Dielectric properties of betaine phosphite-betaine phosphate solid-solution crystals in the improper ferroelastic phase

Temperature dependences of dielectric permittivity in the improper ferroelastic phase, including the region of the improper ferroelastic phase transition occurring at T=T_c1, were studied in the betaine phosphite-betaine phosphate solid-solution crystals. At a betaine phosphate (BP) concentration of 10%, the phase transition temperature T_c1 was found to shift toward higher temperatures by about 5 K compared to betaine phosphite (BPI) crystals, where T_c1=355 K. The phase transition remains in the vicinity of the tricritical point. As the BP concentration in BPI is increased, the dielectric anomaly at T=T_c1 weakens substantially compared to pure BPI. The nonlinear temperature dependence of reciprocal dielectric permittivity in the improper ferroelastic phase of BPI_xBP_1?x crystals is described in the concentration region 0.9≤x≤1 in terms of a thermodynamic model taking into account the biquadratic relation of the nonpolar order parameter of the improper ferroelastic phase transition to polarization. The decrease in the ferroelectric phase transition temperature T_c1 (or in the temperature of loss of improper ferroelastic phase stability) with increasing BP concentration in the above limits is due to the decreasing effect of the nonpolar mode on the polar instability, which is accompanied by a weakening of the dielectric anomaly at T=T_c1     

51V nuclear magnetic resonance in polycrystalline ferroelastic BiVO4

Nuclear magnetic resonance studies on polycrystalline ferroelastic BiVO₄ indicate that the ⁵¹V electric field gradient asymmetry parameter is an order parameter in the ferroelastic transition. Using ∩ = A(T?T_c)^B, B is found to be 0.48(5), in good agreement with earlier studies of this material. Near the phase transition above and below, the vanadium nuclear quadrupole coupling is constant with a value of 4.8(1) MHz.     

The influence of phase transitions in the Rb<Subscript>2</Subscript>CdI<Subscript>4</Subscript> ferroelastic on the exciton absorption spectrum

The parameters of the long-wavelength exciton band for Rb₂CdI₄ films are investigated in the temperature range 90–410 K. It is found that the Rb₂CdI₄ films undergo a sequence of phase transitions at temperatures T_c1=380 K (paraphase → incommensurate phase), T_c2=290 K (incommensurate phase → ferroelastic phase I), and T_c3 = 210 K (ferroelastic phase I → ferroelastic phase II). The parameters of the exciton band (such as the spectral position and the half-width) measured during heating and cooling of the Rb₂CdI₄ film differ significantly. This is especially true for the incommensurate phase. Upon heating of the incommensurate phase, the domain boundaries become frozen, whereas the cooling of this phase is accompanied by the generation of solitons and their pinning, which, in turn, results in a first-order phase transition at the temperature T_c2. It is revealed that the oscillator strength of the exciton band anomalously increases in the range of existence of commensurate phase I (T_c3<-T<-T_c2) due to ordering of the Rb₂CdI₄ crystal lattice.     

H nuclear magnetic resonance study of the ferroelastic and superionic phase transitions of (NH4)4LiH3(SO4)4 single crystals

We investigated the temperature dependences of the line shape, spin-lattice relaxation time, T₁, and spin-spin relaxation time, T₂, of the ¹H nuclei in (NH₄)₄LiH₃(SO₄)₄ single crystals. On the basis of the data obtained, we were able to distinguish the “ammonium” and “hydrogen-bond” protons in the crystals. For both the ammonium and hydrogen-bond protons in (NH₄)₄LiH₃(SO₄)₄, the curves of T₁ and T₂ versus temperature changed significantly near the ferroelastic and superionic phase transitions at T_C (=232 K) and T_S (=405 K), respectively. In particular, near T_S, the ¹H signal due to the hydrogen-bond protons abruptly narrowed and the T₂ value for these protons abruptly increased, indicating that these protons play an important role in this superionic phase transition. The marked increase in the T₂ of the hydrogen-bond protons above T_S indicates that the breaking of O-H?O bonds and the formation of new H-bonds with HSO₄^- contribute significantly to the high-temperature conductivity of (NH₄)₄LiH₃(SO₄)₄ crystals.     

Esr study of (SO4)2− dynamics in relation to the ferroelectric phase transition in ammonium sulfate

Ferroelectric phase transition in ammonium sulfate has been studied by ESR of CrO₄^3? radical substituting for SO₄^2? ion in (NH₄)₂SO₄. In addition to discontinuous changes at T_c, certain continuous changes are observed in ESR parameters of this probe below T_c, which reflect the role of the sulfate ion in the phase transition. A microscopic mechanism of the phase transition is proposed and discussed in terms of the change of orientation of the sulfate tetrahedron through a finite angle. The degree of the change of orientation below T_c is thought to be the possible order parameter of the phase transition.     

Proton Dynamics in Letovicite, (NH4)3H(SO4)2: A H and N NMR Spectroscopic Study

The improper ferroelastic phase letovicite (NH₄)₃H(SO₄)₂ has been studied by ¹H MAS NMR as well as by static ¹⁴N NMR experiments in the temperature range of 296–425 K. The ¹H MAS NMR resonance from ammonium protons can be well distinguished from that of acidic protons. A third resonance appears just below the phase transition temperature which is due to the acidic protons in the paraelastic phase. The lowering of the second moment M₂ for the ammonium protons takes place in the same temperature range as the formation of domain boundaries, while the signals of the acidic protons suffer a line narrowing in the area of T_c. The static ¹⁴N NMR spectra confirm the temperature of the motional changes of the ammonium tetrahedra. Two-dimensional ¹H NOESY spectra indicate a chemical exchange between ammonium protons and the acidic protons of the paraphase.     

NMR investigations of dynamical processes in orientationally ordered and disordered NaCN,RbCN and CsCN

The nuclear spin lattice relaxation timeT ₁ of the²³Na,⁸⁵Rb,⁸⁷Rb,¹³³Cs,¹⁴N nuclei is measured in NaCN, RbCN and CsCN as a function of temperature below and above the ferroelastic phase transition temperatureT _c. BelowT _c the behaviour ofT ₁ of the alkali nuclei renders possible to determine the flip frequency of the CN molecules and its temperature dependence. AboveT _c from the¹⁴NT ₁ the correlation time τ_c of the rotational motions of the CN molecules and its temperature dependence is determined. An empirical rule is verified demonstrating that atT _c the correlation times take nearly the same values for all cyanides. For the high and low temperature phases one obtains atT _c about τ_c=5·10^?13s and τ_c=5·10^?11s, respectively. The results are discussed with respect to the mechanism of the phase transition.     

A nuclear magnetic resonance study of the structural properties and molecular motions of Li2KH(SO4)2 and LiKSO4 single crystals

The structural properties and relaxation mechanisms of Li₂KH(SO₄)₂ crystals were determined using the temperature dependences of NMR spectra and the spin-lattice relaxation times (T₁) of their ¹H, ⁷Li, and ³⁹K nuclei. The results obtained were compared with the previously reported physical properties of LiKSO₄ crystals. The substitution of the potassium ions with protons in the LiKSO₄ crystals were variations in the phase transition temperatures, and the non-appearance of ferroelastic properties. The ⁷Li T₁ for the Li₂KH(SO₄)₂ crystals was much shorter than the ⁷Li T₁ for the LiKSO₄ crystals, and these findings indicate that the presence of the protons in Li₂KH(SO₄)₂ causes the Li ions to move with greater freedom.     

Ferroic phase transitions in β-LiNH4SO4

Abstract

The paper reviews the results of experimental and theoretical studies of ferroic phase transitions in β-LiNH₄SO₄ and its deuterated analogue. β-LiNH₄SO₄ undergoes succesive phase transitions: a paraelectric - ferroelectric phase transition at T₁ ? 462 K, a ferroelectric - ferroelastic phase transition at T₂ ? 283 K and a transition from one ferroelastic phase to the other at T₃ ? 28 K. Attention is focused on the influence of the order of phase transitions on the pattern of ferroelectric and ferroelastic domain structure, and also on the role played by the dynamics of molecular groups in the mechanism of transitions. The pre-transition effect connected with the ferroelectric-paraelectric transition: heterophase, capable of accounting for anomalies in different physical properties present 1-3 K below T₁ is shown. The anomalous temperature variation of spontaneous polarisation of the crystal is discussed within the framework of the phenomenological model of weak ferroelectrics.     

Manifestation of an intermediate phase in a ferroelastic K3Na(CrO4)2:MnO 4 2− in raman and IR absorption spectra

In a broad temperature range of 4–300 K, we have performed a complex combined investigation of phase transitions in crystals of a ferroelastic K₃Na(CrO₄)₂:MnO ₄ ^2? using methods of Raman light scattering and IR light absorption. Considerable changes that we have observed in both Raman and IR spectra in the range of T ≈ 150 K testify to the occurrence of another phase transition that has not been observed before at this temperature. We have performed a group-theoretical analysis and compared its results with experimental spectra, which has allowed us to conclude that there are two phase transitions in this crystal, \(P\bar 3m1 \to C2/m \to C2/c\) , which occur at temperatures T _c1 ≈ 230 K and T _c2 ≈ 150 K, respectively.     

Proton diffusion in the room-temperature phase of [(NH4)1−xRbx]3H(SO4)2 as studied by 1H spin-lattice relaxation in the rotating frame

Proton diffusion in the room-temperature phase (phase II) of [(NH₄)_1?xRb_x]₃H(SO₄)₂ (0≤x≤1) has been studied by means of ¹H spin-lattice relaxation times in the rotating frame, T_1ρ. The ¹H T_1ρ values were measured at 200.13 MHz in the range of 380–490 K. The ammonium protons and the acidic protons have independent T_1ρ values in the higher temperature range of phase II, suggesting that the spin diffusion between the two species is ineffective. The translational diffusion of the acidic protons is the most dominant mechanism to relax both the ammonium protons and the acidic protons in phase II. The ¹H T_1ρ values in phase II are analyzed theoretically and the motional parameters are obtained. The results of NMR well explain the macroscopic proton conductivity.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

High pressure study of BaPb0.7Bi0.3O3 films

The resistance R, the superconducting transition temperature T_c and the energy gap Δ(T) have been measured on the BaPb_0.7Bi_0.3O₃ films up to 14 kbar. We have found that up to 14 kbar: (1) pressure suppresses T_c and Δ(T) while enhances R, (2) the value of 2Δ(0)/kT_c is 3.8±0.1, independent of pressure, and (3) the Δ(T)/Δ(0) varies with T/T_c in a BCS fashion but only for T/T_c<0.75 and independent of pressure. The results show that BaPb_1?xBi_xO₃ is a weak-coupling superconductor, but fail to provide information about the cause for the high T_c of the compound.     

Ferroelastic phase transition and anomalous elastic and thermal properties of betaine borate (CH3)3NCH2COO·H3BO3

The temperature and pressure derivatives of the elastic constants of orthorhombic betaine borate, (CH₃)₃NCH₂COO·H₃BO₃, have been determined by measuring temperature and stress induced shifts of resonance frequencies of thick plates at ca. 15 MHz in the range between 140 and 300 K and 0 and 3 kbar. The elastic ‘shear’ resistance c₄₄ exhibits a value as low as 0.0492×10¹⁰Nm^-2at 293 K. With decreasing temperature c₄₄ approaches zero at ca. 142.5 K, indicating an acoustic soft mode behaviour connected with a ferroelastic phase transition. The softening of c₄₄ is described in a good approximation by c₄₄(T)_p=0 =alogT/T₀ with a=0.0663×10¹⁰Nm^-2 and T₀ = 139.5 K. Further, c₄₄ decreases with increasing pressure according to the linear relation c₄₄(p)_{T=293 K} = 0.0492?0.184×10^-4p (p in bar, c₄₄ in 10¹⁰ Nm^-2). All other elastic constants show a quite normal temperature and pressure dependence. At 293 K the transition is induced by a pressure of 2.65 kbar. The transition temperature T_c depends linearly on pressure according to T_c = 142.5+0.0568 p (pinbar, T_cinK). Passing through the transition no discontinuous change of the lattice constants is observed. The three principal coefficients of thermal expansion and the pressure derivatives of the dielectric constants exhibit discontinuities at the transition. The transition is of strongly second order.     

High pressure behaviour of KHSO4 studied by electrical impedance spectroscopy

Measurements of the electrical conductivity were performed in KHSO₄ at pressures between 0.5 and 2.5 GPa and in the temperature range 120-350 °C by the use of the impedance spectroscopy. The temperatures of the α-β phase transition (T_Tr) and of the melting (T_m), determined from the Arrhenius plots ln(σT) vs. 1/T, increase with pressure up to 1.5 GPa having dT/dP∼+45 K/GPa. Above the pressure 1.5 GPa, the pressure dependencies of T_Tr and T_m are negative dT/dP∼−45 K/GPa. At pressures above 0.5 GPa, the reversible decomposition of KHSO₄ into K₃H(SO₄)₂+H₂SO₄ (and probably into K₅H₃(SO₄)₄+H₂SO₄) affects the electrical conductivity of KHSO₄, with the typical values of the protonic electrical conductivity, c. 10⁻¹ S/cm at 2.5 GPa.     

The temperature dependence of the ALO-modes in Pb5Ge3O11

The temperature dependence of the LO-TO splitting of the A-modes of Pb₅Ge₃O₁₁ between room temperature and T_c=450K was determined from the Raman spectrum. The finite splitting of two A-modes above T_c leads to the conclusion that the space group of Pb₅Ge₃O₁₁ in the paraelastic phase deviates from P6 which was determined by X-ray and other physical methods.     

The elastic behaviour of ferroelastic Sb5O7I polytype 2MC studied by ultrasonic experiments and Brillouin scattering

The temperature dependence of the elastic functions of the improper ferroelastic polytype 2MC-Sb₅O₇I has been investigated in the temperature range from room temperature to well above the structural phase transition atT _c=481 K. The stiffnessesc(c^*c^*),c(a,a),c ₂₂ andc(c^*a) show a considerable softening up to 20% aroundT _c whereasc ₄₄ remains unaffected by the phase transition. The experimental results are discussed considering cubic and quartic anharmonic coupling between two components of the zone boundary order parameter and elastic waves.Carried out in Laboratories RCA Ltd, Zürich, SwitzerlandCarried out in Fakultät für Physik der Universität, Regensburg, Federal Republic of Germany     

Structures and phase transition in Rb2NaHoF6

The phase transition at T_c=172(2) K and high as well as the low temperature structures at 205 K and 17 K were studied with a low temperature Guinier diffractometer and camera. A second order phase transition (Γ-condensation of the T_1g mode) lowers the symmetry from Fm3m at T>;T_c to I4/m at T<T_c. In the low temperature phase the octahedra are tilted (5.2 degrees at 17 K) and slightly stretched. The increase of the tilt angle and the linear increase of the tetragonal distortion suggests a mean field power law. This classical behaviour would agree with the assumption of a Jahn Teller splitting of the Ho³⁺ electronic state.     

Effect of γ-irradiation on the heat capacity of an [NH2(CH3)2]2 · CuCl4 crystal in the temperature range 80–300 K

The heat capacity of [NH₂(CH₃)₂]₂ · CuCl₄ crystals prior to and after γ-irradiation with doses of 1, 5, 10, and 50 MR is measured by the calorimetric method in the temperature range 80–300 K. It is found that, as the temperature decreases, the temperature dependence C _p (T) exhibits two anomalies which correspond to phase transitions from the incommensurate to the ferroelectric phase at T _c =281 K and from the ferroelectric to the ferroelastic phase at T ₁=255 K. The nature of the anomalies is typical of a first-order phase transition. In addition, a smeared anomaly in the form of a small increase in the heat capacity of the ferroelectric phase is observed at T≈275 K. It is demonstrated that when the dose of γ-irradiation increases, the anomalies decrease in magnitude and the phase transition temperatures are displaced: T _c increases and T ₁ decreases.     

The origin of the pseudogap phase: precursor superconductivity versus a competing energy gap scenario

In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature T_c is different from the energy gap onset temperature T^∗. In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter Δ_sc is to be distinguished from the excitation gap Δ; in this way, pseudogap effects persist below T_c. It has been argued by many in the community that the presence of these distinct energy scales demonstrates that the pseudogap is unrelated to superconductivity. In this paper, we show that this inference is incorrect. We demonstrate that the difference between the order parameter and excitation gap and the contrasting dependences of T^∗ and T_c on hole concentration x and magnetic field H follow from a natural generalization of BCS theory. This simple generalized form is based on a BCS-like ground state, but with self-consistently determined chemical potential in the presence of arbitrary attractive coupling g. We have applied this mean field theory with some success to tunneling, transport, thermodynamics, and magnetic field effects. We contrast the present approach with the phase fluctuation scenario and discuss key features which might distinguish our precursor superconductivity picture from that involving a competing order parameter.