Order Structural Phase Transition Research Articles

First order structural phase transition in BaPb 1−xBi xO 3 and the scaling law

Measuring the ultrasound velocity change ΔV s V s as a function of temperature T in BaPb 1− x Bi x O 3 (x = 0.4), we have found a remarkably large jump and hysteresis in ΔV s V s versus T. This first order phase transition accompanies a prominent critical slowing down phenomenon against the time after fixing T in the cooling process. Scaling the time appropriately, all curves with different time dependences can be folded into only one curve, following the scaling law in the first order phase transition. An X-ray diffraction analysis shows that this first order phase transition is associated with a structural phase transition from the orthorhombic structure to the monoclinic one.

Phase transition in In 3Sb 5O 12 by NQR of 115In nuclei

Results of investigations of In 3Sb 5O 12 crystals by means of the 115In NQR method in the temperature range 77–500 K are presented. The quadrupole coupling parameters for two structurally inequivalent centres are equal: e 2 Qq = 228 MHz and 213 MHz and η = 0.46 and 0.475, respectively. It is shown that a first order structural phase transition takes place at a temperature of T 2 = 165 K.

STUDY THE PHASE TRANSITION FOR THE PTS SINGLE CRYSTAL AT LOW TEMPERATURE BY PHOTOACOUSTIC EFFECT

The photoacoustic signal and phase angle have been measured for the single crystal of Polybis-(p-toluence sulfonate) of 2,4-(hexadiyne)-l,6-diol(PTS) in the temperature range of 175-225 K based on the photoacoustic effect (PAE.) The jump of photoacoustic signal and phase angle at 200 ±0.5 K was observed. We suggested that the jump can be attributed to the second order structural phase transition in PTS.

Lattice Parameters and the First Order Structural Phase Transition in Cu4Sn1-xGexS4(x≤0.3)

Lattice Parameters and the First Order Structural Phase Transition in Cu₄Sn_1-<i>x</i>Ge_<i>x</i>S₄(<i>x</i>≤0.3)

Temperature dependence of EXAFS intensities near second order phase transitions

Extended x-ray absorption fine structure (EXAFS) measures near neighbor bond lengths. Thermal damping of the oscillatory absorption modulation is caused by bond-length fluctuations and is predicted to show a weak change in temperature derivative at the temperature T c of a second order structural phase transition. The size of the slope change is a measure of the sensitivity of T c to changes in the bond-stretching force constant.

Basic Properties in Superconducting Perovskite-Type Oxide BaPb1-xBixO3

The BaPb1-xBixO3(BPB) system is orthorhombic for x<0.9 at room temperature, and for x≤0.4, exhibits a second order structural phase transition at low temperatures. Next, electron transfer in BPB is strongly influenced by electron localization due to oxygen vacancies and Bi ions, which may explain the composition-induced metal-insulator transition at x=0.35. The magnetic penetration depth is about 2 µm at 4.2 K, which is twice larger than the value calculated from the GL theory. Furthermore, polycrystalline BPB films make highly sensitive infrared optical detectors.

Optical phenomena in BaMnF4 near its phase transition temperatures

Measurements of indeces of refraction, birefringence, rotation of optical ellipsoid and optical activity have been made near incommensurate phase transition temperature and near two-and three-dimensional magnetic ordering temperatures in BaMnF4. The results are compatible with a single first order structural phase transition at TI = 251 K. The point group symmetry below TI is shown to be 2(C2) or lower. Magnetic contribution to the refractive index at low temperatures is obtained, the highest value being δncm≈1 10-3.

Observation of Magnetic and Structural Phase Transition in CsFeS2

Both neutron diffraction and Mössbauer investigation reveal that CsFeS 2 remains paramagnetic down to 70 K, at which a sudden first order magnetic and structural phase transition takes place. Antiferromagnetic coupling of spins both along the c -axis and along the diagonal direction in the a - b plane of the orthorhombic crystal structure of the high temperature phase accounts best for the observed low temperature neutron diffraction data. Mössbauer parameters determined over the temperature range from 4.2 K to room temperature indicate that the iron in CsFeS 2 is in a ferric state having large covalent bonding to sulfur ligands. The measured hyperfine field of 193.0±0.1 kOe at 4.2 K is a quite reduced value compared with those of other high spin ferric compounds.

DIRECTION OF SECOND ORDER STRUCTURAL PHASE TRANSITION AT г POINT OF hn SPACE GROUPS

By calculating the minimum of thermodynamic potential in Landau's theory of second order phase transition, the direction of second order structural phase transition at Γ point of Ohn space groups are obtained. "Maximal subgroup" condition is discussed.

An ESR study of phase transitions in crystals of M(BF 4) 2·6H 2O (M = Fe, Co, Ni, Zn)

From a temperature dependent ESR study of Mn 2+-doped crystals of M(BF 4) 2·6H 2O, M Zn, Co and Ni, new structural phase transitions have been detected and studied. First order structural phase transitions occur in Co(BF 4) 2·6H 2O at T 1 ~ 281K, T 2~189 K and T 3~172K (during cooling), in Zn(BF 4) 2·6H 2O at T 1 ~ 286 K and in Ni(BF 4) 2·6H 2O at T 1 ~ 301 K. A continuous phase transition occurs in Co(BF 4) 2·6H 2O at T p ~ 257 K, in Zn(BF 4) 2·6H 2O at T p ~ 277 K and in Ni(BF 4) 2·6H 2O at T p ~ 294 K. The ESR spectral characteristics suggest similarities in the structures of these fluoroborate compounds in the phase above T 1 with the room temperature structure of Mg(ClO 4) 2·6H 2O. All these compounds are found to have a tendency to crystallise in a triply-twinned pseudo-hexagonal form, although the unit cell above T 1 is found to be orthorhombic. The structural changes related to the water octahedron around the metal at T 1 were found to be very small and basically the same for these three compounds. Although the unit cell structure of Fe(BF 4) 2·6H 2O above the first order phase transition temperature T 1 was found to be similar to that of the other fluoroborate compounds, the structural changes occurring at T 1 appeared to be quite different. The low temperature thermal behaviour differs considerably in the Co, Fe and Zn compounds.

NQR Study of the Structural Phase Transition in 1,2-Diphenylhydrazine

14 N NQR lines in 1,2-diphenylhydrazine have been investigated between 4.2 K and 370 K by using a pulsed spectrometer. With increasing temperature, the number of resonance line in NQR spectra decreased from six lines to three lines above 115 K. The temperature dependence of resonance lines reveals that 1,2-diphenylhydrazine makes a second order structural phase transition around 115 K. An information about the molecular structure is also obtained.

On the kinetics of the first order phase transitions

An attempt is made to analyse the kinetics of the first order structural phase transitions on the basis of the Landau-Ginzburg equation. Two simple solutions are proposed: One in the form of one-dimensional solitary wave which can be considered as a planar interface separating two phases and travelling along direction normal to the interface. Any direction of propagation is possible. The other solution has a form of a onedimensional kink-antikink couple which under supercooling conditions reveals properties of a critical nucleus. A short discussion of the free energy density form for one- and multidimensional order parameters, and of the symmetry of the quadratic gradient term is included.

ESR study of phase transitions in single crystals of Cd(BF 4) 2, 6H 2O

From an ESR study of Mn 2+ doped single crystals of Cd(BF 4) 2, 6H 2O, two first order structural phase transitions at 324 ± 2 K (monoclinic to trigonal) and at 177 ± 2 K (trigonal to monoclinic or triclinic) are detected and studied for the first time.

Lattice Dynamics of 1T-TiSe2

Phonon dispersion curves for the high temperature phase of a layer compound 1 T -TiSe 2 , which reveals a second order structural phase transition at T c =200 K, are calculated using the rigid ion model and the shell model, The calculated phonon dispersion curves, especially with the shell model, are in good agreement with the observation with regard to their gross features. In particular, the calculated dispersion curve for acoustic phonons propagating in the layer and polarized perpendicular to the layer shows an upward bend as this is observed. However,the observed dip at the L point cannot be reproduced. with our models in which only central two-body forces are assumed; the L point corresponds to the wave vector of the observed lattice distortion. The results are discussed in connection with other possible effects.

Electron diffraction and infrared study of the semimetallic layered compound Ti 1−xV xSe 2

The crystals of the system Ti 1−xV xSe 2 (C ≤ x ≤ 0.05) undergo a second order structural phase transition. Electron diffraction studies show that the transition temperature decreases with progressive V-doping. The phase transition considerably affects the infrared reflectivity, measured at 300 and 77 K in the spectral range 40 cm −1 to 4000 cm −1. The presence of free carriers and the existence of optical infrared active E u phonon modes ( E ⊥ c) confer their characteristic appearance to the spectra. At room temperature one phonon structure is measured at 143 cm −1. At 77 K a new series of phonon peaks appears up to a V-concentration of 5 % as a direct consequence of superlattice formation. At room temperature the plasma-edge shifts towards higher frequencies as the vanadium concentration increases. This effect is caused by a large increase of N m ∗ , associated with the mixing of impurities. It is indicative of the small density of states at the Fermi level in semimetallic TiSe 2. Our results suggest a phase transition driven by lattice dynamical effects.

Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions

The classical φ6-field theory in (1+1) dimensions, is considered as a model for the first order structural phase transitions. The equation of motion is solved exactly; and the presence of domain wall (kink) solutions at and below the transition point, in addition to the usual phonon-like oscillatory solutions, is demonstrated. The domain wall solutions are shown to be stable, and their mass and energies are calculated. Above the transition point there exists exotic unstable kink-like solutions which takes the particle from one hill top to the other of the potential. The partition function of the system is calculated exactly using the functional integral method together with the transfer matrix techniques which necessitates the determination of the eigenvalues of a Schrodinger-like equation. Thus the exact free energy is evaluated which in the low temperature limit has a phonon part and a contribution coming from the domain wall excitations. It was shown that this domain wall free energy differs from that calculated by the use of the domain wall phenomenology proposed by Krumhansl and Schrieffer. The exact solutions of the Schrodinger-like equation are also used to evaluate the displacement-displacement, intensity-intensity correlation functions and the probability distribution function. These results are compared with those obtained from the phenomenology as well as the φ4-field theory. A qualitative picture of the central peak observed in structural phase transitions is proposed.

NMR Studies of Quasi-One-Dimensional Conductor β-Na0.33V2O5

NMR of 23 Na and 51 V in β-Na 0.33 V 2 O 5 has been studied between 90 K and room temperature. The results of 23 Na NMR show that sodium atoms are monovalent cations in β-Na 0.33 V 2 O 5 and occupy two non-equivalent positions in equal probability. The reported anomalies of the transport and calorimetric properties were found to be originated from the first order structural phase transition by the observation of the jump of 51 V nuclear quadrupole satellites of β-Na 0.33 V 2 O 5 in the temperature range between 130 K and 170 K.

Anharmonic oscillator model for first order structural phase transition

Exact solutions for the motion of a classical anharmonic oscillator in the potentialV(φ)=Bφ 2 − |A|φ 4 +Cφ 6 are obtained in (1 + 1) dimensions. Instanton-like solutions in (imaginary time) which takes the particle from one maximum of the potential to the other are obtained in addition to the usual oscillatory solutions. The energy dependence of the frequencies of oscillation is discussed in detail. This can be used as a model for the first order structural phase transition in the mean field approximation. The high and low temperature behaviour of the static susceptibility is obtained. Finally, a qualitative explanation is offered for the observed central peak in ferroelectrics like SrTiO2.

Magnetic and structural phase transitions in NiTiF6⋅6H2O

At 300 K, NiTiF6⋅6H2O crystallizes in the trigonal NiSnCl6⋅6H2O structure with one axially distorted [Ni(H2O)6]++ complex per unit cell. This structure is retained on rapid cooling, enabling us to measure χ∥, χ⊥, and Cp between ∼0.05 and 4.2 K in a 3He-4He dilution refrigerator. χ∥ and χ⊥ are those of a uniaxial ferromagnet with Tc?0.14 K and the easy direction along the trigonal axis. These data, as well as Cp with H∥=300 and 1500 Oe are well described by an Oguchi model in which pairs of exchange-coupled spins are treated exactly and interactions among pairs are replaced by a mean field. The pair Hamiltonian is 𝒞H=D (S2zi+S2zj) −2JSi⋅Sj+gμB(Si+Sj)2. Heff where Si=Sj=1, Heff=H+2J (q−1)M/Ng2μ2B with q=6. We find D/k=−1.83 K, g=2.26 and J/k?+0.012 K. We have also measured Cp for NiTiF6⋅6H2O under equilibrium conditions between 1.7 and 270 K. A first order structural phase transition is observed at 136.5 K with a latent heat of ∼662 cal/mole.

Electron spin resonance investigation of the structural phase transitions in Alurea 6(ClO 4) 3 and Ga urea 6(ClO 4) 3

Second order structural phase transitions in Alur 6(ClO 4) 3 and Gaur 6(ClO 4) 3 with T c ∼ 300 K are studied by means of ESR on single crystals doped with the analogous Cr(III) compound. The transitions are antiferrodistortive and of the displacive type, the displacements resulting from the condensation of a X 2 mode (k = (0 1 2 1 2 )) of the ClO 4 ions. The ESR parameters have the same temperature dependence as the order parameters and can be described by D and E∼φ∼. The space group describing the structure changes from S 6 2 to S 2 1, and the number of domains is multiplied by three. Above 300 K the crystals already consist of two domains, resulting from a ferrodistortive phase transition D 3 d 6 → S 6 2. The actual transition temperature of the latter phase transition lies at some temperature above the decomposition temperature of the crystals.