Fe-Cr-Ni alloys, resulting from the non-linear variation of atomic magnetic moments as functions of alloy composition, are observed. Accuracy of the CE model is assessed against the DFT data, where for ternary Fe-Cr-Ni alloys the cross-validation error is found to be less than 12 meV/atom. A set of cluster interaction parameters is defined for each alloy, where it is used for predicting new ordered alloy structures. Fcc Fe2CrNi phase with Cu2NiZn-like crystal structure is predicted to be the global ground state of ternary Fe-Cr-Ni alloys, with the lowest chemical ordering temperature of 650K. DFT-based Monte Carlo (MC) simulations are applied to the investigation of order-disorder transitions in Fe-Cr-Ni alloys. Enthalpies of formation of ternary alloys predicted by MC simulations at 1600K, combined with magnetic correction derived from MCE, are in excellent agreement with experimental values measured at 1565K. The relative stability of fcc and bcc phases is assessed by comparing the free energies of alloy formation. Evaluation of the free energies involved the application of a dedicated algorithm for computing configurational entropies of the alloys. Chemical order is analyzed, as a function of temperature and composition, in terms of the Warren-Cowley Short-Range Order (SRO) parameters and effective chemical pairwise interactions. In addition to compositions close to binary intermetallic phases CrNi2, FeNi, FeNi3 and FeNi8, pronounced chemical order is found in fcc alloys near the centre of the ternary alloy composition triangle. The calculated SRO parameters compare favourably with experimental data on binary and ternary alloys. Finite temperature magnetic properties of fcc Fe-Cr-Ni alloys are investigated using an MCE Hamiltonian parameterized using a DFT database of energies and magnetic moments computed for a large number of alloy configurations. MCE simulations show that the ordered ternary Fe2CrNi alloy phase remains magnetic up to 850-900 K due to strong anti-ferromagnetic coupling between (Fe,Ni) and Cr atoms in the ternary Fe-Cr-Ni matrix.

An ab initio-based magnetic-cluster-expansion treatment developed for body-and face-centered cubic phases of iron and iron-chromium alloys is applied to modeling the ␣-␥ and ␥-␦ phase transitions in these materials. The Curie, Néel, and the structural phase-transition temperatures predicted by the model are in good agreement with experimental observations, indicating that it is the thermal excitation of magnetic and phonon degrees of freedom that stabilizes the fcc ␥ phase. The model also describes the occurrence of the ␥ loop in the phase diagram of Fe-Cr alloys for a realistic interval of temperatures and Cr concentrations.

Iron-chromium alloys are characterized by a complex phase diagram, by the small negative enthalpy of mixing at low Cr concentrations in the bcc ␣-phase of Fe, and by the inversion of the short-range order parameter. We present Monte Carlo simulations of the binary Fe-Cr alloy based on the cluster expansion approximation for the enthalpy of the system. The set of cluster expansion coefficients is validated against density functional calculations of energies of small clusters of chromium in bcc structure. We show that in the limit of small Cr concentration the enthalpy of mixing remains negative up to fairly high temperatures, and individual Cr atoms remain well separated from each other. Clustering of Cr atoms begins at concentrations exceeding approximately 10% at 800 K and 20% at 1400 K, with Cr-Fe interfaces being parallel to the ͓110͔ planes. Calculations show that the first and the second short-range order parameters change sign at approximately 10.5% Cr, in agreement with experimental observations. Semi-grand-canonical ensemble simulations used together with experimental data on vibrational entropy of mixing give an estimate for the temperature of the top of the ␣-␣Ј miscibility gap. We find that the complex ordering reactions occurring in Fe-Cr, as well as the thermodynamic properties of the alloy, can be reasonably well described using a few concentrationindependent cluster expansion coefficients.

We present density matrix renormalisation group calculations of the PariserParr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (1 3 B + u ) and even-parity singlet (2 1 A + g ) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1 1 B − u ) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2 1 A + g state lies below that of the 1 1 B − u state. We observe an attraction between the soliton-antisoliton pairs in the 2 1 A + g state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.