A LATTICE STATISTICS MODEL DERIVED FROM THE TWO-LAYER ADSORPTION PROBLEM

1965 ◽  
Vol 43 (6) ◽  
pp. 980-985
Author(s):  
D. D. Betts ◽  
D. L. Hunter
Keyword(s):  
Nearest Neighbor ◽  
Chemical Potential ◽  
Physical Adsorption ◽  
Square Lattice ◽  
Lateral Interaction ◽  
Lattice Statistics ◽  
Regular Lattice ◽  
Adsorption Sites ◽  
Layer Adsorption ◽  
Gas Molecules

A model is proposed for the physical adsorption of two layers of gas molecules at the sites of a regular lattice with lateral interaction between nearest-neighbor molecules. The model is more complicated than the two-dimensional Ising model. However, for a particular relation among the three energy parameters and at a particular value of the chemical potential the model simplifies considerably. For the simplified model and a square lattice of adsorption sites, high- and low-temperature series expansions for the specific heat have been obtained and the transition temperature estimated.

Two-Dimensional Ising Model in an Annealed Random Field

1998 ◽  
Vol 12 (06n07) ◽  
pp. 231-237 ◽  
Author(s):  
C. E. Cordeiro ◽  
L. L. Gonçalves
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Nearest Neighbor ◽  
Chemical Potential ◽  
Square Lattice ◽  
Arbitrary Distribution ◽  
Exchange Constant ◽  
Uniform Field ◽  
Two Dimensional ◽  
Coupled Equations

The critical behavior of the two-dimensional Ising model (square lattice, exchange constant J) in an uniform field, and in an annealed random field is considered. The random field is generated by decorating the horizontal and vertical bonds of the lattice, and it satisfies an arbitrary distribution which is imposed by introducing a pseudo-chemical potential. By decimating the decorating variables the model can be mapped onto a homogeneous Ising model with effective exchange constant J′ and effective external field h′, dependent on the temperature. These parameters, which satisfy a set of coupled equations, depend on the spin average and nearest-neighbor two-spin correlation, and are obtained numerically. For the symmetric field distribution [Formula: see text] the mapping of the critical frontier on the (K′=βJ′,H′=βh′) plane onto the (K=β J,H=βh) plane is determined and, as in the model introduced by Essam and Place, there is a region on the (K, H) plane which cannot be reached from any real values of (K′, H′). The critical exponents are determined numerically, and it is shown that they do not satisfy renormalization relations obtained for their model.

scholarly journals Magnetic Properties of Quantum Square Heisenberg Antiferromagnet with Frustration: an Auxiliary Fermion Approach

2014 ◽  
Vol 24 (3) ◽  
pp. 193 ◽  
Author(s):  
Pham Thi Thanh Nga ◽  
Nguyen Toan Thang
Keyword(s):  
Nearest Neighbor ◽  
Chemical Potential ◽  
Local Coordinate System ◽  
Exchange Interactions ◽  
Square Lattice ◽  
Heisenberg Antiferromagnet ◽  
Ordered Phases ◽  
Fermionic Representation ◽  
Antiferromagnetic Model ◽  
Exchange Parameters

We study the magnetic ordered phases of the spin \(-\frac{1}{2}\) Heisenberg antiferromagnetic model with nearest \(J_1\) and next nearest neighbor \(J_2\) exchange interactions on the square lattice using fermionic representation of spin operators within Popov-Fedotov approach.The unphysical states are eliminated on each site by introducing an imaginary chemical potential. Working in local coordinate system for every site we investigate the different ordered phases in dependence on exchange parameters. At \(T = 0\) we recover the conventional spin wave results. 

scholarly journals Quantitative Evaluations of Hydrogen Diffusivity in V-X (X = Cr, Al, Pd) Alloy Membranes Based on Hydrogen Chemical Potential

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 67
Author(s):  
Asuka Suzuki ◽  
Hiroshi Yukawa
Keyword(s):  
Nearest Neighbor ◽  
Chemical Potential ◽  
Hydrogen Permeability ◽  
First Principle ◽  
Hydrogen Diffusivity ◽  
Hydrogen Atoms ◽  
First Principle Calculations ◽  
Blocking Effects ◽  
Pd Alloy ◽  
Quantitative Evaluations

Vanadium (V) has higher hydrogen permeability than Pd-based alloy membranes but exhibits poor resistance to hydrogen-induced embrittlement. The alloy elements are added to reduce hydrogen solubility and prevent hydrogen-induced embrittlement. To enhance hydrogen permeability, the alloy elements which improve hydrogen diffusivity in V are more suitable. In the present study, hydrogen diffusivity in V-Cr, V-Al, and V-Pd alloy membranes was investigated in view of the hydrogen chemical potential and compared with the previously reported results of V-Fe alloy membranes. The additions of Cr and Fe to V improved the mobility of hydrogen atoms. In contrast, those of Al and Pd decreased hydrogen diffusivity. The first principle calculations revealed that the hydrogen atoms cannot occupy the first-nearest neighbor T sites (T1 sites) of Al and Pd in the V crystal lattice. These blocking effects will be a dominant contributor to decreasing hydrogen diffusivity by the additions of Al and Pd. For V-based alloy membranes, Fe and Cr are more suitable alloy elements compared with Al and Pd in view of hydrogen diffusivity.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

Normal-Strain Induced Change in Lattice-Type for Confined Cyclohexane Films

1996 ◽  
Vol 464 ◽  
Author(s):  
J.E. Curry ◽  
J.H. Cushman
Keyword(s):  
Triangular Lattice ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Computer Experiments ◽  
Square Lattice ◽  
Melting Transition ◽  
Normal Strain ◽  
Surface Forces Apparatus ◽  
Bulk Fluid ◽  
Lattice Type

ABSTRACTOne to three layer cyclohexane films confined between mica-like surfaces are studied to elucidate changes in the films' lattice-type. The laterally confined film is in equilibrium with the bulk fluid that is well into the liquid regime of its phase diagram. Monte Carlo simulations are conducted at constant chemical potential, temperature, and V=Ah, where A is the lateral area and h is the separation between the walls. One and two layers of fluid freeze as h increases. The one layer fluid has a triangular lattice, while the two layer fluid exhibits first a square lattice and then a triangular lattice with increasing surface separation. In contrast to previous studies, solidlike order is induced primarily by the strong fluid-solid interaction and is largely a function of pore width. A shift in the relative alignment of the surfaces perturbs the solidlike fluid structure but does not cause the sudden shear melting transition associated with epitaxial alignment of the fluid atoms with the surface. There is a correlation between the shear stress calculated in the computer experiments and that measured in Surface Forces Apparatus experiments.

THE EXACT SOLUTION OF SOME LATTICE STATISTICS MODELS WITH FOUR STATES PER SITE

1964 ◽  
Vol 42 (8) ◽  
pp. 1564-1572 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Partition Function ◽  
Nearest Neighbor ◽  
Quaternary Alloy ◽  
Interesting Property ◽  
Two Dimensions ◽  
Lattice Statistics ◽  
Critical Temperatures ◽  
Different Types ◽  
Interacting Systems ◽  
Statistical Mechanical

Statistical mechanical ensembles of interacting systems localized at the sites of a regular lattice and each having four possible states are considered. A set of lattice functions is introduced which permits a considerable simplification of the partition function for general nearest-neighbor interactions. The particular case of the Potts four-state ferromagnet model is solved exactly in two dimensions. The order–disorder problem for a certain quaternary alloy model is also solved exactly on a square net. The quaternary alloy model has the interesting property that it has two critical temperatures and exhibits two different types of long-range order. The partition function for the spin-3/2 Ising model on a square net is expressed in terms of graphs without odd vertices, but has not been solved exactly.

Ascertaining the nanocluster formation within an ion-irradiated Pt/Ni/C multi-trilayer with X-ray absorption spectroscopy

2012 ◽  
Vol 20 (1) ◽  
pp. 137-144
Author(s):  
Nitya Ramanan ◽  
Sumalay Roy ◽  
Debdutta Lahiri ◽  
Surinder M. Sharma ◽  
B. N. Dev
Keyword(s):  
Absorption Spectroscopy ◽  
Structural Changes ◽  
Nearest Neighbor ◽  
Ion Irradiation ◽  
Physical Adsorption ◽  
X Ray ◽  
Bimetallic Nanoclusters ◽  
Wave Technique ◽  
Wide Scale ◽  
X Ray Absorption

In this work nanoclusters formed in a Pt/Ni/C multi-trilayer by the ion-irradiated method of synthesis are characterized. In particular, an attempt to understand the role of interfaces in the synthesis is made. With this objective, ion-irradiation-induced structural changes in a Pt/Ni/C multi-trilayer using X-ray absorption spectroscopy (at the NiK-edge) in conjunction with the X-ray standing-wave technique are investigated. The XANES analysis identifies chemical binding at pristine Ni/C and Ni/Pt interfaces, in contrast with physical adsorption at the Pt/C interface. The chemical nature of the interfaces determines their relative stability with respect to irradiation and controls the extent of metallic diffusion. The most interesting structural change, upon irradiation, is the disruption of the Pt/C interface and subsequent migration of Pt atoms towards pre-diffused Ni atoms within the C layer, leading to the formation of Ni-centered Ni–Pt bimetallic nanoclusters (with Ni:Pt = 60:40). These clusters are highly disordered beyond their nearest neighbor and find wide-scale applications as, for example, magnetic devicesetc. The implications of these findings on the design goals are discussed.

SUPERCONDUCTING CLASSES IN THE EXTENDED HUBBARD MODEL

1996 ◽  
Vol 10 (12) ◽  
pp. 1397-1423 ◽  
Author(s):  
MASA-AKI OZAKI ◽  
EIJI MIYAI ◽  
TOMOAKI KONISHI ◽  
KAORU HANAFUSA
Keyword(s):  
Hubbard Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
S Wave ◽  
Ferromagnetic Order ◽  
Numerical Studies ◽  
The Mean

This paper describes group theoretical classification of superconducting states (SC) in the extended Hubbard model with on-site repulsion (U), nearest neighbor attraction (V) and nearest neighbour exchange interaction (J) on the two-dimensional square lattice using the mean field approach. By decomposing the pairing interaction into irreducible parts; A1g, B1g and Eu of D4h point symmetry, we have derived two singlet SCs (s-wave and d-wave) from A1g and B1g, eight triplet SCs from Eu. The first three types of triplet SC have pairing by electrons with antiparallel spin, the second two types have pairing by electrons with equal spin and the last three types are non-unitary and have pairing by only up-spin electrons. We showed that three non-unitary states have to be accompanied with a ferromagnetic order from the structure of the maximal little groups. We performed numerical studies for these SCs. For parameters and electron density favorable for the ferromagnetic order, a non-unitary SC coexistent with ferromagnetism is most stable.

A Theoretical Study of H2S Toxic Gas Adsorption on Pristine and Doped Monolayer (AlN)21 Using Density Functional Theory

2020 ◽  
Vol 12 (02) ◽  
pp. 99-111
Author(s):  
Jamal A. Shlaka ◽  
◽  
Abbas H. Abo Nasria
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Theoretical Study ◽  
Gas Adsorption ◽  
Aluminium Nitride ◽  
Functional Theory ◽  
Adsorption Sites ◽  
Gas Molecules ◽  
Toxic Gas ◽  
Center Ring

Been studying the interactions between graphene - like aluminium nitride P(AlN)21 nano ribbons doped and defect (AlN)21Sheet, Molecules and small toxic gas molecules ( H2S), were built for two different adsorption sites on graphene like aluminium nitride P(AlN)21. this was done by employing B3LYP density functional theory (DFT) with 6-31G*(d,p) using Gaussian 09 program, Gaussian viw5.0 package of programs and Nanotube Modeller program 2018. the adsorptions of H2S on P(AlN)21, (C) atoms-doped P(AL-N)20 sheet, D-P(AL-N)20 and D-(C)atoms-doped P(AL-N)19 (on atom) with (Ead) (-0.468eV),(-0.473 eV), (-0.457 eV), (-0.4478 eV) and (-0.454 eV), respectively, (Ead) of H2S on the center ring of the P(AL-N)21, (C) atoms-doped P(AL-N)20 sheet, D-P(AL-N)20 and D-(C,B)atoms-doped P(AL-N)19 sheet are (-0.280 eV),(-0.465 eV), (-0.405 eV), (-0.468 eV) and -0.282 eV), respectively, are weak physisorption . However, the adsorptions of H2S, on the ((AlN)20 -B and D- (AlN)19 -B), (on atom N and center ring the sheet) are a strong chemisorption because of the (Ead) larger than -0.5 eV, due to the strong interaction, the ((AlN)20-B and D-(AlN)19-B), could catalyst or activate, through the results that we obtained, which are the improvement of the sheet P(AlN)21 by doping and per forming a defect in, it that can be used to design sensors. DOI: http://dx.doi.org/10.31257/2018/JKP/2020/120210

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