Incipient Phase Transition Research Articles

Complex phase diagram and supercritical matter.

The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquidlike and gaslike, however, suggest "supercritical boundaries." Here we provide a mathematical description of these phenomena by revisiting the Yang-Lee theory and introducing a complex phase diagram, specifically a four-dimensional (4D) one with complex T and p. While the traditional 2D phase diagram with real temperature T and pressure p values (the physical plane) lacks Lee-Yang (LY) zeros beyond the critical point, preventing the occurrence of criticality, the off-plane zeros in this 4D scenario still induce critical anomalies in various physical properties. This relationship is evidenced by the correlation between the Widom line and LY edges in van der Waals, 2D Ising model, and water. The diverged supercritical boundaries manifest the high-dimensional feature of the phase diagram: e.g., when LY zeros of complex T or p are projected onto the physical plane, boundaries defined by isobaric heat capacity C_{p} or isothermal compression coefficient K_{T} emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.

Two fluoradene derivatives: pseudosymmetry, eccentric ellipsoids and a phase transition.

Structures of two derivatives of the curved fluoradene ring system (C(19)H(12)) have been determined. Both have phases that are highly pseudosymmetric. At room temperature crystals of 7b-triisopropylsilylfluoradene (C(28)H(32)Si) have a P1 cell that contains two independent molecules (Z' = 2) and that is almost centered. Crystals of 7b-(2,4-dinitrophenyl)fluoradene (C(25)H(14)N(2)O(4)) have both a P2(1)/c cell with Z' = 1 and a P2(1)/c cell with Z' = 2. The molecular volumes in these two P2(1)/c structures differ by 0.7%, but the structures are otherwise virtually the same; the two independent molecules in the larger cell are related by a pseudotranslation. Some of the atomic ellipsoids in the P2(1)/c, Z' = 1 structure are very large and eccentric, and there are some hints in the diffraction pattern of an incipient phase transition, but the Z' = 1 and Z' = 2 phases are clearly different. The P2(1)/c, Z' = 2 crystal at 295 K probably contains some volume fraction of the Z' = 1 phase; when the temperature is lowered to 273 K this fraction is decreased markedly. The pronounced pseudosymmetry in the P1 and P2(1)/c structures that have Z' = 2 has been investigated by analysing the atomic coordinates, by performing refinements in the smaller pseudocells and by making separate Wilson plots for the classes of reflections which are systematically strong and systematically weak. All three approaches are informative, but they reveal different information. Least-squares fits of coordinates of corresponding atoms measure the similarity of the molecular conformations. The Wilson plots allow a quantitative comparison of the intensities of the strong and weak reflections and thus an assessment of the deviations of the true structure from the smaller pseudocell structure. Comparison of the atomic displacements obtained in the full and pseudocell refinements shows where the structural distortions are largest and provides an indication of their directions.

Diffuse x-ray scattering in the Hg2I2 model incipient ferroelastics

This paper reports the first detection and study of diffuse maxima in x-ray scattering in Hg2I2 incipient ferroelastics. These maxima originate from the formation of clusters of the incipient orthorhombic phase in the paraelastic tetragonal matrix. The nucleation and growth of the clusters are caused by spatial and temporal fluctuations of the order parameter (which correspond to the TA soft mode at the X point of the Brillouin zone edge) and are induced by the incipient phase transition. Information is obtained on the temperature behavior of the susceptibility and correlation length and on the shape and anisotropy of clusters, and the critical indices are determined.

The elastic behaviour of Ce3S4 and La3S4

The hydrostatic pressure and temperature dependences of the elastic stiffnesses of the cubic, Th3P4 structure compounds Ce3S4 and La3S4 have been measured using the ultrasonic pulse echo overlap technique. Although Ce3S4, unlike La3S4 (T c = 103 K), does not undergo a phase transition when its temperature is lowered to 16 K, its elastic stiffnesses (C11-C12)/2 and C11 soften with decreasing temperature (in a similar manner but less markedly than those of La3S4); this lattice instability indicates an incipient phase transition. In both compounds the elastic constants increase under pressure: the long-wavelength acoustic-mode Gruneisen parameters are all positive, and the application of pressure does not induce acoustic phonon-mode softening.

The Observation of Incipient Phase Transitions in K2PtCl6, K2PdCl6, and K2IrCl6

Measurements of the temperature dependence of the nuclear quadrupole resonance (NQR) frequencies and spin–lattice relaxation times for the 35Cl nuclei in Cs2PtCl6, Rb2PtCl6, K2PtCl6, and K2PdCl6 provide information on the temperature dependence of two averages of the rotary lattice mode frequency over the-Brillouin zone. An iterative method is introduced to analyze the NQR frequency data and simultaneously yield the static lattice resonance frequencies and the temperature dependence of one of the average rotary mode frequencies. The results show that previous analyses of the data yielded erroneous values of the static lattice resonance frequencies. What is more interesting, the analysis presented clearly indicates incipient phase transitions in both K2PtCl6 and K2PdCl6 but shows that the structures of Cs2PtCl6 and Rb2PtCl6 remain stable to 0 K. The interpretation of the relaxation time data yields the temperature dependence of the second average rotary mode frequency and substantiates the conclusions drawn from the frequency data. A comparison of data for K2PtCl6 and K2IrCl6 reveals an incipient phase transition in the latter substance as well.