Showing papers on "Phase transition published in 1968"
TL;DR: In this paper, it was shown that the Percus-Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite.
Abstract: It is shown that the Percus–Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite. The results show a first‐order phase transition which appears to be of the type observed numerically for the Lennard‐Jones 12–6 potential.
1,089 citations
TL;DR: The structure of SrTiO3 has been the subject of X-ray, infrared, [2] ESR, [3-5] neutron, [6] and Raman [7-10] spectroscopic investigations since 1962 as discussed by the authors.
Abstract: The structure of SrTiO3 has been the subject of X-ray, [1] infrared, [2] ESR, [3–5] neutron, [6] and Raman [7–10] spectroscopic investigations since 1962. While the high-temperature phase is acknowledged to be simple cubic perovskite 0 h 1 , with one formula group per unit cell, there have been, until recently, apparent inconsistencies in the diverse data and a lack of agreement concerning the symmetry of the crystal at low temperatures. Following discovery of anomalies in the sound velocity of SrTiO3 near 110°K [11], ESR studies [3] showed the presence of a cubic to tetragonal phase transition. This was verified by means of X-ray analysis [1]; in the latter study the c/a ratio was determined to be 1.000 56, and two other phase transitions were inferred to be at 65 and 35°K. Infrared and neutron studies [2, 6] supported the X-ray symmetry assignment of structure at 77 °K: the crystal was viewed as having domain structure with one of the equivalent (100) axes in each domain slightly elongated in the tetragonal phase; below 110°K the crystal was thought to retain a single formula group per unit cell and all atoms at inversion centers. The distortion from cubic symmetry was apparently so slight, in fact, that even the predicted F1u → Eu + A2u doubling below 110°K of each of the Oh -phase IR-active vibrations was unobservable in infrared studies. [2]
526 citations
TL;DR: In this paper, the ferroelectric phase transition in [K-PO 4 ]-type crystals is explained by the coupling between the proton tunneling mode and the optical mode vibration of the complexes along the c-axis.
Abstract: Dynamical aspects of the ferroelectric phase transition in KH 2 PO 4 -type crystals are elucidated on the basis of the coupling between the proton tunneling mode and the optical mode vibration of the [K-PO 4 ] complexes along the c-axis. Two coupled modes are obtained within the framework of a linear theory. The mode in which both systems oscillate in phase is shown to be responsible for the ferroelectric phase transition. The isotope effect in the Curie point is explained qualitatively and the Curie constant is estimated.
326 citations
TL;DR: In this paper, the propagation of an electromagnetic field in a fluctuating laser-active medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space.
Abstract: The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.
269 citations
TL;DR: In this paper, the critical conditions for the phase transition of a gel in free swelling and under uniaxial tension were calculated for the gel under tension and free swelling, respectively, and it was concluded that it would be difficult to attain the conditions necessary for the transition in the free-swelling case, but that it should be possible under tension.
Abstract: It is predicted that the net repulsion between the segments of a polymer network and a poor solvent can cause a phase transition marked by a sudden change in the degree of swelling. This is analogous to the “coil–globule” transition recently predicted by Ptitsyn to occur for a macromolecule in solution. The critical conditions for the transition. as well as phase diagrams, are calculated for the gel in free swelling and under uniaxial tension, which facilitates the transition. The transition depends on the gel being formed of chains crosslinked while greatly swollen by a diluent and also having a high degree of crosslinking. It is concluded that it would be difficult to attain the conditions necessary for the transition in the free-swelling case, but that it should be possible for gel under tension.
257 citations
TL;DR: In this paper, the crystal distortion of each phase was determined and it was shown that BiMnO 3 is ferromagnetic below 103°K, while BiCrO 3 was inferred to be antiferromagnetic under 123°K accompanied with weak ferromagnetic moment.
Abstract: Magnetic perovskites BiMnO 3 and BiCrO 3 were synthesized under very high pressures. There are phase transitions at 500°K and 410°K at atmospheric pressure for BiMnO 3 and BiCrO 3 respectively, and the crystal distortion of each phase was determined. BiMnO 3 is ferromagnetic below 103°K, while BiCrO 3 is inferred to be antiferromagnetic below 123°K accompanied with weak ferromagnetic moment. BiCrO 3 has an abnormally large effective Bohr magneton number at room temperature phase. The distortion of BiMnO 3 decreases slightly below the ferromagnetic Curie point.
186 citations
TL;DR: In this article, a general dynamical scaling theory of phase transitions is established by exploiting the absence of a characteristic length in an extended system at its phase transition, which imposes strong constraints on the frequency and wave-number dependence of the fluctuation spectrum and leads to unambiguous predictions concerning the critical properties.
182 citations
TL;DR: In this article, the authors analyzed the high-field magnetization of Neel ferrimagnets and applied this analysis to their measurements of YbIG and DyIG and showed that in some ferrimagnetic systems, as the temperature is increased at fixed field strength, the magnetization can decrease in one temperature interval, be temperature independent in another and rise or fall in a third.
Abstract: In this paper we analyze the high‐field magnetization of Neel ferrimagnets and apply this analysis to our measurements of YbIG and DyIG. We show that in some ferrimagnetic systems, as the temperature is increased at fixed field strength, the magnetization can decrease in one temperature interval, be temperature independent in another, and rise or fall in a third. Conversely, at fixed temperature, as the field is increased, there can be intervals of small and large susceptibility with abrupt discontinuities between them, even in the absence of anisotropy. This behavior is ascribed to the formation of angles between the various sublattice moments and the external field. The angled region can be described by a phase diagram in the H‐T plane. There are second‐order phase transitions at all boundaries, along which the order parameter (the angles) undergoes critical fluctuations. Two features appear technologically promising for some ferrimagnets: (a) a temperature range over which the moment of the ferrimagnet...
154 citations
TL;DR: The connection between Landau's theory of phase transitions and the lattice-dynamical theory of a displacive transition in a crystal is discussed in this article, where it is shown that at a second-order phase transition the frequency of one normal mode becomes zero.
Abstract: The connection between Landau's theory of phase transitions and the lattice-dynamical theory of a displacive transition in a crystal is discussed. At a second-order displacive transition the frequency of one normal mode becomes zero. By investigating the displacements of the atoms from special positions of the lattice for a number of crystals having the distorted perovskite structure, we have shown that several modes are involved in the various transitions, except in the case of LaAlO3, where the transition is probably second-order or nearly so, and is associated with a mode of low frequency. The wave vector of this mode is at the point (1/2 1/2 1/2) of the Brillouin zone, and its irreducible representation is Γ25.
152 citations
TL;DR: In this paper, the authors investigated the transport and related thermodynamic properties of TiNi at and around its ''martensitic'' transition temperature, and established the existence of a critical range extending over a 60°C interval.
Abstract: Through an investigation of the transport and related thermodynamic properties of TiNi at and around its ``martensitic'' transition temperature, the existence of a critical range extending over a 60°C interval is established. Within this critical range, the phase transition is second order. Irreversibility of various properties within the critical range is interpreted in terms of irreversible shear movement of atoms. On the basis of transport data, the band structure of TiNi is inferred to be a single or ``nearly'' single positive band within the temperature range investigated. The postulate that some of the valence electrons undergo a ``covalent''→``conduction'' electronic transformation in the course of the second‐order transition is consistent in large measure with experimental data.
144 citations
IBM1
TL;DR: In this paper, a simple model Hamiltonian for phase transitions in perovskite compounds was introduced for the study of phase transitions involving rotations of $B{\mathrm{O}}_{6}$ octahedra.
Abstract: We introduce a simple model Hamiltonian for the study of phase transitions in perovskite compounds $\mathrm{AB}{\mathrm{O}}_{3}$ involving rotations of $B{\mathrm{O}}_{6}$ octahedra. Depending on the relative magnitude of the anharmonic coefficients, we find a transition to the tetragonal or to the trigonal phase. We obtain the temperature dependence of the rotation angle below the transition temperature ${T}_{a}$, and of the soft-mode frequencies associated with the transition both above and below ${T}_{a}$. The coupling to an elastic deformation field is briefly discussed.
TL;DR: In this paper, the change in the easy axis of magnetization observed in some ferrimagnets has been studied using a phenomenological description, and it was found that two second-order phase transitions can occur.
Abstract: The change in the easy axis of magnetization observed in some ferrimagnets has been studied using a phenomenological description. It is found that two second-order phase transitions can occur.
TL;DR: The high temperature phase transition in KH2PO4 has been investigated by differential thermal analysis, thermogravimetric analysis, proton magnetic resonance and relaxation, infrared spectroscopy, and x-ray and quasielastic cold-neutron scattering as mentioned in this paper.
Abstract: The high‐temperature phase transition in KH2PO4 has been investigated by differential thermal analysis, thermogravimetric analysis, proton magnetic resonance and relaxation, infrared spectroscopy, and x‐ray and quasielastic cold‐neutron scattering. The transition is not connected with a static breaking up of the hydrogen‐bond network but rather with the onset of disordered hindered rotation of the H2PO4 groups around all three axes. It seems that rotation of H2PO4 groups is as well rate determining for the proton conductivity of this crystal.
TL;DR: In this paper, single crystals of Pb(Fe1/2Ta 1/2)O3 were grown from ternary melts with excess PbO. The crystals, having cubic perovskite structure at room temperature, undergo a ferroelectric phase transition at about 243°K, changing to rhombohedral structure.
Abstract: Single crystals of Pb(Fe1/2Ta1/2)O3 were grown from ternary melts with excess PbO. The crystals, having cubic perovskite structure at room temperature, undergo a ferroelectric phase transition at about 243°K, changing to rhombohedral structure. The dielectric constant passes through a maximum of nearly 9500 at 1 KHz. The spontaneous polarization along [100] direction is ca 28 µC/cm2 at liquid nitrogen temperature. A magnetic anomaly at about 180°K is related to the onset of antiferromgnetic ordering.
TL;DR: In this paper, an attempt has been made to calculate the change in lattice energy accompanying the rotational phase transition cocurring in the paraffins, based on the assumption that the changes in the lattice energies corresponding to discontinuous change in the crystal structure may be approximated by the difference in the theoretical lattice potential energies of the crystal before and after the transition has occurred.
Abstract: An attempt has been made to calculate the change in lattice energy accompanying the rotational phase transition cocurring in the paraffins. The calculation is based on the assumption that the change in the lattice energy corresponding to the discontinuous change in the crystal structure may be approximated by the difference in the theoretical lattice potential energies of the crystal before and after the transition has occurred. A specific model for the rotation mechanism has been postulated, and a method devised for calculating the average repulsive energy of a system of cooperatively rotating rigid chains. The results of the calculation indicate that the change in lattice energy is of the same order as the experimental heat of transition.
TL;DR: In this article, it is shown that the symmetry group of the ordered phase cannot be any subgroup of the symmetry groups of the disordered phase, and that the elastic constants of the second-order phase transition can be computed.
TL;DR: In this article, the effect of the olivine-spinel phase transition on thermal diffusivity of poly crystalline Mg2SiO4 was studied at 48.5 kb for the temperature range 350° to 650°K.
Abstract: The pressure and temperature variations of thermal diffusivity of poly crystalline Mg2SiO4 have been measured for the range 24 to 50 kb and 400° to 1300°K. Effect of the olivine-spinel phase transition on thermal diffusivity of Fe2SiO4 was studied at 48.5 kb for the temperature range 350° to 650°K. Synthetic samples with grain size 1 to 5 microns were used. For the pressure range studied, the reciprocal of thermal diffusivity 1/κ of Mg2SiO4 increases almost linearly with temperature up to about 1200°K, as expected from the theory of phonon conduction, but is nearly constant above that temperature. The 1/κ versus temperature curve of Fe2SiO4 (olivine) is nearly straight up to 700°K, where it becomes slightly convex. The thermal diffusivity of NaCl is measured under similar conditions for comparison with Bridgman's data. The agreement is reasonably good. The pressure derivative ∂κ/∂P, at P = 40 kb is 1.8 × 10−4 cm2/sec kb (at 700°K) and 0.8 × 10−4 cm2/sec kb (at 1100°K) for Mg2SiO4, and 4.7 × 10−4 cm2/sec kb (at 700°K) for NaCl. This pressure dependence can be explained by the theory of phonon conduction. The thermal diffusivity of Fe2SiO4 (spinel) is about 1.5 times that of Fe2SiO4 (olivine) over the range 350° to 650°K. The effect of radiative heat transfer in Mg2SiO4 is discussed. The photon mean free path is estimated to be 0.3 mm at 1400°K.
TL;DR: In this article, a theory of the first-order phase transition in U${\mathrm{O}}_{2}$ is presented and discussed in the molecular field approximation, where an isotropic nearest-neighbor exchange and local quadrupole-lattice interaction are taken as the basic interactions in the model.
Abstract: A theory of the first-order phase transition in U${\mathrm{O}}_{2}$ is presented and discussed in the molecular-field approximation. An isotropic nearest-neighbor exchange and local quadrupole-lattice interaction are taken as the basic interactions in the model. Interesting behavior is obtained due to the two distinct ways in which the collective ground-state degeneracy can be removed at $T=0\ifmmode^\circ\else\textdegree\fi{}$K: a cooperative Jahn-Teller distortion or a polarization of the sublattice magnetization by the exchange field. Depending on the relative gain in free energy obtained by these two mechanisms, one obtains four different types of behavior near the critical point: (1) a second-order transition to a distorted state with no magnetic ordering; (2) a second-order transition to a distorted state followed by a second-order magnetic transition; (3) a first-order transition yielding a discontinuous change in lattice distortion and sublattice magnetization; (4) a second-order magnetic transition accompanied by a weak distortion. The temperature dependence of the elastic constant ${C}_{44}$ is also derived. The parameters required to give a first-order transition in agreement with the measured discontinuity in sublattice magnetization and the correct behavior for ${C}_{44}$ are found to be consistent with the parameters obtained from the measured spin-wave excitations.
TL;DR: In this paper, the electron-phonon interaction of two bands is considered in small-gap semiconductors and the Helmholtz free energy of the system is obtained on the basis of the electron spectrum renormalized by the interaction.
Abstract: Displacive phase transitions are considered in small-gap semiconductors due to the electron-phonon interaction of two bands. The Helmholtz free energy of the system is obtained on the basis of the electron spectrum renormalized by the interaction. The temperature dependent low-symmetry lattice distortion, renormalized frequencies of the active “soft”; optical branch in both phases, the Curie temperature, etc., are obtained. By means of the Green's function method combinative vibronic frequencies of the system are found. The dielectric susceptibility which is essentially determined by active vibrations is calculated and the general picture of similar (ferroelectric) phase transitions is discussed.
[Russian Text Ignored].
TL;DR: In this paper, the thermodynamics of transitions between uniformly and nonuniformly magnetized states of an isotropic ferromagnet in an external field is described in the molecular-field approximation.
Abstract: The thermodynamics of transitions between uniformly and nonuniformly magnetized states of an isotropic ferromagnet in an external field is described in the molecular-field approximation. These results are found to be in substantial agreement with many experiments.
TL;DR: In this article, the crystal structures of ferroelectric and paraelectric (Glycine) 2 HNO 3 were determined by X-ray as well as by neutron diffraction methods at -150°C and at room temperature, respectively.
Abstract: The crystal structures of ferroelectric and paraelectric (Glycine) 2 HNO 3 were determined by X-ray as well as by neutron diffraction methods at -150°C and at room temperature, respectively. One of the glycine molecules has the zwitter-ion configuration and another is mono-protonated. Thus the chemical formula should be written as NH 3 + CH 2 COO - ·NH 3 + CH 2 COOH·NO 3 - . Both glycine ions as well as the nitrate ion are nearly planar within the experimental error. A short O-H…O bond, about 2.45A, connects two glycine ions of the different configuration and a proton is attached to the oxygen of the glycinium ion. The paraelectric structure is a disordered one based upon the ferroelectric structure. Such a type of the order-disorder phase transition and the above-mentioned strong hydrogen bond may play an important role for the ferroelectric behaviour of the crystal, which is very similar to the case of (Glycine) 3 H 2 SO 4 .
TL;DR: In this article, the theory of fermion phase transitions is reviewed from a unified field theoretic standpoint, based on the diagrammatic perturbation expansion of a generalized matrix propagator.
Abstract: The theory of fermion phase transitions is reviewed from a unified field theoretic standpoint, based on the diagrammatic perturbation expansion of a generalized matrix propagator. Transitions from a normal to a condensed phase are characterized by the spontaneous appearance of long-range order and (in the presence of a suitable infinitesimal external field) broken symmetry. This is illustrated by the ferromagnetic, solid, superconducting and spindensity wave ground states. The phenomenon is explained qualitatively as caused by the creation of a long-range internal field, F, due to the interactions between particles. This field establishes long-range order in the system, and is in turn itself established by the long-range order, in a self-consistent fashion. The mechanism here is expressed quantitatively in terms of a self-consistent Dyson equation relating a generalized matrix propagator, G, to a proper self-energy matrix, Σ. The off-diagonal elements of G describe ‘anomalous’ propagation process...
TL;DR: Tetragonal ZrO2 can be formed directly from the mono-clinic form at 25°C by applying pressures greater than 37 kbar as discussed by the authors, but the transition is reversible and cannot be retained in a metastable condition at ambient conditions.
Abstract: Tetragonal ZrO2 can be formed directly from the mono-clinic form at 25° C by applying pressures greater than 37 kbars. The transition is reversible, and the tetragonal phase cannot be retained in a metastable condition at ambient conditions.
TL;DR: In this article, the entropy changes associated with these anomalies is explained by proposing structural changes at the transition points, and the upper phase transition is discussed in terms of a model based on the coexistence of the two crystalline phases.
Abstract: The heat capacities of the sodium cyanide crystal were measured from 14 to 310°K by an adiabatic calorimeter. The two anomalous regions reported by Ziegler et al. are confirmed. The entropy changes associated with these anomalies is explained by proposing structural changes at the transition points. Analysis of the lattice heat capacity gives the average librational frequency of the cyanide ion at the lowest temperatures as 210 cm−1 in the Einstein approximation. For the higher temperature range, the cyanide ions may be described as undergoing a hindered rotation, with a barrier height of approximately 2 kcal/mol. The upper-phase transition is discussed in terms of a model based on the coexistence of the two crystalline phases. The lower transition and the analogous one reported previously for potassium cyanide are interpreted together as order-disorder phenomena with respect to the behavior of the cyanide ions. The thermodynamic functions of the crystal are also calculated by the graphical integration of...
TL;DR: A cholesteric-nematic phase transition can be induced by relatively weak electric fields, and the threshold field varies inversely with the pitch of the helix in corroboration of recent theoretical suggestions.
Abstract: A cholesteric-nematic phase transition can be induced by relatively weak electric fields, and the threshold field varies inversely with the pitch of the helix in corroboration of recent theoretical suggestions. The phase change is accompanied by a change in the activation energy for charge-carrier production and can easily be observed by both conductivity measurements and direct optical examination.
TL;DR: In this article, the motions of the propionate anions in strontium-, lead-, and barium-dicalcium propionates were examined with the proton magnetic resonance method at low temperatures.
Abstract: The motions of the propionate anions in strontium-, lead-, and barium-dicalcium propionates were examined with the proton magnetic resonance method at low temperatures. It was found that the methyl groups rotate about the C3-axes even at 20°K in the Sr-, and the Ba-salts. In the Sr-salt the gradual decrease of the second moment below the ferroelectric transition point was observed and this phenomenon was related to the large angle torsional oscillations of the ethyl groups about the C3′-axes as introduced in Part I: Near the ferroelectric transition point the observed second moment shows the possibility of excitation of the C3′-rotation which would make the crystal to be paraelectric above the transition point. It was expected that the C3′-torsion is to some extent excited in the Pb-salt at liquid nitrogen temperature, a slight discrete change being observed at the lower transition point. A sharp line width transition was also observed in the Ba-salt and this fact resulted in the finding of a new λ-type p...
TL;DR: In this paper, the authors investigated the thermodynamic properties of a hard core on a triangular lattice and concluded that there is a first-order phase change of the fluid-solid type, similar to the transition observed for hard disks and hard spheres.
Abstract: The thermodynamic properties of assemblies of molecules with a hard core on a triangular lattice have been investigated by the matrix method and by series expansions. Three particular cases have been considered (denoted as B, C, D), corresponding, respectively, to exclusion ranges extending up to second‐, third‐, and fourth‐neighboring sites. Case A (i.e., exclusion on first‐neighboring sites only) has been studied previously by other authors, who concluded to the existence of a second‐order continuous transition at high density. For all three cases B, C, and D, there is a good evidence for a first‐order phase change of the fluid–solid type, similar to the transition observed for hard disks and hard spheres.
TL;DR: In this article, a new high pressure ordered phase, denoted as OII, has been discovered in this temperature range and the acoustic properties of the new OII phase were investigated with emphasis on the regions of the first-order phase transition from OII to the ordered tetragonal phase.
Abstract: The abiabatic elastic constants of single‐crystal ammonium bromide have been measured at 20 MHz as functions of temperature and pressure in the region from 180°–240°K and from 0–6 kbar. A new high‐pressure ordered phase, denoted as OII, has been discovered in this temperature range. The acoustic properties of the new OII phase were investigated with emphasis on the regions of the first‐order phase transition from the OII phase to the ordered tetragonal phase and the lambda transition from the OII phase to the disordered cubic phase. The region of the lambda transition from the ordered tetragonal phase to the disordered cubic phase was also studied. A detailed comparison is made with the behavior of ammonium chloride near its order–disorder phase transition.