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Register a new userCoarse grained Density Functional theory of order-disorder phase transitions in metallic alloys
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The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing non-perturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. By taking advantage of a coarse grained formulation of the density functional theory [Bruno et al., Phys. Rev. B 77, 155108 (2008)] we develop a MonteCarlo technique, based on an ab initio Hamiltonian, that allows for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and Ni$_3$V support that our theory provides an appropriate description of order-disorder phase transitions.
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The class of the Generalized Coherent Potential Approximations (GCPA) to the Density Functional Theory (DFT) is introduced within the Multiple Scattering Theory formalism for dealing with, ordered or disordered, metallic alloys. All GCPA theories are based on a common ansatz for the kinetic part of the Hohenberg-Kohn functional and each theory of the class is specified by an external model concerning the potential reconstruction. The GCPA density functional consists of marginally coupled local contributions, does not depend on the details of the charge density and can be exactly rewritten as a function of the appropriate charge multipole moments associated with each lattice site. A general procedure based on the integration of the qV laws is described that allows for the explicit construction the same function. The coarse grained nature of the GCPA density functional implies great computational advantages and is connected with the O(N) scalability of GCPA algorithms. Moreover, it is shown that a convenient truncated series expansion of the GCPA functional leads to the Charge Excess Functional (CEF) theory [E. Bruno, L. Zingales and Y. Wang, Phys. Rev. Lett. {bf 91}, 166401 (2003)] which here is offered in a generalized version that includes multipolar interactions. CEF and the GCPA numerical results are compared with status of art LAPW full-potential density functional calculations for 62, bcc- and fcc-based, ordered CuZn alloys, in all the range of concentrations. These extensive tests show that the discrepancies between GCPA and CEF are always within the numerical accuracy of the calculations, both for the site charges and the total energies. Furthermore, GCPA and CEF very carefully reproduce the LAPW site charges and the total energy trends.
The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern research of material science. Here we study the crucial problem of representing DFT Hamiltonian for crystalline materials of arbitrary configurations via deep neural network. A general framework is proposed to deal with the infinite dimensionality and covariance transformation of DFT Hamiltonian matrix in virtue of locality and use message passing neural network together with graph representation for deep learning. Our example study on graphene-based systems demonstrates that high accuracy ($sim$meV) and good transferability can be obtained for DFT Hamiltonian, ensuring accurate predictions of materials properties without DFT. The Deep Hamiltonian method provides a solution to the accuracy-efficiency dilemma of DFT and opens new opportunities to explore large-scale materials and physics.
The distribution of local charge excesses (DLC) in metallic alloys, previously obtained as a result of the analysis of order N electronic structure calculations, is derived from a variational principle. A phenomenological Charge Excess Functional (CEF) theory is obtained which is determined by three concentration dependent, material specific, parameters that can be obtained from {it ab initio} calculations. The theory requires modest computational efforts and reproduces with an excellent accuracy the DLC and the electrostatic energies of ordered, substitutionally disordered or segregating metallic alloys and, hence, can be considered an efficient approach alternative to conventional electronic structure calculations. The substantial reduction of computing time opens new perspectives for the understanding of metallic systems and their mechanical properties.
We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.
Formation energy of the sigma-phase in the Fe-V alloy system, Delta E, was computed in the full compositional range of its occurrence (34 < x < 60) using the electronic band structure calculations by means of the KKR method. Delta E-values were found to strongly depend on the Fe concentration, also its variation with different site occupancies was characteristic of a given lattice site. Calculated magnetic and configuration entropy contributions were used to determine sublattice occupancies for various compositions and temperatures. The results agree well with those obtained from neutron diffraction measurements.
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