Ground-state structures and the random-state energy of the Madelung lattice (original) (raw)
Related papers
Predicting structural energies of atomic lattices
Physical Review B, 1991
The complexity of current ab initio quantum-mechanical calculations of the total energy of given distributions of atoms on a periodic lattice often limits explorations to just a few configurations. We show how such a small number of calculations can be used instead to compute the interaction energies of a generalized Ising model, which then readily provides predicted energies of many more interesting configurations. This is illustrated for A1As/GaAs systems.
An extended Falicov-Kimball model on a triangular lattice
EPL (Europhysics Letters), 2011
The combined effect of frustration and correlation in electrons is a matter of considerable interest of late. In this context a Falicov-Kimball model on a triangular lattice with two localized states, relevant for certain correlated systems, is considered. Making use of the local symmetries of the model, our numerical study reveals a number of orbital ordered ground states, tuned by the small changes in parameters while quantum fluctuations between the localized and extended states produce homogeneous mixed valence. The inversion symmetry of the Hamiltonian is broken by most of these ordered states leading to orbitally driven ferroelectricity. We demonstrate that there is no spontaneous symmetry breaking when the ground state is inhomogeneous. The study could be relevant for frustrated systems like GdI2, N aT iO2 (in its low temperature C2/m phase) where two Mott localized states couple to a conduction band.
A new approach for modelling lattice energy in finite crystal domains
Evaluation of internal energy in a crystal lattice requires precise calculation of lattice sums. Such evaluation is a problem in the case of small (nano) particles because the traditional methods are usually effective only for infinite lattices and are adapted to certain specific potentials. In this work, a new method has been developed for calculation of lattice energy. The method is a generalisation of conventional geometric probability techniques for arbitrary fixed lattices in a finite crystal domain. In our model, the lattice energy for wide range of twobody central interaction potentials (including long-range Coulomb potential) has been constructed using absolutely convergent sums. No artificial cut-off potential or periodical extension of the domain (which usually involved for such calculations) have been made for calculation of the lattice energy under this approach. To exemplify the applications of these techniques, the energy of Coulomb potential has been plotted as the function of the domain size.
Charge Ordering and Phase Separations in the Molecular Crystal Model
Acta Physica Polonica A, 2010
We analyse the ground state phase diagrams and thermodynamic properties of charge orderings in narrow band materials using the molecular crystal model in the static limit. We present results for the hypercubic lattices in dimensions d = 2 and d = ∞. We focus our study on the problem of phase separations involving charge orderings and the effects of next-nearest-neighbor hopping (t 2) on the charge ordered states in these systems. The ground state phase diagrams are evaluated for a few representative cases. Results for the molecular crystal model are compared with those obtained previously for the spinless fermion model with repulsive intersite interaction W .
Two types of global space-group optimization (GSGO) problems can be recognized in binary metallic alloys A q B 1−q : (i) configuration search problems, where the underlying crystal lattice is known and the aim is finding the most favorable decoration of the lattice by A and B atoms and (ii) lattice-type search problems, where neither the lattice type nor the decorations are given and the aim is finding energetically favorable lattice vectors and atomic occupations. Here, we address the second, lattice-type search problem in binary A q B 1−q metallic alloys, where the constituent solids A and B have different lattice types. We tackle this GSGO problem using an evolutionary algorithm, where a set of crystal structures with randomly selected lattice vectors and site occupations is evolved through a sequence of generations in which a given number of structures of highest LDA energy are replaced by new ones obtained by the generational operations of mutation or mating. Each new structure is locally relaxed to the nearest total-energy minimum by using the ab initio atomic forces and stresses. We applied this first-principles evolutionary GSGO scheme to metallic alloy systems where the nature of the intermediate A-B compounds is difficult to guess either because pure A and pure B have different lattice types and the (i) intermediate compound has the structure of one end-point (Al 3 Sc, AlSc 3 , CdPt 3 ), or (ii) none of them (CuPd, AlSc), or (iii) when the intermediate compound has lattice sites belonging simultaneously to a few types (fcc, bcc) (PdTi 3 ). The method found the correct structures, L1 2 type for Al 3 Sc, D0 19 type for AlSc 3 , 'CdPt 3 ' type for CdPt 3 , B2 type for CuPd and AlSc, and A15 type for PdTi 3 . However, in such stochastic methods, success is not guaranteed, since many independently started evolutionary sequences produce at the end different final structures: one has to select the lowest-energy result from a set of such independently started sequences. Interestingly, we also predict a hitherto unknown (P2/m) structure of the hard compound IrN 2 with energy lower than all previous predictions.
Lattice dynamics in PbMg1∕3Nb2∕3O3
Physical Review B, 2004
Lattice dynamics for five ordered PbMg 1/3 Nb 2/3 O3 supercells were calculated from first principles by the frozen phonon method. Maximal symmetries of all supercells are reduced by structural instabilities. Lattice modes corresponding to these instabilities, equilibrium ionic positions, and infrared reflectivity spectra were computed for all supercells. Results are compared with our experimental data for a chemically disordered PMN single crystal.
Lattice Element Models and Their Peculiarities
Archives of Computational Methods in Engineering, 2017
Your article is protected by copyright and all rights are held exclusively by CIMNE, Barcelona, Spain. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
Multiple-histogram Monte Carlo study of the Ising antiferromagnet on a stacked triangular lattice
Physical Review B, 1993
The nearest neighbor Ising antiferromagnet on a stacked triangular lattice is a frustrated cooperative system in which it is known that at least two long-range ordered states exist at low temperature. This model has also been of considerable interest as it is known to be a reasonable description of two antiferromagnetic insulators, CsCoBrs and CsCoC13. It has also been the subject of previous theoretical and simulation studies which have yielded con8icting results for the critical phenomena displayed near the transition from the paramagnetic to the high-temperature ordered phase. We have carried out a detailed Monte Carlo study of this system using the recently developed multiplehistogram technique and finite-size scaling analysis, with the purpose of extracting estimates for the critical exponents relevant to this continuous transition. Our results give P = 0.311(4), p = 1.43(3), o. =-0.05(3), and v = 0.685(3) which are not in agreement with previous Monte Carlo work. In addition, although they are close to the expectations from previous symmetry arguments, there are systematic differences between our results and these theoretical predictions. A possible interpretation of these Monte Carlo exponent estimates is that they do not correspond to those calculated for any known universality class, and add to the growing number of simple models of interacting spins, in which geometrical frustration is relevant, which appear to exhibit novel critical behavior. Finally, we have examined the evolution of real-space spin configurations and have seen that a buildup of correlations between anti-phase-domain walls, or solitons, along the stacking direction precedes the transition, an observation which is consistent with recent neutron-scattering measurements on CsCoBr3.
Ground-state energies of antiferromagnetic lattices
Physica A: Statistical Mechanics and its Applications, 1980
Approximate values for the ground-state energy of one-and two-dimensional antiferromagnetic systems are determined with ceils of an even number of spins. The interaction between the cells is treated as a perturbation.