Order-disorder Transition Point Research Articles

Mechanical properties and fractographic analyses of FeCo-2V alloy heat-treated around order-disorder transition temperature

The effect of heat treatment on the mechanical properties of FeCo-2V alloy was investigated at temperatures slightly above and below its order-disorder transition point with varied holding times and cooling rates. The fracture surface, grain size, and recrystallized microstructure were characterized by SEM and EBSD. The correlation between yield strength and microstructural features was analysed. Yield strength was found to decrease with the elevation of heating temperature, extension of holding time, and decrease in cooling rate. Fast cooling significantly improved the mechanical strength and ductility. The quenched samples exhibited microscopically ductile fracture features with shallow dimples on the fractured surface, while the slow-cooled ones displayed brittle microscopic fracture features, regardless of the heating temperature and holding time. The yield strength follows two separate Hall-Petch relationships for samples dominantly in the ordered and disordered states. Our analyses reveal that the mechanical strength of FeCo-2V alloy is mainly controlled by the grain size, thus it is important to regulate the grain recrystallization and growth during the heat treatment process.

Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation.

Effects of three-point direct correlation on properties of the phase field crystal (PFC) modeling are examined for the control of various ordered and disordered phases and their coexistence in both three-dimensional and two-dimensional systems. Such effects are manifested via the corresponding gradient nonlinearity in the PFC free-energy functional that is derived from classical density functional theory. Their significant impacts on the stability regimes of ordered phases, phase diagrams, and elastic properties of the system, as compared to those of the original PFC model, are revealed through systematic analyses and simulations. The nontrivial contribution from three-point direct correlation leads to the variation of the critical point of order-disorder transition to which all the phase boundaries in the temperature-density phase diagram converge. It also enables the variation and control of system elastic constants over a substantial range as needed in modeling different types of materials with the same crystalline structure but different elastic properties. The capability of this PFC approach in modeling both solid and soft matter systems is further demonstrated through the effect of three-point correlation on controlling the vapor-liquid-solid coexistence and transitions for body-centered cubic phase and on achieving the liquid-stripe or liquid-lamellar phase coexistence. All these provide a valuable and efficient method for the study of structural ordering and evolution in various types of material systems.

Comment on “Quantify the contribution of chain length heterogeneity on block copolymer self-assembly”

The effects of molecular weight distribution on the self-assembly of lamella-forming AB-diblock copolymers with polydisperse A-blocks are examined using the self-consistent field theory applied to the freely-jointed chain (FJC) model of polymers. The experimentally observed domain spacing and order-disorder transition point are well described by the theory. The excellent agreement between experiments and theory indicates that the FJC model is capable of describing the phase behaviour of low-molecular block copolymers. A combination of experimental techniques and theoretical modelling offers exciting opportunities to engineering desirable block copolymer morphologies using block copolymers with designed chain length heterogeneities.

Investigation of possible phase transition of the frustrated spin-1/2 J1-J2-J3 model on the square lattice

The frustrated spin-1/2 J1-J2-J3 antiferromagnet with exchange anisotropy on the two-dimensional square lattice is investigated. The exchange anisotropy is presented by η with 0 ≤ η < 1. The effects of the J1, J2, J3 and anisotropy on the possible phase transition of the Néel state and collinear state are studied comprehensively. Our results indicate that for J3 > 0 there are upper limits {J}_{3}^{c} and ηc values. When 0 < J3 ≤ {J}_{3}^{c} and 0 ≤ η ≤ ηc, the Néel and collinear states have the same order-disorder transition point at J2 = J1/2. Nevertheless, when the J3 and η values beyond the upper limits, it is a paramagnetic phase at J2 = J1/2. For J3 < 0, in the case of 0 ≤ η < 1, the two states always have the same critical temperature as long as J2 = J1/2. Therefore, for J2 = J1/2, under such parameters, a first-order phase transition between the two states for these two cases below the critical temperatures may occur. When J2 ≠ J1/2, the Néel and collinear states may also exist, while they have different critical temperatures. When J2 > J1/2, a first-order phase transition between the two states may also occur. However, for J2 < J1/2, the Néel state is always more stable than the collinear state.

Frozen states and active-absorbing phase transitions of the Ising model on networks

A zero temperature quench of the Ising model is known to lead to a frozen steady state on random and small world networks. We study such quenches on random scale free networks (RSF) and compare the scenario with that in the Barab\'asi-Albert network (BA) and the Watts Strogatz (WS) addition type network. While frozen states are present in all the cases, the RSF shows an order-disorder phase transition of mean field nature as in the WS model as well as the existence of two absorbing phases separated by an active phase. The WS network also shows an active-absorbing (A-A) phase transition occurring at the known order-disorder transition point. The comparison of the RSF and the BA network results show interesting difference in finite size dependence.

Order–disorder transition in the two-dimensional interacting monomer-dimer model: Ising criticality

We study the order–disorder transition of the two-dimensional interacting monomer-dimer model (IMD) which has two symmetric absorbing states. To be self-contained, we first estimate numerically the dynamic exponent z of the two-dimensional Ising model. From the relaxation dynamics of the magnetization at the critical point, we obtain , or , where and are exactly known exponents. We then compare the critical relaxation of the order parameter at the transition point of the IMD with that of the Ising model. We find that the critical relaxation exponent is in good agreement with the Ising model, unlike the recent claim by Nam et al (2014 J. Stat. Mech. P08011). We also claim that the Binder cumulant is not an efficient quantity to locate the order–disorder transition point of the model with two symmetric absorbing states.

Self-assembly of cyclic rod-coil diblock copolymers

The phase behavior of cyclic rod-coil diblock copolymer melts is investigated by the dissipative particle dynamics simulation. In order to understand the effect of chain topological architecture better, we also study the linear rod-coil system. The comparison of the calculated phase diagrams between the two rod-coil copolymers reveals that the order-disorder transition point (χN)ODT for cyclic rod-coil diblock copolymers is always higher than that of equivalent linear rod-coil diblocks. In addition, the phase diagram for cyclic system is more "symmetrical," due to the topological constraint. Moreover, there are significant differences in the self-assembled overall morphologies and the local molecular arrangements. For example, frod = 0.5, both lamellar structures are formed while rod packing is different greatly in cyclic and linear cases. The lamellae with rods arranged coplanarly into bilayers occurs in cyclic rod-coil diblocks, while the lamellar structure with rods arranged end by end into interdigitated bilayers appears in linear counterpart. In both the lamellar phases, the domain size ratio of cyclic to linear diblocks is ranged from 0.63 to 0.70. This is attributed to that the cyclic architecture with the additional junction increases the contacts between incompatible blocks and prevents the coil chains from expanding as much as the linear cases. As frod = 0.7, the hexagonally packed cylinder is observed for cyclic rod-coil diblocks, while liquid-crystalline smectic A lamellar phase is formed in linear system. As a result, the cyclization of a linear rod-coil block copolymer can induce remarkable differences in the self-assembly behavior and also diversify its physical properties and applications greatly.

Properties of clinopyroxene LiFeGe2O6

The polycrystalline compound LiFeGe2O6 has been synthesized by the solid-phase reaction. The X-ray diffraction, Mossbauer, calorimetric, and magnetic investigations have been carried out. The Mossbauer spectrum at 300 K represents a single quadrupole doublet. The isomer shift with respect to the metal iron α-Fe is 0.40 mm/s, which is characteristic of the Fe3+ high-spin ion in the octahedral coordination. The quadrupole splitting of 0.42 mm/s indicates a distortion of the oxygen octahedron around the iron cation. The results of the measurement of the temperature dependence of the heat capacity in the range 2–300 K have shown the presence of the only anomaly with a maximum at T m ∼ 20.5 K, which indicates the occurrence of a magnetic phase transition in this point. The data of the measurement of the temperature dependence of the magnetization have confirmed that the magnetic order with the dominant antiferromagnetic interaction of magnetically active ions exists in LiFeGe2O6 at a temperature below 20.5 K. The investigation of the temperature dependence of the heat capacity in the magnetic field H up to 9 T has demonstrated that the external factor insignificantly changes the order-disorder transition point (at H = 9 T, there occurs a shift of ∼0.5 K toward the low-temperature range).

Effects of average degree of network on an order–disorder transition in opinion dynamics

We have investigated the influence of the average degree (k) of network on the location of an order-disorder transition in opinion dynamics. For this purpose, a variant of majority rule (VMR) model is applied to Watts–Strogatz (WS) small-world networks and Barabási–Albert (BA) scale-free networks which may describe some non-trivial properties of social systems. Using Monte Carlo simulations, we find that the order–disorder transition point of the VMR model is greatly affected by the average degree (k) of the networks; a larger value of (k) results in a more ordered state of the system. Comparing WS networks with BA networks, we find WS networks have better orderliness than BA networks when the average degree (k) is small. With the increase of (k), BA networks have a more ordered state. By implementing finite-size scaling analysis, we also obtain critical exponents β/ν, γ/ν and 1/ν for several values of average degree (k). Our results may be helpful to understand structural effects on order–disorder phase transition in the context of the majority rule model.

Micro-Meter Size Organogelator with Tri-Color Luminescence (Blue, Green and Red) Activated by Dy3+, Tb3+ and Eu3+ ions

The preparation of a novel type of low-molecular-weight amphiphilic organogelator bearing three long 14-alkyl chains and hydrophilic oligo(oxyethylene) groups was described. Ultra-violet absorption and fluorescence spectra give evidence of the energy transfer between organic ligands to lanthanide ions. Characteristic green, blue and red luminescence of the organogels were obtained and interesting emission properties of terbium, dysprosium and europium ions were unexpectedly observed at the first time during the order-disorder phase transition point (29 degrees C).

Quantum phase transition as a result of magnetic frustrations in a ferrimagnetic Heisenberg system

Using density-matrix renormalization group (DMRG) method, we studied the effect of magnetic frustrations due to next-nearest- neighbor bonds in a system of quasi-one-dimensional Heisenberg antiferromagnetic chain but with ferrimagnetic properties. In this paper, the ground state energy per unit cell, spin correlation function and spin gap are calculated. As a result of the frustrations, the quantum disordered phase with the spin gap appears at the spin order-disorder phase transition point αC≈0.412 to α＝1. And in the region of magnetic-order phase, the increasing magnetic frustrations reduce the magnetic order.

Study of self-assembly of symmetric coil-rod-coil ABA-type triblock copolymers by self-consistent field lattice method

The self-assembly of symmetric coil-rod-coil ABA-type triblock copolymer melts is studied by applying self-consistent field lattice techniques in a three-dimensional space. The self-assembled ordered structures differ significantly with the variation of the volume fraction of the rod component, which include lamellar, wave lamellar, gyroid, perforated lamellar, cylindrical, and spherical-like phases. To understand the physical essence of these phases and the regimes of occurrence, we construct the phase diagram, which matches qualitatively with the existing experimental results. Compared with the coil-rod AB diblock copolymer, our results revealed that the interfacial grafting density of the separating rod and coil segments shows important influence on the self-assembly behaviors of symmetric coil-rod-coil ABA triblock copolymer melts. We found that the order-disorder transition point changes from f(rod)=0.5 for AB diblock copolymers to f(rod)=0.6 for ABA triblock copolymers. Our results also show that the spherical-like and cylindrical phases occupy most of the region in the phase diagram, and the lamellar phase is found stable only at the high volume fraction of the rod.

Block Copolymers in Electric Fields: A Comparison of Single-Mode and Self-Consistent-Field Approximations

We compare two theoretical approaches to dielectric diblock copolymer melts in an external electric field. The first is a relatively simple analytic expansion in the relative copolymer concentration, and includes the full electrostatic contribution consistent with that expansion. It is valid close to the order-disorder transition point, the weak segregation limit. The second employs self-consistent field (SCF) theory and includes the full electrostatic contribution to the free energy at any copolymer segregation. It is more accurate but computationally more intensive. Motivated by recent experiments, we explore a section of the phase diagram in the three-dimensional parameter space of the block architecture, the interaction parameter and the external electric field. The relative stability of the lamellar, hexagonal and distorted body-centered-cubic (bcc) phases is compared within the two models. As function of an increasing electric field, the distorted bcc region in the phase diagram shrinks and disappears above a triple point, at which the lamellar, hexagonal and distorted bcc phases coexist. We examine the deformation of the bcc phase under the influence of the external field. While the elongation of the spheres is larger in the one-mode expansion than that predicted by the full SCF theory, the general features of the schemes are in satisfactory agreement. This indicates the general utility of the simple theory for exploratory calculations.

Unified Interpretation of the Short- and Long-Range Ordered States in Cu–Pt Alloys

This paper describes a unified interpretation of unusual short-range order diffuse scattering intensity distribution, the appearance of intensity maxima simultaneously at the special points L and X of the reciprocal space, and of the formation of a variety of long-range ordered structures, including less common structures, in the face-centered cubic Cu–Pt alloys. Reassessment is first made of the ordered structures on the Pt-rich composition side and then it is shown that all the structures in the alloys are systematically described adopting the static concentration wave model, originally developed by Khachaturyan, with the two kinds of waves, L1 1 wave and L1 2 wave, and their combination. These waves are assumed to be still alive at temperatures above the order–disorder transition point with appreciably decreased amplitude and coherency length and lead to the appearance of the two types of diffuse intensity maxima. Comparison is made with the ordering behaviors in the well-known Cu–Au alloys, in which o...

Molecular dynamics simulation of the phase behavior of lamellar amphiphilic model systems

Using efficient simplified continuum amphiphile models-AB dimers, A2B2 tetramers, and A4B4 octamers-as models for diblock copolymers, surfactants and liquid crystals, the phase behavior of the corresponding lamellar systems is investigated by large-scale parallelized dissipative particle dynamics type of molecular dynamics simulation. We not only observe the first order nature of the order–disorder transition, but also find that this first order phase transition becomes weaker as the block length of the models increases. The theoretically predicted “chain stretching” effect is reproduced as the like-monomer attractive potential well depth is increased. At the order–disorder transition point, a singular discontinuous jump in the stretching amplitude is accompanied with a distinctive orientation-induced stretching effect in the layer normal direction and an orientation induced-compressing effect in the layer plane directions. The configuration of the lamellar phase is very sensitive to the commensurability of its equilibrium layer spacing with the cell size. Too large layer spacings lead to the formation of a slightly tilted lamellar structure in the “quasistatic-cooling” process and to an undulation instability in the “quasistatic-heating” process. The relation between equilibrium layer spacing and like-monomer attraction is examined.

Thermal Motion in Sodium Nitrite: The Temperature Dependence of Debye-Waller Factors

In order to understand the relation between the transition mechanism and the thermal vibration, the temperature dependence of the Debye-Waller factor is investigated in NaNO 2 by single-crystal X-ray diffractometry. The crystal parameters are refined by least squares calculations both in paraelectric and ferroelectric phases. The maximum entropy method is also employed to estimate the spontaneous polarization. The Debye-Waller factor displays a minor anomaly at the order-disorder transition point. The result is compared with K 2 SeO 4 , a typical displacive crystal.

Order-disorder transition in hcp binary alloys: Next-nearest-neighbor interactions

The order-disorder transition in hcp binary alloys is investigated by Monte Carlo simulations and the renormalization-group methods. The inclusion of the interactions beyond the nearest neighbors induces qualitative changes of the phase boundaries. Especially, the contribution from second-neighbor interactions explains the shift along the concentration axis of the congruent point of order-disorder transition observed in the $\ensuremath{\alpha}/{\ensuremath{\alpha}}_{2}$ phase boundaries in the Ti-Al binary system.

Block copolymer films between neutral walls: A Monte Carlo study

We study thin, symmetric AB-copolymer films between neutral walls using the bond fluctuation model. Near the surface, the monomer distribution with respect to the chains’ center of mass is nonisotropic: The chains flatten on the surface. The resulting A- and B-lamellae have interfaces practically perpendicular to the walls, as also observed in recent experiments. Our simulations indicate the onset of long-range surface ordering before the bulk orders. The strongest effects take place between the spinodal and the order–disorder transition point of the diblock copolymer melt.

Coexistence of ordered and disordered phases in a nearly symmetric diblock copolymer near an order-disorder transition point.

We investigated the phase behavior near the order-disorder transition (ODT) temperature in a nearly symmetric diblock copolymer, using ultra-small-angle x-ray scattering method. In a narrow temperature range very close to the ODT temperature, we observed the scattering profiles that can be interpreted as a linear combination of the scattering from the disordered state and that from the ordered lamellar state. These profiles were stable during the observation time (50 h), revealing that the two-phase coexistence occurs at thermal equilibrium within this temperature range.

Transitions between modulated phases in an Ising model with third-neighbour interactions (mean-field approximation)

We study order–disorder transitions in a three-dimensional Ising lattice in which all the spins belonging to the same xy plane have the same degree of disorder, so that the structure can be effectively reduced to a chain of layers. The layers interact with each other up to third neighbours. Employing the mean-field approximation, we find the different configurations that undergo the transition to total disorder in terms of the interaction constants and work out a diagram displaying the possible sequences of modulated phases that can be found when the temperature goes from 0 to the order–disorder transition point. At intermediate temperatures the average values of the spins of the layers for periodic structures are found by solving an equation system. Substitution of these values into the expression of the free energy allows one to determine the most stable structure for each set of interaction constants and for each temperature. The model predicts a transition between two modulated structures with the same wavelength but different unit cells, for suitable values of the interaction constants. The formalism is also applied to substances like UNi 2Si 2, with only a partial agreement with experiment.