A quenched-in state of thermal equilibrium (at 723 K) in a single crystal of Cr-Fe-Co-Ni close to equal atomic percent was studied. Atom probe tomography revealed a single-phase state with no signs of long-range order. The presence of short-range order (SRO) was established by diffuse x-ray scattering exploiting the variation in scattering contrast close to the absorption edges of the constituents: At the incoming photon energies of 5969, 7092, and 8313 eV, SRO maxima that result from the linear superposition of the six partial SRO scattering patterns, were always found at X position. Electronic structure calculations showed that this type of maximum stems from the strong Cr-Ni and Cr-Co pair correlations, that are furthermore connected with the largest scattering contrast at 5969 eV. The calculated effective pair interaction parameters revealed an order-disorder transition at approximately 500 K to a L1 2-type (Fe,Co,Ni) 3 Cr structure. The calculated magnetic exchange interactions were dominantly of the antiferromagnetic type between Cr and any other alloy component and ferromagnetic between Fe, Co, and Ni. They yielded a Curie temperature (T C) of 120 K, close to experimental findings. Despite the low value of T C , the global magnetic state strongly affects chemical and elastic interactions in this system. In particular, it significantly increases the ordering tendency in the ferromagnetic state compared to the paramagnetic one.
Atomic ordering in Au-Pd alloys was studied by diffuse x-ray scattering and first-principles methods. Diffuse scattering was done of a single crystal of Au-48 at.% Pd that was aged at 703 K for 24 days. The weakly modulated short-range-order scattering exhibits diffuse maxima with an incommensurate wave vector, which can be related to a Fermi-surface nesting mechanism. From effective pair interaction parameters determined by the inverse Monte Carlo method, a one-dimensional long-period superstructure of the CH structure, LPS1, was found for AuPd. Concurrent electronic-structure calculations of the effective cluster interaction (ECI) parameters indicated the presence of another closely related superstructure, LPS2, at 0 K. At the same time, direct first-principles calculations of the total energies of the CH structure and further one-dimensional long-period superstructures predicted the stabilization of LPS4. Although the energy differences between these structures are small and a complex behavior of the effective interactions is expected due to the Fermi-surface nesting, experimental data and theoretical results both support the stabilization of a long-period superstructure of the CH structure for AuPd at 0 K. The ECI parameters determined by the screened generalized perturbation method also predicted a groundstate structure different from Au 7 Pd 5 , previously obtained from cluster expansion calculations. Its energetic preference was confirmed by direct total-energy calculations.
Interactions in Fe-Pd were studied using diffuse x-ray scattering and first-principles calculations. Diffuse x-ray scattering was performed from single crystals of Fe-38.2 at. % Pd and Fe-81.0 at. % Pd to investigate states of thermal equilibrium at 1023 K and 1073 K, respectively. Short-range-order scattering was separated and effective pair interaction (EPI) parameters were determined using the inverse Monte Carlo method. The EPI parameters are found to strongly vary with respect to data from a previous investigation of Fe-50 at. % Pd. Electronic-structure calculations of effective cluster interaction (ECI) parameters for these states showed the importance of considering multibody interactions and applying the disordered local moment model of the magnetic state: in the ferromagnetic model, the strength of the interactions gets overestimated. Close agreement is reached for short-range order between calculations and the present scattering experiments. Using either a linear compositional variation of the EPI parameters or ECI parameters for alloys with other Pd fractions, the shape of the order-disorder transition line on the Pd-rich side could be reproduced.
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