Cubic-tetragonal Transition Research Articles

Displacive-order-disorder crossover at the ferroelectric-paraelectric phase transitions of BaTiO3 and LiTaO3

A detailed comparison between accurate infrared reflectivity data and dielectric constant e0(T) measurements has been carried out in ABO3 ferroelectrics. In BaTiO3, the ferroelectric mode saturates above the cubic-tetragonal transition, whereas e0( T) tends to diverge. This supports an intrinsic crossover from displacive to order-disorder behaviour on approaching Tc because the critical dimensionality in these cubic dipolar systems is dc = 4 > d = 3. In the uniaxial LiTaO3 with d = d c = 3, the crossover is less pronounced.

Soft mode spectroscopy in barium titanate

Infrared reflectivity measurements are performed with a scanning interferometer on a single crystal over a wide range of temperature (300-1350K) especially in the cubic paraelectric phase of barium titanate (Tc=395K). The temperature dependence of TO and LO frequencies, dampings and TO oscillator strengths is reported. An overdamped soft mode, which follows a Curie-Weiss law over 800 degrees , is evidenced. A deviation from this law occurs over a hundred degrees above the tetragonal-cubic transition. The discrepancy of the value of dielectric constant obtained from optical mode frequencies and that obtained by direct dielectric measurements is discussed in terms of the possibility of a disorder which would appear progressively on cooling, in the cubic phase, and which complicates the displacive-type mechanism.

A new tricritical point in Co doped barium titanate

Abstract By means of X-ray diffraction of a polydomain single crystals of Co doped BaTiO3 we have measured the c/a ra io as a function of temperature. We found that the first order character of the tetragonal-cubic transition disappears by increasing the Co amount. We conclude that samples with 2.5% atom of Co exhibit a tricritical point. This point seems to be different than the tricritical point which is observed in pure BaTiO3 under hydrostatic pressure.

On the symmetry of deformable crystals

This study was motivated by my recognition of some difficulties in the theory of phase transitions. LANDAU* [1] proposed a theory of phase transitions in crystals, covering cases where the crystal symmetry undergoes some change. Briefly and roughly, it excludes the possibility of various types of changes in symmetry. Unfortunately for the theory, various excluded transitions are observed. I do not know of a good reference describing the known exceptions. The discussion which follows refers to cubic-tetragonal transitions, 'which are observed in some superconductors. According to conversations I have had with experimentists, other types of exceptions are observed. It is not impossible to be fooled, for the distinction between a second order and weak first order transition is a fine one. However one assesses this, we have good reason to look at the theory with a critical eye, and to remove its imperfections. In discussing one such exception, ANDERSON • BLOUNT [3] claim to show that such transitions "... usually involve some change in internal symmetry other than mere strain ...". Said differently, thermoelasticity theory should be replaced by a theory involving a larger list of variables in the constitutive equations. If the suggested cure is to work, it should change the conclusions of LANDAU, most probably to decrease the number of changes excluded. Considering the nature of the calculations involved, it seems to me less than clear that merely enlarging the list of state variables will accomplish this, and they do not prove that it will. Thus, I think that we should look at other weak spots in the LANDAU theory. ANDERSON & BLOUNT mention, but discount another, involving matters of continuity. I focus on another. It might well be that thermoelasticity theory is inadequate, but it should be given a fair hearing. As far as I know, we do not have a theory, accepted by knowledgeable workers, to replace LANDAU's. Again considering the nature of LANDAU'S reasoning, it might help if we could attribute to thermodynamic potentials more invariance than is commonly done. Common molecular theories predict a rather unconventional theory of

Raman scattering study of phase transitions in RbCaF 3

Recent experiments on RbCaF 3 have indicated the occurence of structural phase transitions at low temperature. The Raman data presented here confirm the transition at 200 K to be similar to the cubic-tetragonal transition occuring in SrTiO 3 and KMnF 3: soft modes of A 1 g and Eg symmetry are observed and the spectrum is consistent with D 4 h crystal symmetry. At 45 K the frequency and damping of the A 1 g mode begin to increase with further decrease in temperature, both of which suggest the the emergence of a new low-frequency mode of A 1 symmetry at this temperature.

Critical dynamics at the structural phase transitions in NaNO 2 and NaNbO 3 and quadrupole relaxation T1 and T1 ϱ in high fields

Measurements of quadrupole spin-lattice relaxation in the laboratory and in the rotating frames for 23Na in NaNO 2 and for 23Na and 93Nb in NaNbO 3 are reported and discussed. From the analysis of the temperature dependence of the critical contribution to T 1 and T 1 ϱ , information is obtained on the dimensionality and the characteristic frequencies of fluctuations. For the ferroelectric order-disorder transition in NaNO 2, the orientational fluctuations in adjacent chains of the NO 2 − dipoles are uncorrelated and their frequencies remain greater than ω L = 130 MHz even at the transition. For the typical displacive cubic-tetragonal transition in NaNbO 3 at T c = 641°C the fluctuations of the oxygen octahedra have a quasiplanar character and a strong slowing down occurs so that at T ≅ T c + 4°C the characteristic frequency at the critical wave vector is about 270 MHz. An analysis of T 1 ϱ near the phase transition is given, taking into account the fact that a further mechanism of relaxation due to vacancy diffusion is present, as revealed by the high-temperature measurements.

Pressure Dependence of the Structural Phase Transition Temperature in SrTiO3and KMnF3

The pressure dependence of the structural phase transition temperature, T a , in SrTiO 3 has been measured up to 30 kbar. The initial slope of 1.8 deg/kbar by Sorge et al. (1970) has been reaffirmed contrary to the prediction by Fossheim and Berre (1972): d T a /d p =0.5 deg/kbar. Above 8.5 kbar the transition temperature shifts nonlinearly with increasing pressure. As for the cubic-tetragonal transition temperature of KMnF 3 the measurements to 10 kbar show a linear shift: d T a /d p =3.9 deg/kbar. Above 10 kbar a deviation from linearity seems to set in.

Studies on Mn 3O 4MgAl 2O 4 system

Structural, electrical and magnetic properties of solid solutions of tetragonal Mn 3O 4 (c/a>1) and cubic MgAl 2O 4 over the whole composition range have been investigated. All the samples were found to be monophasic and exhibited either tetragonal or cubic symmetry at room temperature/ Tetragonal-cubic transition appeared to be of the first order. Electrical conductivity decreases with increasing concentration of MgAl 2O 4 and conduction presumably occurs via ‘hopping’ of holes from Mn 3+ + Mn 2+ at B sites at 600<T<800 K. Magnetic susceptibility results indicate that all compositions are paramagnetic in the range 80–340 K and would order ferrimagnetically at lower temperatures, except (Mn 3O 4) 0·2 (MgAl 2O 4) 0·8, which may exhibit antiferromagnetism.

Effect of hydrostatic pressure on the phase transition of ferroelectric PbTiO 3

The effect of hydrostatic pressure on the dielectric constant of the Nb-doped lead titanate ceramics was measured up to 60 kbar at room temperature. From the previously observed pressure dependence of lattice parameters and the present results, it is concluded that the tetragonality decreases linearly with a slope of −7.6×10 −4/kbar and that the pressure dependence of the tetragonal-cubic transition temperature is −8.4K/kbar.

On the RbClCdCl 2 system

The RbClCdCl 2 phase diagram was re-examined and new data on the sub-solidus behaviour were collected. The tetragonal-cubic transition occurs reversibly at 114 ± 2°C. An anomalous polymorphism of RbCdCl 3 is influenced by the presence of water which favours the formation of an orthorhombic phase at room temperature.

The structure of sodium niobate (T2) at 600°C, and the cubic-tetragonal transition in relation to soft-phonon modes

Abstract The structure of NaNbO3, phase T2 (immediately below the cubic phase), has been determined from lattice parameters and difference reflections. It is tetragonal C-face-centred, with a= 7·8698(8) Å, c=3·9428(4) Å at 600°c. It corresponds to condensation of an M3 soft-phonon mode from the cubic phase, in contrast to SrTiO3 where the condensing mode is Γ25. The anomalous changes in mean square values of atomic displacements have been derived from changes in lattice parameters. Hence the intensities of x-ray scattering are calculated and compared with direct measurements of diffuse scattering by other workers, with satisfactory agreement. A mechanism for the transition is postulated.

A crystallographic study of the system FeCr 2O 4Fe 3O 4 (Fe 2+Fe 3+xCr 2−xO 4)

Materials in the system Fe 2+Fe 3+ xCr 2−xO 4 (x = 0 to x = 2) were prepared by thermal decomposition of the mixed Fe 3+ and Cr 3+ ammonium sulphates to form appropriate solid solutions of Fe 2O 3 and Cr 2O 3. Subsequent heating of the materials at 1100°C in a flowing CO CO 2 gas mixture resulted in single phase spinels with compositions which have been confirmed by chemical analysis and Mössbauer spectra. X-ray measurements, between 4.2°K and room temperature, have shown that FeCr 2O 4 undergoes a cubic-orthorhombic phase transition at 138°K, contrary to the cubic-tetragonal transition previously reported. The cubic-orthorhombic transition takes place for compositions x = 0 to x = 0.3. Between x = 0.4 and x = 0.6 a cubictetragonal-orthorhombic transition takes place. From x = 0.68 to x = 0.75 a cubic-tetragonal transition takes place and the tetragonal phase persists to 4.2°K. Materials for which x = 0.8 to x = 2 exhibit the cubic spinel structure from room temperature to 4.2°K. The cubic-to-orthorhombic transition which occurs in Fe 3O 4 is observed.

Effect of high pressure on the lattice constants of chromites having the spinel structure

In order to examine the pressure dependence of the compressibility for Ni and Cu chromites with the spinel structure the lattice constants have been measured up to 70kb by the use of a cubic anvil X-ray diffraction press. The high compressibility of NiCr 2O 4 was explained by softening of the lattice for temperatures near the cubictetragonal transition. The change of lattice constant of CuCr 2O 4 under high pressure was anomalous.

X-Ray and Mössbauer Studies in the Sr(FeTa)1/2O3 and Sr(CrTa)1/2O3 System

Sr(FeTa) 1/2 O 3 is a disordered perovskite, tetragonal at room temperature, while Sr(CrTa) 1/2 O 3 is an ordered perovskite, cubic at room temperature. These compounds make solid solutions in the whole range of composition. Tetragonal-cubic transition occurs at about 90 mol% of Sr(FeTa) 1/2 O 3 . Intensity of superstructure line of X-ray diffraction which shows the ordered arrangement of the B ions decreases gradually with increase of Sr(FeTa) 1/2 O 3 . Isomer shift is nearly constant, 0.64 mm/sec, for all compounds, the value of which is reasonable for Fe 3+ . The curve of the quadrupole splitting vs composition is rather complicated. We can give it a qualitative interpratation in terms of local distortion arising from the disordered distribution of the Ta, x Fe and (1- x )Cr ions.

Cation migration, cation valencies and the cubic-tetragonal transition in Mn xFe 3− xO 4

Thermal expansion measurements of polycrystalline, single crystalline and textured specimens Mn x Fe 3− x O 4 are reported. The experimental data are interpreted in terms of two cation migration processes, namely the cation exchange between the octahedral and tetrahedral sublattices, and an octahedral Mn 3+ clustering. The changes in the crystal structure of cubic Mn 1·9Fe 1·1O 4 in the temperature range of 250–350°C indicate a shift in the cation distribution of 0·15–0·20 ions per unit AB 2O 4, which is stabilised by the macroscopic tetragonal distortion of the lattice. The tetragonal distortions of the specimens x=1·9 in combination with electrical conductivity measurements on x=2·0 reveals unequivocally that in the spinel structure octahedral Mn 3+ and Fe 2+ are the stable cation valencies at low temperatures.

Pyroelectric Effect in Barium Titanate Ceramic

The pyroelectric coefficient (at constant stress) of a 95 wt% BaTiO3, 5 wt% CaTiO3 ceramic composition (Clevite Ceramic B) was measured over the temperature range from 4.9° to 400°K. Extrema in the pyroelectric coefficient were observed at the rhombohedral-orthorhombic transition point (150°–170°K), the orthorhombic-tetragonal transition point (240°–260°K), and the tetragonal-cubic transition point (Curie point, at 387°K). The pyroelectric coefficient showed no anomalous behavior below 150°K. A spontaneous polarization curve derived from the pyroelectric results is compared with published single-crystal measurements. The ceramic results can be completely interpreted by means of a model describing switching of domain orientations at phase transitions.

A new structural phase transition in CsPbCl 3

A new phase transition into a superstructure has been found in CsPbCl 3 crystal at about 40°C below the previously reported cubic-tetragonal transition point. A remarkable anomaly in the sound velocity was observed there.

Photoluminescence, Photocurrent, and Phase-Transition Correlations in SrTiO3

Photoluminescence emanating from ``pure'' high resistivity SrTiO3 has been examined between 4000 and 13 000 Å as a function of temperature and 3650 Å irradiation. One strong narrow peak (7929 Å at 95°K; half-width ≤1 Å) and 9 associated peaks (7852, 8005, 8051, 8098, 8280, 8304, 8469, 8574, 8726 Å), each of which exhibit maximum intensity at 35° and 95°K, which are within the temperature ranges associated with the ferroelectric-paraelectric transition, and the tetragonal-cubic transition, respectively. As this emission extinguishes below 35°K, an asymmetric structureless broadband emission begins, which extends from ≈4200–≈8000 Å, and peaks near 5000 Å. Concurrent photocurrent measurements show: a maximum at 105°K and a minimum at 35°K; the existence of extensive trapping effects, including long-duration (hours to days) dark-current relaxation, a field-induced persistent internal polarization (due to spacial separation of trapped electrons and holes), and an interaction between irradiation and ferroelectric hysteresis. Sublinear responses exist common to the photoluminescence peaks and photocurrents at various temperatures, viz. response ∝ Jβ(T) where ½&amp;lt;β(T)&amp;lt;1. The behavior observed is in part interpretable on the basis of recombination processes via multiple defects.

Phase Transitions in the System BaTiO3-KnbO3

Solid solution formation in the system BaTiO3—KnbO3 was established by X-ray diffraction and dielectric measurements. Solid solutions with cubic symmetry were observed in the composition range from 4 to 90 mole % KnbO3 at room temperature. The lattice parameter for the BaTiO3 solid solutions increased with increasing KNbO3; that for the KnbO3 solid solutions decreased with the addition of BaTiO3. A distinct discontinuity in lattice parameter was observed at the composition containing about 65 mole % BaTiO3. Dielectric measurements were made from-195° to 400°C. The cubic-tetragonal transition temperature of BaTiO3 was rapidly lowered with increasing addition of KNbO3, whereas the two lower phase transition temperatures were raised. All three phase transitions of KnbO3 were rapidly lowered with increasing addition of BaTiO3. The observed phase transitions, lattice parameters, and electron probe data suggest a complex region in the subsolidus which extends from 35 to about 75 mole % KNbO3.

Magnetic Properties and Optical and Paramagnetic Spectra of Divalent Nickel in Sr2(NiW)O6

Small single crystals of ordered perovskite Sr 2 (NiW)O 6 were synthesized by the flux method using SrCl 2 6H 2 O. The crystal becomes antiferromagnetic below 59°K and undergoes a tetragonal-cubic transition at 523°K. Optical and paramagnetic spectra of divalent nickel in Sr 2 (NiW)O 6 were investigated. The optical absorption lines are interpreted as transitions between the singlet ground state and possible Stark levels, following the scheme given by Low for MgO:Ni. Parameters of the energy levels were determined as follows: 10 D q =8575 cm -1 , E p =13430 cm -1 , E D =10860 cm -1 and E G =17120 cm -1 . Paramagnetic resonance occurred at the field strength of 7562 Oe and the frequency of 23.73 GC /sec. Values of g and spin-orbit coupling constant λ were evaluated at 2.242 and -256 cm -1 respectively.