Λ-type Phase Transition Research Articles

Phase transition of [2,2]-paracyclophane--an end to an apparently endless story.

In this contribution, the solid-state low-temperature phase structure of [2,2]-paracyclophane is unambiguously characterised by single-crystal X-ray analysis. Additionally, a heat capacity measurement was undertaken, which proves the existence of a λ-type phase transition at 45 K, a transition that is connected with the formation of a secondary Cp/T feature at 60 K. The low-temperature phase (<45 K) crystallises in the lower symmetry space group P4n2, whereas the high-temperature phase (>60 K) crystallises in space group P4(2)/mnm. This proves what has been postulated both by experimental and theoretical chemists but has repeatedly been dismissed as speculation many times.

Analysis of the Raman intensities near the phase transitions in ammonium halides

This study concentrates on the temperature dependence of the Raman intensities for the lattice modes in ammonium halides (NH 4Cl and NH 4Br) close to phase transitions. We predict their intensities using the results of a shell model for the Raman polarizability within the framework of an Ising pseudospin–phonon coupled model. From our observed Raman intensities of those phonon modes studied here, we extract the values of the critical exponent for the order parameter in these crystalline systems. The exponent values indicate that the Raman intensities show a logarithmic divergence at higher pressures in NH 4Cl, whereas they predict a λ-type phase transition at zero pressure in NH 4Br.

Low-temperature dielectric behavior of (NH 4) 3H(SO 4) 2 crystal

Dielectric investigations on (NH 4) 3H(SO 4) 2 single crystals below room temperature are reported. Dielectric dispersions are observed in the two regions of temperature above 200 K and below 70 K. Glass-like dielectric relaxations found in the dielectric constant and loss at T>200 K are considered due to reorientation of some dipoles derived by the random freezing of protons in the statically disordered hydrogen bonds. The dielectric loss at T<70 K is analyzed to result from the contribution of two Debye type relaxations. One of the corresponding relaxation times as a function of temperature shows a good fit to the modified Arrhenius equation at 29 K≤T≤70 K. The other one exhibits a critical slowing down on approaching a critical temperature, which seems to be closely associated with the λ-type phase transition at T∼67 K.

APPLICATION OF THE PIPPARD RELATIONS TO AMMONIA NEAR THE MELTING POINT

This study gives our application of the Pippard relations to the ammonia near its melting point. The Pippard relations between the specific heat C P , the thermal expansivity α P and the isothermal compressibility κ T , have been established for the ammonia near its melting point. We have obtained that the Pippard relations are valid for the ammonia. We give here an evidence that on the basis of the experimental data the critical transition in this system near its melting point can be considered as the λ-type phase transition.

Stable and metastable phase equilibria in the GeSe2-Se system

Stable and metastable phase equilibria in the binary system GeSe2-Se have been investigated by means of optical and electron microscopy, electron probe microanalysis (EPMA), x-ray diffraction (XRD), thermal analysis, and adiabatic calorimetry. A revised equilibrium phase diagram is presented. A not previously observed λ-type phase transition was observed near ∼420 K (147 °C) for GeSe2. The intermediate phase, φ, which earlier had been considered as metastable, is shown to be stable through extensive annealing experiments and by adiabatic calorimetry. The φ phase, with composition near Ge3Se7, melts incongruently at 658±5 K (385±5 °C) to GeSe2 and a liquid with 85±2 at.% Se. The liquidus of GeSe2 and φ was determined by EPMA of annealed-and-quenched samples. Both a stable (φ-Se-liquid) and a metastable (GeSe2-Se-liquid) eutectic point were observed. The stable one was observed at 480±2 K (207±2 °C) and 92.5±1.0 at.% Se, whereas the temperature of the metastable eutectic (GeSe2-Se-liquid) was observed to be ∼10 K lower. Metastable phase equilibria, obtained on thermal evolution of glasses with different compositions, are described and discussed.

Raman studies of a lambda -type phase transition in solid Cs2CdCl4.

An unusual second-order-like phase transition in the perovskite-type layered compound ${\mathrm{Cs}}_{2}$${\mathrm{CdCl}}_{4}$ has been observed by Raman studies of the solid. The phase transition took place over a range of temperatures from 435 \ifmmode^\circ\else\textdegree\fi{}C to about 460 \ifmmode^\circ\else\textdegree\fi{}C. At any temperature within this temperature range Raman bands characteristic of the different cadmium coordination in each of the separate phases were detected simultaneously with relative intensities that were dependent on the temperature. Analysis of the Raman spectra indicated that the structure of ${\mathrm{Cs}}_{2}$${\mathrm{CdCl}}_{4}$ transformed from the ${\mathrm{K}}_{2}$${\mathrm{NiF}}_{4}$-type layered-perovskite-like low-temperature phase II (octahedral cadmium coordination) to the ${\mathrm{K}}_{2}$${\mathrm{SO}}_{4}$-type-structure high-temperature phase I (tetrahedral cadmium coordination). Relative-intensity measurements of bands characteristic of each cadmium coordination as a function of temperature indicated an equilibrium distribution. The enthalpy and entropy associated with the change of coordination were of the order of those usually observed on fusion. These large values are consistent with the major structural rearrangement from a network octahedral structure to discrete tetrahedral coordination. Although local order around the cadmium ion increased in the high-temperature phase the overall order of the lattice was considerably reduced because of the orientational disorder of the spherical, discrete ${\mathrm{CdCl}}_{4}^{2\mathrm{\ensuremath{-}}}$. Similar studies have been performed for solids of composition ${\mathrm{Cs}}_{2}$${\mathrm{CdCl}}_{4}$\ensuremath{\cdot}0.5CsCl, ${\mathrm{Cs}}_{2}$${\mathrm{CdCl}}_{4}$\ensuremath{\cdot}CsCl, and ${\mathrm{Cs}}_{2}$${\mathrm{CdCl}}_{4}$\ensuremath{\cdot}2CsCl to follow the formation of ${\mathrm{Cs}}_{3}$${\mathrm{CdCl}}_{5}$ which is stable above 395 \ifmmode^\circ\else\textdegree\fi{}C. The presence of the peak due to ${\mathrm{CdCl}}_{4}^{2\mathrm{\ensuremath{-}}}$ at temperatures as low as 365 \ifmmode^\circ\else\textdegree\fi{}C signaled the onset of the reaction to ${\mathrm{Cs}}_{3}$${\mathrm{CdCl}}_{5}$.

High Tc Superconductivity and S-I Transition in Ba–Y–Cu–O

Superconductor-Insulator transition and superconductivity have been studied by the measurements of resistivity, specific heat, XPS, a.c.magnetic susceptibility and X-ray diffraction in Ba–Y–Cu–O system. The experimental results show that the S-I (superconductor-insulator) transition which might be driven by the electrons occurs near x=0 and the high electronic density of states at Fermi level usually associated with the high Tc in this system. A λ-type phase transition which is probably related to the antiferromagnetism was also observed near 12K.

Continuous and discontinuous phase transitions in ammonium halides

Raman spectra of NH 4Cl and NH 4Br have been recorded as functions of temperature and pressure. The λ-type phase transition in NH 4Cl has been studied as (i) a weakly first order. (ii) a tricritical and (iii) a second order transition. A strongly first order transition has been studied in NH 4Br. The analysis of the data has concentrated on the correlation of frequency shift with volume change across the phase change regions. This correlation has been established for the frequencies of the ν 2 and ν 5 Raman modes of NH 4Cl at zero pressure (1st order) 1.6 kbar (tricritical) and 2.8 kbar (2nd order), and the frequencies of the ν 5 Raman mode of NH 4Br at zero pressure (1st order). A single Y (mode Grünelsen parameter) has been shown to describe each frequency shift right through the phase change region once an order-disorder contribution has been introduced at and below the transition temperatures.

Disintegration Energy of Ferrocene Crystal in Triclinic Phase and Kinetic Study on Monotropic Transition from Monoclinic to Orthorhombic Phase

Abstract Cooling of single crystals of ferrocene below the λ-type phase transition at 163.9 K leads to crystal disintegration with explosive violence independently of the λ-type transition. The strain energy evolved at the disintegration (“the disintegration energy” for short) was determined to be (1.10 ± 0.11) kJ mol–1 by a drop calorimetry system using a low-temperature Calvet microcalorimeter. The disintegration energy was independent of the crystal size with four sieve fractions in the range 2.5–0.25 mm. The violent disintegration is interpreted here in terms of an energy transfer from the strain energy accumulated in the domain boundaries in a form of elastic energy to the kinetic energy of disintegrated crystallites. The speed of a crystallite with the grain size of 60–70 pm was estimated to be 110 m s 1. On the other hand, kinetic aspect of a monotropic transition from the undercooled monoclinic to the stable orthorhombic phase at around 190 K. has been investigated with the same drop calorimetry s...

Heat capacity in the range 13–300 K and phase transitions of ferrocene- d10

The high-temperature (HT) phase of Fe(C 5D 5) 2 is easily undercooled to exhibit a λ-type phase transition at 164.1 K in the metastable state. The stable low-temperature (LT) phase is obtained by annealing the undercooled HT phase around 190 K. A first-order phase transition characterized by a superheating effect occurs at 251 K between the stable LT and HT phases. A comparison with Fe(C 5H 5) 2 has been made.

Heat capacity of a five-coordinated iron(III) complex, iodobis (N, N-Dimethyldithiocarbamato) iron(III), between 0.4 and 300 K

The heat capacity of iodobis ( N, N-dimethyldithiocarbamato)iron(III) has been measured between 0.4 and 300 K. Based on the heat capacity and entropy at low temperatures it was found that the present sample consists of a mixture of monomer ( ca. 40%) and dinier ( ca. 60%); the former brings about a λ-type phase transition from an antiferromagnetic to a paramagnetic state at T N = (1.65 ±0.04) K while the latter exhibits a Schottky-ype anomaly due to antiferromagnetic dimeric coupling, the effect of which becomes dominant below ca. 0.7 K. The zero-field splitting parameter of a single ferric ion was estimated to be D k = D D k = 14 K for the monometer and the dimer, while the dimeric coupling constant was J D k = −0.15 K . The entropy at low temperatures cannot be accounted for solely by the spin manifold. Additional contribution from a tunnel-splitting of the rotational levels of four constituent methyl-groups has been discussed. In this case, the level splitting of the ground state is 2.5 J mol −1 and the barrier height of hindering potential is 2.3 kJ mol −1.

The high temperature structure of β-SnS and β-SnSe and the B16-to-B33 type λ-transition path

Abstract The high temperature modifications β-SnS and β-SnSe crystallize in the orthorhombic TlI-type structure [Cmcm, No. 63; SnS at 905 K: a = 4.148(2), b = 11.480(5), c = 4.177(2) Å; SnSe at 825 K: a = 4.410(6), b = 11.705(7), c = 4.318(4) Å]. For the λ-type phase transition α → β from the GeS-type (B16) to the TlI-type (B33) the atomic shifts were determined from about 200° below the critical temperature to Tc (878 K and 807 K). They show a continuous transition from threefold to fivefold bonded atoms. This change in topology and bond character corresponds to the model of a SN2 chemical reaction. There is an indication of a possible first-order transition near Tc .

Dynamics and structure of disordered hydrogen-bonded crystals

Since the problem of the structure and of the molecular and lattice dynamics of solid methanol seems yet unsolved, new contributions are presented coming from theoretical calculations and lattice dynamical calculations. The α and β structures of solid methanol are accounted for on the basis of CNDO and packing-forces calculations. It turns out that a structurally disordered model for the β phase is likely to occur. A mechanism for the λ-type phase transition at 157·4° K is proposed which qualitatively accounts for the data from specific heat, dielectric constants, N.M.R. line-width and X-ray studies. The vibrational spectrum is discussed and compared with the interpretations available in the previous literature. Attempts are made to find evidence in the infra-red of the disordered model proposed from theoretical calculations. k = 0 phonons are calculated and their geometry dependence studied. While the O-H stretching motion is independent from an out-of-plane deformation of the molecular chain, O-H … O de...

Phase Transitions in Crystalline Divalent Metal Dicalcium Propionates. II. Proton Magnetic Resonance Investigation

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 phase transition with the peak at about 204°K by the differential thermal analysis. A slight decrease of the second moment was observed at the upper transition point and the C3′-rotation was assumed to be fully excited above that point.