Nearest-neighbor Pair Interactions Research Articles

Thermodynamic calculations using reverse Monte Carlo.

We introduce the theoretical background needed to perform thermodynamic calculations using reverse Monte Carlo (RMC). The theory is developed for binary A_{x}B_{1-x} lattice systems. The main assumption is that the arrangement of A and B atoms can be described using short-ranged order (SRO) parameters. The detailed balance equation, which is expressed in terms of SRO parameters, is solved to obtain the equilibrium SRO parameter value for the given material interactions, temperature, and composition. Thermodynamic properties, such as the chemical potential, are evaluated using the equilibrium SRO parameter value. RMC enables the calculation of the probability distribution of the local atomic environments, which is needed in the detailed balance equation. We illustrate the application of our method to bulk lattice materials with different first nearest neighbor pair interactions. The main advantage of our approach is that the probability distribution from RMC can be stored in form of look-up tables, and used with a variety of interaction strengths and temperature for rapid estimation of thermodynamic properties. In all examples, the chemical potential is accurately evaluated in the matter of a few seconds on a desktop computer.

Investigations of the Co-Pt alloy phase diagram with neutron diffuse scattering, inverse cluster variation method, and Monte Carlo simulations

The short-range order in a CoPt alloy was determined at 1203 and 1423 K using neutron diffuse scattering measurements. The effective pair interactions provided by data analysis reproduce well the experimental order-disorder transition temperature in Monte Carlo simulations. They complete previous results reported for the Co-Pt system and are compared to those obtained within tight-binding and ab initio formalisms. Our results show that the important dependence of the nearest-neighbor pair interactions with composition is not related to the sample magnetic state at the measured temperatures. Interactions measured in the paramagnetic domain for the CoPt alloy behave like those in the ferromagnetic domain for the ${\mathrm{Co}}_{3}\mathrm{Pt}$ and ${\mathrm{Co}}_{0.65}{\mathrm{Pt}}_{0.35}$ alloys. The effective pair interactions related to the tight-binding Ising model provide a relatively good description of the CoPt alloy thermodynamics close to the ordering temperature (short-range order and temperature of phase transformation), even if they strongly differ from those measured in this study. The average magnetic moment of Co atoms at high temperatures was determined from the analysis of the intensity contribution that is not dependent on the scattering vector. The obtained value is very close to the moment measured at room temperature or determined from ab initio calculations. This confirms the Curie-Weiss behavior of the CoPt alloy. Finally, transmission electron microscope observations carried out on samples annealed for about 30 days confirmed that the order-disorder transition takes place in the 830--843 K temperature interval at the ${\mathrm{Co}}_{3}\mathrm{Pt}$ composition.

Dynamic magnetic hysteresis loop features of molecular-based magnetic materials and ferrimagnetic systems by the path probability method

Dynamic magnetic hysteresis loops (DMHL) features of molecular-based magnetic materials and ferrimagnetic systems are investigated by a mixed spin (1/2, 1) model by means of the path probability method (PPM). The PPM contains two rate constants; hence the DMHL features have been studied by using the method with two rate constants. In particular, the effects of the repulsive (J<0) and attractive (J>0) bilinear nearest-neighbor pair interactions, temperature (T), crystal-field interaction (D), angular frequency (ω) of the oscillating magnetic field and especially the rate constant (k2), which corresponds to the wheel speed in the melt spinning technique (MST), on the DMHL are investigated. The shapes and areas of hysteresis loops are affective sensibility by these system parameters. We also investigate the magnetic coercive fields and remanents magnetizations as a function ω. We found that the most of our results are in a good agreement with some theoretical and experimental reported works. We also observe the novel and interesting DMHL behaviors for lower values of T, and higher values of ω, k2 and D.

Finite-field phase transitions and criticality in a generalized kagomé Ising ferromagnet: Exact solutions

The standard two-parameter (nearest-neighbor pair-interaction J2 and magnetic field h) planar Ising model ferromagnet only has phase transitions in zero field. We generalize a standard kagomé Ising model ferromagnet by adding localized triplet Ising interactions J3. Exact solutions are obtained for the phase diagrams of the three-parameter model, demonstrating finite-field phase transitions and criticality. Necessary conditions for the latter findings include the pair-interaction parameter being ferromagnetic (J2>0), the applied field parameter competing against the intrinsic triplet-interaction parameter, the ratio of the triplet- and pair-interaction parameters residing within a determined finite symmetrical interval, and the field parameter being properly tuned, viz., tracing the pertinent field vs temperature phase boundary curve. The curvilinear shape of the phase boundary facilitates the relative strength |J3|∕J2 of the triplet interaction to be experimentally accessible. Employing generalized fluid–magnet correspondence relations, it is mathematically convenient and informative to affiliate the above magnetic phase diagrams with the corresponding fluid phase diagrams of the associated generalized kagomé lattice-gas model.

Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

A generalised perturbation-based equation of state for thermodynamic modelling of fluids over a wide range of density

ABSTRACTA new generalized perturbed thermodynamic nonlinear isotherm regularity (GPTNLIR) equation of state (EoS) has been proposed for the fluids over the entire density range from gas to liquid. The GPTNLIR has been derived on the basis of an effective nearest neighbor pair interaction of an extended average effective pair potential (AEPP) in the framework of the thermodynamic perturbation theory (TPT). The selected AEPP is an extended Lennard-Jones (12, 6, 3) type which considers the repulsive, dispersion, dipole-dipole and longer-range interactions between pair molecules, respectively. Based on the EoS, a non-linear relationship exists between (Z– ZCS)v2 and ρ for each isotherm of fluid, where Zis the compression factor, v=1/ρis the molar volume, ZCS is Carnahan–Starling (CS) expression for the compression factor of the reference fluid with the temperature-dependent effective hard-core diameter (σeff). The validity of EoS against the experimental p–v–Tdata were tested for a variety of fluids, including polar, non-polar, hydrogen bonded and quantum fluids. This EoS provides the estimation of σeff at T>Tc, T=Tc and T<Tc, in which Tc is critical temperature, for each real fluid using its experimental p–v–T data and the extension of TPT theory as well.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

First-principles study on thermodynamic properties of CdxZn1-xO alloys

Bandgap engineering is one of the keys to practical applications of ZnO. Using ternary ZnMeO (Me=Be, Mg, Cd, etc.) alloys to regulate the bandgap of ZnO has been widely studied. Alloying ZnO with CdO to form CdxZn1-xO is an effective way to narrow down the bandgap of ZnO. With its narrower bandgap, CdxZn1-xO is a promising candidate for fabricating optoelectronic devices operable in the UV-visible wavelength region. In this work, we study the thermodynamic properties of CdxZn1-xO alloys of both wurtzite (WZ) and rock salt (RS) structures by first-principles calculations based on density functional theory (DFT) combined with the cluster expansion approach. The effective cluster interactions (ECIs) fitted formation energies agree well with the DFT-calculated formation energies for different compositions and structures correspondingly, validating the cluster expansion approach in calculations of the formation energy for CdxZn1-xO alloys. It is found that, for both WZ-CdxZn1-xO and RS-CdxZn1-xO alloys, the ECIs involve pair, triplet and quadruplet interactions: the pair interactions are dominant and contribute mostly to the formation energy. The first-and second-neighbor pair interaction parameters of WZ-CdxZn1-xO are positive, which indicates a tendency of ordering in WZ-CdxZn1-xO. For RS-CdxZn1-xO alloys, the nearest-neighbor pair interaction is negative, indicating a tendency to phase separation. The dominant positive second-neighbor pair interaction, however, appears to favor the ordering tendency. For both the WZ-CdxZn1-xO and RS-CdxZn1-xO alloys, the calculated formation energy of most structures is positive in the whole composition range, except for WZ-CdxZn1-xO with Cd concentrations of 1/3 and 2/3. Then, the crystal and electronic band structures of the metastable WZ-Cd1/3Zn2/3O and WZ-Cd2/3Zn1/3O are calculated. It turns out that both lattice constants a and c increase while the value of c/a and the bond angle of OZn(Cd)O decrease with increasing Cd concentration in the WZ-CdxZn1-xO alloys. Analyses of the band structures, densities of states (DOSs) and partial densities of states of WZ-CdxZn1-xO alloys reveal that the valence band maximum (VBM) is determined by O-2 p states and the conduction band minimum (CBM) stems from the hybrid Cd-5 s and Zn-4 s orbital. The VBM rises while the CBM declines, leading to the decrease of the bandgap of WZ-CdxZn1-xO with increasing Cd concentration. At finite temperatures, the thermal stability of the solid-state system is determined by Gibbs free energy. The bimodal curve, which indicates the equilibrium solubility limits as a function of temperature, can be calculated by the common tangent approach from the Gibbs free energy. The critical temperatures, above which complete miscibility is possible for some concentrations, are 1000 and 2250 K for WZ and RS phases, respectively. The higher critical temperature implies that it is more difficult to form RS-CdxZn1-xO than to form WZ-CdxZn1-xO. Finally, the phase diagrams of WZ-CdxZn1-xO and RS-CdxZn1-xO are derived based on calculations of the Gibbs free energy. At 1600 K, the solubility of Cd in WZ-ZnO amounts to 0.13, while the solubility of Zn in RS-CdO limits to only 0.01, indicating that it is much easier to incorporate Cd into WZ-ZnO than to incorporate Zn into RS-CdO.

Investigation of a core/shell Ising nanoparticle: Thermal and magnetic properties

The phase diagrams and magnetic hysteresis behavior of a spin-12 Ising core/shell nanoparticle are investigated by the use of the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions. Nearest-neighbor pair interactions are incorporated between the Ising spins in the three parts of the nanoparticle that are core, core/shell and surface shell. The effects of the external magnetic field and core/shell exchange interaction on the thermal magnetization and susceptibility of the system are examined.

Magnetic Properties of a Transverse Ising Nanoparticle

We use the effective field theory with a probability distribution technique to investigate the magnetic properties of an antiferromagnetic Ising core/shell nanoparticle with a negative interlayer coupling core/shell in the presence of both the longitudinal and the transverse fields. Nearest-neighbor pair interactions are incorporated between the Ising spins in three parts that are core, core/shell, and surface shell. The effects of the external and the transverse fields and the exchange interactions between core/shell and in surface shell on the hysteresis loops and the susceptibility of the nanoparticle are examined. A number of interesting phenomena have been found.

Order of Phase Transition on a Simple Cubic Lattice Determined by Cluster Variation Method

Detailed analyses of the free energy behavior near the order-disorder transition temperature on a simple cubic lattice are attempted by cluster variation method (CVM). The entropy is formulated within a cubic approximation of the CVM and two kinds of nearest neighbor pair interaction energies are assumed in the internal energy; one is independent of an atomic distance, r, and the other depends on r through Lennard-Jones type pair potential. In both cases, it is found that the order of the transition is of second order.

Dynamic phase diagrams of a mixed spin-1 and spin-5/2 Ising system in an oscillating magnetic field

We study the nonequilibrium aspects of the kinetics of a mixed spin-1 and spin-5/2 Ising system, including the biquadratic nearest-neighbor pair interaction (K) and the crystal-field interaction (D), under the presence of a time-dependent oscillating external magnetic field within a mean-field approach. The set of mean-field dynamic equations is obtained by employing the Glauber transition rates. We investigate the time variations of the average order parameters to find the phases in the system. We also study the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition (DPT) points. The dynamic phase diagrams are presented in three dierent planes. The phase diagrams are discussed, and a comparison is made with the results of other kinetic mixed spin Ising systems.

Vortex core states in a minimal two-band model for iron-based superconductors

The pairing symmetry is one of the major issues in the study of iron-based superconductors. We adopt a minimal two-band tight-binding model with various channels of pairing interaction, and derive a set of two-band Bogoliubov--de Gennes (BdG) equations. The BdG equations are implemented in real space and then solved self-consistently via exact diagonalization. In the uniform case, we find that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing state is most favorable for a nearest-neighbor pairing interaction while the ${s}_{{x}^{2}{y}^{2}}$-wave pairing state is most favorable for a next-nearest-neighbor pairing interaction, which is consistent with that reported by Seo et al. [Phys. Rev. Lett. 101, 206404 (2008)]. We then proceed to study the local electronic structure around a magnetic vortex core for both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and ${s}_{{x}^{2}{y}^{2}}$-wave pairing symmetry in the mixed state. It is found from the local density of states spectra and its spatial variation that the resonance core states near the Fermi energy for the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing symmetry are bound while those for the ${s}_{{x}^{2}{y}^{2}}$-wave pairing symmetry can evolve from the localized states into extended ones with varying electron filling factor. Furthermore, by including an effective exchange interaction, the emergent antiferromagnetic spin-density-wave order can suppress the resonance core states, which provides one possible avenue to understand the absence of resonance peak as revealed by recent scanning tunneling microscopy experiment by Yin et al. [Phys. Rev. Lett. 102, 097002 (2009)].

Dynamic phase transitions and dynamic phase diagrams in the kinetic mixed spin-1 and spin-2 Ising system in an oscillating magnetic field

We study the nonequilibrium aspects of the kinetics of a mixed spin-1 and spin-2 Ising system including the biquadratic nearest-neighbor pair interaction (K) and crystal-field interaction (D) under the presence of a time-dependent oscillating external magnetic field within a mean-field approach. In particular, we calculate the dynamic phase transition (DPT) temperatures and present dynamic phase diagrams. The set of mean-field dynamic equations is obtained by employing Glauber transition rates. We investigate the time variations of average order parameters to find the phases in the system. We also study the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the DPT points. The dynamic phase diagrams are presented in three different planes. Phase diagrams contain disordered (d), ferrimagnetic (i), antiquadrupolar or staggered (a) phases, and four coexistence or mixed phase regions, namely i+d, i+a, i+a+d and a+d mixed phases, that strongly depend on interaction parameters.

Constructing ground state configurations of lattice polymers

In this work we show how to generate ground state configurations of two-dimensional lattice polymers with nearest-neighbor pair interactions between nonbonded monomers. We describe a number of traps that have to be avoided, and how to randomize the configuration.

Spin-1 Model of Noninteracting Nanoparticles

In this work, we presented a spin-1 model to investigate the magnetic properties of noninteracting monodomain nanoparticles based on the pair approximation. Nearest-neighbor pair interactions are incorporated between the Ising spins in three parts that are core, core–surface, and surface within the nanoparticle. Using the spin-1 Ising model of magnetization in the pair approximation, we calculated the free energy and minimized with respect to pair variables to obtain the field-cooled magnetization. Hysteresis loops of the system were plotted for various values of exchange coupling constants, and axial anisotropy of strength which couples the core, core–surface, and surface regions. The coercive field and its linear fit to the data were plotted as a function of radius of ferromagnetic nanoparticles.

Solutions for correlations along the coexistence curve and at the critical point of a kagomé lattice gas with three-particle interactions

We consider a two-dimensional (d=2) kagomé lattice gas model with attractive three-particle interactions around each triangular face of the kagomé lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagomé lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature and are compared with corresponding results in a traditional kagomé lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.

THE FINITE-SIZE SCALING STUDY OF THE SPECIFIC HEAT AND THE BINDER PARAMETER FOR THE FIVE-DIMENSIONAL ISING MODEL

The five-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using finite-size lattices with the linear dimensions L=4, 6, 8, 10, 12, 14, and 16. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically-predicted expression near the infinite-lattice critical temperature. The approximate values for the critical temperature of the infinite-lattice, T c =8.8063, T c =8.7825 and T c =8.7572, are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of T c =8.7787. The value obtained for the critical exponent of the specific heat, i.e. α=0.009, is also in agreement with α=0 predicted by the theory.

Hydrogen-induced Sb atom reconstruction3×3→2×1on Si(111) as an example of a six-state model

A six-state model is proposed to describe the hydrogen-induced $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ $(\text{trimers})\ensuremath{\rightarrow}2\ifmmode\times\else\texttimes\fi{}1$ (zigzag chains) reconstruction of 1 ML of Sb atoms on Si(111). Attractive nearest-neighbor Sb-Sb pair interactions and also triple interaction ${v}_{t}$ are considered. The phase diagram of the system with and without ${v}_{t}$ is calculated when no hydrogen atoms are adsorbed. Second-order phase transitions are obtained between a disordered phase and both ordered phases, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and $2\ifmmode\times\else\texttimes\fi{}1$, when ${v}_{t}=0$. The possibility of phase separation close to the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ensuremath{\rightarrow}2\ifmmode\times\else\texttimes\fi{}1$ phase boundary is discussed when ${v}_{t}$ interaction is included. Corroborating recent experimental data, we demonstrate that adsorption of small coverage of hydrogen atoms turns the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ phase into mixed $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and $2\ifmmode\times\else\texttimes\fi{}1$ structure. The length and number of zigzag chains grow with the increase in hydrogen concentration.

THE FINITE-SIZE SCALING STUDY OF THE SPECIFIC HEAT AND THE BINDER PARAMETER FOR THE 7-DIMENSIONAL ISING MODEL

The 7-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 4, 6, 8. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T c = 12.866(2), T c = 12.871(2) and T c = 12.871(49) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise values of the Creutz cellular automaton results of T c = 12.8700(42), the 1/d-expansion result of T c = 12.8712, the series expansion result of T c = 12.86902(33), the dynamic Monte Carlo result of T c = 12.8667(50). The values obtained for the critical exponent of the specific heat, i.e., α = 0.011(76), α = -0.002, α = 0.011(5) and α = 0.082(32) corresponding to the above T c values, respectively, are in agreement with α = 0 predicted by the theory. Moreover the values for the Binder parameter are calculated as gL(T c ) = -1.022(28), gL(T c ) = -1.09, gL(T c ) = -1.01(12) and gL(T c ) = -1.34(55) corresponding to the above T c values, respectively.