Showing papers on "Phase transition published in 1979"
TL;DR: In this paper, a theory of the underlying metastable phase, the amorphous phase, is developed, which is useful for describing the behavior of the viscosity of dense liquids and glasses.
Abstract: The free-volume model, which has been useful for describing the behavior of the viscosity $\ensuremath{\eta}$ of dense liquids and glasses, is extended to account for their thermodynamic behavior as well. Experimental results for the heat capacity ${C}_{p}$ and the volume $\overline{v}$ show that the system falls out of complete, metastable thermodynamic equilibrium at the glass transition temperature ${T}_{g}$. As a first step in understanding these universal phenomena, a theory of the underlying metastable phase, the amorphous phase, is developed. Recent molecular-dynamic calculations demonstrating the existence of a cellular structure in liquids and the properties of the local free energy of the molecular cells permit us to formulate more precisely and justify in more detail the standard free-volume model. In particular, it is possible to define the free volume and distinguish solid-like and liquidlike cells. This leads to the introduction of percolation theory, which is used to describe the gradual development of the communal entropy of the amorphous phase. We then determine the probability distribution of the cellular volume as a function of the fraction of liquidlike cells, $p$. The equilibrium liquid-glass transition is associated with the increase of $p$ with temperature. This occurs via a phase transition which is most probably first order. The results of our theory give a generalized equation for the viscosity which agrees accurately with experimental results at all temperatures. Results for ${C}_{p}$ and $\overline{v}$ are also obtained. This equilibrium theory can provide the basis for a relaxation theory of the kinetic effects observed around and below ${T}_{g}$. The relationship between the entropy theory and the free-volume model is also clarified.
1,000 citations
01 Jan 1979
TL;DR: In this article, the authors present an approach to perturbation approach to Lattice Instabilities in Quasi-One-Dimensional Conductors (QODC) in the context of TTF-TCNQ.
Abstract: 1 Introduction to Highly Conducting One-Dimensional Solids.- 1. Introduction.- 2. Some Preliminary Thoughts.- 3. Excitonic Superconductivity.- 4. TCNQ Salts and KCP.- 4.1. NMP-TCNQ.- 4.2. TTF-TCNQ.- 4.3. KCP.- 5. TTF-TCNQ and TSeF-TCNQ.- 5.1. Structural Transitions in TTF-TCNQ.- 5.2. Electromagnetic Properties of TTF-TCNQ.- 5.3. ESR and Alloys of TTF-TCNQ and TSeF-TCNQ.- 6. Theory.- 7. Some Concluding Thoughts.- References.- 2 X-Ray and Neutron Scattering from One-Dimensional Conductors.- 1. Introduction.- 1.1. Lattice Instabilities and Phonon Anomalies.- 1.2. X-Ray Diffuse Scattering.- 1.3. Neutron Scattering.- 2. Structural Studies of KCP and Related Platinum Chain Complexes.- 2.1. Structure and One-Dimensional Electrical Properties of KCP.- 2.2. X-Ray Diffuse Scattering from KCP.- 2.3. Neutron Scattering Studies of KCP.- 2.4. Study of Other Platinum Complexes.- 3. Structural Studies of Organic One-Dimensional Conductors.- 3.1. Structure and TTF-TCNQ Crystals.- 3.2. High-Temperature Precursor Scattering in TTF-TCNQ.- 3.3. The Modulated Phases of TTF-TCNQ.- 3.4. Spin Waves in TTF-TCNQ?.- 3.5. The Interpretation of the Sequence of Modulated Phases in TTF-TCNQ.- 3.6. Study of Other Organic One-Dimensional Conductors.- 4. Concluding Remarks.- References and Notes.- 3 Charge-Density Wave Phenomena in One-Dimensional Metals: TTF-TCNQ and Related Organic Conductors.- 1. Introduction.- 2. Strength of Interactions Bandwidth, Electron-Electron and Electron-Phonon Interactions.- 2.1. One-Electron Energies Band Structure.- 2.2. Electron-Electron Interactions: Nuclear Magnetic Resonance and Magnetic Susceptibility.- 2.3. Electron-Phonon Interaction.- 3. The Peierls Instability in TTF-TCNQ: Structural Aspects and Phonon Softening.- 4. The Pseudogap: Optical Properties.- 5. Electrical Conductivity.- 5.1. DC Measurements.- 5.2. Microwave Measurements.- 6. The Transition Region 38 K
745 citations
TL;DR: In this paper, an electron-liquid to electron-crystal phase transition in a sheet of electrons on a liquid-He surface has been shown to occur at a temperature between 0.35 and 0.65 K.
Abstract: Experimental evidence is presented for an electron-liquid to electron-crystal phase transition in a sheet of electrons on a liquid-He surface. The phase transition has been studied for electron areal densities from 3\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{cm}}^{\ensuremath{-}2}$ to 9\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{cm}}^{\ensuremath{-}2}$ and has yielded melting temperatures between 0.35 and 0.65 K. The phase transition occurs at $\ensuremath{\Gamma}=137\ifmmode\pm\else\textpm\fi{}15$, where $\ensuremath{\Gamma}$ is a measure of the ratio of potential energy to kinetic energy per electron.
736 citations
TL;DR: In this article, it is shown that at a sufficiently large temperature a phase transition takes place after which almost all elementary particles in the hot super-dense matter become massless and weak interactions become long-range like electromagnetic interactions.
Abstract: Reviews phase transitions in super-dense matter, which consists of particles interacting in accordance with the unified gauge theories of weak, strong and electromagnetic interactions It is shown that at a sufficiently large temperature a phase transition takes place after which almost all elementary particles in the hot super-dense matter become massless and weak interactions become long-range like electromagnetic interactions Analogous phenomena may take place with an increase of fermion density in cold dense matter, and also in the presence of external fields and currents Phase transitions in gauge theories lead to a time dependence of the masses of particles, of coupling constants and of the cosmological term in the expanding Universe, to the appearance of a domain structure of vacuum, to substance energy non-conservation, to a possibility of obtaining the 'hot' Universe starting with a 'cold' one, and to some other unusual effects important for cosmology and for elementary particle physics
605 citations
Abstract: The consequences of a vortex unbinding picture of two-dimensional superconductivity are worked out. Although there is no true finite-temperature phase transition, dirty superconducting films should display anomalous behavior below the BCS transition temperature and above an effective Kosterlitz-Thouless vortex unbinding temperature. In particular, both the conductivity and fluctuation diamagnetism behave like ξ
+
2
in this regime, where ξ+ is the correlation length calculated by Kosterlitz, ξ+-ξ
c
exp (B/T − T
c)1/2. We estimate ξc, B, and the vortex unbinding temperature, and determine the nonlinear resistivity below T
c. A recent theory of vortex dynamics, together with a time-dependent Ginzburg-Landau theory, lead to a determination of the frequency-dependent conductivity.
570 citations
TL;DR: A condensed monolayer of carbon on the surface of C-doped nickel single crystals has been observed at different bulk doping levels in the range of 10−1 to 1 at as discussed by the authors.
470 citations
TL;DR: In this article, a phenomenological theory is developed to describe the change of the local spontaneous polarization in the vicinity of a free surface of a ferroelectric thin film which is kept between metallic electrodes.
Abstract: A phenomenological theory is developed to describe the change of the local spontaneous polarization in the vicinity of a free surface of a ferroelectric thin film which is kept between metallic electrodes. It is shown that depolarizing field effects reduce the deviation of this local polarization from its bulk value, as compared to surface effects on phase transitions in other systems. In particular, the critical exponents describing the behavior of the local polarization in the vicinity of the Curie temperature ${T}_{C}$ are the same as the bulk exponents and only critical amplitudes are changed. This behavior contrasts to phase transitions in other systems (antiferroelectrics, ferro- and antiferromagnets, ordering alloys etc.) where different exponents are predicted. In order to improve upon this Landau-type theory by taking into account the effects of statistical fluctuations near ${T}_{C}$, recent results of renormalization-group theory are used to estimate logarithmic correction factors which should modify the critical behavior of the local polarization. Finally the experimental implications of our results are briefly discussed, and also a discussion of surface effects on the phase transition of dipolar magnets is given.
462 citations
TL;DR: This analysis indicates that d62-dipalmitoyl phosphatidylcholine in excess H2O undergoes a sharp phase transition at approximately 37 degrees C and that there appears to be hysteresis in the phase transition of approximately 1 degree C.
402 citations
TL;DR: A comparison of monolayer and bilayer systems on the basis of the absolute value of the molecular area of the phospholipid in the bilayer gel phase and the change in area at the bilayers and monolayers transition leads to the following conclusions.
376 citations
TL;DR: In this paper, the authors derive a criterion for the appearance of rounding due to local fluctuations in thermodynamic phase, which occurs when the free energy lowering due to taking advantage of local fluctuation in impurity density more than offsets the free-energy cost of the interface produced.
Abstract: Microscopic random quenched impurities may or may not produce rounding of a first-order phase transition. We derive a criterion for the appearance of rounding due to local fluctuations in thermodynamic phase. Such fluctuations occur when the free-energy lowering due to taking advantage of local fluctuations in impurity density more than offsets the free-energy cost of the interface produced. The argument also predicts the spatial scale of such phase fluctuations, when they occur. In some situations this scale is just the coherence length $\ensuremath{\xi}$; in others, the inhomogeneity develops over "domains," which may be much larger than $\ensuremath{\xi}$. Near a second-order transition our criterion reduces to the one due to Harris. We specifically discuss what happens when a first-order transition becomes second order as an external parameter is varied.
370 citations
PARC1
TL;DR: In this paper, the physics of superionic conductors with emphasis on the new insights that the research of the past few years has brought about is discussed. But the authors focus on the excitation spectrum and their relationship to high ionic conductivities.
TL;DR: In this article, the authors studied pure SU(2) gauge fields in four and five space-time dimensions and a compact SO(2)-gauge field in four dimensions.
Abstract: Using Monte Carlo techniques, we study pure SU(2) gauge fields in four and five space-time dimensions and a compact SO(2) gauge field in four dimensions. Ultraviolet divergences are regulated with Wilson's lattice prescription. Both SU(2) in five dimensions and SO(2) in four dimensions show clear phase transitions between the confining regime at strong coupling and a spin-wave phase at weak coupling. No phase change is seen for the four-dimensional SU(2) theory.
01 Jan 1979
TL;DR: In this article, the authors proposed a model for superionic conductors based on EXAFS, and showed that the model can be extended to other superionic properties, such as high frequency and low frequency.
Abstract: 1. Introduction.- References.- 2. Structure and Its Influence on Superionic Conduction: EXAFS Studies.- 2.1 Technique of EXAFS.- 2.1.1 Theory.- 2.1.2 Experiment.- 2.1.3 Data Reduction and Analysis.- 2.1.4 Contrast with Diffraction Studies.- 2.2 Structural Considerations for Superionic Conduction.- 2.2.1 General Considerations.- 2.2.2 Pair Potentials.- 2.2.3 Anharmonic Model.- 2.2.4 Excluded Volume Model and Cation-Anion Correlations.- 2.3 EXAFS Investigations of bcc Superionic Conductors: AgI.- 2.3.1 Early Structural Studies.- 2.3.2 EXAFS Study.- 2.3.3 Other Recent Structural Studies.- 2.3.4 Structural Model for Superionic Conduction in bcc Conductors.- 2.4 EXAFS Investigations of fcc Superionic Conductors: Cuprous Halides.- 2.4.1 CuI Structural Studies.- 2.4.2 EXAFS and Structural Models for CuI.- 2.4.3 CuBr.- 2.4.4 CuCl.- 2.4.5 Discussion.- 2.5 Summary.- References.- 3. Neutron Scattering Studies of Superionic Conductors.- 3.1 Neutron Scattering.- 3.1.1 Scattering function.- 3.1.2 Elastic Scattering.- 3.1.3 Inelastic Scattering.- 3.2 Structural Studies.- 3.2.1 AgI.- 3.2.2 Fluorites.- 3.2.3 ?-Alumina.- 3.3 Inelastic Studies.- 3.3.1 AgI.- 3.3.2 RbAg4I5.- 3.3.3 Fluorites.- 3.3.4 ?-Alumina.- 3.4 Conclusions.- References.- 4. Statics and Dynamics of Lattice Gas Models.- 4.1 General Theory of the Lattice Gas Model for Superionic Conductors.- 4.1.1 Definition of the Lattice Gas Model.- 4.1.2 Liouvillian Approach to Lattice Gas Dynamics.- 4.1.3 Master-Equation Approximation.- 4.1.4 High-Frequency Limit.- 4.1.5 Extension to All Frequencies.- 4.2 Extended Dynamical Theory.- 4.2.1 ?trap and Its Relation to a Soliton Model.- 4.2.2 Low-Frequency Conductivity.- 4.3 Applications to Silver Iodide and Hollandite.- 4.3.1 Silver Iodide: Structural Properties, Lattice Gas Representation.- 4.3.2 The Disorder Entropy of AgI.- 4.3.3 Dynami c Properties of ?-AgI.- 4.3.4 Collective Excitations in One-Dimensional Systems: Hollandite.- 4.4 Conclusions.- Appendix A.- Appendix B.- Appendix C.- References.- 5. Light Scattering in Superionic Conductors.- 5.1 Raman Scatteri ng.- 5.1.1 Silver Iodide.- 5.1.2 M+Ag4I5 (M+ = Rb+, K+, NH+4).- 5.1.3 Copper Halides.- 5.1.4 ?-Aluminas.- 5.1.5 Anion Conducting Fluorites.- 5.2 Low-Frequency Raman and Brillouin Scattering.- 5.2.1 Theoretical Considerations.- 5.2.2 Silver Halides.- 5.2.3 Other Superionic Conductors.- 5.3 Infrared Absorption and Frequency Dependent Conductivity.- 5.4 Conclusion.- References.- 6. Magnetic Resonance in Superionic Conductors.- 6.1 Theory of NMR Relaxation of and by Rapidly Diffusing Ions.- 6.1.1 General Correlation Functions and Interactions.- 6.1.2 Calculation of T1 and T2 from Correlation Functions.- 6.1.3 T1/T2 Ratio.- 6.1.4 Simple Random-Walk Values.- 6.1.5 Diffusion in Lower Dimensions.- 6.1.6 Effects of Correlated Hopping.- 6.2 Comparison with Experiment.- 6.2.1 Thermal Activation.- 6.2.2 Frequency Dependence.- 6.2.3 Prefactors.- 6.2.4 Coupling to Paramagnetic Impurities.- 6.3 Electron Paramagnetic Resonance.- 6.4 Structure Determination.- 6.5 Summary and Conclusions.- References.- 7. Phase Transitions in Ionic Conductors.- 7.1 Modern Theory of Phase Transitions.- 7.1.1 Landau Criteria.- 7.1.2 Renormalization Group.- 7.2 Models for Critical Behavior in Superionic Conductors.- 7.2.1 Quasi-Chemical Models.- 7.2.2 Lattice Gas Models.- 7.2.3 The Order Parameter for RbAg4I5.- 7.3 Critical Behavior of Physical Properties.- 7.3.1 Specific Heat.- 7.3.2 Ionic Conductivity.- 7.3.3 Acoustic Properties.- 7.3.4 Other Properties.- 7.4 Conclusions.- References.- 8. Continuous Stochastic Models.- 8.1 Models for Superionic Conductors.- 8.1.1 The Hamiltonian.- 8.1.2 Comparison of the Models from Microscopic Considerations.- 8.1.3 Correlation Functions.- 8.2 Continuous Models.- 8.2.1 Langevin Equation.- 8.2.2 Fokker-Planck Equation and Liouvillian.- 8.2.3 Continued-Fraction Expansion.- 8.2.4 Static Mobility, Diffusion Constant, dc Conductivity.- 8.2.5 Dynamic Mobility, ac Conductivity.- 8.2.6 Approximate Solutions and Similar Models.- 8.2.7 Dynamic Structure Factor for Jump Diffusion.- 8.2.8 Dynamic Structure Factor for Large Friction.- 8.2.9 Dynamic Structure Factor for General Friction.- 8.2.10 Light Scattering: Continuous and Continuum Models.- 8.2.11 Microscopic Foundation.- 8.3 Computer Simulations.- 8.4 Correlations Among the Mobile Ions.- References.- Additional References with Titles.
TL;DR: In this article, the authors studied phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement, and they applied the lessons learned from lattice Higgs models to understand the behavior of weak interactions at high temperature.
TL;DR: In this article, a spatial averaging of the equations describing two single-phase media is separately considered regarding the volumes occupied by either phase with allowance for the boundary conditions on phase interfaces.
TL;DR: In this paper, the authors applied the Renormalization group method to a new situation, that is, to critical fluids in the presence of uniform shear flow, where distortion and suppression of long wavelength fluctuations (k k c ) by the flow become essential, and the following unexpected features are encountered in the steady state: (i) Order parameter fluctuations with k k c are highly anisotropic but are suppressed on the average below their equilibrium levels.
TL;DR: In this paper, phase transitions and critical behaviour of covalently crosslinked polyacrylamide gels were described and analyzed in terms of the Flory-type mean field theory and the mode coupling theory.
TL;DR: In this paper, the electroclinic effect of chiral molecules was studied in the second-order, smectic-$A$-smectic-C$ phase transition.
Abstract: When a smectic-$A$ phase is composed of chiral molecules, it exhibits an electroclinic effect, i.e., a direct coupling of molecular tilt to applied field. The pretransitional behavior of the electroclinic effect in the $A$ phase is used to study the critical behavior near the second-order, smectic-$A$---smectic-$C$ phase transition. This behavior is measured by monitoring the change in birefringence of a sample as the electroclinic effect causes a tilt of the molecules. A large pretransitional effect is measured, and constants describing the critical behavior are determined.
TL;DR: In this article, a pressure-induced phase transition is observed at pressures above 25.6 kbar for anatase at 1 atm and at room temperature for the 197 cm-1 mode of six Raman active modes.
TL;DR: A wall-induced birefringence in a nematic liquid crystal above the nematicisotopic phase transition point has been observed for the first time in this article, and it is expected that this phenomenon will provide a useful tool to study the nature of aligning forces at liquid-crystal--solid interfaces.
Abstract: A wall-induced birefringence in a nematic liquid crystal above the nematic-isotopic phase transition point has been observed for the first time. It is expected that this phenomenon will provide a useful tool to study the nature of aligning forces at liquid-crystal--solid interfaces.
01 Mar 1979-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, an associated solution model is applied to describe the thermodynamic behavior of Fe-S liquid, assuming the existence of FeS species in addition to Fe and S in the liquid.
Abstract: An associated solution model is applied to describe the thermodynamic behavior of Fe-S liquid. This model assumes the existence of ‘FeS’ species in addition to Fe and S in the liquid. With two solution parameters for each of the binaries Fe-‘FeS’ and ‘FeS’-S, this model accounts for the compositional dependence of the thermodynamic properties of Fe-S liquid from pure Fe to pure S over a wide range of temperature. The binary Fe-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘FeS’ to Fe and S. Using this model for the liquid phase and a defect thermodynamic model for the pyrrhotite phase, the Fe-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of pyrrhotite at all temperatures. Both the thermodynamic and phase diagram data are obtained from the literature.
TL;DR: A model for protein-lipid interactions in bilayer membranes where the proteins are very dilute is extended to higher protein concentration, and it is found that proteins may change the lipid phase transition temperature and that they weaken the phase transition.
Abstract: A model for protein-lipid interactions in bilayer membranes where the proteins are very dilute is extended to higher protein concentration, where appreciable lipid-mediated protein-protein interactions occur. It is found that proteins may change the lipid phase transition temperature and that they weaken the phase transition. There exists a critical protein concentration above which the sharp lipid phase transition is abolished. The model also qualitatively reproduces several experimental observations on the physical behavior of bilayers formed from mixtures of cholesterol and phosphatidylcholines.
TL;DR: BaMnF4 as mentioned in this paper is a pyroelectric ferromagnet which displays a number of unusual physical characteristics, some of which are unique, such as its dielectric anomalies at its Neel temperature.
Abstract: BaMnF4 is a pyroelectric ferromagnet which displays a number of unusual physical characteristics, some of which are unique. It has the only known continuous antiferroelectric phase transition. It has two- and three-dimensional antiferromagnetic ordering temperatures. It is a weak ferromagnet with ferromagnetism caused by the linear magnetoelectric effect-the only case yet known. It exhibits dielectric anomalies at its Neel temperature. At high temperatures its dielectric constant diverges with increasing temperature; a ferroelectric phase transition would occur if the crystals did not melt first. At high temperatures BaMnF4 is also an anisotropic ionic conductor. The antiferroelectric phase is incommensurate. The incommensurate phase appears unusual in that its translation vector is temperature-independent. Sound velocity measurements made near the antiferroelectric phase transition temperature demonstrate the presence of and characteristics for a relaxational mode; this mode couples strongly to transverse acoustic phonons and is probably the 'phason' predicted theoretically for incommensurate lattices. This article reviews theory and experiment for this unusual material, including neutron, Raman and Brillouin scattering; X-ray, dielectric and conductivity measurements; magnetic resonance and susceptibility studies.
TL;DR: In this paper, the Euclidean vacuum in quantum chromodynamics (QCD) can be regarded as a four-dimensional ensemble of permanent color magnetic dipoles (instantons and meron pairs), with a positive paramagnetic susceptibility.
Abstract: We show that the Euclidean vacuum in quantum chromodynamics (QCD) can be regarded as a four-dimensional ensemble of permanent color magnetic dipoles (instantons and meron pairs), with a positive paramagnetic susceptibility. Standard techniques are used to discuss the interactions of this medium for moderate densities. In the presence of color fields (due to quarks), large scale instantons (and other fluctuations) are suppressed, the density is low, and the system is easily treated. Below a critical field strength, this dilute phase is unstable and a first-order phase transition occurs to a dense phase consisting of closely packed instantons and merons, and possibly other things. In this dense phase, we believe that the permeability is infinite (perfect paramagnetism) and thus the normal QCD vacuum cannot tolerate color fields. This leads to a strikingly simple baglike picture of hadrons, as consisting of quarks confined to a region of space-time which is in a very dilute (abnormal) vacuum phase, in equilibrium with the dense vacuum (normal) phase outside the bag. The quarks are confined to the region of dilute phase where their dynamics are simple; and, as we show, they are shielded from the large-scale fluctuations outside the bag. We present a derivation of the static bag for heavy quarks and an estimate (to within a factor of two) of the bag constant. We further discuss some features of the resulting bag model including chiral-symmetry breaking and surface effects.
TL;DR: In this article, the Monte Carlo renormalization-group method was used to study the three-state Potts model in three and four dimensions, and they found a first-order transition without an associated discontinuity fixed point.
Abstract: We have used the Monte Carlo renormalization-group method to study the three-state Potts model in three and four dimensions. In both cases, we find a first-order transition without an associated discontinuity fixed point. The transition in three dimensions is ''almost second order'' in the sense that some evidence was found for the existence of second-order fixed points associated with singularities in the metastable region just beyond the first-order transition.
TL;DR: The spinodal decomposition (SD) mechanism is based on the Ginzburg-Landau expression for the free energy of an inhomogeneous system as mentioned in this paper, and it has been shown to be effective in the experimental study of SD in alloys, glasses, and binary liquid mixtures.
Abstract: Considerable deviations from equilibrium conditions are observed for nonstatic, first-order phase transitions. In some cases, unstable (labile) phase states may precede the onset of the phase transition. The relaxation of the system is then accompanied by an enhancement of random inhomogeneities and the appearance of a modulated intermediate structure. This mechanism of the initial stage of a phase transition is called spinodal decomposition (SD). Theoretical and experimental studies of SD in two-component systems are reviewed in this paper. Thermodynamic stability and the possibility of SD in one-component liquid-vapor systems and an alternative nucleation mechanism are discussed. The phenomenological theory of SD is based on the Ginzburg-Landau expression for the free energy of an inhomogeneous system. A linearized diffusion equation is derived, for which thermodynamically unstable states have exponentially increasing solutions for the Fourier components of composition. Subsequent refinements of SD theory take into account thermal fluctuations and involve the derivation of the kinetic equation for the distribution functional. Diffraction methods are the most effective in the experimental study of SD in alloys, glasses, and binary liquid mixtures. So far, the agreement between theory and experiment must be regarded as only qualitative.
TL;DR: A second order phase transition has been found in Na3Zr2Si2PO12 by three independent techniques as mentioned in this paper, including ac-impedance and X-ray diffraction powder patterns, and specific heat measurements showed a clear indication of a phase transition at 420 K with ΔH = 2.07 kJ mol−1.
TL;DR: In this paper, it was shown that even the preferred directions of the molecules in a smectic A phase will make a nonzero angle with the layer normal, and from the data examined, this angle, ϑm, appears to be about 10-15° for the compound TCOOB (trans‐1,4−cyclohexane−di−n−octyloxybenzoate).
Abstract: A previous paper demonstrated that the orientational disorder present in all smectic A phases causes most molecules to make fairly large angles with the normal to the smectic plane. Thus, the molecular directions form a diffuse cone around the layer normal. It is now argued that even the preferred directions of the molecules in a smectic A phase will make a nonzero angle with the layer normal, and from the data examined, this angle, ϑm, appears to be about 10–15 ° for the compound TCOOB (trans‐1,4‐cyclohexane‐di‐n‐octyloxybenzoate). The smectic A‐to‐C phase transition is found to have two aspects in the diffuse‐cone model: the distribution of the molecular directions around the layer normal loses its rotational symmetry at the phase transition temperature TA–C, and the angle ϑm starts increasing sharply at a temperature Tt. In most cases these two temperatures are probably equal. The increase of ϑm with decreasing temperature in the smectic C phase of TCOOB can be described by a (Tt−T)0.35 dependency superimposed on a much smaller linear temperature dependency already present in the smectic A phase.