A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Studies of electronic structure by x-ray Raman and emission spectroscopy: applications to MgB2 superconductors and high pressure physics

X-ray Raman scattering and x-ray emission spectroscopies were used to study the electronic properties and phase transitions in several condensed matter systems. The experimental work, carried out at the European Synchrotron Radiation Facility, was complemented by theoretical calculations of the x-ray spectra and of the electronic structure. The electronic structure of MgB2 at the Fermi level is dominated by the boron σ and π bands. The high density of states provided by these bands is the key feature of the electronic structure contributing to the high critical temperature of superconductivity in MgB2. The electronic structure of MgB2 can be modified by atomic substitutions, which introduce extra electrons or holes into the bands. X ray Raman scattering was used to probe the interesting σ and π band hole states in pure and aluminum substituted MgB2. A method for determining the final state density of electron states from experimental x-ray Raman scattering spectra was examined and applied to the experimental data on both pure MgB2 and on Mg(0.83)Al(0.17)B2. The extracted final state density of electron states for the pure and aluminum substituted samples revealed clear substitution induced changes in the σ and π bands. The experimental work was supported by theoretical calculations of the electronic structure and x-ray Raman spectra. X-ray emission at the metal Kβ line was applied to the studies of pressure and temperature induced spin state transitions in transition metal oxides. The experimental studies were complemented by cluster multiplet calculations of the electronic structure and emission spectra. In LaCoO3 evidence for the appearance of an intermediate spin state was found and the presence of a pressure induced spin transition was confirmed. Pressure induced changes in the electronic structure of transition metal monoxides were studied experimentally and were analyzed using the cluster multiplet approach. The effects of hybridization, bandwidth and crystal field splitting in stabilizing the high pressure spin state were discussed. Emission spectroscopy at the Kβ line was also applied to FeCO3 and a pressure induced iron spin state transition was discovered.

Models for spin-state transitions in solids

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

Raman study of pressure-induced structural transitions in CsIO4 to 12 GPa

High pressure Raman scattering studies have been carried out on cesium periodate (CsIO4) using the diamond anvil cell. Three pressure-induced phase transitions occur in the range 0.1�12 GPa as indicated by abrupt changes in the Raman spectra, and pressure dependence of the phonon frequencies. The transitions are observed at 1.5, 4.5 and 6.2 GPa in the increasing pressure cycle. A large hysteresis is noticed for the reverse transition when releasing the pressure. The high pressure phase is nearly quenchable to ambient pressure. The nature of the pressure-induced transitions are discussed in terms of the sequence of pressure-induced transitions expected for scheelite-pseudoscheelite structure ABO4 compounds from crystal chemical considerations. For the softening of the two high frequency internal modes, a pressure-induced electronic change involving the 5 d states of cesium and 5 p states of iodine is invoked.

First-order structural transition in the magnetically ordered phase of Fe(1.13)Te

Specific heat, resistivity, magnetic susceptibility, linear thermal expansion (LTE), and high-resolution synchrotron x-ray powder diffraction investigations of single crystals Fe(1+y) Te (0.06 <= y <= 0.15) reveal a splitting of a single, first-order transition for y <= 0.11 into two transitions for y >= 0.13. Most strikingly, all measurements on identical samples Fe(1.13)Te consistently indicate that, upon cooling, the magnetic transition at T(N) precedes the first-order structural transition at a lower temperature T(s). The structural transition in turn coincides with a change in the character of the magnetic structure. The LTE measurements along the crystallographic c axis display a small distortion close to T(N) due to a lattice striction as a consequence of magnetic ordering, and a much larger change at T(s). The lattice symmetry changes, however, only below T(s) as indicated by powder x-ray diffraction. This behavior is in stark contrast to the sequence in which the phase transitions occur in Fe pnictides.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Effect of Molecular Flexibility on the Nematic-to-Isotropic Phase Transition for Highly Biaxial Molecular Non-Symmetric Liquid Crystal Dimers

In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the alpha-(4-cyanobiphenyl-4'-yloxy)-omega-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N-B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N-U)-isotropic (I) phase transition is first-order in nature, whereas the N-B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).

Study of crystal structure and phase transition studies in perovskite-type oxides using powder-diffraction techniques and symmetry-mode analysis.

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Effect of information transmission on cooperative behavior

Considering the fact, in the real world, that information is transmitted with a time delay, we study an evolutionary spatial prisoner's dilemma game where agents update strategies according to certain information that they have learned. In our study, the game dynamics are classified by the modes of information learning as well as game interaction, and four different combinations, i.e. the mean-field case, case I, case II and local case, are studied comparatively. It is found that the time delay in case II smoothes the phase transition from the absorbing states of C (or D) to their mixing state, and promotes cooperation for most parameter values. Our work provides insights into the temporal behavior of information and the memory of the system, and may be helpful in understanding the cooperative behavior induced by the time delay in social and biological systems.

Phase transition and transition kinetics of a thermotropic poly(amide-imide) derived from 70% pyromellitic dianhydride, 30% terephthaloyl chloride, and 1,3-bis[4-(4 '-aminophenoxy)cumyl]benzene

The phase transition and transition kinetics of a liquid crystalline copoly(amide-imide) (PAI37), which was synthesized from 70 mol% pyromellitic dianhydride, 30 mol% terephthaloyl chloride, and 1,3-bis[4-(4'-aminophenoxy)cumyl]benzene, was characterized by differential scanning calorimetry, polarized light microscopy, X-ray diffraction, and rheology. PAI37 exhibits a glass transition temperature at 182 degreesC followed by multiple phase transitions. The crystalline phase starts to melt at similar to 220 degreesC and forms smectic C (S-C) phase. The Sc phase transforms into smectic A (S-A) phase when the temperature is above 237 degreesC. The S-C to S-A transition spans a broad temperature range in which the S-A phase vanishes and forms isotropic melt. The WARD fiber pattern of PAI37 pulled from the anisotropic melt revealed an anomalous chain orientation, which was characterized by its layer normal perpendicular to the fiber direction. The transition kinetics for the mesophase and crystalline phase formation was also studied.

Phase identification in a series of liquid crystalline TPP polyethers and copolyethers having highly ordered mesophase structures. 7. Phase structures in a series of copolyethers containing odd and even numbers of methylene units of different compositions

A series of liquid crystalline copolyethers have been synthesized from 1-(4-hydroxy-4'-biphenyl)-2-(4-hydroxyphenyl)propane with 1,7-dibromoheptane and 1,12-dibromododecene [coTPPs(7/12)], which represents copolyethers containing both odd and even numbers of methylene units. The molar ratio of odd to even methylene units in this series ranges from 1/9 to 9/1. The coTPPs(7/12) exhibit multiple phase transitions during cooling and heating in differential scanning calorimetry experiments. For all these thermal transitions, a small undercooling and superheating dependence is observed upon cooling and heating at different rates. Three types of phase behaviors can be classified in coTPPs(7/12) on the basis of the structural analyses by wide-angle X-ray diffraction on powder and fiber samples and by electron diffraction experiments in transmission electron microscopy. At room temperature, highly ordered smectic and smectic crystal (SC) phases are identified in coTPPs(7/12: 1/9 and 2/8), which is similar to the homopolymer TPP(m = 12). The coTPPs(7/12: 3/7, 4/6, and 5/5) possess a hexagonal columnar (Phi(H)) phase in which the molecular and columnar axes are parallel to the fiber direction and perpendicular to the hexagonal lateral packing. The coTPPs(7/12: 6/4, 7/3, and 8/2) possess a tilted hexagonal columnar (Phi(TH)) phase with a single tilt angle which increases with the increasing composition of the seven-numbered methylene units. However, in coTPP(7/12: 9/1), a Phi(TH) phase with multiple tilt angles is found. Upon heating, phase structures in most coTPPs(7/12) involving the columnar phases enter directly into the nematic (N) phase, while the coTPP(7/12: 1/9) exhibits a highly ordered smectic F (S-F) phase before it reaches the N phase. One exception is found in coTPP(7/12: 2/8), wherein the transformation from the S-F to Phi(H) occurs prior to the N phase. Combining the copolymer phase behaviors observed with the corresponding homopolymers TPP(n = 7) and TPP(m = 12), a phase diagram describing transition temperatures with respect to the composition can be constructed.

Phase identification in a series of liquid crystalline TPP polyethers and copolyethers having highly ordered mesophase structures. 6. Structure changes from smectic to columnar phases in a series of copolyethers containing odd and even numbers of methylene units in equal molar composition

A series of liquid crystalline copolyethers has been synthesized from 1-(4-hydroxy-4'-biphenyl)-2-(4-hydroxyphenyl)propane and different alpha,omega-dibromoalkanes [coTPP(n/m)]. In this report, coTPPs having n = 5, 7, 9, 11 and m = 12 are studied, which represent copolyethers having both varying odd number and a fixed even number of methylene units. The compositions were fixed at an equal molar ratio (50/50). These coTPPs(nlm) show multiple phase transitions during cooling and heating in differential scanning calorimetry experiments. The undercooling dependence of these transitions is found to be small, indicating that these transitions are close to equilibrium, Although the coTPPs possess a high-temperature nematic (N) phase, the periodicity order along the chain direction is increasingly disturbed when the length of the odd-numbered methylene units decreases from n 11 to 5. in the coTPPs(5/12, 7/12, and 9/12), wide-angle X-ray diffraction experiments at different temperatures show that, shortly after the N phase formation during cooling, the lateral molecular packing improves toward a hexagonal lattice, as evidenced by a gradual narrowing of the scattering halo. This process represents the possible existence of an exotic N phase, which serves as a precursor to the columnar (Phi(H)) phase. A further decrease in temperature leads to a (PH phase having a long-range ordered, two-dimensional hexagonal lattice. In coTPP(11/12), the phase structures are categorized as highly ordered and tilted, smectic and smectic crystal phases, similar to homoTPPs, such as the smectic F (S-F) and smectic crystal G (SCG) phases. An interesting observation is found for coTPP(9/12), wherein a structural change from the high-temperature Phi(H) phase to the low-temperature S-F phase occurs. It can be proven that, upon heating, the well-defined layer structure disappears and the lateral packing remains hexagonal. The overall structural differences in this series of coTPPs between those of the columnar and highly ordered smectic phases are related to the disorders introduced into the layer structure by the dissimilarity of the methylene unit lengths in the comonomers.

Nonlinearity of the complex crystals with O-H bond

A systematic and quantitative research on the structure-property correlation has been carried out in KH2PO4 (KDP), NH4H2PO4 (ADP) and HIO3, based on the dielectric theory of complex crystals and the Levine bond charge model. We, for the first time, successfully solve the problems in the calculation of the nonlinearities of the complex inorganic nonlinear optical (NLO) crystals, which have O-H bonds in their crystal structures. We do this by introducing the bond-valence equation we have set up, calculating the nonlinear optical tensor coefficients d(ijk) of these three compounds, quantitatively determining the contributions of each type of bond to the total second-order NLO tensor coefficient (d(ijk)) of the crystal, and presenting the bond parameters and the linear properties of each kind of bond. For the first time, the NLO coefficient d(36) for ADP was calculated. All calculated results are in good agreement with experimental data. We found that O-H bonds also play an important role in these crystals, except for in the important anionic groups (PO4 groups and IO3 groups). All the results thus calculated show that our method is useful in evaluating the NLO coefficients of the inorganic NLO crystals containing O-H bonds in their structures, and should be a useful tool toward the future research into new nonlinear optical materials of this kind.