Order Phase Transition Temperature Research Articles

Dielectric relaxation in pure and doped with Cu lead germanate single crystal

Dielectric permittivity of pure and doped with copper lead germanate Pb5Ge3O11 (PGO) crystal was studied in wide frequency (20 Hz to 3 GHz) and temperature (120 K to 450 K) range. The ferroelectric phase transition in PGO crystals is mixed “order-disoder” and displacive. Second order phase transition temperature shifts to lower temperature with increase the concentration of Cu2+ dopant. At low temperatures the dielectric relaxation caused by off center Cu2+ ion dynamics was detected. Dielectric dispersion in PGO:Cu crystals is attributed to domain wall dynamics and dipole glass freezing. It is shown that the domain relaxation requires lower energy then for the random freezing dipoles.

Reentrant and spin compensation phenomena in an Ising type ferrimagnetic system

A mixed spin-1 and spin-2 Ising ferrimagnetic system is investigated on a square lattice of spins S=±2,±1,0 and Q=±1,0 in the presence of an h′ external magnetic field, such that S and Q are nearest-neighbors antiferromagnetically coupled. Using Monte Carlo simulations we calculate the finite temperature phase diagrams of the magnetization and the specific heat. We consider ferromagnetic interactions between next-nearest neighbors, S spins (J2′), as well as between the Q spins (J3′), and crystal field and external magnetic field interactions at each point of the lattice. Under these conditions the system exhibits spin compensation temperatures and a first-order reentrant behavior in a certain range of the parameters of the Hamiltonian. We analyze the behavior of the critical and compensation temperatures, as well as the first order phase transition temperatures, with the external magnetic and crystal fields, and the next-nearest neighbors interaction between S spins. We found that the existence of compensation temperatures and a first order phase transition depends on the strength of h′, J2′ and D′.

Optical anisotropy, order parameter and its critical behavior in temperature-dependent refractive indices of nematic liquid crystals

The temperature dependence of optical birefringence, order parameter, effective geometry parameter, and normalized polarizability was determined for nematic liquid crystal mixtures by measuring the refractive indices. The effects of the adjustable parameters obtained from temperature-dependent refractive indices were analyzed appropriately for the crossover temperature and order parameter values. Besides, a four-parameter power law expression method was used for the optical birefringence measurement to address inappropriate fits in the weak first-order phase transition region. From this method, the effective second order phase transition temperature T⁎⁎ was determined by showing the slightly higher values than phase transition temperature. The value of the order parameter critical exponent λ obtained from this method showed a good agreement with the mean field theory by demonstrating closeness to the tricritical hypothesis (β = 0.25). As a consequence, the measurement of the temperature-dependent optical birefringence was successfully verified the pre-transitional phenomena accurately, and it can facilitate an insightful description of that region.

Accelerated search for perovskite materials with higher Curie temperature based on the machine learning methods

Curie temperature (Tc), the second order phase transition temperature, is also one of the important physical properties of perovskite materials. It is a meaningful work to quickly and efficiently predict Tc of new perovskite materials before doing a considerable amount of experimental work. In the work, SVM (support vector machine), RVM (relevance vector machine) and RF (random forest) were employed to establish the prediction models of Tc with the physicochemical parameters, respectively. The results reveal that the three models all have high precision and reliability. According to K-fold cross validation, the SVR model had better prediction performance than the RVM and RF models. Meanwhile, the potential perovskite material with higher Tc was found by using the SVR model integrated with the search strategy of genetic algorithm from the virtual samples. The methods outlined here can provide valuable hints into the exploration of materials with desired property and can accelerate the process of materials design.

Magnetostructural phase transitions and magnetocaloric effect in (Gd5-xScx)Si1.8Ge2.2

Future advancements in magnetocaloric refrigeration/heat pumping technologies depend on the discovery of new materials that demonstrate large, tunable magnetocaloric effects (MCEs) in the vicinity of coupled magnetic and structural phase transitions that occur reversibly with minimum hysteresis. With this in mind, we investigate phase transitions, microstructure, magnetic, thermal, magnetocaloric, and transport properties of (Gd5-xScx)Si1.8Ge2.2 compounds. Replacement of magnetic Gd with non-magnetic Sc in Gd5-xScxSi1.8Ge2.2 increases the ferromagnetic to paramagnetic first order phase transition temperature, TC, with only a minor reduction in MCE when x ≤ 0.2. We also demonstrate that hydrostatic pressure further increases TC and reduces the hysteresis of the first order phase transition in Gd4.8Sc0.2Si1.8Ge2.2 from 7 to 4 K. Temperature-dependent x-ray powder diffraction study of Gd4.8Sc0.2Si1.8Ge2.2 confirms the monoclinic ↔ orthorhombic structural transformation at TC, in agreement with magnetic, calorimetric, and electrical transport measurements. In addition to the substantial magnetocaloric effect, a large magnetoresistance of ∼20% is also observed in Gd4.8Sc0.2Si1.8Ge2.2 for ΔH = 50 kOe in the vicinity of the magnetostructural transition. In a drastic reversal of the initial doping behavior further additions of Sc (x > 0.2) suppress formation of the monoclinic phase, change the nature of the transition from first-to second-order, and reduce both the transition temperature and magnetocaloric effect.

An alternative perspective to observe the critical phenomena of dilaton black holes

The critical phenomena of dilaton black holes are probed from a totally different perspective other than the P–v criticality and the q–U criticality discussed in former literature. We investigate not only the two point correlation function but also the entanglement entropy of dilaton black holes. For both the two point correlation function and the entanglement entropy we consider 4times 2times 2=16 cases due to different choices of parameters. The van der Waals-like behavior can be clearly witnessed from all the T–delta L (T–delta S) graphs for q<q_c. Moreover, the effects of dilaton gravity and the spacetime dimensionality on the phase structure of dilaton black holes are disclosed. Furthermore, we discuss the stability of dilaton black holes by applying the analogous specific heat definition and remove the unstable branch by introducing a bar T=T_*. It is shown that the first order phase transition temperature T_* is affected by both alpha and n. The analogous equal area laws for both the T–delta L graph and the T–delta S graph are examined numerically. The relative errors for all cases are small enough so that we can safely conclude that the analogous equal area laws hold for T–delta L (T–delta S) graph of dilaton black holes.

Revisiting van der Waals like behavior of f(R) AdS black holes via the two point correlation function

Van der Waals like behavior of f(R) AdS black holes is revisited via two point correlation function, which is dual to the geodesic length in the bulk. The equation of motion constrained by the boundary condition is solved numerically and both the effect of boundary region size and f(R) gravity are probed. Moreover, an analogous specific heat related to δL is introduced. It is shown that the T−δL graphs of f(R) AdS black holes exhibit reverse van der Waals like behavior just as the T−S graphs do. Free energy analysis is carried out to determine the first order phase transition temperature T⁎ and the unstable branch in T−δL curve is removed by a bar T=T⁎. It is shown that the first order phase transition temperature is the same at least to the order of 10−10 for different choices of the parameter b although the values of free energy vary with b. Our result further supports the former finding that charged f(R) AdS black holes behave much like RN-AdS black holes. We also check the analogous equal area law numerically and find that the relative errors for both the cases θ0=0.1 and θ0=0.2 are small enough. The fitting functions between log⁡|T−Tc| and log⁡|δL−δLc| for both cases are also obtained. It is shown that the slope is around 3, implying that the critical exponent is about 2/3. This result is in accordance with those in former literatures of specific heat related to the thermal entropy or entanglement entropy.

Gd5(SixGe1−x)4 system – updated phase diagram

Gd5(SixGe1−x)4 for 0.41<x<0.5 is orthorhombic and ferromagnetic at lower temperature, monoclinic and paramagnetic at higher temperature, and shows a first order magnetic-structural phase transition between the two. In this range, the magnetic moment vs. magnetic field (MH) isotherms measured just above the first order transition temperature carry information about all magnetic and structural transitions. Here, the Curie–Weiss law was applied to the paramagnetic portions of the MH isotherms which allowed identification of the second order magnetic phase transition temperature of the monoclinic phase, a region where the second order transition does not occur due to the existence of the first order transition. The calculated second order phase transition temperatures of the monoclinic phase were added to the existing phase diagram. The completed magnetic-structural phase diagram carries now all the information including the magnetic transition temperatures of both monoclinic and orthorhombic phases. It was also found that the magnetic transition temperature of the monoclinic phase and the first order transition temperature are interrelated.

Ultrasonic and Dielectric Studies of Polyurea Elastomer Composites with Inorganic Nanoparticles

The temperature dependence of ultrasonic velocity and ultrasonic attenuation were measured in polyurea elastomer composites with inorganic nanoparticles. The decrease in the ultrasonic velocity along with an attenuation maximum was observed above the glass transition temperature, Tg. The shape and position of this peak are directly proportional to the amount of embedded nanoparticles. In addition, the sharp anomalies in the ultrasonic velocity and ultrasonic attenuation were observed above the glass transition temperature in semicrystalline polyurea elastomers. These anomalies are related to the corresponding first order phase transition of these crystalline domain-containing networks. The ultrasonic attenuation peak related to glass transition is considerably smaller in these polyurea networks showing a small influence of the soft domains below the melting temperature, Tm. The first order phase transition in the semicrystalline polyurea elastomers shows a large temperature hysteresis of more than 10 K, which was confirmed by dielectric investigations. The addition of small amounts of inorganic nanoparticles resulted in a shift of the first order phase transition temperature in semicrystalline nanocomposites.

Second order phase transition temperature of single crystals of Gd5Si1.3Ge2.7 and Gd5Si1.4Ge2.6

Gd5(SixGe1−x)4 has mixed phases in the composition range 0.32 &amp;lt; x &amp;lt; 0.41, which have not been widely studied. In this paper, we have synthesized and indexed single crystal samples of Gd5Si1.3Ge2.7 and Gd5Si1.4Ge2.6. We have investigated the first order and second order phase transition temperatures of these samples using magnetic moment vs. temperature and magnetic moment vs. magnetic field at different temperatures. We have used a modified Arrott plot technique that was developed and reported by us previously to determine the “hidden” second order phase transition temperature of the orthorhombic II phase.

Fast switching response and dielectric behaviour of fullerene/ferroelectric liquid crystal nanocolloids

The electro-optical and dielectric responses of the fullerenes C60-doped ferroelectric liquid crystal (FLC) nanocolloids are reported. Order parameter and phase transition temperature remain invariant as a function of varying dopant concentration (0.10 wt% to 0.50 wt%). Faster switching response of nanocolloids comparing to that of the non-doped FLC is manifested by increase in the localised electric field (around 76% increment for 0.50 wt%), while reduction in the spontaneous polarisation could be the result of anti-parallel correlation amid dopant and FLC dipoles. Decrease in dielectric constant, absorption strength, dielectric strength and rotational viscosity of FLC nanocolloids than that of non-doped FLC is the other consequence of C60 doping. Goldstone-mode relaxation frequency is found to be increased with increasing doping concentration of C60 in FLC.

A simple model to predict long-range atomic ordering temperatures in Cu-based shape memory alloys

The order–disorder and order–order phase transition temperatures in the austenitic phase of Cu-based shape memory alloys were used to obtain a set of first- and second-neighbour pair interchange energies. To this end, a mean field model was postulated. Then, the applicability to different alloys of this simple model was analysed. It was found that a good agreement with the experimental phase diagram is obtained for Cu–Zn–Al, Cu–Al–Ni and Cu–Al–Be alloys using composition-independent parameters. It was also found that for Cu–Al–Mn alloys, composition-dependent pair interchange energies need to be employed.

Study of the Second-Order “Hidden” Phase Transition of the Monoclinic Phase in the Mixed Phase Region of ${\rm Gd}_{5}{({\rm Si}_{\rm x}{\rm Ge}_{1-{\rm x}})}_{4}$

Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> (Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> exhibits a first order phase transition for the compositions 0 <; x <; 0.575 leading to a magnetic phase transition as well. It is not possible to measure the second order phase (magnetic) transition temperatures of the individual phases with direct measurements. This is because the first order phase transition occurs before the second order phase transition. With modified Arrott plots we have shown previously that it is possible to estimate the second order phase transition of the Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> -type orthorhombic phase. In this paper we have estimated the second order phase transition temperature of the Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -type monoclinic phase using a single crystal sample of Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.5</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sub> (0.375) which falls in the mixed phase region of the sample.

Magnetocrystalline Anisotropy in Single Crystal Gd$_{5}$Si$_{2.7}$Ge$_{1.3}$ and Gd$_{5}$Si$_{2}$Ge$_{2}$

Gd5(SixGe1-x)4 exhibits uniaxial magnetocrystalline anisotropy. There are few reports on direct magnetic measurements on principle and non-principal axis to determine the uniaxial nature of magnetocrystalline anisotropy. In this paper we confirm the nature of magnetocrystalline anisotropy to be uniaxial in single crystal Gd5Si2.7Ge1.3 (x=0.675) sample using magnetic moment versus angle of rotation measurements. The first order magnetocrystalline anisotropy constant was also calculated on single crystal Gd5 Si2.7 Ge1.3 (x=0.675) sample using magnetic moment versus magnetic field measurements on easy and hard axes. Effect of magnetocrystalline anisotropy on determination of the first order phase transition temperature of the sample was determined to be negligible in single crystal Gd5Si2Ge2 sample using magnetic moment versus temperature measurement at various orientations of the sample.

Order Parameter Distribution and Phase Transition Temperature for a Thin Film With Asymmetric Boundaries

The phenomenological theory was developed for the ferroic phase transition in a thin film with asymmetric boundary conditions which simulate the real situation of a film on the substrate or a layer between two different materials. The solutions of the boundary value problem for the order parameter were obtained numerically for some particular sets of phenomenological parameters in the Landau expansion and extrapolation lengths. The main attention was focused on the case of opposite signs of the extrapolation lengths at film surfaces. It was shown that the mean order parameter is close to that in bulk and phase transition temperature remains weakly dependent on film thickness when the extrapolation lengths have similar absolute values and opposite signs.

Minimum shear viscosity over entropy density at phase transition?—A counterexample

The ratio η/s, shear viscosity (η) to entropy density (s), reaches its local minimum at the (second order) phase transition temperature in a wide class of systems. It was suspected that this behavior might be universal. However, a counterexample is found in a system of two weakly self-interacting real scalar fields with one of them condensing at low temperatures while the other remains in the symmetric phase. There is no interaction between the two fields. In our mean field analysis the resulting η/s is monotonically decreasing in temperature despite the second order phase transition.

Monte Carlo Simulation of First Order Phase Transitions

Monte Carlo simulation with Metropolis algorithm has been performed on a cubic Ising lattice with four-spin couplings. Temperature dependence of the spin average and average energy has been obtained. We found that the phase transition is of first order when the strength of four-spin coupling is stronger a critical value, and this critical value is of lattice size dependence. Binder cumulants still can be used to determine the second order phase transition temperature. For first order phase transition, the spin average disappears abruptly at the temperature of the average energy being a third of the ground state energy.

Quantum mechanical aspect of first order phase transition of crystals

It has been generally believed that some external physical porperties, e.g. volume, enthalpy, and entropy, etc. change discontinuously at first order phase transition temperatures, since Ehrenfest’s proposition. However, the deviation from this proposition was often found in many crystals. As the progress of experimental methods and the accuracy develop the number of crystals that manifest unusual transition processes is increasing. Notably aberrant phenomena are as follows. An intermediate phase appears whose crystal structure is undoubtedly different from those of the low and high temperature forms. The peak of differential thermal analysis of specific heat is splitted into two as if one transition inevitably induces another. The interpretation of these abnormal behaviors in the vicinity of the transition is certainly beyond reach of thermodynamic ideas. We assumed that the eigenkets of Boltzmann’s H of each phase in the vicinity of the transition temperature interact to produce perturbing state. Then the intermediate phase named M phase emerges, and its eigenket is the superposition of eigenkets of commuting Hamiltonian of the two temperature phases. It is natural that the new M phase has different structure from those of the two phases. The above mentioned phenomena occurring in dichlorobenzophenone, NaNO2, 1-Ethyl-3-(4-methylpentanoyl)urea, and VO2 are explained by this quantum mechanical theory.

Investigation of the dielectric and piezoelectric properties of potassium sodium niobate ceramics close to the phase boundary at (K 0.35Na 0.65)NbO 3 and partial substitutions with lithium and antimony

Potassium sodium niobate (KNN) piezoelectric ceramics and KNN substituted with lithium (Li +) and antimony (Sb 5+) have been synthesized by the conventional solid state sintering method. This work focuses on the phase transition in the KNN system at potassium (K +) content of approximately 0.35. Therefore, K amount was altered from 0.31 to 0.35. Additionally, Li + and Sb 5+ were used for partial substitution (up to 8% for Sb) thereby enhancing the piezoelectric and dielectric properties. However, addition of Li + and Sb 5+ also lead to a decrease in both the Curie temperature ( T C ) and the first order phase transition temperature ( T T-O ) of the ceramics. Addition of more than 4 mol% of Li + led to the formation of extra phases. The piezoelectric properties within the given composition range were found to be optimum at (K 0.34Na 0.64Li 0.02)(Nb 0.96Sb 0.04)O 3. A piezoelectric charge coefficient ( d 33 * ) of 404 pm/V for this composition was obtained from unipolar strain hysteresis measurements.

Kerr Effect Studies on Mixtures of the Two Tolane Base Liquid Crystals

The static Kerr effect and third order non-linearity were investigated for mixtures of the tolane-base liquid crystals within the isotropic phase in the neighborhood of the nematic phase. The nematic mixtures are characterized by components having similar molecular structure, i.e., the mixtures comprised by 4′-pentyl-3-fluoro-4-isothiocyanatotolane (5TOLF) and 4′-heptyl-3 fluoro-4-isothiocyanatotolane (7TOLF) which have a positive and large Kerr constant. The nematic to isotropic transition temperatures and nematic to crystalline temperatures for these mixtures were measured using DSC and polarizing microscopy methods. The nematic mixture of M3 (%50 5TOLF + %50 7TOLF) shows the largest nematic range. The linear dependence of (T − T*)−1 on the Kerr constant is found to be in good agreement with the predications of the Landau-De Gennes model. The hypothetical second order phase transition temperatures and susceptibility values were determined for these compounds.