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We develop an effective theory approach to investigate the phase properties of globular proteins. Instead of interactions between individual atoms or localized interaction centers, the approach builds directly on the tertiary structure of a protein. As an example we construct the phase diagram of (apo)myoglobin with temperature (T) and acidity (pH) as the thermodynamical variables. We describe how myoglobin unfolds from the native folded state to a random coil when temperature and acidity increase. We confirm the presence of two molten globule folding intermediates, and we predict an abrupt transition between the two when acidity changes. When temperature further increases we find that the abrupt transition line between the two molten globule states terminates at a tricritical point, where the helical structures fade away. Our results also suggest that the ligand entry and exit is driven by large scale collective motions that destabilize the myoglobin F-helix.

The Raman spectra of an Rb2KLuF6 crystal are studied in the temperature range from 8 to 375 K, which includes two phase transitions: one of which proceeds from a cubic to a tetragonal phase, while the other transition takes place from a tetragonal to a monoclinic phase. An analysis of the temperature dependences of parameters of spectral lines shows that the former transition is of the second kind, while the latter transition is of the first kind, close to the tricritical point. It is shown that the structural phase transitions in the Rb2KLuF6 double perovskite are not associated with disordering. The former transition is associated with rotations of LuF6 octahedra around the fourth-order axis, while the latter transition is related with rotations of octahedra and displacements of rubidium ions.

A detailed study of the effect of temperature and pressure on heat capacity, entropy and hysteresis phenomena near the ferroelectric phase transition in ammonium sulfate (AS) was performed. An analysis of experimental results within the framework of the phenomenological theory showed that taking into account the temperature-dependent part of the anomalous entropy leads to a significant increase in the barocaloric effect (BCE). The maximum values of extensive and intensive BCE near the tricritical point are outstanding: &Delta, S B C E m a x &asymp, 85 J/kgK, &Delta, T A D m a x &asymp, 12 K and can be achieved at low pressure &sim, 0.5 GPa.

Developing high dielectric permittivity material is vital to satisfy the ongoing demands for the miniaturization of electronic and energy storage devices. Recent investigations uncover the role of a thermodynamical tricritical phenomenon on enhancing the dielectric response. However, such a tricritical point always locates in an extremely narrow composition region, which makes it time-consuming for exhaustive experimental searching of the optimal dielectric permittivity in a given material system. In the present paper, we employ an accelerated discovery strategy to seek the largest dielectric permittivity in Ba(Ti1–x%Hfx%)O3 ceramic material by using an iterative method between computational machine learning and the experimental synthesis and property measurement. The optimal composition is found to be x = 11 with the highest permittivity of er = 4.5 × 104 after 4 loops of iteration involving 6 compositions, which shows higher efficiency compared with conventional experimental searching. Further thermal a...

Ferrimagnet HoFe6Al6 (tetragonal ThMn12-type crystal structure) has a compensation point for the Ho and Fe magnetic sublattices at a temperature close to absolute zero. The experimental study was carried out in fields up to 60 T. H-T phase diagrams and a full magnetization process along the principal crystallographic directions of a single-crystalline sample are obtained theoretically by using a model of a f-d ferrimagnet with two anisotropic sublattices, coupled by weak exchange interaction. The two first-order phase transitions, found experimentally along the [110] and [100] axes, were explained theoretically. The transition along the [110] direction occurs between noncollinear and collinear phases, it starts at the compensation point and ends at a tricritical point around 60 T. The transition along the [100] direction goes also from the point of compensation to the point of the liquid-vapor type at 40 T. This transition was shown to occur between two distinct noncollinear phases. The crucial role of the strong rare-earth anisotropy for the positions of the obtained critical points was revealed.

Thermal and dielectric studies of (ND4)2MoO2F4 crystals undergoing successive phase transitions at T1 = 272 K and T2 = 181 K showed that deuteration is accompanied by an increase in the chemical pressure in the crystal lattice (Δp ≈ 0.02 GPa), which shifts the Cmcm ↔ Pnma transformation for the first order to the tricritical point. The direct participation of ammonium groups in the mechanism of structural distortions is demonstrated by a decrease in the entropy of the high-temperature phase transition (ΔS1 = R ln 6.0). An external hydrostatic pressure leads to an expansion of the temperature interval of the intermediate antiferroelectric Pnma phase. The triple point on the T–p phase diagram, where the Cmcm, Pnma, amd Pnma* phases coexist, can be realized at a negative pressure of ptrp ≈ −0.8 GPa.

When compressed in a slit of width $D$, a $\Theta$-chain that displays the scaling of size $R_0$ (diameter) with respect to the number of monomers $N$, $R_0\sim aN^{1/2}$, expands in the lateral direction as $R_{\parallel}\sim a N^{\nu}(a/D)^{2\nu-1}$. Provided that the $\Theta$ condition is strictly maintained throughout the compression, the well-known scaling exponent of $\Theta$-chain in 2 dimensions, $\nu=4/7$, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from $R_0/D0$ (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain., Comment: 31 pages, 4 figures

Motivated by recent reports of H_{3}LiIr_{2}O_{6} as a spin-orbital-entangled quantum liquid, we investigate via a combination of density functional theory and nonperturbative exact diagonalization the microscopic nature of its magnetic interactions. We find that while the interlayer O─H─O bond geometry strongly affects the local magnetic couplings, these bonds are likely to remain symmetrical due to large zero-point fluctuations of the H positions. In this case, the estimated magnetic model lies close to the classical tricritical point between ferromagnetic, zigzag, and incommensurate spiral orders, what may contribute to the lack of magnetic ordering. However, we also find that substitution of H by D (deuterium) as well as disorder-induced inhomogeneities destabilizes the O─H or D─O bonds, modifying strongly the local magnetic couplings. These results suggest that the magnetic response in H_{3}LiIr_{2}O_{6} is likely sensitive to both the stoichiometry and the microstructure of the samples and emphasize the importance of a careful treatment of hydrogen for similar systems.

Single crystals of (ND4)2MoO2F4 containing 95% deuterium were produced by repeated recrystallization of (NH4)2MoO2F4 in heavy water. The effect of deuteration on the parameters of successive phase transitions was investigated by differential scanning microcalorimetry and polarization optics. X-ray analysis of the original and distorted phases was performed. It was found that deuteration does not change the sequence of crystal phases typical for (NH4)2MoO2F4, but leads to a shift in the phase transition Cmcm → Pnma towards the tricritical point. The mechanism of phase transitions in (ND4)2MoO2F4 was associated with both the ordering and the displacement of atoms.

The mechanisms of temperature and high pressure phase transitions have been studied by Raman spectroscopy. Room temperature (295 K) experiments under high hydrostatic pressure up to 3.6 GPa for (NH 4 ) 2 MoO 2 F 4 have been carried out. Experimental data indicates a phase transition into a new high-pressure phase for (NH 4 ) 2 MoO 2 F 4 at 1.2 GPa. This phase transition is related to the ordering anion octahedron groups [MoO 2 F 4 ] 2− and is not associated with ammonium group. Raman spectra of small non-oriented crystals ranging from 10 to 350 K have been observed. The experiment shows anion groups [MoO 2 F 4 ] 2− and ammonium in high temperature phase are disordered. The phase transition at T 1 = 269.8 K is of the first-order, close to the tricritical point. The first temperature phase transition is related to the ordering anion octahedron groups [MoO 2 F 4 ] 2− . Second phase transitions T 2 = 180 K are associated with the ordering of ammonium. The data presented within this study demonstrate that 2D correlation analysis combined with traditional Raman spectroscopy are powerful tool to study phase transitions in the crystals.

Electron paramagnetic resonance (EPR) and pulse electron–nuclear double resonance (ENDOR) spectroscopies are applied to investigate the structural phase transition and the low temperature phase in manganese- and copper-doped [NH3(CH2)4NH3][Zn(HCOO)3]2 dense metal–organic framework. Continuous-wave (CW) EPR measurements indicate successful incorporation of Mn2+ and Cu2+ ions at the Zn2+ lattice sites. Pulse ENDOR spectrum reveals at least four different proton species in the vicinity of the Mn2+ center showing excellent agreement with the X-ray diffraction experiments. Temperature-dependent CW EPR spectra demonstrate that Mn2+ and Cu2+ local paramagnetic probes are sensitive to the phase transition in the studied compounds. The analysis of the temperature dependence of the Cu2+ hyperfine coupling parameter reveals a first-order phase transition at Tc = 235 K into an antiferroelectric phase that is close to the tricritical point. The obtained logarithmic divergence of the line width of the Mn2+ EPR spectrum...

Phase behavior of methane–pentane mixture and anomalies of the isochoric heat capacity Cρ,x and the derivative (∂P/∂T)ρ,х have been studied experimentally in the vicinity of liquid–vapor critical point at three pentane concentrations, namely, for 0.0196, 0.0345, and 0.096 mol fraction of pentane. It has been shown that for two low pentane concentrations the behavior of the heat capacity Cρ,x and (∂P/∂T)ρ,х differs substantially from both theoretically predicted and experimentally observed behavior of the properties in other mixtures. We suggest that the reason of such unusual behavior is caused by the proximity of the mixture critical locus to the tricritical point at low pentane concentrations. On the other hand dew–bubble curves (DBC) of the methane–pentane mixtures for all studied concentrations do not exhibit any special features and thus can be described theoretically within the scope of the conventional scaling approach.

The dielectric properties of deuterated betaine phosphite crystals with a high degree of deuteration in the region of the antiferrodistorsive (at T = T c1) and ferroelectric (at T = T c2) phase transitions have been investigated. The temperature behavior of the dielectric permittivity of betaine phosphite and deuterated betaine phosphite has been described within the framework of the Landau thermodynamic model taking into account the biquadratic coupling between the polar order parameter of the ferroelectric transition and the nonpolar order parameter of the antiferrodistorsive phase transition. It has been shown that an increase in the degree of deuteration leads to a decrease in the coupling between the order parameters. An increase in the temperature of the ferroelectric phase transition due to the deuteration of betaine phosphite is caused by an increase in the dielectric permittivity in the symmetric phase above the temperature of the antiferrodistorsive phase transition.

Lipid phase heterogeneity in the plasma membrane is thought to be crucial for many aspects of cell signaling, but the physical basis of participating membrane domains such as "lipid rafts" remains controversial. Here we consider a lattice model yielding a phase diagram that includes several states proposed to be relevant for the cell membrane, including microemulsion - which can be related to membrane curvature - and Ising critical behavior. Using a neural network-based machine learning approach, we compute the full phase diagram of this lattice model. We analyze selected regions of this phase diagram in the context of a signaling initiation event in mast cells: recruitment of the membrane-anchored tyrosine kinase Lyn to a cluster of transmembrane of IgE-Fc{\epsilon}RI receptors. We find that model membrane systems in microemulsion and Ising critical states can mediate roughly equal levels of kinase recruitment (binding energy ~ -0.6 kBT), whereas a membrane near a tricritical point can mediate much stronger kinase recruitment (-1.7 kBT). By comparing several models for lipid heterogeneity within a single theoretical framework, this work points to testable differences between existing models. We also suggest the tricritical point as a new possibility for the basis of membrane domains that facilitate preferential partitioning of signaling components., Comment: 33 pages, 7 figures, 16 supplementary pages, 10 supplementary figures

Phase equilibria were studied in the Li2SO4–LiCl–H2O system with boundary subsystems of various types: type 1 subsystem LiCl–H2O and type 2 subsystem Li2SO4–H2O. The ternary critical curves (G=L–S) and (L1=L2–S) originating at the terminal critical points p and Q of the type 2 binary system do not combine to form a single curve with the binary homogeneous critical point (G=L–S) ⇔ (L1=L2–S) but end at the invariant points (G=L1–L2–S) and (G–L1=L2–S) connected by the monovariant four-phase curve (G–L1–L2–S) at a temperature below 490°C. It was found that, at 490–520°C, there are no critical phenomena in the solutions, and the solubility of each of the salts varies continuously from the solubility in the binary aqueous system to the solubility in an anhydrous melt. Above the temperature of the four-phase equilibrium (G–L1–L2–S), a region (G–L1–L2) of phase separation of unsaturated solutions in the presence of gas is observed, which is bounded by the monovariant critical curves (G=L1–L2) and (G–L1=L2). With increasing temperature, this region shrinks and collapses at the tricritical point (G=L1=L2) at ~520°C.

The temperature and order of the phase transition are studied for a less-coarsened Bell–Lavis model. The interactions exist between triangular molecules being on third-neighbour (3NN) sites, while the nearest-neighbour (1NN) interactions are subject to a hard core exclusion. Using Monte Carlo calculations, we obtain the temperature, T, and chemical potential μ phase diagram for a whole range of μ values, where the honeycomb phase exists. We find that the entropy gain prevails at low molecular densities (high μ). Therefore, the first-order disordered-to-honeycomb phase transition found in the 3NN model has lower temperature than that of the 1NN model. At higher molecular densities (low μ), below the tricritical point, the exclusions start to play some role and the entropy decreases. This leads to the occurrence of the intermediate short-range ordered phase in between disordered and honeycomb phases. The upper phase transition is found at higher temperature, while the lower one at the same temperature as th...

A comprehensive study of the influence of classical anisotropy fields on the magnetic properties of Heisenberg antiferromagnets within unified molecular field theory versus temperature T, magnetic field H, and anisotropy field parameter hA1 is presented for systems comprised of identical crystallographically-equivalent local moments. The anisotropy field for collinear z-axis antiferromagnetic (AFM) ordering is constructed so that it is aligned in the direction of each ordered and/or field-induced thermal-average moment with a magnitude proportional to the moment, whereas that for XY anisotropy is defined to be in the direction of the projection of the moment onto the xy plane, again with a magnitude proportional to the moment. Properties studied include the zero-field Neel temperature TN, ordered moment, heat capacity and anisotropic magnetic susceptibility of the AFM phase versus T with moments aligned either along the z axis or in the xy plane. Also determined are the high-field magnetization perpendicular to the axis or plane of collinear or planar noncollinear AFM ordering, the high-field magnetization along the z axis of a collinear z-axis AFM, spin-flop (SF), and paramagnetic (PM) phases, and the free energies of these phases versus T, H, and hA1. Phase diagrams at T = 0 in the Hz-hA1 plane and at T > 0 in the Hz-T plane are constructed for spins S = 1/2. For hA1 = 0 the SF phase is stable at low field and the PM phase at high field with no AFM phase present. As hA1 increases, the phase diagram contains the AFM, SF and PM phases. Further increases in hA1 lead to the disappearance of the SF phase and the appearance of a tricritical point on the AFM-PM transition curve. Applications of the theory to extract hA1 from experimental low-field magnetic susceptibility data and high-field magnetization versus field isotherms for single crystals of AFMs are discussed., 41 pages, 35 captioned figures including 81 subfigures

Combining Statistical Mechanics and Quantum Chemistry it is possible to study solvent effects in spectroscopy and understand chemical reactivity in solution. However, once the thermodynamic condition can be incorporated, it is possible to advance in other important regions of the phase diagram. Hence supercritical fluids with temperature and pressure beyond the critical point can be studied. Supercritical fluids are of interest both for their remarkable physical chemical properties and the industrial interests. The critical point, however, is apparently not a thermodynamic condition amenable to quantum chemical calculations. This is because it is characterized by intense fluctuations and density inhomogeneity. The correlation length becomes infinite at the critical point. But for points close enough to the critical point the fluctuations disappear, and it is possible to get very close to this rather interesting point in the phase diagram. In this work we review some results for the spectroscopy of molecular systems in the supercritical region and the static dipole polarizability and the refractive index of Ar only 2 K above the critical point. The refractive index presents some peculiarities, but it is well behaved as we pass at the critical point. The numerical value obtained of 1.083 is in very good agreement with the experimental value of 1.086. We contend that the proximity of the critical point is amenable to theoretical quantum mechanical studies possibly accessing new physical phenomena.

We present an improved analysis of the reentrant nematic and tricritical behavior of the nematic to smectic A phase transition in liquid crystal mixture within phenomenological theory. To describe the nematic–smectic A–reentrant nematic phase sequence in binary mixture, nematic and smectic order parameters have been coupled with the concentration. We show that reentrant nematic and the tricritical point on the N–SmA phase transition line can be achieved in the same phase diagram under certain conditions. We predict two tricritical points. One corresponds to nematic to smectic A phase transition and other corresponds to reentrant nematic to smectic A phase transition. A comparison of the results with experimental phase diagrams is described in great details. The predictions of the theory are in good agreement with available experimental data.

The temperature dependence of the orientational order parameters 〈P_{2}(cosβ)〉 and 〈P_{4}(cosβ)〉 in the nematic (N) and twist-bend nematic (N_{tb}) phases of the liquid crystal dimer CB7CB have been measured using x-ray and polarized Raman scattering. The 〈P_{2}(cosβ)〉 obtained from both techniques are the same, while 〈P_{4}(cosβ)〉, determined by Raman scattering is, as expected, systematically larger than its x-ray value. Both order parameters increase in the N phase with decreasing temperature, drop across the N-N_{tb} transition, and continue to decrease. In the N_{tb} phase, the x-ray value of 〈P_{4}(cosβ)〉 eventually becomes negative, providing a direct and independent confirmation of a conical molecular orientational distribution. The heliconical tilt angle α, determined from orientational distribution functions in the N_{tb} phase, increases to ∼24^{∘} at ∼15 K below the transition. In the N_{tb} phase, α(T)∝(T^{*}-T)^{λ}, with λ=0.19±0.03. The transition supercools by 1.7 K, consistent with its weakly first-order nature. The value of λ is close to 0.25 indicating close proximity to a tricritical point.

A mean-field density-functional model for three-phase equilibria in fluids (or other soft condensed matter) with two spatially varying densities is analyzed analytically and numerically. The interfacial tension between any two out of three thermodynamically coexisting phases is found to be captured by a surprisingly simple analytic expression that has a geometric interpretation in the space of the two densities. The analytic expression is based on arguments involving symmetries and invariances. It is supported by numerical computations of high precision, and it agrees with earlier conjectures obtained for special cases in the same model. An application is presented to three-phase equilibria in the vicinity of a tricritical point. Using the interfacial tension expression and employing the field variables compatible with tricritical point scaling, the expected mean-field critical exponent is derived for the vanishing of the critical interfacial tension as a function of the deviation of the noncritical interfacial tension from its limiting value, upon approach to a critical endpoint in the phase diagram. The analytic results are again confirmed by numerical computations of high precision. ispartof: JOURNAL OF CHEMICAL PHYSICS vol:150 issue:16 ispartof: location:United States status: published

The first theoretical observation of the tricritical point for the isotropic to biaxial nematic phase transition of biaxial nematic liquid crystals in the presence of an external field is reported. The influence of an external magnetic field on the isotropic to biaxial nematic phase transition have been studied using Landau phenomenological theory. Topological classification of phase diagrams in the field – temperature coordinates is performed. It is shown that for a particular value of the magnetic field, the first order isotropic to biaxial nematic phase transition becomes second order phase transition at a tricritical point.

Bragg and diffuse X-ray reflections from the M points of the Brillouin zone boundary of a benzil crystal paraphrase, the integral intensity of which is associated with the order parameter and its fluctuations, are studied. Original data on the temperature behavior of the order parameter and diffuse scattering are obtained. The relevant critical exponents are determined. A conclusion is drawn as to the proximity of the phase transition in these crystals to the tricritical point. A phase transition model is discussed.

The reasons for nonmonotonous changing of surface coverage as function of chemical potential in the multisite adsorption models (with allowance for the possibility that molecules can be oriented in a different manner with respect to the solid surface) are revealed in this work. It is demonstrated that this behavior of the surface coverage as function of chemical potential is determined by either the sequence of ordered structures being formed or by the emergence of a stable interface between the ordered phases at temperatures above the tricritical point.

Experimental studies have shown that the chain flexibility plays an important role in the properties of the liquid crystal phase transitions. We examine the effect of the chain flexibility on the nematic to smectic-A phase transition within the Landau phenomenological theory. We show how the flexibility of the chains influences the critical behavior of the nematic to smectic-A phase transition. The possibility of the tricritical point at the nematic to smectic-A phase transition is discussed in a phenomenological way. The theoretical predictions are found to be in good qualitative agreement with available experimental results.

The broad band spectrum of the optical conductivity of the quasi-one dimensional organic conductor (FA) 2 PF 6 (FA = fluoranthene) has been investigated in a wide temperature range including the Peierls transition temperature T p = 180 K. A semiconducting gap has been observed both below and above T p varying between 150 meV at 10 K and 80 meV at 300 K. The (T p − T) 1 4 temperature dependence for the order parameter has been deduced from an analysis of the integrated band intensity of phase phonons thus giving evidence that the Peierls transition is a 2nd order phase transition near the tricritical point.

nofulltext# --- Tarı İlgin, Özlem (Arel Author) --- Conference: 9th International Physics Conference of The Balkan Physical Union (BPU-9)., Chromium (Cr) undergoes a first order Neel transition as an antiferromagnetic material. When V, Mo and Mn atoms are substituted in the Cr lattice, a weak first order Neel transition in pure Cr changes toward a second order transition and a possible tricritical point in CrV occurs close to 0.2 at %V, as observed experimentally from the measurements of the thermal expansivity at various temperatures. In this study, we analyze the experimental data for the thermal expansivity from the literature as a function of temperature using the power - law formula for Cr alloys (Cr - 0.1V, 0.2V, 0.5V and Cr - 0.1Mn, Cr - 0.2Mo, 0.3Mo, 0.4Mo). Our results are interpreted near the tricritical point in dilute chromium alloys.

This paper reports on a Raman spectroscopy investigation of phase transitions in (NH 4 ) 3 ZrF 7 crystal. Raman spectra were obtained and analyzed in a wavenumber range from 3800 to 15 cm −1 and in the temperature range from 7 to 360 K. The anomalies caused by a series of subsequent structural phase transitions have been analyzed. A soft phonon mode restoring in the distorted phase was found. The spectral changes observed in the current study are similar to those typically found in phase transitions near a tricritical point. The spectral changes in the middle wavenumber range, 700–150 cm −1 , indicate that the phase transitions are due to structural ordering of pentagonal ZrF 7 3− bipyramids. Spectral data also show that a phase transition near 225 K is accompanied by an increase of the unit cell volume. In addition, spectral changes in the range of internal vibrations of ammonium ions indicate that the ion's motion slows down with decrease of temperature.

A phenomenological approach to the description of the smectic-A-hexatic-B-crystal-B phase sequence in a liquid crystal mixture is proposed. The problem of the first or second-order nature of the smectic-A-hexatic-B transition is explored by means of the variation in the concentration. The influence of the concentration on the smectic-A-hexatic-B-crystal-B phase sequence is discussed by varying the coupling between crystalline order parameter, hexatic order parameter and the concentration variable. We show that a tricritical point on the smectic-A to hexatic-B phase transition line can be achieved under certain conditions. The theoretical prediction is found to be in good qualitative agreement with experimental results.

The temperature dependences of the specific heat, unit cell parameters, susceptibility to hydrostatic pressure, and permittivity of cryolite (NH4)3Nb(O2)2F4 have been studied. Phase transitions of nonferroelectric nature have been detected. Entropy parameters point to the relation of structure distortions to ordering processes.

A thermodynamic dataset for the ternary system Cr–Fe–Ni which has been reported in the literature for the range from medium to high temperatures has been supplemented with datasets from the binary sub-systems at lower temperatures. The magnetic and the chemical ordering transitions which are known from the binary Fe–Ni system were extrapolated into the ternary system Cr–Fe–Ni. The phase diagram of Cr–Fe–Ni alloys at temperatures below 500 °C was predicted. The magnetic contribution to the Gibbs energy of Ni-rich alloys induces a miscibility gap which appears in the binary phase diagram of Fe–Ni as a small triangle-like field ending in a tricritical point. In the ternary system Cr–Fe–Ni the miscibility gap is present as a broad two-phase field in the vicinity of the composition FeNi 3 . At lower temperatures this miscibility gap participates in a sequence of changing equilibria when it interferes with the chemically ordered L1 2 phase.

Based on the results for temperature dependences of optical birefringence and optical indicatrix rotation derived for Sn2P2S6 crystals, we show that at the atmospheric pressure, those crystals are under the conditions of tricritical point, with the critical exponent of the order parameter . At the same time, we have found that the temperature behaviour of the rotation angle of spontaneous electric polarization obeys the law . The action of hydrostatic pressure leads to only small changes in the critical exponent β, thus suggesting that the tricritical point on the P, T-diagram of Sn2P2S6 should occur in the pressure range .

We examine the effect of pressure on the nematic to smectic-A N–SmA) transition within the Landau phenomenological theory. The influence of pressure on the N–SmA transition is discussed by varying the coupling between the orientational and translational order parameters. The possibility of the tricritical point at the N–SmA transition is discussed in a phenomenological way. The theoretical predictions are found to be in good qualitative agreement with experimental results.

Ionic mobility and phase transitions in ammonium titanyl pentafluoride (NH{sub 4}){sub 3}TiOF{sub 5} were studied using the {sup 19}F and {sup 1}H NMR data. The high-temperature phase (I) is characterized by spherically symmetric (isotropic) reorientation of [TiOF{sub 5}]{sup 3-} anions and by uniaxial reorientation of these anions in the ferroelastic phase II. A previously unknown second-order phase transition to the low-temperature modification (NH{sub 4}){sub 3}TiOF{sub 5}(III) was found at 205 K. The transition is accompanied by hindering of uniaxial rotations of [TiOF{sub 5}]{sup 3-} anions and by noticeable change of {sup 19}F magnetic shielding tensor associated with the influence of pseudo-Jahn-Teller effect. A pressure-induced tricritical point with coordinates p{sub TCR{approx}}2 kbar and T{sub TCR{approx}}170 K is estimated on the base of {sup 19}F NMR chemical shift data, and previously studied p-T diagram of (NH{sub 4}){sub 3}TiOF{sub 5}. - Graphical abstract: p-T phase diagram of (NH{sub 4}){sub 3}TiOF{sub 5}.

A review of theoretical and experimental results obtained for the triglycine selenate (TGSe) ferroelectric has been presented. It has been stressed that the critical character of paraelectric–ferroelectric phase transition in TGSe or that close to tricritical had been confirmed in many articles. However, in the paraelectric region the properties of TGSe can be characterized as being between the Landau critical point type of behaviour and that of the Landau tricritical point. Different examples of such a discrepancy have been cited. Some properties of TGSe have been discussed in relation to those of the structurally isomorphous triglycine sulphate ferroelectric. The theoretical models used for TGSe in the literature have been briefly discussed.

In the present work, we have experimentally studied and analysed the dilatometric properties of Sn2P2(Se0.28S0.72)6 crystals during ferroelectric phase transition. A complete matrix of thermal expansion tensors as well as the characteristic surface of the thermal expansion tensor has been obtained. The critical exponent for the volume thermal expansion coefficient in Sn2P2(Se0.28S0.72)6 crystals has been determined to be equal to 0.50 ± 0.06, which is peculiar to tricritical behaviour. Non-agreement in the values of the critical exponents evaluated from the temperature dependencies of relative elongation (0.17 ± 0.01) and volume thermal expansion coefficient (0.50 ± 0.06) is shown to be due to the possible temperature rotation of the spontaneous polarisation vector.

Measurements of the p, V, T data and phase equilibrium of a water-n-pentane system were performed. It was established that the phase diagram of this system belongs to the third type in the Scott and Van Koninenburg classification. The intervals and parameters of the lower and upper branches of the critical line and the parameters of the upper critical endpoint and the double homogeneous point were determined.

The spin-3/2 Ising model is studied on a two-layer Bethe lattice with antiferromagnetic/antiferromagnetic (AFM/AFM) intralayer and either FM or AFM type of interlayer interactions by using the pairwise approach for the coordination numbers q = 3, 4, and 6. In the guidance of the ground-state phase diagrams, the thermal variations of the magnetizations, susceptibility and specific heat are examined in detail to obtain the critical behaviors of the model. Thus, it was found that the model presents second- and first-order phase transitions; where their lines are combined is a tricritical point. In addition, the model also presents two Neel temperatures, the existence of which leads to the re-entrant behavior.

Tricritical points (TCPs), contained in two-phase holes in three-phase surfaces, are of great importance in industrial applications of near-critical and supercritical technology because they occur in a range of temperatures, pressures and compositions where the technological processes are carried out. Their predictions are also important for mapping the transitions between different types of fluid phase behavior, when using molecular parameters in theoretical thermodynamic models, since these parameters take into account the different molecular interactions in the phase transition. In ternary systems, the tricritical point (TCP) has zero degrees of freedom; in other words, it exists only at a unique condition of pressure, temperature and composition. On the other hand, in quaternary systems, the tricritical state has one degree of freedom, and a line of tricritical points may exist. In this work, a theoretical procedure was developed and implemented using the theoretical, non-cubic Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) for computing and predicting the tricritical points of various ternary systems with single tricritical points, and tricritical lines of quaternary systems (involving n-alkanes, branched alkenes, alcohols, water, carbon dioxide, nitrogen and hydrogen sulfide) without fitting the binary interaction parameter. The results were compared with experimental tricritical data obtained from literature and an excellent agreement was obtained within a range of temperatures and pressures of practical interest in engineering.

A thermal study of the liquid crystals tridecylcyanobiphenyl and tetradecylcyanobiphenyl has been performed by means of adiabatic scanning calorimetry. Both compounds exhibit only the smectic-A mesophase between the normal liquid and the crystalline phase and their phase transitions are strongly first order. A summary of the enthalpies and transition temperatures for all the smectic homologues of the cyanobiphenyl family is given, based on high-resolution measurements of the present work and previous studies.

There is a well-known de Gennes coupling between the scalar nematic order parameter S and the smectic density-wave amplitude /Psi/, which causes the nematic-smectic-A phase transition to cross over from second order to first order via a tricritical point. This sort of crossover is observed for numerous liquid crystals (LCs) with small to moderate nematic ranges. Recent studies of LC+aerosil systems, where the aerosil particles form a soft thixotropic gel, have shown that such aerosil gels can greatly reduce or completely suppress this coupling. The underlying LC critical exponents once de Gennes coupling is absent are discussed and compared with theory.

KF-doped BaTiO 3 single crystals were grown by a KF-flux method, changing the molar ratios of the liquid-solution consisting of KF: BaO: TiO 2 = 10: 1: 1+α where a is a variable in a range up to 1.2. By using an electron-probe micro-analyzer; the content x in the chemical formula, Ba 1-x K x TiO 3-x F x , was evaluated: it changes continuously from approximately 0.01 to 0.12 as α increases from 0 to 1.2. The dielectric constant was measured for these crystals with different x-values. The Curie-temperature Tc decreases monotonously from 390 K to 280 K with increasing x, while the maximum value of the dielectric constant e max at T c exhibits a peak around x = 0.1 (near the tricritical point) where the transition changes the character from the first-order to the second-order. The phase-diagram of KF-doped BaTiO 3 was determined.

Phase equilibria of perfluoroalkane + alkane binary mixtures have been studied according to the perturbed chain-statistical associated fluid theory (PC-SAFT) molecular-based equation of state together with a simple monoparametric mixing rule. These systems, for a fixed perfluoroalkane, show transitions from type II phase behaviour, according to the van Konynenburg classification, for the short members of each homologous series, to type III for the largest ones which are properly predicted by the model. These transitions are described by the model via a type IV zone which is studied according to a quasi-binary approach inferring a double critical endpoint (DCEP) and a tricritical point (TCP) in the intermediate transitional zone. The barotropic inversion phenomena for the type III mixtures are also analyzed with the studied equation of state. The general shape of the global phase diagrams of these mixtures is correctly predicted in a qualitative way by the model with a binary interaction parameter temperature independent of the whole temperature range, but the simultaneous correlation of critical loci, three-phase equilibria and equilibrium compositions is not possible with just a single parameter in a quantitative way. The accurate correlation of the complex phase behaviour of these mixtures would require temperature-dependent binary interaction parameters or more complex mixing rules that should take account of the complex weak intermolecular forces rising in these mixtures.

The thermal anomalies associated with the Ia3d → I41/acd → I41/a transition sequence of phase transitions in leucite have been studied by differential scanning calorimetry and interpreted with Landau theory. Both transitions are close to the tricritical point. The coupling between the two transitions is biquadratic, and reduces the stability of the I41/a phase.

This study gives our calculation for the specific heat using our Raman frequency shifts of the ν 5 ( 174 cm - 1 ) mode close to the tricritical ( P = 1.6 kbar ) and second order ( P = 2.8 kbar ) phase transitions in NH 4 Cl . For this calculation we use as the values of the critical exponent for the specific heat, a = 0.11 ( T T c and T > T c ) for the tricritical ( T c = 257.17 K ) , and a = 0.18 ( T T c ) , a = 0.64 ( T > T c ) for the second order ( T c = 268 K ) phase transitions, which we deduce from our analysis of the Raman frequency shifts of this mode studied here, on the basis of an Ising model. Our calculated specific heats agree well with those measured thermodynamically for both tricritical and second order phase transitions in NH 4 Cl .

The three-liquid-phase equilibria data of the quaternary system water (1) + tert-butanol (2) + n-decane (3) + n-undecane (4) in the tricritical region are reported. It has been found that the mass fraction of n-decane in (n-decane + n-undecane) controls the size of the three-phase region and the approach to the tricritical point. The experimental data have been analyzed to obtain the tricritical temperature and the tricritical composition.

Recently, it turned out that nanostructured reaction media containing highly inert solvents as tetrahydrothiophen-1,1-dioxide (sulfolane) are beneficial for strongly oxidizing or reductive reactions. Because of their ability of solubilizing polar and nonpolar solvents with a large nanostructured interface in particular microemulsions provide such interesting reaction media. Starting from the pseudoternary microemulsion H2O-n-octane-C12E4/C12E5 (polyoxyethylene n-alkyl ether), water was successively replaced by the highly inert tetrahydrothiophen-1,1-dioxide (sulfolane). We found that an increasing sulfolane content drives the system beyond the tricritical point. Replacing the already long chain surfactants C12E4 and C12E5 by a mixture of the even longer chain surfactants C18E6 and C18E8, we were able to prepare nonaqueous sulfolane microemulsions for the first time. We also teach how in a second step the phase behavior of the hydrophilic sulfolane-n-octane-C18E8 system can be tuned at constant temperature (as required by the reaction conditions) by addition of the hydrophobic cosurfactant 1-octanol (C8E0). The change in curvature that occurs by adding 1-octanol is demonstrated measuring the size of reverse micelles by DLS. We found that the radius varies from at least 8 to 16 nm, a suitable sizes for inverse nanoreaction vessels.

The critical properties of the mixed manganite La 0.67− x Y x Ba 0.23 Ca 0.1 MnO 3 with x =0.10 and x =0.15 around the paramagnetic (PM)-ferromagnetic (FM) phase transition were investigated through various techniques. These involved modified Arrott plots, Kouvel-Fisher method and Widom scaling relation. Magnetic data, analyzed in the critical region, using the above methods, yielded the critical exponents for ( x =0.10) La 0.57 Y 0.10 Ba 0.23 Ca 0.1 MnO 3 (β=0.312±0.002 and γ=1.147±0.003 at T C =299.23±0.05 K). Moreover, the estimated critical exponents of ( x =0.15) La 0.52 Y 0.15 Ba 0.23 Ca 0.1 MnO 3 were β=0.286±0.004 and γ=0.943±0.002 at T C =289.53±0.06 K. The critical exponents' values were close to the theoretical values of 3D-Ising model and tricritical mean-field model. These results suggested that the present composition should be close to a tricritical point in the La 0.67− x Y x Ba 0.23 Ca 0.1 MnO 3 phase diagram. Expressing the field dependence as Δ S M ∝ H n allowed us to establish a relationship between the exponent n and the critical exponents of the material and to propose a phenomenological universal curve for the field dependence of Δ S M .

The para-ferroelectric tricritical phase transition of a single crystal of triglycine selenate (TGSe) has been studied in the neighbourhood of the transition temperature, under weak electric fields, E, using a highly sensitive calorimetric technique. The specific heat, c E , under fields in the range between 5 and 175 V cm -1 and close to transition temperature (0.2 K), shows different behaviour on cooling and on heating at a temperature variation rate of ±0.03 K h -1 ; for T < T c - 0.5 K all sets of data match each other. The experimental data have been fitted to the 2-6 Landau potential obtained for E = 0; a term -ξ Q, taking into account the coupling between E (ξ being dependent on E) and the order parameter Q, is included. This potential fits well with the experimental data in the ferroelectric phase. The different relation between and E obtained on heating and on cooling runs is discussed and it is concluded that data on heating correspond to the thermal equilibrium.

The magnetic susceptibility of a MnSi single crystal is measured in the region of the ferromagnetic phase transition under pressures up to 0.8 GPa in compressed helium. It is found that the tricritical point on the phase-transition curve corresponds to a much lower pressure and a considerably higher temperature (P tr ≈ 0.355 GPa and T tr ≈ 25.2 K) than was reported earlier (P tr ≈ 1.2 GPa and T tr ≈ 12 K). New results impose certain limitations on theoretical analysis of tricritical phenomena in MnSi.