Order-disorder Transformation Research Articles

Synthesis, magnetic and structural properties of (1-x)LiFe5O8–(x)LiZn2.5Ti2.5O8 spinel solid solutions

Compounds with the spinel structure present a technologically important class of materials. Spinels show a great variety of magnetic and magnetoelectric phenomena owing to the facile entrance of transition metals in the cationic sublattices. One of such examples is lithium ferrite LiFe5O8 with high ferrimagnetic phase transition temperature and cationic order-disorder transformations. The latter are important as they influence the crystal symmetry, which is crucial for physical properties. In this work we synthesize a series of (1-x)LiFe5O8–(x)LiZn2.5Ti2.5O8 (0≤x≤1) solid solutions and characterize them with various experimental and theoretical methods. The solid solutions experience a series of concentrational phase transformations between atomically ordered (P43(1)32) and disordered (Fd3¯m) phases. The variation with concetration x of Fe3+ occupancies in cationic sublattices is studied using Mössbauer spectroscopy. The Mössbauer and magnetic measurements reveal sharp suppression of magnetic properties at x≥0.5 when the number of Fe3+ ions in the A-sublattice vanishes. The magnetic behaviour in the studied series of solid solutions is confirmed by Monte Carlo calculations with magnetic exchange interactions determined using the density functional theory.

On the order–disorder transformation within a main hardening precipitate in Al–Mg–Si alloys

ABSTRACT The earliest stages of solid-state precipitation in age hardenable alloys, before the first ordered phase formation, are notoriously elusive, yet often of central importance to material properties quantification. The order–disorder precipitate transformations are currently accepted to proceed by long-range chemical ordering on a substructure extending through the particle, with the Al–Mg–Si alloy Guinier-Preston (GP) zone → β″ transformation representing the most well-documented example. It is shown here that the structurally distinct β″ phase arises directly from solute diffusion-controlled precipitation within a precipitate, providing an alternative pathway for the transformation of one precipitate to a more thermodynamically stable precipitate. The emergence of dispersed β″ nuclei in the otherwise fcc-based particle is revealed by structural and chemical signs of a significant spatial solute variation. Furthermore, upon reduced aging temperature, heavily structurally flawed final particles result from increasingly challenging nucleus coalescence. The highly localised origin of this process suggests that early-stage precipitate transformation mechanisms be revisited for other age hardenable alloys.

Sodium Octahydridotriborate as a Solid Electrolyte with Excellent Stability Against Sodium-Metal Anode.

Solid-state sodium metal batteries have been extensively investigated because of their potential to improve safety, cost-effectiveness, and energy density. The development of such batteries urgently required a solid-state electrolyte with fast Na-ion conduction and favorable interfacial compatibility. Herein, the progress on developing the NaB3H8 solid-state electrolytes is reported, which show a liquid-like ionic conductivity of 0.05 S cm-1 at 56°C with an activation energy of 0.35eV after an order-disorder phase transformation, matching or surpassing the best single-anion hydridoborate conductors investigated up to now. The steady polarization voltage and significantly decreased resistance are achieved in the symmetric Na/NaB3H8/Na cell, indicating the great electrochemical stability and favorable interfacial contact with the Na metal of NaB3H8. Furthermore, a Na/NaB3H8/TiS2 battery, the first high-rate (up to 1C) solid-state sodium metal battery using the single-anion hydridoborate electrolyte, is demonstrated, which exhibits superior rate capability (168.2 mAh g-1 at 0.1 C and 141.2 mAh g-1 at 1 C) and long-term cycling stability (70.9% capacity retention at 1 C after 300 cycles) at 30°C. This work may present a new possibility to solve the interfacial limitations and find a new group of solid-state electrolytes for high-performance sodium metal batteries.

Structural characteristics of Bi2O2CO3 nanosheets synthesized by nano-pulsed discharges in water

A comprehensive analysis of Bi2O2CO3 nanosheets, which were synthesized using nanosecond-pulsed discharges in water between bismuth electrodes, was conducted in order to investigate the crystallographic features of this material. Electron diffraction, X-ray diffraction and electron energy-loss spectrometry techniques revealed the presence of a stoichiometric tetragonal Bi2O2CO3 structure, labelled BOC in this study. It crystallizes in the body-centred tetragonal Bravais lattice and belongs to the I4/mmm space group (No. 139), with the following lattice parameters: a = 3.91, c = 13.77 Å. The nanosheets adopt square shapes. This shape is dictated by the symmetry elements of its point group (4/mmm) under the prevailing local conditions. From the energetic point of view, this shape, dictated by the 4/m2/m2/m point group and therefore a pinacoid, corresponds to an absolute extremum, an indicator of the stability of these BOC nanosheets. Most nanosheets are crossed by equal-inclination fringes or bend contours. These bend contours reflect the fact that the BOC nanosheets contain crystal defects and/or are so thin that they bend elastically, leading to rotation of the lattice planes towards the diffracting Bragg position. The diffraction patterns corresponding to bend contours intersecting along the [001] zone axis have been studied in detail. Extra reflections are superimposed on the diffraction pattern of the BOC crystallographic structure. These extra reflections are essentially attributed to two phenomena: multiple diffraction and local disorder–order transformations of the BOC crystal structure, passing from a body-centred tetragonal to a primitive Bravais lattice. A mechanism related to the ledge mechanism (kinks and jogs), explaining the formation of nanosheets in a metallic matrix, has been adapted and proposed for the formation of BOC nanosheets in water. When the nanosheets are removed from the water, they become carbonated once in the air, leading to the formation of BOC that inherits the nanosheet morphology.

Second-Order Nonlinear Switching and Photoluminescence Properties of Cd-Based Hybrid Perovskite with High-Temperature Phase Transition.

Recently, organic-inorganic hybrid perovskites exhibiting facile structural phase transitions have accumulated significant attention due to their switchable second-order nonlinear optical (NLO) properties, which hold significant promise for next-generation intelligent optoelectronic devices. In this study, we present a novel one-dimensional hexagonal hybrid perovskite, (4-methoxypiperidinium)CdCl3, which undergoes a reversible high-temperature structural phase transition at 389 K. Notably, (4-methoxypiperidinium)CdCl3 demonstrates switchable second-order NLO and dielectric properties, accompanied by symmetry breaking from the centrosymmetric Pnma to noncentrosymmetric Pna21 space group. Variable-temperature structure analyses reveal that this transition is mainly driven by the order-disorder transformation of the 4-methoxypiperidinium cations. Furthermore, it also features a promising photoluminescence performance with blue-light emission and a long lifetime of 25.34 ns. It is anticipated that this study will expand the family of hybrid perovskites exhibiting high-temperature phase transitions and offer valuable guidance for the design of new NLO switching materials with superior optoelectronic properties.

Ultra-large strain response in BNT-BT-KNN thin films boosted by electric field-induced inversion of long-range ordered polarization

Bismuth sodium titanate (BNT)-based piezoelectric materials are the most promising candidates for lead-free actuator applications. With the request for integration and size miniaturization of devices, it is urgent to develop thin films for microdevices to be compatible with semiconductor processes. Through composition engineering, BNT-based thin films were fabricated on silicon substrates, with ultra-high strain response and negligible hysteresis in strain curves. The DC-dependent and temperature-dependent dielectric properties were collected to investigate the relaxor state of thin films. The structure and polarization transition and evolution as a function of electric field and time were analyzed based on the electric characterization, in-situ Raman measurements, and dynamics PFM. The reversible phase transition and polarization order-disorder transformation are the most significant features for reaching a large strain of >1.6% in BNT-based thin films.

Atomic level mechanism of disorder-order transformation kinetics at nanoscale in FePt based systems

L10 ordered FePt is one of the most promising materials for spintronic and recording media applications. In the present work, the mechanism of L10 phase transformation in FePt based films with varying initial structures is examined at the nanoscale to understand the ordering process using synchrotron based GIXRD, MOKE, VSM, and techniques with sub nanometer depth selectivity like XRR and SIMS. Precisely controlled compositions of the films are deposited using magnetron sputtering. Rapid thermal annealing is used for post-deposition processing. It is evaluated experimentally that for a shorter annealing time of 70 s at 400 °C, besides volume diffusion, short circuit diffusion paths along the intercrystallite region owing to the presence of nanostructured grains play a dominant role in alloying behavior. A study of the L10 ordering process reveals the crucial role of film structure in controlling the transformation kinetics, texturing of nanograins, and magnetic coercivity. Diffusion studies disclose that type B diffusion kinetics is activated for the annealing time during which L10 transformation occurs in the films.

Room-Temperature Phase Transition Material with Switchable Second-Order Nonlinear Optical Properties.

Phase transition materials with switchable second-order nonlinear optical (NLO) properties have attracted extensive attention because of their great application potential in photoelectric switches, sensors, and modulators, while metal-free organics with NLO switchability near room temperature remain scarce. Herein, we report a hydrogen-bonded metal-free organic crystal, 2-methylpropan-2-aminium 2,2-dimethylpropanoate (1), exhibiting a room-temperature phase transition and favorable NLO switchability. Through investigations on its thermal anomalies, dielectric properties, and crystal structures, we uncover that 1 holds a near-room-temperature phase transition at 303 K from noncentrosymmetric point group C2v to centrosymmetric one D2h, which is attributed to the order-disorder transformations of both tert-butylamine cations and dimethylpropionic acid anions. Accompanied by symmetry change during the phase transition, 1 exhibits reversible and repeatable NLO "on-off" switchability with a desirable switching contrast ratio of ca. 19 between high and low NLO states. This discovery demonstrates a metal-free organic crystal with NLO switching behavior near room temperature, serving as a promising candidate in smart and ecofriendly photoelectric functional materials and devices.

Discovering the Order-Disorder Transition in Quinoline Intercalated Vanadium Oxide with Superior Calcium Storage via Polyhedral Distortion.

Calcium-ion batteries (CIBs) are considered as potential next-generation energy storage systems due to their abundant reserves and relatively low cost. However, irreversible structural changes and weak conductivity still hinder in current CIBs cathode materials. Herein, an organic molecular intercalation strategy is proposed, in which V2O5 regulated with quinoline, pyridine, and water molecules are studied as cathode material to provide fast ion diffusion channels, large storage host, and high conductivity for Ca ions. Among them, V2O5-quinoline (QVO) owns the largest interplanar spacing of 1.25 nm and the V-O chains are connected with organic molecular by hydrogen bond, which stabilizes the crystal structure. As a result, QVO exhibits a specific capacity of 168 mAh g-1 at 1 A g-1 and capacity retention of 80% after 500 cycles at 5 A g-1 than the other materials. Furthermore, X-Ray diffraction and X-ray absorption spectroscopy results reveal a reversible order-disorder transformation mechanism of Ca2+ for QVO, which can make full use of the abundant active sites for high capacity and simultaneously achieve fast reaction kinetics for excellent rate performance. These results demonstrate that QVO is a promising cathode material for CIBs, providing more choices for the development of high-performance CIBs.

Tuning Dielectric Constant of P3HT by Ultrasound-Induced Aggregation

Poly(3-hexylthiophene) (P3HT), a semiconducting polymer, is integral to the development of organic electronic devices. Its optoelectronic properties are significantly influenced by the nature of its intermolecular interactions, predominantly classified as J-type and H-type couplings. This study investigates the effect of sonication on the dielectric properties of P3HT, focusing on the transition from J-type (or less prominent H-type) to H-type intermolecular interactions, accompanied by disorder-order transformation. The research determined that sonication leads to a significant change in the dielectric properties of P3HT by forming distinct ordered regions interspersed within disordered or quasi-ordered areas. Specifically, there is an observable transition from J-type to H-type aggregation, which has profound effects on the material's electronic structure and optoelectronic performance. This transition was confirmed by changes in the absorption and photoluminescence spectra, indicating a more localized electronic character and the formation of non-emissive excitons in the case of H-aggregates. Increased dielectric constant after sonication is attributed to interface polarization, especially the Maxwell-Wagner-Sillars polarization. This effect is likely because new interfaces are created between the ordered regions and disordered/quasi-ordered regions within the P3HT material, where charges can accumulate as a result of disorder-order transformation. Our research contributes to the broader understanding of polymer physics and the development of organic electronic devices by showing how the manipulation of microstructural environments can control material properties.

Colloid and nanoparticle-driven phase behavior in weakly perturbed nematic liquid crystals

We study theoretically weakly colloidal particle or nano-particle perturbed nematic liquid crystal (LC) order. We consider cases where the particles are essentially homogeneously dispersed in LC matrix. A mesoscopic Landau-de Gennes approach is used where we focus on the temperature variations in the amplitude order parameter field for different particle volume concentrations ϕ. In the dilute regime, we describe the nematic order in terms of interface and volume amplitude order fields. This modeling suggests that the temperature-driven order-disorder crossover exhibits a two-step transformation. In the case that particles locally support LC order, on decreasing temperature firstly the interface order is established, followed by the build-up of volume order. The latter appears via the 1st order phase transition. On the other hand, the interface order growth is formed either gradually or via the 1st order interfacial transition. In the regime of relatively high values of ϕ the system can be effectively described in terms of a single amplitude order parameter field. In this case, the temperature-driven phase behaviour is qualitatively similar to the interface order temperature response in the diluted regime. We analytically express phase transition temperatures and determine critical points in the temperature-interface interaction phase space. Key novelties of the paper are the determination of conditions for particle-LC interface-driven discontinuous change of nematic ordering and nanoparticle-enabled critical point condition in pressure-driven order-disorder phase transformations. Experimental evidences supporting the predicted phase behavior are presented.

A High-Rate and Long-Life Sodium Metal Battery Based on a NaB3H8 ⋅ xNH3@NaB3H8 Composite Solid-State Electrolyte.

All-solid-state sodium metal batteries are promising for large-scale energy storage applications owing to their intrinsic safety and cost-effectiveness. However, they generally suffer from sodium dendrite growth or rapid capacity fading, especially at high rates, mainly due to poor wettability, sluggish ionic transport, or low interfacial stability of the solid electrolytes. Herein, we report a novel composite, NaB3H8 ⋅ xNH3@NaB3H8 (x<1), as a new class of solid electrolyte for high-rate batteries. NaB3H8 ⋅ xNH3@NaB3H8 is obtained from the sticky NaB3H8 ⋅ NH3 after removal of NH3 partially at room temperature. It delivers an ionic conductivity of 0.84 mS cm-1 at 25 °C and reaches 20.64 mS cm-1 at 45 °C after an order-disorder phase transformation. It also reveals a good capability of dendrite suppression and remarkable stability against sodium metal. These performances enable the all-solid-state Na//TiS2 battery with a high capacity of 232.4 mAh g-1 (97.2 % of theoretical capacity) and long-term cycling stability at 1 C. Notably, this battery shows superior long-life cycling stability even at 5 and 10 C, which has been rarely reported in all-solid-state sodium metal batteries. This work opens a new group of solid electrolytes, contributing to fast-charging or high-power-density sodium metal batteries.

Structural Order-Disorder Analysis of Thermally-Activated Water-Washed Kaolin Particles Using Fourier Transform Infrared Spectroscopy

During the calcination of kaolin particles, kaolinite is thermally activated at high temperatures, causing the crystal structure to collapse and yielding amorphous metakaolinite through dehydroxylation. This metakaolinite is used as a supplementary cementitious material, and one of the most important factors influencing the pozzolanic properties is calcination conditions. Fourier transform infrared spectroscopy (FTIR) has become useful in distinguishing and obtaining information about structural order-disorder and phase transformation following the calcination process. In this study, water-washed kaolin particles were thermally activated at elevated temperatures ranging from 600 to 800 °C for 3–4 h at a rate of 10 °C/min before being analyzed with FTIR to determine the optimum conditions for calcining kaolin particles by examining functional groups, and also to study structural order-disorder or crystallinity of calcined kaolin particles. The most reactive metakaolinite state of water-washed kaolin particles was achieved after 3 h of calcination at 800 °C. Using both empirical and numerical approaches, variations in the position and relative intensity of O-H stretching and deformation of hydroxyl groups in the infrared spectrum can be used to classify the degree of structural order of water-washed kaolin particles. By increasing the calcination temperatures and period, the well-ordered and partially-ordered structures of kaolin particles were transformed into well-ordered, partially-ordered, and poorly-ordered structures. These structural disorder and crystallinity have a significant impact on pozzolanic activity because well-ordered kaolinite can be transformed into less reactive metakaolinite, whereas poorly-ordered kaolinite with high defects can be transformed into more reactive metakaolinite. However, in this study, the structure of water-washed kaolin particles that achieved complete dehydroxylation was discovered to be partially-ordered to poorly-ordered and can be transformed into highly reactive pozzolans.

Thermotropic Structure Phase Transitions and Two Types of Thermochromic Behaviors in a Bromoargentate Cluster [Pr-dabco]2Ag4Br6.

Organic-inorganic silver halide hybrids show abundant phase transitions and thermochromism. However, it is very rare that silver halides exhibit thermochromism related to thermotropic structure phase transition. Herein, a bromoargentate hybrid, [Pr-dabco]2Ag4Br6 (1) (Pr-dabco+ = 1-propyl-1,4-diazabicyclo-[2.2.2]octan-1-ium), with tetranuclear [Ag4Br6]2- clusters was prepared and characterized by microanalysis, ultraviolet-visible (UV-vis) diffuse reflectance spectroscopy, and thermogravimetric (TG) and differential scanning calorimetry (DSC) techniques. Interestingly, 1 undergoes an irreversible structure phase transition at ∼436 K in the first heating process, which is accompanied by an abrupt color change from colorless to yellow; however, a reversible color change between pale yellow and yellow is observed in the next heating-cooling cycles. Notably, DSC measurement revealed that a reversible phase transition is associated with the change in color between pale yellow and yellow, while the powder X-ray diffraction (PXRD) patterns corresponding to pale yellow and yellow phases are quite similar to each other. These observations demonstrate that thermochromism in the next heating-cooling runs is associated with a reversible structure phase transition, which perhaps concerns the disorder-order transformation of alkyl chains in the cationic ligand [Pr-dabco]+, and relevant to the anharmonic fluctuations of the Ag-Br and Ag-N bonds, a strong electron-phonon coupling effect is seen within the bromoargentate cluster.

Effect of Chlorine on Copper Electrodissolution

A computational study on the role of adsorbed Cl ions on copper dissolution is presented. Extensive grand canonical Monte Carlo (GCMC) calculations using reactive force-field (ReaxFF) are used to check the formation chlorine (Cl) adlayer structures on Cu (100) surface as a function of the chemical potential (µ). From experimental studies conducted by other researchers it has been observed that Cl adlattice on Cu in c(2X2) at maximum coverage. We observe that at low µ, Cl adlayer is disordered and moves to ordered c(2X2) structure at high µ. The binding energy of Cl, oxygen (O), hydroxide (OH-) and H2O on Cu at different sites is calculated and compared with Density-functional theory (DFT) values. Metal surface is often highly uneven and rough during electrodissolution process. Therefore, we also discuss the adsorption isotherm, disorder-order transformation, and preferential adsorption sites for rough surfaces. Specific anion adsorption (SAA) of Cl involves partial charge transfer to Cu substrate and these effect the type of bond and bond strength which is also briefly discussed. The electrodissolution of Cu in the presence of Cl is modelled using kinetic Monte Carlo simulation to obtain the polarization curve.Keywords: Adsorbed chlorine, electrodissolution, grand canonical monte carlo, molecular dynamics, ReaxFF, kinetic monte carlo.

Structure-dependent oxidation behavior of Au-Cu nanoparticles

Thermal oxidation is an easily controlled method to change the physical and chemical properties of nanoparticles, thus optimizing and expanding their applications. Unfortunately, less attention has been paid to the role of the crystal structure whose atomic arrangements can be critical for oxidation. Au-Cu nanoparticles showing a fast order-disorder transformation are oxidized at two temperatures of ordered (L10) and disordered (A1) phase regions. The oxidation rates between the two phases are compared by the Arrhenius equation, and a lower oxidation rate is determined in the L10 lattice than in the A1 lattice based on the time required for the complete oxidation. One possible reason is attributed to the longer diffusion length in the L10 lattice compared to the A1 lattice due to the anisotropic diffusion path of the former while isotropic diffusion of the latter, resulting in longer oxidation time and then slower oxidation for the ordered sample. The crystalline phase of Au-Cu nanoparticles can be straightforwardly tuned and the resulting atomic disposition is a powerful tool to control oxidation evolution.

The phase transformation behavior of Mn-Al rare-earth-free permanent magnets

Rare-earth-free permanent magnet materials based on Mn show great promise for applications in electric motors and devices. The metastable ferromagnetic τ phase of the Mn-Al system has magnetic properties between those of the high-performance Nd-Fe-B magnets and the lower-performance ferrite magnets. However, the hybrid displacive-diffusional pathway of τ formation, from the parent ε phase through the intermediary ε’ phase, is still not fully understood. This phase transformation progression was studied in-situ using diffractive, calorimetric, and magnetometric techniques to show that the progression from ε to τ in Mn54Al46 at <450 °C involves the ordering of ε into ε’. Density functional theory calculations were performed on each phase and confirmed the experimental observation that the ε to ε’ to τ pathway is energetically favorable. Isothermal annealing of quenched-in ε at 350 °C demonstrated that ε’ is ferromagnetic, also in agreement with theoretical results, with a moderate coercivity of at least 50 kA/m. The τ phase was observed to nucleate along the prior ε phase grain boundaries and grow into the ε’ phase regions. A boundary front of ε’ was observed between the τ and ε phases. Both Kissinger and Flynn-Wall-Ozawa methods were used to determine the activation energies for the ε’ and τ phase transformations with values of ∼140 kJ/mol obtained for both phases. Therefore, the ordering transformation to ε’ and the hybrid displacive-diffusional transformation to τ were shown to overcome the same magnitude energy barrier. Both activation energies were less than previous τ phase activation energies measured on Mn55Al45 in the absence of a significant ε’ ordering exotherm, providing a kinetic benefit to the ε to ε’ to τ pathway at 350 °C. The results of this study give insight into the phase transformation of L10 binary materials as well as materials that undergo a disorder–order transformation followed by displacive shear.

A combined study on microstructure, microchemistry and magnetic behavior of (Sm0.12Co0.88)95Hf1B4 nano-composite ribbons by electron microscopy and atom probe tomography

In this work, Hf and B modified ribbon produced by RSP (rapid solidification process) method have been studied to investigate the microstructure, phase formation and magnetic properties of the Sm-Co-based alloy. (Sm0.12Co0.88)95Hf1B4 ribbon has been synthesized and annealed at various temperatures (700 °C, 800 °C & 900 °C) to analyze the effect of temperature on magnetic properties and structure. X-ray diffraction (XRD) phase analysis has confirmed the 1:7 H phase as a significant phase in the as-spun ribbon. A combination of 1:5 H and 2:17 R phases were found in the ribbon annealed at 900 °C due to disorder-order transformation upon heat treatment. The development of ordered structure and grain growth upon annealing at 800 °C and 900 °C have deteriorated the magnetic properties. Scanning electron microscopy (SEM) and Transmission electron microscopy (TEM) analysis also revealed the grain growth and the development of the ordered 2:17 R structure upon annealing. The ribbon annealed at 700 °C showed better magnetic properties, Hc≈ 8.6 kOe, Mr ≈ 49 emu/g and (BH)max≈ 5.63 MGOe with an average grain size of ∼149 ± 5 nm. TC of the as-spun ribbon was found to be ⁓750 °C, and the temperature co-efficient of magnetization (α) and coercivity (β) were about − 0.008 and − 0.161%/°C, respectively. The APT analysis confirmed the fine borides in both as-spun and annealed (700 °C & 900 °C) ribbons.

Self-oscillatory instability of the driven phase front propagation induced by liberation of latent heat.

We theoretically address crystals exhibiting first-order phase transformations subjected to a steadily propagating temperature gradient. The latter drives a nonisothermal propagation of a phase front. We theoretically demonstrate that for the phase transformations of the displacive type, the phase front always steadily follows the isotherm. In contrast, in the case of the order-disorder or hybrid phase transformations in a crystal containing pinning defects, one finds a velocity of the isotherm, the first critical velocity, at which the steady front motion becomes unstable, and a stick-slip front propagation starts. Upon reaching the second critical velocity, the stick-slip behavior vanishes, and the motion becomes steady again. Our results enable one to determine the activation energy of the leading order-disorder process from the measurements of the driven motion of the phase front. In light of these results, we discuss experimental findings for PbTiO_{3} and NaNbO_{3}.

Short-Range Order Modeling in Alloys

The short and long-range orders in alloys can be assessed based on a new expression for the combinatorial factor, which is more convenient and intuitive than the traditionally used form. This novel expression can be directly applied to reproduce the results of several well-known statistical-thermodynamic models that are typically considered independent or even inconsistent. The short list of models includes Quasichemical Theory, Associated Solution Model, Surrounded Atom Model, and Cluster Site Approximation. As a result, the formalism and interpretation of these models are significantly clarified, allowing us to identify and fix several long-standing errors that might otherwise have gone unnoticed. Multicomponent generalization of these models is also greatly simplified. For systems undergoing a phase transition, an extended version of the theory provides a mechanism that allows the correct critical temperature of phase transition to be reproduced, as well as a significant increase in the accuracy of thermodynamic functions. In the case of order–disorder transformations, the new theory ensures an integrated description of short and long-range orders, which has long been considered an important and difficult problem.