Random-bond Model Research Articles

Surface Controlled Silicon Nanoparticles Production and Their Effects on High Capacity and High Cyclability of All-Solid-State Lithium-Ion Batteries

Si nanoparticle is expected as anode for high density Lithium-ion batteries as as it facilitates high capacity and high cyclability simultaneously owing to its structural robustness to suppress fracture during cycled (de)lithiation reactions. Direct TEM observation has revealed that the particle size of 150 nm is the threshold for facture and the particles smaller than 150 nm are anticipated to contribute to the structural stability during cycles. However, the surface of silicon nanoparticle is oxidized spontaneously and the specific surface area increases significantly with decreasing the particle size. Accordingly, the specific oxygen content of the Si active material becomes inevitably high for smaller nanoparticles. High oxygen content in Si anode decreases the initial efficiency and capacityas a result of irreversible silicate formation. Therefore, smaller nanoparticle with a limited amount of oxidation would be ideal and necessary to attain high capacity and high cyclability. However, there is few report on the approach to suppress oxidation of smaller silicon nanoparticles and discuss the effect of size and oxygen content separately. Also, no general understanding of the effect of the particle size and oxygen for the case of all-solid-state batteries (ASSBs). In this work, we have produced Si nanoparticles with differently controlled size and oxygen content by plasma flash evaporation (PFE) from low-cost powder feedstock, and the effect of characteristic oxide surface structure on the battery performance of ASSBs with Argyrodite electrolyte has been identified.We have successfully produced the nanoparticles as small as 20 nm and reduced the oxygen content x in SiOx representation from the standard amount of 0.24 to 0.049. As a result, the initial discharged capacity can be improved by 110% while attaining similar cyclabilities. When we compare the nanoparticles with different sizes ranging from 20 nm to 165 nm and having small oxygen content x < 0.05, although the initial discharged capacities are almost the same for these particles, only the particle with 165 nm shows rapid capacity decay in 10 cycles, whereas the 20 nm and 84 nm particles tend to maintain the capacity similarly. This confirms that the particles smaller than 100 nm are effective to maintain high capacity also in ASSBs under a low 0.1 C-rate condition. Furthermore, XPS analysis revealed that the surface of the particles with less oxidation is composed of suboxide Si-O bond oxide preferentially and the amount of Si-O4 bond is less than the conventional particles covered by the oxide shell, with which the Si-O bond ratio is described by the conventional random bond model. No apparent dependence of the capacity with the amount of Si-O4 bond. However, the surface oxide shell thickness estimated by the Si-O bond amount and the total oxygen content has shown a clear linear correlation with the charged capacity, irrespective of the particle size. This suggests that the surface oxide thickness affects significantly the amount of the lithiation reaction and is ideally as thin as possible to attain high capacity, especially for the case of ASSBs.

Randomness and frustration in a S=12 square-lattice Heisenberg antiferromagnet

Chemical substitution in Sr${}_{2}$CuTe${}_{1\ensuremath{-}x}$W${}_{x}$O${}_{6}$ introduces a combination of randomness and frustration in the square-lattice Heisenberg quantum antiferromagnet. Neutron scattering is used to probe the ground and excited states of the mixed compounds in this series. It is demonstrated that the random network of interactions is only mildly frustrated. A semiclassical mean-field treatment of the random-bond model, which produces a ground state of small and weakly interlinked ordered patches hosting spin-wave-like excitations, agrees well with the experimental observations.

Hysteresis loops and dielectric properties of compositionally graded (Ba,Sr)TiO3 thin films described by the transverse Ising model

Using the effective field theory with a probability distribution technique that accounts for the self-spin correlations, we apply the transverse spin-1/2 Ising model to study the intrinsic hysteresis of compositionally graded Ba1−xSrxTiO3 (BST) thin films with x decreasing from 0.20 to 0.10 in successive slabs. The random bond model of related parameters is applied to mimic doping. The effects of the thickness, the concentration of Sr, the number of slabs and the temperature on the polarization and the hysteresis are discussed.

Roughening of an interface in a system with surface or bulk disorder

We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also away from it, in the bulk. The dynamical structure factor shows a rich crossover pattern from the form of a pure system at large wavevectors k, to a different behavior, typical of the kind of disorder, at smaller k's. For the random field model a second crossover is observed from the typical behavior of a system where disorder is only effective on the surface, as the random bond model, to the truly large scale behavior, where bulk-disorder is important, that is observed at the smallest wavevectors.

Neighborhood Identity Ordering and Quenched to Annealed Transition in Random Bond Models

Systems with many different interactions pose a challenge to traditional methods of statistical physics. In this paper, we develop the random bond model, which has a huge number of randomly chosen interaction parameters (quenched variables). Using heuristic arguments and Monte-Carlo simulations, we show that for any temperature there exists a sufficiently large system size above which one can forego the complicated quenched averaging familiar from spin glasses, and calculate statistical averages using standard methods of equilibrium statistical mechanics.

Silicon Monoxide at 1 atm and Elevated Pressures: Crystalline or Amorphous?

The absence of a crystalline SiO phase under ordinary conditions is an anomaly in the sequence of group 14 monoxides. We explore theoretically ordered ground-state and amorphous structures for SiO at P = 1 atm, and crystalline phases also at pressures up to 200 GPa. Several competitive ground-state P = 1 atm structures are found, perforce with Si-Si bonds, and possessing Si-O-Si bridges similar to those in silica (SiO2) polymorphs. The most stable of these static structures is enthalpically just a little more stable than a calculated random bond model of amorphous SiO. In that model we find no segregation into regions of amorphous Si and amorphous SiO2. The P = 1 atm structures are all semiconducting. As the pressure is increased, intriguing new crystalline structures evolve, incorporating Si triangular nets or strips and stishovite-like regions. A heat of formation of crystalline SiO is computed; it is found to be the most negative of all the group 14 monoxides. Yet, given the stability of SiO2, the disproportionation 2SiO(s) → Si(s)+SiO2(s) is exothermic, falling right into the series of group 14 monoxides, and ranging from a highly negative ΔH of disproportionation for CO to highly positive for PbO. There is no major change in the heat of disproportionation with pressure, i.e., no range of stability of SiO with respect to SiO2. The high-pressure SiO phases are metallic.

Critical behavior of the three-dimensional random-bond Potts model with many states

The critical behavior of the three-dimensional random-bond Potts models with many states ( and ) is studied by the finite-time dynamic method. We evaluate the static and dynamic critical exponents as well as the critical temperatures. The asymptotic critical behavior for is identified with , and but the exponents obtained for with are the only effective ones. Our results support that is positive and the intrinsic can escape the bound suggested by previous work. By comparing with the results for various , we infer that the asymptotic critical behavior of the three-dimensional random-bond Potts model with many states is -dependent.

Universality in the critical dynamics of the three-dimensional large-q Potts model with bond randomness

The critical behavior of the three-dimensional random-bond Potts model for large state numbers with q=16 and q=32 is studied by the finite-time dynamics combining with Monte Carlo renormalization group method. The correlation length and dynamic exponents as well as the critical temperatures are calculated through reducing the influence of finite-size effects. According to the variations of critical exponents with disorder amplitude, we identify the asymptotic critical exponents with ν=0.424(14), z=3.03(12) and find that they are q-independent. The results further confirm that the intrinsic ν, instead of finite-size one, can escape the bound ν>2/d suggested previously.

Structurally determined directionality identifies the boundary between mobile and immobile domains in a disordered material

The structure and available degrees of freedom of an amorphous configuration can determine the location of dynamic heterogeneities. In the same way, these features can also determine the directionality of the particle motion. In this paper we propose that directionality can be attributed to those particles that only participate in a single unconstrained motion. The consequences of this suggestion in terms of the spatial distribution of particles with high directionality are explored using a random bond model.

Universality in disordered systems: The case of the three-dimensional random-bond Ising model

We study the critical behavior of the d=3 Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed by the same universality class as the site- and bond-diluted models, clearly distinct from that of the pure model, thus providing a complete set of universality in disordered systems.

Randomized and Distributed Self-Configuration of Wireless Networks: Two-Layer Markov Random Fields and Near-Optimality

This work studies the near-optimality versus the complexity of distributed configuration management for wireless networks. We first develop a global probabilistic graphical model for a network configuration which characterizes jointly the statistical spatial dependence of a physical- and a logical-configuration. The global model is a Gibbs distribution that results from the internal network properties on node positions, wireless channel and interference; and the external management constraints on physical connectivity and signal quality. A local model is a two-layer Markov Random Field (i.e., a random bond model) that approximates the global model with the local spatial dependence of neighbors. The complexity of the local model is defined through the communication range among nodes which corresponds to the number of neighbors in the two-layer Markov Random Field. The local model is near-optimal when the approximation error to the global model is within a given bound. We analyze the tradeoff between approximation error and complexity. We then derive sufficient conditions on the near-optimality of the local model. For a fast decaying wireless channel with power attenuation factor α > 4 , a node only needs to communicate with O(1) neighbors for a local model to be near optimal. For a slowly decaying channel with a power attenuation factor 2 ≤ α ≤ 4, a node may have to communicate with more than O(N(4-α)/4) neighbors to result in a bounded approximation error. If the communication range is kept to be O(1), a bounded approximation error can also be achieved by reducing the density of active links to O(N(α-4)/(α+4)) for α 4 . The two-layer Markov Random Fields enable a class of randomized distributed algorithms such as the stochastic relaxation that allows a node to self-configure based on information from neighbors. We validate the model, the analysis and the randomized distributed algorithms through simulation.

Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase-transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double-logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.

Uncovering the secrets of the 2D random-bond Blume–Capel model

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume–Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the system onto a network and we search for a minimum cut by a maximum flow method. At finite temperatures the system is studied by an efficient two-stage Wang–Landau (WL) method for several values of the crystal field, including both the first- and second-order phase transition regimes of the pure model. We attempt to explain the enhancement of ferromagnetic order and we discuss the critical behavior of the random-bond model. Our results provide evidence for a strong violation of universality along the second-order phase transition line of the random-bond version.

On the short-range order of the SiO x (0 ≤ x ≤ 2) surface

Fine (oscillating) structure (FS) in the elastically scattered electron spectra (ESES) [O. Bondarchuk, S. Goysa, I. Koval, P. Melnik, M. Nakhodkin, Surf. Sci. 258 (1991) 239; O. Bondarchuk, S. Goysa, I. Koval, P. Melnik, M. Nakhodkin, Surf. Rev. Lett. 4 (1997) 965] was used to investigate surface structure of the SiO x (0 ≤ x ≤ 2). SiO x surface with different stoichiometry was prepared by implantation of 500 eV oxygen ions into a silicon wafer. Fourier transformation of the FS ESES contains one peak at 2.32 Å for Si, two peaks at 1.62 Å and 2.65 Å for a-SiO 2 and three peaks centered at 1.6–1.7 Å, 2.1–2.2 Å and 2.65–3.04 Å for SiO x . Peaks at 1.62 Å and 2.65 Å are assigned to Si–O and O–O nearest distances correspondently. Ratio of the area under the peak at 2.65 Å to the area under the peak at 1.62 Å turned out to be not constant but grows linearly with the composition parameter x. The latter is considered to prove validity of the Random Bond Model to describe short-range order on the surface of non-stoichiometric silicon oxide.

Critical dynamics of the two-dimensional random-bond Potts model with nonequilibrium Monte Carlo simulations

We study two-dimensional q -state random-bond Potts models for both q=8 and q=5 with a linearly varying temperature. By applying a successive Monte Carlo renormalization group procedure, both the static and dynamic critical exponents are obtained for randomness amplitudes (the strong to weak coupling ratio) of r_{0}=3 , 10, 15, and 20. The correlation length exponent nu increases with disorder from less than to larger than unity and this variation is justified by the good collapse of the specific heat near the critical region. The specific heat exponent is obtained by the usual hyperscaling relation alpha=2-dnu and thus indicates no possibility of the activated dynamic scaling. Both r_{0} and q have effects on the critical dynamics of the disordered systems, which can be seen from variations of the rate exponent, the hysteresis exponent, and the dynamic critical exponent. Implications of these results are discussed.

Molar volume minimum and adaptative rigid networks in relationship with the intermediate phase in glasses

We propose that the molar volume minimum observed in barium silicate glasses $(1\ensuremath{-}x){\text{SiO}}_{2}\ensuremath{-}x\text{BaO}$ is related to the onset of an adaptative rigid glassy network. We obtain in the compositional window $29%&lt;x&lt;33%$ a dramatic decrease in stressed rigid local units from the Raman analysis and at $x=31%$ the onset of barium ionic conduction. A random bond model [J. Barr\'e et al., Phys. Rev. Lett. 94, 208701 (2005)] and constraint counting algorithms permit defining of the free energy of the system, and analyzing of the elastic nature of three compositional ranges of interest: a stressed rigid phase at low $x$, a flexible phase at high $x$, and a stress-free intermediate phase where space filling is optimized.

Exactly Solvable Models of Adaptive Networks

A satisfiability-unsatisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.

Dielectric properties of compositionally graded Ba1–xSrxTiO3 thin films described by the transverse‐field Ising model

AbstractThis investigation reports on the phase transition and dielectric properties of compositionally graded Ba1–xSrxTiO3 (BST) thin films with x decreasing from 0.20 to 0.10 in successive slabs, based on the transverse‐field Ising model (TIM) within the framework of mean field theory. The random bond model of related parameters is applied to mimic doping. The effect on polarization and dielectric susceptibility arising from a gradient in composition is taken into account. The peaks of dielectric susceptibility versus temperature become comparatively flat by modulating appropriate thickness in each slab in compositionally graded BST thin films, which means that the thickness may weaken the effect of composition gradient. When increasing the number of slabs of thin films, the dielectric susceptibility shows good temperature stability in a wide temperature range, which is useful for reducing the temperature coefficient of dielectric susceptibility without depressors. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Coupling between the magnetism and dielectric properties inEu1−xBaxTiO3

The dielectric constant of the quantum paraelectric ${\mathrm{EuTiO}}_{3}$ exhibits a sharp decrease at about 5.5 K, at which temperature antiferromagnetic ordering of the Eu spins simultaneously appears, indicating coupling between the magnetism and dielectric properties. A similar feature has also been detected in ${\mathrm{Eu}}_{1\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{TiO}}_{3}$ $(0&lt;x&lt;~0.2).$ The random-bond model within the framework of the transverse-field Ising model and the site dilution model based on the Heisenberg model are successfully applied to the ${\mathrm{Eu}}_{1\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{TiO}}_{3}$ electrical and magnetic subsystems, respectively. By adding an appropriate coupling term between the magnetic and electrical subsystems, which is related to the interaction of the Heisenberg spin and pseudospin, we investigate intrinsic coupling between the magnetic and electrical subsystems and successfully obtain its special dielectric constant, which is in good agreement with the experimental data.

A study on critical universality of the random-bond Potts models with self-dual quenched randomness

In this paper we present our numerical study on short-time critical dynamics for the q-state random-bond Potts model with self-dual quenched disorders. By exploring the universal power-law scaling behavior, the results of magnetic exponent η and dynamic exponent z are estimated for the q=3 and q=8 cases with two specific disorder distribution functions. Our Monte Carlo simulations show evidence that the results of magnetic exponent η are independent of distribution forms, which verifies the existence of universality for the general quenched random-bond models numerically.