Second-order Phase Transition Temperature Research Articles

Effect of Al ions on the hyperthermia properties of oleic acid-coated Sr2-xAlxFeMoO6 nanoparticles

A self-regulating magnetic fluid with a suitable second-order phase transition temperature for achieving hyperthermia treatment temperatures is investigated for use as a possible mild cancer treatment. Current studies have focused on the optimization of magnetic fluids. In this work, magnetic fluids of Al-doped Sr2FeMoO6 nanoparticles are investigated based on their relatively high saturation magnetization. The nanoparticles are synthesized using a simple sol–gel method, successfully nanomized, and then coated by oleic acid through ball milling to prevent oxidation and improve biocompatibility. The crystal structure, morphology, basic magnetic properties and heating properties of the samples in a high-frequency magnetic field are investigated. It is found that oleic acid-coated Sr1.98Al0.02FeMoO6 nanoparticles with a particle diameter of ~ 140 nm and a maximum heating temperature of 47.8 °C at a concentration of 2 mg·ml−1 possess excellent induction heating properties. The saturation magnetization, coercive force, specific absorption rate and effective specific absorption rate are 18 emu/g, 5.14 mT, 41.8 W·g−1 and 0.0193 W·g−1·kHz·(kA·m−2), respectively.

The crystal-field dependency of sound attenuation in the spin-3/2 ising model

The effects of crystal-field (D) on sound attenuation are considered for the spin-3/2 Ising model by using Onsager theory of irreversible thermodynamics. It is assumed that the sound wave couples to the order-parameter fluctuations, therefore, it decays mainly via order-parameter relaxation process. The order-parameters, magnetization and quadrupole moment, are defined in terms of exact recursion relations (ERR) on Bethe lattice (BL). After our analysis, two relaxation times are obtained and they are used to calculate the sound attenuation coefficient (α). Consequently, the critical behaviors of sound attenuation coefficient are investigated in terms of frequency (w) and Onsager coefficient (γ) for the coordination numbers q=3, 4 ad 6 near the second-order (Tc) and first-order (Tt) phase transition temperatures in the ferromagnetic phase regions for the negative and positive D values and the results are presented on the (kBT/J, α) planes. It is found that the peaks about Tt’s are observed at the same temperature, but the peaks about Tc’s are observed shifted to lower and higher temperatures in increasing (w)’s and (γ)’s, respectively. In addition, the peaks are also obtained near the tricritical points for all q.

Ehrenfest equations for second-order phase transition under hydrostatic and uniaxial stresses

ABSTRACTFor 40 years, many research works have been confusing the linear part of the Ehrenfest equation for the shift of the second-order phase transition temperature in solids by the hydrostatic pressure with the equation for the shift caused by the uniaxial pressure . While the sum of the three slopes is trivially equal to the slope due to hydrostatic pressure , the sum of calculated from the exact Ehrenfest equation for the uniaxial pressure generally does not coincide with and may differ from by the sign and by the absolute value by more than three times.

Dispersion behaviors of Gaussian-type distribution of Curie temperature in relaxor ferroelectrics

ABSTRACTWhen the contributions of dipole and soften vibration mode are assigned to a complex impermeability and a real impermeability, respectively, the total complex permeability with frequency can be derived to modify the classical Landau-Devonshire theory. In a gaussian distribution and a skewed gaussian distribution of Curie temperature of second-order phase transition, the functions derived have the form of dispersion behavior of relaxor ferroelectrics. By comparing with experiment result, slight deviations appear on the two sides of peak of permittivity for the gaussian distribution, and improved by the skewed gaussian distribution. The relevant problems to be solved are proposed.

The thermodynamic functions of ferroelectric and paraelectric SbSI

A first-principle method is used to calculate phonon density of states, Helmholtz free energy, internal energy, and entropy for ferroelectric and paraelectric SbSI. Theoretical phase transition temperature was obtained using the difference of the Helmholtz free energy, internal energy, and entropy term between ferroelectric and paraelectric phases on temperature. The obtained value is in reasonable agreement with the experimental second-order phase transition temperature Tc2 = 233 K.

±J model on the Bethe lattice with crystal field interaction

±J model was exploited on the Bethe lattice for the spin-1 Blume–Capel model. Either ferromagnetic (J>0) or antiferromagnetic (J<0) interactions are assumed between the nearest-neighbor (NN) spins on the Bethe lattice for given probabilities p or 1−p, respectively. The phase diagrams of the model were calculated exactly on the temperature (T)–probability (p) or crystal field (D) planes for given coordination numbers q=3, 4 and 6. In addition to the first- and second-order phase transitions, another kind phase transition with zero magnetization and quadrupolar order-parameter presenting a jump was obtained above the second-order phase transition temperature which seems to be indicating the spin glass phase. When the lines of these three phases combine is a multicritical point and the first two combine is a tricritical point. In the (T,p) planes, the lower critical dimensions (the value of q) of obtaining any phase transition increase with increasing negative D values.

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (w), Onsager coefficient (γ) and external magnetic field (H) near the second-order (Tc) and first-order (Tt) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α). Our investigations revealed that only one peak is obtained near Tt and three peaks are found near Tc when the Onsager coefficient is varied at a given constant frequency for q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4 and 6 near Tc. The sound attenuation peaks are observed near Tt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.

Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

We derive a cluster mean-field theory for an Ising Hamiltonian using a cluster-lattice Fourier transform with a cluster of size ${N}_{\mathrm{c}}$ and a coarse-grained (CG) lattice into cells of size ${N}_{\mathrm{cell}}$. We explore forms with ${N}_{\mathrm{cell}}\ensuremath{\geqslant}{N}_{\mathrm{c}}$, including a non-CG (NCG) version with ${N}_{\mathrm{cell}}\ensuremath{\rightarrow}\ensuremath{\infty}$. For ${N}_{\text{c}}={N}_{\mathrm{cell}}$, the set of static, self-consistent equations relating cluster and CG lattice correlations is analogous to that in dynamical cluster approximation and cellular dynamical mean-field theory used in correlated electron physics. A variational ${N}_{\mathrm{c}}$-site cluster grand potential based on ${N}_{\mathrm{c}}={N}_{\mathrm{cell}}$ CG lattice maintains thermodynamic consistency and improves predictions, recovering Monte Carlo and series expansion results upon finite-size scaling; notably, the ${N}_{\mathrm{c}}=1$ CG results already predict well the first- and second-order phase boundary topology and transition temperatures for frustrated lattices. The NCG version is significantly faster computationally than the CG case and more accurate at fixed ${N}_{\mathrm{c}}$ for ferromagnetism, which is potentially useful for cluster expansion and quantum cluster applications.

High-field metamagnetism in the antiferromagnetCeRh2Si2

A study of the antiferromagnet CeRh$_2$Si$_2$ by torque, magnetostriction, and transport in pulsed magnetic fields up to 50 Tesla and by thermal expansion in static fields up to 13 Tesla is presented. The magnetic field-temperature phase diagram of CeRh$_2$Si$_2$, where the magnetic field is applied along the easy axis $\mathbf{c}$, is deduced from these measurements. The second-order phase transition temperature $T_{N}$ and the first-order phase transition temperature $T_{1,2}$ (=~36 K and 26 K at zero-field, respectively) decrease with increasing field. The field-induced antiferromagnetic-to-paramagnetic borderline $H_c$, which equals 26 T at 1.5 K, goes from first-order at low temperature to second-order at high temperature. The magnetic field-temperature phase diagram is found to be composed of (at least) three different antiferromagnetic phases. These are separated by the first-order lines $H_{1,2}$, corresponding to $T_{1,2}$ at H=0, and $H_{2,3}$, which equals 25.5 T at 1.5 K. A maximum of the $T^2$-coefficient $A$ of the resistivity is observed at the onset of the high-field polarized regime, which is interpreted as the signature of an enhanced effective mass at the field-induced quantum instability. The magnetic field dependence of the $A$ coefficient in CeRh$_2$Si$_2$ is compared with its pressure dependence, and also with the field dependence of $A$ in the prototypal heavy-fermion system CeRu$_2$Si$_2$.

Phase diagram and electro-optical Kerr effect of nematic mixtures containingtolane and biphenyl cores

An experimental phase diagram for two types of nematic liquid crystals and their binary mixtures was established by polarised optical microscopy and differential scanning calorimetry methods. The mixtures comprised a tolane-base liquid crystal, 4-heptyl-3-fluoro-4-isothiocyanatotolane (7TOLF), and a biphenyl-base nematogen, 4-heptyl-3-fluoro-4-isothiocyanatobiphenyl (7BF). The static Kerr effect and third-order non-linearity were investigated for 7TOLF and 7BF and their nematic mixtures within the isotropic phase. Both the compounds have a positive and large Kerr constant. The second-order phase-transition temperatures, T*, were determined for these mixtures. 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 third-order non-linear susceptibility,χ(3), values were determined for these mixtures.

DC electric field effects on Ehrenfest-like relations at the glass transition

There have been numerous studies on the effects of dc and alternating electric fields on phase transitions in small-molecule mixtures and high-molecular weight polymers. Furthermore, textbook examples discuss modifications in the melting temperature of pure materials that are subjected to uniform dc fields. This thermodynamic analysis extends some of these predictions to second-order phase transitions. Upon invoking both volume and entropy continuity via the integral approach to phase equilibrium at second-order transitions, electric field effects on the glass transition are developed that parallel the Ehrenfest equations for the pressure dependence of Tg. Both Tg-field equations predict small changes in the glass transition temperature that scale as the square of the electric field strength. If one equates the dependence of Tg on the magnitude of the electric field via (i) volume continuity and (ii) entropy continuity, it is possible to obtain the electric-field analog of the Prigogine–Defay equality, in which thermophysical properties and discontinuous observables at the zero-field and field-dependent second-order phase transition temperatures are related. When the temperature and pressure dependencies of the relative electric permittivity (i.e., dielectric constant) are neglected in the absence of external fields, one recovers the classic Prigogine–Defay equality (i.e., the lower limit of the Prigogine–Defay ratio) that was developed from a consideration of volume and entropy continuity for the pressure dependence of Tg, by invoking the differential approach to phase equilibrium.

Sideways dynamics of ferroelectric domain walls

Characteristic features of the sideways motion of domain walls in ferroelectrics are considered. The proposed model for calculating the mobility of domain walls for this type of motion is based on the approaches developed by D. G. Sannikov and M. A. Collins et al. We examine the dynamics of domain walls in the vicinity of second-order phase transitions. The calculated domain wall mobility is in agreement with experiment in Pb 5Ge 3O 11, Pb 5− x Ba x Ge 3O 11, Rochelle salt, gadolinium molybdate, terbium molybdate, triglycine sulphate, and barium titanate. It is shown that the velocity of domain walls is proportional to the difference between the applied field and a threshold field. Good agreement with experiments in a number of ferromagnets and ferroelectrics is obtained in this aspect. The coupling of the spontaneous polarization to the strain is shown to induce propagation of solitary stress waves during the domain wall motion in ferroelectrics. We analyse some properties of stress wave propagation within the framework of the suggested model as well the elastic, electrostrictive and piezoelectric effects on the domain wall motion. The contribution of inertia to the velocity of domain walls is calculated. The domain wall mass for 180° walls in barium titanate estimated in the framework of the model is in accordance with its known value. Magnetic-field-induced motion of ferroelectric domain walls is considered. The finite-size effect on the mobility of domain walls is calculated. The mobility exhibits a critical increase when the sample thickness decreases. This behaviour is similar to the temperature growth of the mobility in the vicinity of the second-order phase transition temperature obtained in this model.

Kerr Effect Investigations in Liquid Crystals Containing the Isothiocyanato and Cyano Groups with Identical Flexible Tails

Electro-optical Kerr effect data have been obtained for 6CB, 6CHBT, 6PCH, and 6BOBT at temperatures greater than the nematic–isotropic transition temperature. Using these data, the real parts of the third-order nonlinear susceptibility χ(3) are determined for all the liquid crystals. All the compounds had a positive Kerr constant, which increased with decreasing of temperature. The second-order phase-transition temperatures, T*, were determined for these compounds. The replacement of aromatic ring by a flexible cyclohexyl group or a bulkier bicyclooctane has a marked effect on the birefringence. Hexyl 4-(4-isothiocyanato-phenyl) bicycle [222] octane, 6BOBT, with the highest transition temperature, had the lowest Kerr constant. In contrast, hexyl cyanobiphenyl, 6CB, showed the largest Kerr constant (6BOBT → 6CHBT ≈ 6PCH → 6CB). The effect of the rigid core and polar head group of the liquid crystals was investigated.

On the glassy state of multiphase and pure polymer materials

In this work we formulate a new glass theory and investigate its suitability for describing the mechanical response of thermoplastic elastomers composed of styrenic-block copolymers. These materials are composed of glassy domains of polystyrene, which physically link soft rubbery chain segments made of either polybutadiene or polyisoprene. We demonstrate that the crossover in the shift factors, observed experimentally to change from Williams–Landel–Ferry to Arrhenius behavior passing through a characteristic crossover temperature T∗ from below, coincides with the crossover from power-law to stretched-exponential behavior of the stress relaxation found in recent tensile experiments. Moreover, we show that the characteristic crossover temperature T∗ is identical with the underlying true equilibrium second-order phase transition temperature T2 of the polystyrene crosslinks, predicted by the thermodynamic theory of Gibbs and Di Marzio for pure glassy polystyrene in the infinite-time limit. By combining the recently introduced theory of Di Marzio and Yang with the significant-structure theory of Eyring and Ree, we develop a new glass theory, which is capable of explaining the mechanical response of multiphase as well as pure glassy materials. Moreover, we show a clear evidence for the existence of T2 postulated in 1950s for pure glasses and hotly debated since then.

Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n) = n(-2beta/nu)[phi0 + phi1n(1/nu)(T-T(c)) + O(n(2/nu)(T-T(c))2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature T(c) = 1.784 J/k(B) and critical exponents 2beta/nu approximately 0.668 and nu approximately 1.0. The self-diffusion constant and the chain dimensions (R2) and (S2) do not obey such a scaling law.

Critical sound attenuation of three-dimensional Ising systems

The field-theoretic description of dynamic critical effect s of the disorder on acoustic anomalies near the temperature of second-order phase transition is considered for three-dimensional Ising-like systems. The calculations of sound attenuation in high temperature phase for pure and diluted Ising-like systems near the critical point are presented. The dynamic scaling function for critical attenuation coefficient is calculated. The effect of the quenched disorder on asymptotic behaviour of the critical ultrasonic anomalies is discussed.

Theory of relaxation phenomena in a spin- [formula omitted] Ising system near the second-order phase transition temperature

The relaxation behavior of the spin- 3 / 2 Ising model Hamiltonian with bilinear and biquadratic interactions near the second-order phase transition temperature or critical temperature is studied by means of the Onsager's theory of irreversible thermodynamics or the Onsager reciprocity theorem (ORT). First, we give the equilibrium case briefly within the molecular-field approximation in order to study the relaxation behavior by using the ORT. Then, the ORT is applied to the model and the kinetic equations are obtained. By solving these equations, three relaxation times are calculated and examined for temperatures near the second-order phase transition temperature. It is found that one of the relaxation times goes to infinity near the critical temperature on either side, the second relaxation time makes a cusp at the critical temperature and third one behaves very differently in which it terminates at the critical temperature while approaching it, then showing a “flatness” property and then decreases. We also study the influences of the Onsager rate coefficients on the relaxation times. The behavior of these relaxation times is discussed and compared with the spin- 1 / 2 and spin-1 Ising systems.

Pair-approximation method for the quantum transverse spin-2 Ising model with a trimodal-random field

The form of the field distribution in a random-field Ising model is known to play an important role in determining the order of the phase transition and the existence of the tricritical points. Therefore, we have investigated the trimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. This is done by introducing a parameter p which simulates the fractions of the spins exposed to h 0 , − h 0 and 0 external longitudinal magnetic fields. The variation of the critical reduced transverse and longitudinal magnetic fields with the parameter p is studied for different coordination numbers, i.e., z = 4 , 6 , 8 , 12 and ∞ (leads to the mean-field results), and it is found that the system exhibits tricritical points for only p ⩽ 0.22 . The phase diagrams with respect to the external longitudinal random-field and the second-order phase transition temperature are calculated for the given values of the transverse field, z and p. It was also observed that the system exhibits reentrant phenomena which may be caused by the competition between the randomness of the external longitudinal magnetic field and the quantum effects.

The quantum transverse spin-2 Ising model with a bimodal random-field in the pair approximation

In this paper, we have investigated the bimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. The exact equations for the second-order phase transition lines and tricritical points are obtained in terms of the random field H, the transverse field G and the coordination number z. It is found that there are some critical values for H and G where the tricritical points disappear for given z. We have also observed that the system presents reentrant behavior which may be caused by the quantum effects and randomness. The phase diagram with respect to the random field and the second-order phase transition temperature are studied extensively for given values of the transverse field and the coordination number.

Crystal Structure and Thermal Expansion of La1−xSrxFeO3−δ Materials

Crystal structure and thermal properties of La1−xSrxFeO3−δ (x= 0, 0.1, 0.3, 0.4, 0.5, and 0.75) have been studied by high‐temperature X‐ray diffraction and thermal analysis in air and nitrogen (p(O2) ∼ 10−3 atm) atmosphere. The first‐order phase transition from orthorhombic‐to‐rhombohedral La1−xSrxFeO3−δ (x= 0, 0.1) was strongly shifted to lower temperatures with increasing Sr content. The phase‐transition temperature was observed significantly lower in polycrystalline ceramics compared with fine powders. The temperature depression of the phase transition in the ceramics was qualitatively explained by stresses induced both by the anisotropic thermal expansion of LaFeO3 and the observed volume contraction of the phase transition. Rhombohedral La1−xSrxFeO3−δ (x= 0.3, 0.4, 0.5) were observed to transform to the cubic perovskite structure during heating. The second‐order phase‐transition temperature decreased with increasing Sr content and decreasing partial pressure of oxygen. On the basis of the present findings, a pseudobinary phase diagram of the LaFeO3–SrFeO3−δ system is presented. Finally, a severely nonlinear thermal expansion was observed for the Sr‐rich materials at high temperature. The high thermal expansion in this region is due to a chemical expansion resulting from a reduction of the valence state of Fe.