Experimental constraints on the phase diagram of elemental zirconium

The phase diagram of zirconium metal has been studied using synchrotron X-ray diffraction and time-of-flight neutron scattering at temperatures and pressures up to 1273 K and 17 GPa. The equilibrium phase boundary of the α-ω transition has a dT/dP slope of 473 K/GPa, and the extrapolated transition pressure at ambient temperature is located at 3.4 GPa. For the ω-β transition, the phase boundary has a negative dT/dP slope of 15.5 K/GPa between 6.4 and 15.3 GPa, which is substantially smaller than a previously reported value of −39±5 K/GPa in the pressure range of 32-35 GPa. This difference indicates a significant curvature of the phase boundary between 15.3 and 35 GPa. The α-ω-β triple point was estimated to be at 4.9 GPa and 953 K, which is comparable to previous results obtained from a differential thermal analysis. Except for the three known crystalline forms, the β phase of zirconium metal was found to possess an extraordinary glass forming ability at pressures between 6.4 and 8.6 GPa. This transformation leads to a limited stability field for the β phase in the pressure range of 6-16 GPa and to complications of high-temperature portion of phase diagram for zirconium metal.     

Transition order and dynamics of a model with competing exchange and dipolar interactions

We performed Monte Carlo simulation of phase transitions from isotropic stripe phase with short-range order to long-range stripe phase in a model with competing ferromagnetic exchange and antiferromagnetic dipolar interactions on triangular lattice. We calculated phase diagram for different values of exchange and dipolar interaction constants ratio, η. We also determined the order of the transitions to stripe phases AFh of different stripe widths h: first-order phase transition was found to transitions into AF1 and AF2 phases, while transitions to AF3 and AF4 phases were of the second order. In the phase diagram the tricritical point was determined at the AF2 and AF3 phase boundary. We observed the peak of nematic phase at the transition region to the AF1 phase, but found it metastable at low values of η. We have also found that in AF1 phase spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to logt.     

Experimental constraints on the phase diagram of titanium metal

The phase transformations of titanium metal have been studied at temperatures and pressures up to 973 K and 8.7 GPa using synchrotron X-ray diffraction. The equilibrium phase boundary of the α-ω transition has a dT/dP slope of 345 K/GPa, and the transition pressure at room temperature is located at 5.7 GPa. The volume change across the α-ω transition is ΔV=0.197 cm³/mol, and the associated entropy change is ΔS=0.57 J/mol K. Except for ΔV, our results differ substantially from those of previous studies based on an equilibrium transition pressure of 2.0 GPa at room temperature. The α-ω-β triple point is estimated to be at 7.5 GPa and 913 K, which is comparable with previous results obtained from differential thermal analysis and resistometric measurements. An update, more accurate phase diagram is established for Ti metal based on the present observations and previous constraints on the α-β and ω-β phase boundaries.     

The pressure influence on the incommensurate-commensurate ferroelectric phase transition in [4-NH2C5H4NH][SbCl4]

The dielectric properties of the [4-NH₂C₅H₄NH] SbCl₄ (abbreviated as 4-APCA) crystal were investigated under hydrostatic pressure up to 300 Mpa. The pressure-temperature phase diagram was given. The paraelectric-ferroelectric phase transition (II→III) temperature (T_c) increases linearly with increasing pressure with a slope dT_c/dp=21×10⁻² K/MPa. The pressure dependence of Curie-Weiss constants has been evaluated also. In the paraelectric phase (II) the Curie constant (C₊) was pressure dependent whereas the C₋ constant over the ferroelectric phase (III) was almost constant. The results are interpreted in terms of improper and displacive type phase transition model with a soft phonon at a zone boundary.     

Enhanced ferroelectric, magnetic and magnetoelectric properties of Bi1−xCaxFe1−xTixO3 solid solutions

We report on the enhanced electromechanical, magnetic and magnetoelectric properties of Bi_1−xCa_xFe_1−xTi_xO₃ solid solutions. The crystal structure of the x≈0.25 compounds are close to the rhombohedral-orthorhombic phase boundary, and the solid solutions are characterized by increased electromechanical properties due to the polarization extension near the polar-nonpolar border. The homogenous weakly ferromagnetic state is established at x>0.15 doping. The chemical doping shifts the magnetic transition close to room temperature, thus enlarging the magnetic susceptibility of the compounds. The solid solutions at the morphotropic phase boundary exhibit a nearly twofold increase in piezoelectric response, whereas the magnetoelectric coupling shows five times enhancement in comparison with the parent bismuth ferrite.     

On the mechanism of the zircon-reidite pressure induced transformation

We report first principles results of a detailed investigation directed to elucidate mechanistic aspects of the zircon-reidite phase transition in ZrSiO₄. The calculated thermodynamic boundary is located around 5 GPa, and the corresponding thermal barrier, estimated from temperatures at which the transition is observed at zero and high pressure, is 133 kJ/mol. Under a martensitic perspective, we examine two different transition pathways at the thermodynamic transition pressure. First, the direct, displacive-like, tetragonal I4₁/a energetic profile is computed using the c/a ratio as the transformation parameter, and yields a very high activation barrier (236 kJ/mol). Second, a quasi-monoclinic unit cell allows us to characterize a transition path from zircon (β=90^°) to reidite (β=114.51^°) with an activation barrier of around 80 kJ/mol at β=104^°. This energy is somewhat lower than our previous estimation and supports the reconstructive nature of the transformation at the thermodynamic transition pressure.     

Electric field induced phase transition in first order ferroelectrics with large zero point energy

An electric field induced phase transition in first order ferroelectrics with very large zero point energy is studied on the framework of the effective field approach. It is well known that when the zero point energy of a system is relatively large, the ferroelectric behaviour is depressed and no phase transition can be observed. The critical value Ω_cf of zero point energy for whom the phase transition disappears turns out to be dependant on the order of transition. For zero point energies larger than this critical value, a phase transition may be induced applying an external electric field. This temperature dependence of the induced polarization shows a discontinuous step when the applied electric field is weak, but becoming a continuous one at a strong applied electric field. Another critical value of zero point energy Ω_cp>Ω_cf is deduced for which no phase transition at all can be attained.     

Phase separation of binary systems

In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K>0, the transition is first order with latent heat and if K<0, the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn-Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1/2. This is different from the prediction made by the classical phase diagram. Third, a TL-phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions.     

Pressure-induced polymorphism in enstatite (MgSiO3) at room temperature: clinoenstatite and orthoenstatite

The phase transition of a synthetic clinoenstatite in a diamond-anvil cell has been studied by using Raman spectroscopy at various pressures and room temperature. The phenomena observed in clinoenstatite have been compared with that observed in orthoenstatite. It is found that the pressure-induced phase transitions in the two enstatites are reversible, but with different transition pressures and transition behavior. An analysis of Raman spectra has revealed that the two enstatites have different high-pressure polymorphs. This result suggests that the space group of the high-pressure polymorph of orthoenstatite is not of C2/c, and that orthoenstatite and orthoferrosilite have different transition routes at room temperature and high pressure. The compressional behavior of the high-PC2/c enstatite is also discussed according to the pressure dependences of Raman frequencies.     

Entropy and phase diagram of valence transition

The electronic and lattice entropies associated with the valence transition are estimated. The electronic entropy in metallic phase is evaluated based on the model which includes the mixing between ?-level and d-band states, and the d-band superimposes the hybridized ?-level. The quasiharmonic approximation together with the Debye approximation are used to calculate the lattice entropy. For the first order transition occurring at low temperature the entropy of semiconducting phase is found to be lower than that of metallic phase. The reverse situation is obtained for high transition temperature. This explains the experimental fact that the slope of the phase boundary of valence transition in SmS changes its sign with temperature. The specific heat calculated in this model shows a broad maximum at low temperature.     

Quantum phase transitions in the anisotropic three dimensional XY model

In this paper we study the quantum phase transition in a three-dimensional XY model with single-ion anisotropy D and spin S=1. The low D phase is studied using the self consistent harmonic approximation, and the large D phase using the bond operator formalism. We calculate the critical value of the anisotropy parameter where a transition occurs from the large-D phase to the Néel phase. We present the behavior of the energy gap, in the large-D phase, as a function of the temperature. In the large D region, a longitudinal magnetic field induces a phase transition from the singlet to the antiferromagnetic state, and then from the AFM one to the paramagnetic state.     

Impurity effects on the phase transformations and equations of state of zirconium metals

The in situ high P-T X-ray diffraction experiments were conducted at pressures up to 17 GPa and temperatures up to 1273 K to study the phase transformations and equations of state for two grades of zirconium metals. At ambient temperature, our results reveal significant differences in both the transition pressure and kinetics of the α-ω phase transformation between the ultra-pure Zr (35 ppm Hf and <50 ppm O) and impure Zr (1.03 at% Hf and 4.5 at% O). These observations indicate that impurities, particularly oxygen ions, play important roles in the transformation mechanisms as well as crystal stability. On the other hand, impurities have no measurable effects on either the elastic bulk moduli of both α and ω phases or the volume change across the α-ω phase transformation. At elevated temperature, both impure and ultra-pure Zr show similar transition temperatures for the ω-β phase boundary over a pressure range of 6-16 GPa, suggesting that impure oxygen and hafnium ions can only be an α-Zr stabilizer; they do not seem to significantly increase the stability of the ω-Zr relative to the β-Zr.     

Optical investigations of polycrystalline Mg1−xB2 near metal-insulator transition

We measured reflectivity spectra of polycrystalline Mg_1−xB₂ samples, which show a metal-insulator transition with x. After performing the Kramers-Kronig analysis, the obtained optical conductivity spectra σ(ω) of MgB₂ show a narrow Drude peak in the far-infrared region and a broad peak in the mid-infrared region. As x increases, the spectral weight of the Drude peak is strongly suppressed and that of the broad peak becomes enhanced a little. The existence of the broad mid-infrared peak in the insulating sample suggests that this peak might not be related to the free carriers in MgB₂. In the far-infrared region, we also observe that the low energy dielectric constant of Mg_1−xB₂ diverges near the metal-insulator phase boundary (i.e. x=0.08). This result implies the possibility of a phase separation and a percolative metal-insulator transition in Mg_1−xB₂.     

Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

The stability of a spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field Γ. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues λ_± of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when Γ is increased. Therefore, this result suggests that the study of the replicon cannot be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the λ_± indicate instability problems for the SG solution close to all ranges of a first order boundary.     

Diffuse phase transition of Fe doped lead ytterbium tantalate ceramics

The effect of different concentration of Fe on the phase transition behavior of Lead ytterbium tantalate is investigated by dielectric and differential scanning calrimetry measurements. The samples are prepared through solid state reaction method and it has been found that the sintering temperature significantly lowered when the proportion of Pb(Fe_1/2Ta_1/2)O₃ increased. It has been observed that the doping in small amounts (0≤x≤0.2) of Fe could meliorate the dielectric and ferroelectric properties. The diffuseness in the mode of phase transition increases and the phase transition temperature decreases as a function of Fe content. It is revealed that the dielectric data and heat capacity data follow a similar trend in the variation of the mode of phase transition and phase transition temperatures. The phase transition temperature values obtained from the heat capacity measurement well agreed with the values obtained from dielectric measurement.     

Phase transition, structural and electrical properties of Pb(Zn1/3Nb2/3)O3-doped Pb(Ni1/3Nb2/3)O3-PbTiO3 ceramics prepared by solid-state reaction method

Phase pure perovskite (1−x−y)Pb(Ni_1/3Nb_2/3)O₃-xPb(Zn_1/3Nb_2/3)O₃-yPbTiO₃ (PNN-PZN-PT) ferroelectric ceramics were prepared by conventional solid-state reaction method via a B-site oxide mixing route. The PNN-PZN-PT ceramics sintered at the optimized condition of 1185 °C for 2 h exhibit high relative density and rather homogenous microstructure. With the increase of PbTiO₃ (PT) content, crystal structure and electrical properties of the synthesized PNN-PZN-PT ceramics exhibit successive phase transformation. A morphotropic phase boundary (MPB) is supposed to form in (0.9−x)PNN-0.1PZN-xPT at a region of x=32-36 mol% confirmed by X-ray diffraction (XRD) measurement and dielectric measurement. The MPB composition can be pictured as providing a “bridge” connecting rhombohedral ferroelectric (FE) phase and tetragonal one since crystal structure of the MPB composition is similar to both the rhombohedral and tetragonal lattices. Dielectric response of the sintered PNN-PZN-PT ceramics also exhibits successive phase-transition character. 0.64PNN-0.1PZN-0.26PT exhibits broad, diffused and frequency dependent dielectric peaks indicating a character of diffused FE-paraelectric (PE) phase transition of relaxor ferroelectrics and 0.40PNN-0.1PZN-0.50PT exhibits narrow, sharp and frequency independent dielectric peaks indicating a character of first-order FE-PE phase transition of normal ferroelectrics. The FE-PE phase transition of 0.56PNN-0.1PZN-0.34PT is nearly first-order with some diffused character, which also exhibits the largest value of piezoelectric constant d₃₃ of 462pC/N.     

Vortex lattice in Bi2Sr2CaCu2O8+δ well above the first-order phase-transition boundary

Measurements of non-local in-plane resistance originating from transverse vortex-vortex correlations have been performed on a Bi₂Sr₂CaCu₂O_8+δ high-T_c superconductor in a magnetic field up to 9 T applied along the crystal c-axis. Our results demonstrate that a rigid vortex lattice does exist over a broad portion of the magnetic field-temperature (H-T) phase diagram, well above the first-order transition (FOT) boundary H_FOT(T). The results also provide evidence for the vortex lattice melting and vortex liquid decoupling phase transitions, occurring above the H_FOT(T).     

Phase transformation in (0.90−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3-0.10PbZrO3 piezoelectric ceramic: X-ray diffraction and Raman investigation

Piezoelectric ceramics with compositions of (0.90−x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃-0.10PbZrO₃, x=0.28, 0.31, 0.34, 0.37, 0.40 and 0.43, were prepared using the conventional columbite precursor method, and their structural phase transformation and piezoelectric behaviors near the morphotropic phase boundary (MPB) have been systematically investigated as a function of PbTiO₃ content. X-ray diffraction (XRD) results demonstrate that the structure of the ceramics experiences a gradual transition process from rhombohedral phase to tetragonal phase with the increasing of PbTiO₃ content, and that compositions with x=0.34-0.40 lie in the MPB region of this ternary system. A Raman spectra investigation of the ceramic samples testified to the transformation process of rhombohedral phase to tetragonal phase by comparing the relative intensities of tetragonal E(2TO₁) mode and rhombohedral phase R_h mode. The structure information was also correlated to the parabola change of the piezoelectric constant; the maximum piezoelectric constants were obtained near the MPB region.     

Structural stability and magnetic properties of Bi1−xLa(Pr)xFeO3 solid solutions

In this work, X-ray diffraction data taken on Bi_1−xLa_xFeO₃ solid solutions are used to verify the following structural phase transitions: “polar rhombohedral-antipolar orthorhombic” at x≈0.16 and “commensurate-incommensurate” within the orthorhombic phase at x≈0.18. In contrast, in the Bi_1−xPr_xFeO₃ series, the polar rhombohedral phase transforms into an antipolar orthorhombic one at x≥0.13. The polar rhombohedral phase near the morphotropic phase boundary exhibits an isothermal transformation into an antipolar orthorhombic phase, though the transformation occurs much faster in the case of La-doped compounds. The incommensurate structural phase was not detected in Bi_1−xPr_xFeO₃ solid solutions. The ternary structural phase diagram is constructed for (Bi,La,Pr)FeO₃ systems. In addition, the polar rhombohedral phase exhibits a magnetic field-induced transition from the modulated antiferromagnetic state into a homogeneous weak ferromagnetic state whereas the antipolar phase is a weak ferromagnetic state in the absence of an external field.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.