Nearest-neighbor Interactions Research Articles

Modeling the effects of near-neighbor cooperative interactions on contractile dynamics in murine and porcine myocardium

Modeling the effects of near-neighbor cooperative interactions on contractile dynamics in murine and porcine myocardium

Inducing Ferrimagnetic Exchange in 1D-FeSe2 Chains Using Heteroleptic Amine Complexes: [Fe(en)(tren)][FeSe2]2.

[Fe(en)(tren)][FeSe2]2 (en = ethylenediamine, C2H8N2, tren = tris(2-aminoethyl)amine, C6H18N4) has been synthesized by a mixed-ligand solvothermal method. Its crystal structure contains heteroleptic [Fe(en)(tren)]2+ complexes with distorted octahedral coordination, incorporated between 1D-FeSe2 chains composed of edge-sharing FeSe4 tetrahedra. The twisted octahedral coordination environment of the Fe-amine complex leads to partial dimerization of Fe-Fe distances in the FeSe2 chains so that the FeSe4 polyhedra deviate strongly from the regular tetrahedral geometry. 57Fe Mössbauer spectroscopy reveals oxidation states of +3 for the Fechain atoms and +2 for the Fecomplex atoms. The close proximity of Fe atoms in the chains promotes ferromagnetic nearest neighbor interactions, as indicated by a positive Weiss constant, θ = +53.8(6) K, derived from the Curie-Weiss fitting. Magnetometry and heat capacity reveal two consecutive magnetic transitions below 10 K. DFT calculations suggest that the ordering observed at 4 K is due to antiferromagnetic intrachain interactions in the 1D-FeSe2 chains. The combination of two different ligands creates an asymmetric coordination environment that induces changes in the structure of the Fe-Se fragments. This synthetic strategy opens new ways to explore the effects of ligand field strength on the structure of both Fe-amine complexes and surrounding Fe-Se chains.

Investigation of Nearest Neighbor Interactions in Nickel Substituted Cobalt Using 59Co IFNMR

Co100-x Nix (x = 10, 20, 30, 40) alloys were synthesized via the chemical method by reducing nitrates of cobalt and nickel using hydrazine as a reducing agent. The proportion of solvents, ethanol, and water was maintained constant for all the samples in the series. The structure and morphology of the samples were examined based on X-Ray diffraction (XRD) data and Scanning Electron Microscope (SEM) images. From XRD it was evident that the system had a mixture of hexagonal close packed (hcp) and face centered cubic (fcc) phases. The amount of hcp phase in the composition gradually reduced as the concentration of nickel increased. The effect of substitution of nickel on cobalt was studied using a home built 59Co internal field nuclear magnetic resonance (IFNMR) spectrometer. Further, the saturation magnetization and hence magnetic field anisotropy values, obtained from M vs H loops, are found to vary with nickel concentration. The NMR results show a broadening of the NMR signals in comparison with the pure phase of cobalt. The NMR spectra and the number of peaks were assigned to possible cobalt-nickel neighbors, and the percentage of such combinations is interpreted in terms of the frequency and intensity of the peaks. This percentage of different nickel-cobalt combinations was compared with the random distribution obtained using the binomial distribution function. This comparison shows a clear trend compared to that analysed by the IFNMR experiment.

Electron doping as a handle to increase the Curie temperature in ferrimagnetic Mn3Si2X6 (X = Se, Te).

By analysing the results of ab initio simulations performed for Mn3Si2X6 (X = Se, Te), we first discuss the analogies and the differences in electronic and magnetic properties arising from the anion substitution, in terms of size, electronegativity, band widths of p electrons and spin-orbit coupling strengths. For example, through mean-field theory and simulations based on density functional theory, we demonstrate that magnetic frustration, known to be present in Mn3Si2Te6, also exists in Mn3Si2Se6 and leading to a ferrimagnetic ground state. Building on these results, we propose a strategy, electronic doping, to reduce the frustration and thus to increase the Curie temperature (TC). To this end, we first study the effect of electronic doping on the electronic structure and magnetic properties and discuss the differences in the two compounds, along with their causes. Secondly, we perform Monte-Carlo simulations, considering from the first to the fifth nearest-neighbor magnetic interactions and single-ion anisotropy, and show that electron doping efficiently raises the TC.

Two-dimensional ferromagnetism induced by Jahn-Teller distortion and orbital order

As the dimension of the system decreases, the quantum confinement effect and electronic correlation interaction inside the material will be correspondingly enhanced, often resulting in some novel physical properties. Recently, the freestanding perovskite oxide films down to the monolayer limit have been successfully prepared and can be transferred to any desired substrate, providing a great opportunity to explore the functional properties of two-dimensional perovskites. In perovskite materials, Jahn-Teller distortion and orbital order often cause a variety of correlated electronic behaviors. However, unlike van der Waals materials that retain their structural and chemical bonding characteristics when reduced to the monolayer limit, perovskite materials may undergo structural reconstruction when reduced to two dimensions. Therefore, whether Jahn-Teller distortion and related effects exist in the perovskite monolayer limit, and whether two-dimensional perovskite can exhibit some new properties different from its bulk phase, have become urgent issues to be solved. In this work, perovskite fluoride KCuF<sub>3</sub> and its monolayer have been comparatively studied by means of first-principles calculation, symmetry analysis, and Monte Carlo simulation methods, to reveal the change in lattice dynamics, structural, electronic, and magnetic properties caused by dimensionality reduction in perovskites. The results show that the cooperative Jahn-Teller distortion and the in-plane staggered orbital order occurring in the KCuF<sub>3</sub> bulk can be retained to the monolayer limit. However, unlike the bulk phase, the Jahn-Teller distortion mode appears as a soft mode of the prototype phase in the monolayer, and the insulating property of the monolayer does not rely on the emergence of the Jahn-Teller distortion, but is related to the enhancement of the electronic correlation effect. The staggered orbital order causes the nearest-neighbor exchange interaction to be ferromagnetic, resulting in the monolayer being a two-dimensional ferromagnetic insulator, different from the antiferromagnetic phase in the bulk. Monte Carlo simulations predict that the Curie temperature of the monolayer is about 5 K, which is much lower than the Néel temperature of the bulk phase, indicating that the disappearance of interlayer coupling leads to a significant reduction in the magnetic phase transition temperature. This work provides guidance and reference for the study of two-dimensional perovskite materials and the design of perovskite-based two-dimensional ferromagnets.

Theoretical study of long-range ordered vacancy distribution in two-dimensional boron structures

<sec>In a two-dimensional boron structure, the ordered high-concentration vacancy distribution can enhance structural stability and significantly modulates material properties. Based on recent experimental progress, herein we particularly focus on the two-dimensional boron structures with a striped distribution of hexagonal vacancies, in order to explore the formation of long-period boron structures.</sec><sec>Utilizing the structures of alloy generation and recognition (SAGAR) program developed by our group, we eliminate duplicate structures according to the structural symmetry to reduce computational cost. An effective model system is proposed to investigate the effect of vacancy distribution on the stability of the system, where the interactions between vacancies are utilized for estimating the total energy. By selecting structures with appropriate concentrations and combining first-principles calculations, the parameters in the model are fitted for different vacancy neighbor interactions, which can be further used to predict stable structures at various vacancy concentrations. The feasibility of model analysis is emphasized for structural screening, showing the good agreement between the parameterized model and the first-principles calculations.</sec><sec>Interestingly, under the same vacancy concentration, stable boron structures with different cell sizes exhibit distinct vacancy distributions, indicating a trend of long-period distribution for ground state structures. To address this phenomenon, when the stable candidate structures from the 1/6 series are dominant in number within the computable range and the changes in neighbor statistics can be clearly seen, we select the structures from this concentration series for detailed calculations.</sec><sec>The calculation results indicate that the convergence of the average energy is primarily influenced by the interaction between the fourth nearest neighbor and the sixth nearest neighbor. When considering only these two neighbors, the system energy changes with the increase of cell size as follows: the average energy of structures with a cell size being an even multiple of the minimum cell size keeps unchanged, while the average energy of structure with a cell size being an odd multiple of the minimum cell size gradually decreases, eventually converging to a stable value. When including the interactions between the ninth nearest neighbor and the tenth nearest neighbor, the average energy of structures with a cell size being an even times the minimum cell size also decreases gradually. The average energy decreases with oscillations, with the magnitude gradually diminishing and eventually stabilizing. This discovery reveals that the enhanced stability of long-period structures is attributed to the competitive interactions among different neighboring vacancies.</sec>

Pressure-induced structural and magnetic ordering transitions in the J1-J2 square lattice antiferromagnets AMoOPO4Cl (A = K, Rb).

By means of ab initio density functional theory calculations taking into account electronic correlation and van der Waals force, we conducted comprehensive studies of the electronic and magnetic properties, as well as structural and magnetic ordering evolution under pressure of the square lattice antiferromagnets AMoOPO4Cl (A = K, Rb) containing Mo5+ ions with , theoretically predicted as the potential candidates for achieving quantum phases, existing in the boundary regimes for square lattice magnets. Our results indicate that the columnar antiferromagnetic ordering, experimentally determined, is the magnetic ground state of the ambient P4/nmm phase, stabilized by the predominant antiferromagnetic next nearest neighbor interaction J2 in the diagonal directions of the square lattice, regardless of the effective Hubbard amendment values. More importantly, the P4/n phase, involving the mutual twisting of the MoO5Cl and PO4 polyhedra, satisfactorily reproduces the experimentally observed structural transition and the subsequent magnetic ordering transition from columnar antiferromagnetic ordering to Néel antiferromagnetic one, identified to be the appropriate high pressure structure. Furthermore, the mechanism underlined responsible for the magnetic ordering transition at high pressure has been disclosed in terms of density of states and spin density isosurface analysis across the transition. The loss of mirror plane symmetry in the P4/n phase activates the P 3s orbitals to participate in the magnetic interaction, giving rise to a competitive ferromagnetic superexchange interaction, in addition to antiferromagnetic direct one, and consequently initiating the magnetic ordering transition. The insights revealed here not only deepen our understanding of the electronic properties and structural and magnetic ordering transitions under high pressure of square lattice antiferromagnets AMoOPO4Cl (A = K, Rb), but also push the boundaries of knowledge by recognizing the role of nonmagnetic ions P 3s in magnetic exchange coupling.

Persistent current in a mesoscopic Holstein-Hubbard ring with Dresselhaus interaction

The effect of electron-phonon coupling, onsite repulsive Coulomb interaction and temperature on the persistent current in a quantum ring is studied in the presence of Dresselhaus spin-orbit interaction. The quantum ring threaded by the Aharonov-Bohm flux is modelled by the one-dimensional Holstein-Hubbard-Dresselhaus Hamiltonian. The electron-phonon interaction and Dresselhaus spin-orbit interaction are decoupled by employing the Lang-Firsov coherent transformation and a unitary transformation respectively. Thereafter, a self-consistent diagonalization technique is performed numerically at the Hartree-Fock level to obtain the effective electronic energy and current. It is shown that the intrinsic Dresselhaus spin-orbit interaction enhances the persistent charge and spin currents significantly. On the other hand, the persistent current is reduced by the onsite and nearest-neighbour electron-phonon interaction and Coulomb interaction. Also, the behaviour of the currents is modified by temperature. The spin-splitting of persistent spin current is enhanced considerably by Dresselhaus spin-orbit interaction and this splitting is tuneable in different regimes of magnetic flux, temperature, chemical potential and the interactions present in the system.

GROUND STATES FOR THE SOS MODEL WITH COMPETING BINARY INTERACTIONS ON A CAYLEY TREE OF ORDER THREE

We consider a SOS (solid-on-solid) model with nearest-neighbor interaction prolonged next-nearest-neighbor interaction and one level next-nearest-neighbor interaction where the spin takes values in the set on a Cayley tree of order three. In the paper, we study translation-invariant and periodic ground states of the model SOS.

Signature of elementary excitations in Se-substituted layered triangular-lattice antiferromagnet CuCrS2

Geometrical spin frustration in a layered triangular-lattice system prohibits the long-range magnetic order and could give rise to unusual spin-disordered states of matter in which spins are strongly correlated and highly entangled with low-energy excitations. Here we investigate the low-temperature magnetic and specific heat properties of the layered triangular-lattice system CuCr(S1-xSex)2 within the entire Se-for-S substitution range. In magnetization measurements, the x = 0 phase exhibits a sharp cusp-like antiferromagnetic transition at 38 K, while for all the Se-substituted samples a broad maximum along with a spin-glass-like freezing at low temperatures is seen. The Curie-Weiss temperature systematically increases from −122 K for x = 0 to + 15 K for x = 1. These observations suggest that the magnetic ground state is determined by the competition between antiferromagnetic direct exchange interactions and ferromagnetic super-exchange interactions. For x = 0, the magnetic contribution to heat capacity exhibits a sharp jump at the magnetic transition temperature indicative of 3D long-range magnetic order, while for the x > 0 samples it increases smoothly across the magnetic transition range following a power-law (∼T2.1) behavior. All these results are in line with an existence of unusual gapless spin-liquid like excitations originating from the spin frustrations and competing nearest-neighbor interactions in CuCr(S,Se)2.

Unveiling exotic magnetic phase diagram of a non-Heisenberg quasicrystal approximant

A magnetic phase diagram of the non-Heisenberg Tsai-type 1/1 Au-Ga-Tb approximant crystal (AC) has been established across a wide electron-per-atom (e/a) range via magnetization and powder neutron diffraction measurements. The diagram revealed exotic ferromagnetic (FM) and antiferromagnetic (AFM) orders that originate from the unique local spin icosahedron common to icosahedral quasicrystals (iQCs) and ACs; The noncoplanar whirling AFM order is stabilized as the ground state at the e/a of 1.72 or less whereas a noncoplanar whirling FM order was found at the larger e/a of 1.80, with magnetic moments tangential to the Tb icosahedron in both cases. Moreover, the FM/AFM phase selection rule was unveiled in terms of the nearest neighbour (J1) and next nearest neighbour (J2) interactions by numerical calculations on a non-Heisenberg single icosahedron. The present findings will pave the way for understanding the intriguing magnetic orders of not only non-Heisenberg FM/AFM ACs but also non-Heisenberg FM/AFM iQCs, the latter of which are yet to be discovered.

Ising Ladder with Four-Spin Plaquette Interaction in a Transverse Magnetic Field.

The spin-1/2 quantum transverse Ising model, defined on a ladder structure, with nearest-neighbor and four-spin interaction on a plaquette, was studied by using exact diagonalization on finite ladders together with finite-size-scaling procedures. The quantum phase transition between the ferromagnetic and paramagnetic phases has then been obtained by extrapolating the data to the thermodynamic limit. The critical transverse field decreases as the antiferromagnetic four-spin interaction increases and reaches a multicritical point. However, the exact diagonalization approach was not able to capture the essence of the dimer phase beyond the multicritical transition.

Spin-liquid behavior in the classical antiferromagnetic [formula omitted] spin system on the square-kagome lattice: Exact analysis within recursive-lattice approach

Magnetic and thermodynamic properties of the antiferromagnetic J1−J2−J3 spin system, i.e., the spin system with three different nearest-neighbor antiferromagnetic interactions, on the square-kagome lattice is investigated in the framework of the corresponding exactly solvable spin-1/2 Ising model on the recursive square-kagome lattice. The phase diagram of the model is found and it is shown that, depending on the model parameters, the model exhibits the existence of three long-range order (antiferromagnetic) phases, which are separated from the paramagnetic phase by the second order phase transitions. It is also shown that, in the zero temperature limit, the paramagnetic phase splits into three different ground states realized on the lines that separate antiferromagnetic ground states of the model. Due to the frustration, all these “paramagnetic” ground states are highly macroscopically degenerated with strict hierarchy of their residual entropies. Moreover, the high macroscopic degeneracy of the paramagnetic phase in the vicinity of these ground states together with the presence of strong correlations (given by the proximity of the second order phase transitions) allow one to consider the paramagnetic ground states as well as their immediate paramagnetic surroundings as regions with the classical spin-liquid behavior. It is also shown that the presence of the second order phase transitions in the vicinity of the paramagnetic ground states suppresses expected anomalous (Schottky-type) behavior of the specific heat related to the rapid entropy changes caused by the frustration.

Effects of phosphorylation on Drp1 activation by its receptors, actin, and cardiolipin.

Drp1 is a dynamin family GTPase required for mitochondrial and peroxisomal division. Oligomerization increases Drp1 GTPase activity through interactions between neighboring GTPase domains. In cells, Drp1 is regulated by several factors including Drp1 receptors, actin filaments, cardiolipin, and phosphorylation at two sites: S579 and S600. Commonly, phosphorylation of S579 is considered activating, while S600 phosphorylation is considered inhibiting. However, direct effects of phosphorylation on Drp1 GTPase activity have not been investigated in detail. Here, we compare effects of S579 and S600 phosphorylation on purified Drp1, using phosphomimetic mutants and in vitro phosphorylation. Both phosphomimetic mutants are shifted toward smaller oligomers. Both phosphomimetic mutations maintain basal GTPase activity, but eliminate GTPase stimulation by actin and decrease GTPase stimulation by cardiolipin, Mff, and MiD49. Phosphorylation of S579 by Erk2 produces similar effects. When mixed with wildtype Drp1, both S579D and S600D phosphomimetic mutants reduce the actin-stimulated GTPase activity of Drp1-WT. Conversely, a Drp1 mutant (K38A) lacking GTPase activity stimulates Drp1-WT GTPase activity under both basal and actin-stimulated conditions. These results suggest that the effect of S579 phosphorylation is not to activate Drp1 directly. In addition, our results suggest that nearest neighbor interactions within the Drp1 oligomer affect catalytic activity.

Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice

The quest to understand the nature of superconductivity in the cuprates has spotlighted the pair density wave (PDW)–a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge, and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive tpp case. When the system incorporates moderate near-neighbor interactions, particularly an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When the attractive Vpp increases further, the system gives way to an unconventional d-wave superconductivity.

Voter model under stochastic resetting

The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension d) and is in one of two possible opinion states. The opinion state of each voter flips randomly, at a rate proportional to the fraction of the nearest neighbors that disagree with the voter. If the voters are initially independent and undecided, the model is known to lead to a consensus if and only if . In this paper the model is subjected to stochastic resetting: the voters revert independently to their initial opinion according to a Poisson process of fixed intensity (the resetting rate). This resetting prescription induces kinetic equations for the average opinion state and for the two-point function of the model. For initial conditions consisting of undecided voters except for one decided voter at the origin, the one-point function evolves as the probability of presence of a diffusive random walker on the lattice, whose position is stochastically reset to the origin. The resetting prescription leads to a non-equilibrium steady state. For an initial state consisting of independent undecided voters, the density of domain walls in the steady state is expressed in closed form as a function of the resetting rate. This function is differentiable at zero if and only if .

Characterization of the 2D Su–Schrieffer–Heeger Model with Second‐Nearest‐Neighbor Interactions

It is known that a 2D‐dimerized Su–Schrieffer–Heeger model can produce a nontrivial topological phase. It is a simple nearest‐neighbor model with four lattice sites in 2D. The Su–Schrieffer–Heeger model is easy to analyze but neglects important interaction in physical systems. Herein, an extended version of this model is proposed which includes all possible second‐nearest‐neighbor interactions in order to grant more flexibility when describing realistic systems. The addition of these interactions changes the symmetry of the model and as a result affects the topological properties. In order to characterize the topological changes to the model, a polarization invariant is used. It is further shown that these symmetry breaking interactions can be used to evoke a topological phase transition as well.

Magnetic properties of perovskites Pr0.9Sr0.1 Mn[formula omitted]Mn[formula omitted]O3: Monte Carlo simulations and experiments

This work presents the remarkable experimental magnetocaloric properties of the perovskites Pr0.9Sr0.1Mn0.93+ Mn0.14+O3, including the magnetic entropy change |ΔSm| and the Relative Cooling Power (RCP). To understand these striking properties, we elaborate in this paper a model and use Monte Carlo (MC) simulations to study it for comparison. For the model, we take into account nearest-neighbor (NN) interactions between magnetic ions Mn3+ (S=2) and Mn4+ (S=3/2) and the interactions between these Mn ions with the magnetic Pr ions. The crystal is a body-centered tetragonal lattice where the corner sites are occupied by Mn ions and the center sites by Pr and Sr ions in their respective concentrations given in the compound formula. We use an Ising-like spin model describing a strong anisotropy on the z axis. We show that pairwise interactions between ions cannot reproduce the large plateau of the magnetization experimentally observed below the phase-transition temperature. By introducing for the first time a many-spin interaction between Mn ions, we obtain an excellent agreement with experiments. Fitting the experimental Curie temperature TC with the MC transition temperature, we estimate the value of the effective exchange interaction in the system. From this value, we estimate various exchange interactions between ions: the dominant one is that between Mn3+ and Mn4+ which is at the origin of the ferromagnetic ordering below TC. We also studied the applied-field effect on the magnetization in the region below and above TC. The obtained MC results for |ΔSm| are in agreement with experiments performed for applied fields from 1 to 5 T. MC results of RCP are also shown and compared to experimental ones. Various other physical quantities obtained from MC simulations including internal energy and specific heat, versus temperature are also shown and discussed.

Structure-property relationships in alkoxy substituted benzoates from experimental and computational thermochemistry

The energetics of formation and the phase transitions for isomeric methyl and ethyl methoxy‑benzoates were studied. The vapour pressures of methyl 2‑methoxy-benzoate and methyl 4‑methoxy-benzoate were measured by transpiration method. The high-precision combustion calorimetry was used to derive the liquid-phase enthalpy of formation of methyl 2‑methoxy-benzoate. The new results and the data available in the literature were critically evaluated using the structure-property correlations. Reliable correlations were established between the vaporisation enthalpies and the normal boiling temperatures as well as with the Kovats indices. Moreover, the validity of vaporisation enthalpies of alkyl methoxy‑benzoates was proved using structure-property relationships within families of structurally similar molecules. Mutual validation of the experimental and theoretical gas phase enthalpies of formation was performed using high-level quantum-chemical methods. The enthalpic contributions to the enthalpy of formation in the gas phase, resulting from the nearest and non-nearest neighbour interactions of the substituents in the benzene ring, were developed and used to quantify the intra-molecular hydrogen bond strength in the ortho-substituted species.

The novel oxy-sulfide glassy ionic conductors Na4P2S7-xOx 0 ≤ x ≤ 7: Understanding the features of static and dynamic cations

We present a 23Na nuclear spin dynamics model for interpreting nuclear magnetic resonance (NMR) spin-lattice relaxation and central linewidth data in the invert glass system Na4P2S7-xOx, 0 ≤ x ≤ 7. The glassy nature of this material results in variations in local Na+ cation environments that may be described by a Gaussian distribution of activation energies. A consistent difference between the mean activation energies determined by NMR and DC conductivity measurements was observed, and interpreted using a percolation theory model. From this, the NaNa coordination number in the sodium cation sublattice was obtained. These values were consistent with jumps through tetrahedral faces of the sodium cages for the sulfur rich glasses, x < 5, consistent with proposed models of their short range order (SRO) structures. From NMR spin-echo measurements, we determined the NaNa second moment M2 resulting from the NaNa magnetic dipole interaction of nearest neighbors. Values of M2 obtained as a function of sodium number density N were in agreement with models for uniform sodium distribution, indicating that these invert glass systems form so as to maximize the average NaNa distance. A simple Coulombic attraction model between Na+ cation and X (=S−, O−) anion was applied to calculate the activation energy. In the range 1.5 ≤ x ≤ 7, an increase in activation energy with increasing oxygen content x occurred, and was consistent with the decrease in average anionic radius, and the increase in Coulombic attraction. For small oxygen additions, 0 ≤ x ≤ 1.5, the suggested minimum at low oxygen concentration seen in the activation energies obtained from DC conductivity data is not evident in the model.