Complicated Phase Diagram Research Articles

Cubic phases of 4′-n-alkoxy-3′-nitrobiphenyl-4-carboxylic acids (ANBC-n)

The structure of the thermotropic cubic phases of 4′- n -alkoxy-3′-nitrobiphenyl-4-carboxylic acids (ANBC- n , where n indicates the number of carbon atoms in the alkoxy group) was studied by X-ray diffraction. For the homologues with n = 15, 16, 17, and 18, the cubic phase was of an Ia 3 d type, whereas the homologues with n = 19, 20, and 21 exhibited an Im 3 m cubic structure; for these seven homologues the same type of cubic structure was observed both on heating and cooling. Further lengthening of the alkoxy chain to n = 22 and 26, however, gave two types of cubic structure in the cubic phase region on heating, one with Im 3 m symmetry in the low temperature region and the other with Ia 3 d symmetry in the high temperature region. On cooling, the two homologues exhibited the Ia 3 d cubic structure only. This is the first example in the cubic phase region of a series of homologues containing two types of structure, dependent on temperature and n . Such a complicated phase diagram in the cubic region is clearly understood qualitatively in terms of Gibbs free energy-temperature diagrams. The dependence of structural parameters such as the cubic lattice constant on the alkoxy chain length n are also presented and discussed.

Relationship between local structure and phase transitions of a disordered solid solution.

The Pb(Zr,Ti)O3 (PZT) disordered solid solution is widely used in piezoelectric applications owing to its excellent electromechanical properties. Six different structural phases have been observed for PZT at ambient pressure, each with different lattice parameters and average electric polarization. It is of significant interest to understand the microscopic origin of the complicated phase diagram and local structure of PZT. Here, using density functional theory calculations, we show that the distortions of the material away from the parent perovskite structure can be predicted from the local arrangement of the Zr and Ti cations. We use the chemical rules obtained from density functional theory to create a phenomenological model to simulate PZT structures. We demonstrate how changes in the Zr/Ti composition give rise to phase transitions in PZT through changes in the populations of various local Pb atom environments.

THE FASCINATING NEW PHYSICS OF SOME OLD BCS SUPERCONDUCTORS

We consider the pairing state due to the usual Bardeen-Cooper-Schrieffer mechanism in substances where the Fermi surface forms pockets around several points of high symmetry. The symmetry imposed on the multiple pocket positions can give rise to a multidimensional nontrivial superconducting order parameter. A complicated mechanism is not required for unusual superconductivity to exist, just the usual phonon attraction and Coulomb repulsion. Time reversal symmetry is broken, so the superconducting state also has orbital magnetism. In some sense, these superconductors are similar to superfluid3 He, which is known to have an 18-dimensional order parameter and a complicated phase diagram. We suggest several candidate substances where ordering of this kind may appear and discuss how these phases may be identified. Superconductivity in these new materials is expected to be much less sensitive to impurities than in other non s-wave superconductors.1

Direct observation of the modulation of the 4f-electron orbital state by strong p-f mixing in CeSb.

Low-temperature x-ray diffraction experiment has been carried out to investigate the 4 f-electron state of the low carrier density system CeSb which shows complicated magnetic phase diagrams at low temperatures. The scattering pattern of the satellite peaks observed in the magnetically ordered state AFP3 is explained well by the model which takes into account both the lattice and charge modulations corresponding to the complex magnetic structure. The present result gives direct evidence for the strong modulation of the 4 f-electron orbital state in CeSb due to the combined effect of the strong p-f mixing and carrier localization.

Creating Chiral Surfaces for Enantioselective Heterogeneous Catalysis: R,R-Tartaric Acid on Cu(110)

One of the most successful ways of inducing enantioselectivity in a heterogeneous catalytic system is by the adsorption of chiral “modifier” molecules on the reactive metal surface. However, little is known about the nature of the active sites present on the modified metal surface and how such modifiers bestow chirality to an achiral metal surface. In this paper we report the behavior of R,R-tartaric acid adsorption on a Cu(110) surface using high-resolution surface analytical techniques. R,R-Tartaric acid is known to be an extremely successful modifier molecule for the enantioselective hydrogenation of methyl acetoacetate, the simplest β-keto ester, to the R-enantiomer of the product molecule methyl 3-hydroxybutyrate. A combination of low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), and Fourier transform reflection−absorption infrared spectroscopy (FT-RAIRS) techniques has allowed us to demonstrate that a complicated adsorption phase diagram exists for this system. A rich vari...

Magnetic characterisation of Tm/Y and Tm/Lu superlattices

Single-crystal Tm/Y and Tm/Lu superlattices have been grown using molecular beam epitaxy and their chemical structures have been determined using X-ray diffraction. Magnetisation measurements have revealed a more complicated phase diagram than that of pure Tm. Application of a field along the c-direction gave rise to an extra transition, and transitions were detected for the superlattices when the field was applied along the b-axis. In neutron diffraction studies, c-axis, longitudinally modulated magnetic structures were found for both Tm/Y and Tm/Lu, which propagate coherently through the non-magnetic layers. In the case of Tm/Lu superlattices there is evidence for ordering of the basal plane components.

MAGNETIC PROPERTIES OF Ti-Co SOLID SOLUTIONS

Thermal variation of the magnetic susceptibility for Ti-Co solid solutions is reported. Cobalt, by alloying acts on the transition Néel temperature giving rise to a complicated magnetic phase diagram. The change of the Fermi level is the main mechanism in the critical temperature, T N , shift.

Langmuir monolayers as disordered solids: Strain-tilt-backbone coupling and natural order parameters for the swiveling transitions

Multistability of Langmuir monolayers, in particular those composed of fatty acids, is reflected by a very rich and complicated phase diagram. We argue that strain-tilt-backbone coupling determines the behavior described by that diagram. Following the solid state approach, we show that a natural order parameter set is defined by thermal averages of spherical harmonics and strain tensor components. In addition, we show that the backbone order parameter can be conveniently represented by an elastic dipole tensor. Treating Langmuir monolayers as disordered solids, we have derived an orientational entropy contribution to the free energy. The swiveling transition between L2(L2h) and L2′(L2*) phases is discussed in detail and is conveniently described in terms of the proposed order parameters. We discuss why the change in the distortion direction of the 2D unit cell tracks the change in tilt direction of the molecules, and also why the cell dimensions involved in the swiveling transition are the same in both phases.

Stability of Zr-Al alloys

The Zr-Al alloy system has one of the more complicated binary transition-metal aluminide phase diagrams: ten reported intermediate phases belonging to four different crystal systems. In order to understand the competition among different structures and concentrations, the heats of formation of a number of different possible structures were calculated using both all-electron and pseudopotential methods. The ${\mathrm{Zr}}_{5}{\mathrm{Al}}_{3}$ $(\mathrm{tI}32)$ and ${\mathrm{Zr}}_{5}{\mathrm{Al}}_{4}$ $(\mathrm{hP}18)$ phases are predicted to be high-temperature phases. The existence of the large number of observed phases is attributed to the fact that the heats of formation for ${\mathrm{Zr}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ for $x=0.25--0.75$ fall on a nearly straight line, suggesting that these phases should have narrow composition ranges. In addition, a simple procedure to modify and test the pseudopotentials is presented and shown to yield calculated metallic alloy properties in good agreement with the all-electron results.

Theoretical Studies on Surface Electronics States. Super Structure of Alkali-atom Adsorbed Metal Surfaces-A First-principles Approach.

Several kinds of super structure have been recently observed by LEED measurements in alkali-atom adsorbed metal surfaces and attributed to substitutional adsorption in addition to simple adatom one. A first-principles study on the stable structure and its stability of such alkali-adsorbed systems, Cu(001)-Li and Al(001)-Na, is reviewed. Assuming the alkali-atom coverage of 0.5 and considering simple-adatom type c(2×2) and substitutional (2×1) and c(2×2) geometry, the most stable structure of Cu(001)-Li and Al(001)-Na is found to be substitutional (2×1) and c(2×2), respectively, being consistent with experiments. Mechanism of the stability is interpreted in terms of surface-vacancy formation and chemical bond formation. In any cases, the energy difference between these adsorbed systems is quite small (the order of 0.1 eV per adatom or less) and a complicated phase diagram may be possibly expected.

RECENT PROGRESS IN THEORETICAL UNDERSTANDING OF HEAVY FERMION SYSTEMS

A key to understand the physics of heavy Fermion systems is the competition between the RKKY interaction and the Kondo screening effect of magnetic moments. The Kondo lattice model is a theoretical model for which one can study the interplay. Recently the ground state phase diagram of the one‐dimensional Kondo lattice model has been completed. After reviewing the properties of the three phases in the phase diagram we discuss the Kondo insulator in one‐dimension with particular emphasis on the difference between the spin excitation gap and the charge excitation gap. We argue that the Kondo insulators may be distinguished from the ordinary band insulators by the difference between the two gaps. Another topic which is discussed in this article is the complicated magnetic phase diagram of the low‐carrier‐density system of cerium monopnictides. We propose that the new mechanism which exists for Kondo semimetals may be responsible for the complicated magnetic structures in these compounds.

Mean-Field Theory of an Axial ChiralXYModel with Anisotropy

The finite-temperature phase diagram is studied for an axial chiral X Y model with p -fold anisotropy in which the nearest neighbor spins along a particular direction are coupled through the chiral interaction while those in a plane perpendicular to this direction are coupled ferromagnetically; the ground-state of the model is known to have a complicated phase diagram characterized by the devil's staircase. By using the mean-field theory, the cases of p = 2, 3, 4 and 6 are investigated. The global phase diagram is constructed by employing the minimization eigenvalue method to find the spin configuration that minimizes the free energy. Certain properties of the phase diagram are studied analytically. The structure of the finite-temperature phase diagram is found to change qualitatively with p , though the qualitative feature of the ground-state phase diagram is known to be independent of p ≥2.

Vortex-lattice phase transitions in Bi2Sr2CaCu2 O8 crystals with different oxygen stoichiometry.

The vortex-lattice phase transitions in Bi 2Sr2CaCu2O8 crystals with various oxygen stoichiometry are studied using local magnetization measurements. Three new findings are reported: The first-order phase transition line at elevated temperatures shifts upward for more isotropic overdoped samples. At lower temperatures another sharp transition is observed that results in enhanced bulk pinning in the second magnetization peak region. The two lines merge at a multicritical point at intermediate temperatures forming apparently a continuous phase transition line that is anisotropy dependent. PACS numbers: 74.60.Ec, 74.60.Ge, 74.60.Jg, 74.72.Hs The mixed state of high-temperature superconductors (HTSC) has a very complicated phase diagram. The nature of the different vortex phases and the thermodynamic transitions between them are of fundamental interest, and are the subject of substantial recent theoretical and experimental efforts [1 ‐ 10]. It is generally accepted that the high anisotropy plays a crucial role in the richness of the phase diagram of HTSC. Nevertheless, a systematic study of the anisotropy effects is quite complicated and was limited so far by the lack of a well defined phase boundary that could be monitored as a function of the anisotropy. A recent advance in local measurements has revealed a sharp step in magnetization due to a first-order vortex-lattice phase transition in Bi2Sr2CaCu2O8 (BSCCO) crystals [10]. Such a clearly defined fundamental transition is thus a natural candidate for an investigation of the anisotropy effects in HTSC, and this paper presents a first study in this direction. Another intriguing feature of the phase diagram of many HTSC crystals, and BSCCO in particular, is the anomalous second magnetization peak at lower temperatures. The associated increase of magnetization with magnetic field has been attributed to surface barrier effects [11], crossover from surface barrier to bulk pinning [12], sample inhomogeneities [13], dynamic effects [14], and 3D to 2D transitions [15‐ 17]. Our local measurements indicate that a very abrupt upturn in the bulk critical current occurs at the onset of the second peak in BSCCO. We postulate that this behavior is triggered by an underlying thermodynamic phase transition of the flux-line lattice. Furthermore, for the different anisotropy crystals the two phase transition lines are found to form, apparently, one continuous transition line that changes from first to possibly second order at

Phase Behavior of Ionic Microemulsions

AbstractNon‐polar oils and water can form thermodynamically stable quasi‐homogeneous (colloidal) mixtures (called microemulsions) in the presence of relatively large amounts (several %) of ionic surfactants. If the surfactant contains a single hydrocarbon chain (e.g. Sodium Dodecyl Sulphate) the presence of a non‐ionic cosurfactant (e.g. hexanol) and electrolyte (concentration of the order 0.1 M) is essential. With a double chain surfactant (e.g. Aerosol OT) the cosurfactant can be missed. At increasing concentrations of electrolyte and/or cosurfactant the nature of the microemulsion changes from droplets of oil in water via a presumably bicontinuous pattern to droplets of water in oil. It should be obvious that thermodynamic stability requires the interfacial tension between water and oil to be low (order of 0.01‐0.1 mN m−1) so that the dispersion entropy can offset the interfacial free energy. At these low interfacial tensions the influence of curvature on the interfacial tensions becomes important. It turns out that a given amount of surfactant (and co‐surfactant) can only disperse a limited amount of oil in water or of water in oil or of water and oil into one another and therefore a microemulsion may be in equilibrium with non colloidal oil and/or water phases. In the bicontinuous microemulsion oil and water may have a geometrically irregular interface or they may form lamellae of more or less constant thickness or other structures, such as a “molten cubic phase”. These equilibria lead to very interesting, but rather complicated phase diagrams. It will be discussed by what mechanisms the various components of the mixture influence the interfacial tension and promote the stability of the microemulsion and how this depends on the chemical nature of the components.

CeCu 2Si 2: Renormalized band structure, quasiparticles and co-operative phenomena

The prototype heavy fermion compound CeCu 2Si 2 exhibits a rather complicated phase diagram at low temperatures. Recently, a number of phase transitions at temperatures above the superconducting T c were discovered. These transitions seem to be correlated with the appearance of superconductivity. We calculate the quasiparticles in CeCu 2Si 2 by means of the renormalized band structure method. The results for the Fermi surface suggest that the new phase transition may be driven by a topological transition in the system of the heavy quasiparticles.

Physical properties of antiferromagnetic ternary compound SmPd 2Al 3

Measurements of electrical resistivity, magnetic susceptibility and specific heat have been performed on a new ternary compound SmPd 2Al 3. The results indicate that the valence of Sm ions is almost trivalent and that SmPd 2Al 3 has a complicated magnetic phase diagram below 12 K.

Superstructures and Superconductivity

Heavy fermion materials - so named because their conduction electrons behave as though they had extra mass - are like the cuprates in that they exhibit unusual superconducting properties. By the time the cuprates had been discovered, a good understanding of these materials was in hand. Unlike theories of high-[Tc] superconductivity, however, ideas about heavy fermions have not been the subject of great controversy. Thus, most of the effort in this backwater of condensed matter physics has focused on certain details of the behavior of one particularly well-studied compounds, UPt[sub 3]. The cause for sustained interest was that the process of developing ever more elaborate explanations for ever more elaborate experiments did not seem to converage. A recent paper by Midgley et al. reporting modulations in the crystal lattice of UPt[sub 3] suggests that theory and experiment might finally converge in a way that, while it does not threaten the broad understanding of heavy fermion systems, involves a degree of freedom ignored until now even in the face of past experience with elemental metallic uranium. Their transmission electron micrograph evidence for the existence of an incommensurate lattice modulation in UPt[sub 3] implicates this modulation as a probable source of themore » double superconducting transitions. Remarkably, the superconducting and magnetic coherence lengths, and the now discovered modulation period, are all of the same magnitude. For some time people have felt that stacking faults might be relevant to the properties of UPt[sub 3], but these new results are distinct from this. What Midgley et al. suggest is that the complicated superconducting phase diagram of UPt[sub 3] derives from the internal strain field caused by the modulation, and that this strain field lifts the degeneracy associated with unconventional pairing.« less

Calorimetry and X-ray diffraction investigations of the binary system neopentylglycol-pentaerythritol

Experimental measurements, mainly differential scanning calorimetry (DSC) and variable-temperature X-ray spectra (Guinier-Simon) are presented for different compositions ( X pe ) of the binary system pentaerythritol-neopentylglycol. Calorimetric results are analysed through the “shape factors method”, and compared to those of X-ray recordings, allowing the presentation of the unusually complicated phase diagram proposed here, with the presence of metatectic, peritectic and eutectoi'd invariants.

Magnetic phase diagrams of the antiferromagnetic planar model on a stacked triangular lattice.

The classical antiferromagnetic planar (XY) model on a simple hexagonal lattice with an applied in-plane magnetic field is studied. With only nearest-neighbor exchange interactions along the c axis, ${\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}$==1, and in the basal plane, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, the ground-state (T=0) phase diagram (H,${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$) exhibits an unexpected richness of ordered states. Finite-temperature effects treated within a molecular-field approximation for a number of values of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ reveal complicated (H,T) phase diagrams. Detailed Monte Carlo simulation results are presented for the case of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=1 and compared with recent predictions associated with chiral multicritical behavior.

The magnetic phase transitions in Ce-monopnictides, strong p-f mixing effect

Specific heat of CeBi and CeSb, as well as LaBi and LaSb, was measured from 1.7 to 60 K under magnetic fields of up to 10 T. A Kondo like peak persists in CeBi in whole the studied region. In CeSb the effect of magnetic order is more significant but the similar situation exists, even though crossover from the Γ 7 dominated to Γ 8 dominated Kondo states appears. The γ-value is about 20 mJ/mol K 2 in both materials with weak field dependence. Phonon softening effect was also observed. It was shown that the extended ANNNI model including non-linear interactions can explain the essential feature of the complicated phase diagram in CeSb fairly satisfactorily.