Distortion of Local Order Parameter Caused by Impurities in Displacive Phase Transition*

A simple field model with a scalar order parameter and quartic anharmonic interaction is used to consider a displacive-type phase transition. It is shown that the order of the phase transition can not be determined within the framework of self-consistent phonon approximation. The considerable deviation of the temperature dependence of soft mode frequency from Curie-Weiss law far from the transition point is obtained and justified in the second-order approximation. The latter result is believed to be due to the model under consideration.

Order parameters make it possible to quantify the degree of structural ordering in a material and thus to apply as the reaction coordinates during the free-energy analysis of phase or structure transitions. Furthermore, order parameters are useful in determining the local structures of molecular groups during transition stages. However, identifying or developing local order parameters (LOPs) that are sensitive for specific materials and phases is a non-trivial task. In this study, the ability of LOPs to classify the solid and liquid structures of water at coexistence or triple points is investigated with the aid of supervised machine learning. The classification accuracy of a total of 179,738,433 combinations of 493 LOPs is automatically and systematically compared for water structures at the ice Ih-Ic-liquid coexistence point and the ice III-V-liquid and ice V-VI-liquid triple points. The optimal sets of two LOPs are found for each point, and sets of three LOPs are suggested for better accuracy.

Mechanical recycling is the most efficient way to reduce plastic pollution due to its ability to maintain the intrinsic properties of plastics as well as provide economic benefits involved in other types of recycling. On the other hand, molecular dynamics (MD) simulations provide key insights into structural deformation, lamellar crystalline axis (c-axis) orientations, and reorganization, which are essential for understanding plastic behavior during structural deformations. To simulate the influence of structural deformations in high-density polyethylene (HDPE) during mechanical recycling while paying attention to obtaining an alternate lamellar orientation, the authors examine a specific way of preparing stacked lamella-oriented HDPE united atom (UA) models, starting from a single 1000 UA (C1000) chain of crystalline conformations and then packing such chain conformations into 2-chain, 10-chain, 15-chain, and 20-chain semi-crystalline models. The 2-chain, 10-chain, and 15-chain models yielded HDPE microstructures with the desired alternating lamellar orientations and entangled amorphous segments. On the other hand, the 20-chain model displayed multi-nucleus crystal growth instead of the lamellar-stack orientation. Structural characterization using a one-dimensional density profile and local order parameter {P2(r)} analyses demonstrated lamellar-stack orientation formation. All semi-crystalline models displayed the total density (ρ) and degree of crystallinity (χ) range of 0.90-0.94 g/cm-3 and ≥42-45%, respectively. A notable stress yield (σ_yield) ≈ 100-120 MPa and a superior elongation at break (ε_break) ~250% was observed under uniaxial strain deformation along the lamellar-stack orientation. Similarly, during the MD simulations, the microstructure phase change represented the average number of entanglements per chain (<Z>). From the present study, it can be recommended that the 10-chain alternate lamellar-stack orientation model is the most reliable miniature model for HDPE that can mimic industrially relevant plastic behavior in various conditions.

It is shown that any Ising model with positive coupling constants is related to another Ising model by a duality transformation. We define a class of Ising models Mdn on d-dimensional lattices characterized by a number n = 1, 2, … , d (n = 1 corresponds to the Ising model with two-spin interaction). These models are related by two duality transformations. The models with 1 &amp;lt; n &amp;lt; d exhibit a phase transition without local order parameter. A nonanalyticity in the specific heat and a different qualitative behavior of certain spin correlation functions in the low and the high temperature phases indicate the existence of a phase transition. The Hamiltonian of the simple cubic dual model contains products of four Ising spin operators. Applying a star square transformation, one obtains an Ising model with competing interactions exhibiting a singularity in the specific heat but no long-range order of the spins in the low temperature phase.

Molecular dynamics (MD) simulations have been carried out on the crystallization of single-chain polyethylene (PE) which was adsorbed on a graphite (001) surface on one side and exposed to vacuum on the other at different temperatures. The MD simulation data have been analyzed to provide information about the crystallization process of polymer adsorbed on the solid substrate. The isothermal crystallization of PE proceeds in two steps: (1) adsorption and (2) orientation. The results detail the radial density distribution function, ordered parameters, local bond-orientational order parameters, and the local properties displayed in layers of the polymer parallel to the graphite and vacuum interfaces. It was also shown that the film thickness affected the critical crystallization temperature of the adsorbed polymer on the substrate surface. Furthermore, the influence of the graphite surface area on the crystallization of PE is discussed by comparing the crystallinity evolution of PE on graphite with different coverage.

NaCl-CsCl structural transition in Sr2PdO3 and Sr2TiO4

Reversible martensitic phase transformations in a partially disordered Ni–Al alloy within the composition range from 60to65at.% of Ni are investigated using molecular dynamics simulation. During a complete temperature cycle a wide hysteresis in enthalpy, volume, and shape of the simulated crystals is observed. The temperature T0 of the phase transformation is found from the calculated free energy evolution. To investigate the atomic-scale development during the phase transformation a local order parameter is defined which is based on a combined method of Voronoy tessellation [J. Reine Angew. Math. 134, 198 (1908)] with common-neighbor analysis. This local order parameter allows us to get a detailed localized picture of nucleation and growth of the new phases. Both homogeneous formation of the new phase and heterogeneous nucleation are observed. The velocity of new phase growth front is estimated.

A generalization of the vibronic theory of ferroelectric phase transitions is made and the theory of antiferroelectric and structural modulated phase transitions, caused by the electron‐phonon interaction in dielectrics and semiconductors, is developed. The criteria for the occurrence of such transitions are obtained. The basic characteristics (spontaneous lattice distortion, dielectric susceptibility, frequencies of soft modes, etc.) are calculated. The dispersion of electronic states, corrections to the mean field approximation for the driving vibronic interaction, and phonon anharmonicity are taken into account. The relation between ferroelectric and antiferroelectric phase transitions is discussed.

We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states, and its superextensive size scaling witnesses a critical behaviour due to a phase transition, since all the interaction terms are extensive. Perturbatively in the noise strength, we found superextensive Fisher information at anisotropy $|\Delta|\leqslant1$ and irrational $\frac{\arccos\Delta}{\pi}$ irrespective of the order of two non-commuting limits, i.e. the thermodynamic limit and the limit of sending $\frac{\arccos\Delta}{\pi}$ to an irrational number via a sequence of rational approximants. From this result we argue the existence of a non-equilibrium quantum phase transition with a critical phase $|\Delta|\leqslant1$. From the non-superextensivity of the Fisher information of reduced states, we infer that this non-equilibrium quantum phase transition does not have local order parameters but has non-local ones, at least at $|\Delta|=1$. In the non-perturbative regime for the noise strength, we numerically computed the reduced Fisher information which lower bounds the full state Fisher information, and is superextensive only at $|\Delta|=1$. Form the latter result, we derived local order parameters at $|\Delta|=1$ in the non-perturbative case. The existence of critical behaviour witnessed by the Fisher information in the phase $|\Delta|<1$ is still an open problem. The Fisher information also represents the best sensitivity for any estimation of the control parameter, in our case the anisotropy $\Delta$, and its superextensivity implies enhanced estimation precision which is also highly robust in the presence of a critical phase.

Revisiting thermodynamic topology of Hawking-Page and Davies type phase transitions

Vibrational, DSC and dielectric studies of Cs1.5Li1.5H(SO4)2 crystal

The changes in phase transition temperatures caused by photo-active illumination were studied for a number of ferroelectrics having phase transitions of different types (FE-PE, FE-FE and FE-AFE). The thermodynamic model is proposed which enables one to describe the experimental results obtained.

The structural phase transitions in the intercalate layer in bromine intercalated compounds based on fine crystalline anisotropic graphite are investigated by the Raman spectroscopy method. The changes of Raman spectra with the temperature for a graphite intercalation compound with bromine are considered. The temperature dependences of parameters of the bromine molecular stretching mode are analyzed. It is shown that there are three phase transitions of different types in the bromine layer in the temperature interval from 153 K up to 300 K. It is revealed that the accommodation coefficient at the bromine layer phase transition from one to another lattice commensurate with the graphite layer is changed. The accommodation coefficients in different temperature intervals are estimated.

Reports detailed experimental studies of the onset of hard-mode Raman activity near the cubic-tetragonal structural phase transitions in KMnF3 and RbCaF3. The results are discussed in the context of a theory taking into account the influence not only of the long-range order, reflected in the macroscopic order parameter, but also that of the precursor order reflected in the central peak and phonon sideband of the soft-mode spectral function. The precursor order, dominant near the phase transition, is responsible for the persistence of quasi-first-order hard-mode features above the transition temperature. The extent of this persistence is used as a basis for specific estimates of the degree of precursor order in KMnF3 and RbCaF3.

As a rule, glassy and amorphous solids are characterized by random, irregular structures. More recent examinations, however, indicated that even this group of materials possesses certain structural laws. Glassy and amorphous SiO2 samples were investigated using X‐ray diffraction. The results of this investigation can be interpreted as structural phase transitions. When subjected to a pressure‐temperature treatment (p = 7 GPa, T = 700 °C), a 15 per cent irreversible densification of vitreous silica without crystallization could be achieved. This can be interpreted as a reconstructive transformation of a certain topological structure (vitreous silica having a cristobalite topology) into another topological structure (densified vitreous silica having a quartz topology).Temperature‐dependent measurements of disperse SiO2 (porous glass, silica gels) led to the conclusion that a displacive phase transition (analogous to the α‐β‐transition in cristobalite) had taken place in the amorphous network.