Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

Adsorption of fluids on solid surfaces: A route toward very dense layers

Adsorption of Xe on single planar walls is investigated in the frame of a density functional theory. The strength of the adsorbate-substrate attraction is changed by considering surfaces of Cs, Na, Li, and Mg. The behavior is analyzed by varying the temperature T (between the triple point T_t and the critical T_c) and the coverage Γ_?${\Gamma }_{?}$. The obtained adsorption isotherms exhibit a variety of wetting situations. Density profiles are reported. It is shown that for strongly attractive surfaces the adsorbed liquid becomes very dense reaching densities characteristic of solids.     

Critical and triple point temperatures of the first adsorbed layer of nitric oxide on graphite,boron nitride and lamellar halides

The two-dimensional critical temperature T_c(2D) of the first layer of nitric oxide adsorbed on homogeneous surfaces of graphite, boron nitride, cadmium halides (CdI₂, CdBr₂, CdCl₂) and magnesium bromide has been determined as accurately as possible. A correlation curve between T_c(2D) and the adsorbent crystalline parameter is compared to the correlation curve of this parameter with the two-dimensional triple point temperature T_t(2D) of the same layer on the above substrates and on those previously investigated by Enault and Larher. It appears from this comparison that T_c(2D) is less sensitive than T_t(2D) to the nature of the substrate: the difference between the extreme values of T_c(2D) is 25 K, whereas it is larger than 70 K for T_t(2D). Moreover the lowest values of T_c(2D) correspond to the substrates for which the lowest values of T_t(2D) have also been observed, namely graphite and boron nitride, both standing out by the smoothness of the adsorption potential of their cleavage faces. Furthermore we are led to reconsider the nature of the less dense phase (α phase) which hitherto has been inferred to be a 2D solid essentially composed of dimers lying flat on the surface.     

Anomalous properties of crystalline methane in the range of 60–70 K

Mechanical, structural, thermal, and spectral properties of solid methane in the temperature range 0.5T _tr-T _tr (T _tr is the triple point) at the equilibrium vapor pressure have been analyzed. It has been shown that the totality of observed anomalies in the temperature range of 60–70 K can be explained by the existence of collective rotational degrees of freedom in solid methane.     

Temperature and pressure dependence of molar volume in solid phases of ammonia near the melting point

Temperature and pressure dependencies of the molar volume are studied here along the transition curve between solid I and solid II phases near the melting point in ammonia. The molar volumes are calculated in the temperature range of 217 to 224  K and in the pressure range of 3 to 8 kbar with respect to the triple point (T_t = 217.34 K, P_t = 3.070 kbar) where the melting curves of solid I and solid II coincide with the transition curve in ammonia.     

Homogeneous He-He solid solutions in the pre-separation region

Temperature dependences of the pressure P(T) in homogeneous solid ³He-⁴He mixtures have been studied experimentally in the wide range of concentrations (35.0%, 62.0%, 68.3%, 74.1%, 75.0%, and 89.3% ³He) above and below the equilibrium phase separation temperature T_s. An anomalous behaviour of the pressure in the vicinity of T_s is found for all investigated samples. With decreasing temperature, as T_s is approached, the pressure increases instead of expected reduction due to decrease in the phonon contribution (P_ph∼T⁴). Such an increase in pressure continues in the metastable region below T_s until the mixture separates. Theoretical interpretation of the observed effects based on a rigorous thermodynamic approach is proposed. The found experimentally pressure behaviour can be described only with the consistent account for fluctuations in the impurity subsystem which near T_s dominates over phonon contribution into the pressure. The obtained theoretical results are in good quantitative agreement with the experimental data. Density fluctuations in the concentrated mixtures give rise to a spontaneous formation of impuriton nano-clusters containing several hundreds of atoms. The fluctuation can be rigorously interpreted as a nucleus of the second phase in the pre-separated homogeneous solid mixture. The estimated size of the fluctuation nano-clusters agrees with the corresponding value for second phase nuclei obtained from the Lifshits-Slesov phenomenological theory of homogeneous nucleation.     

A freezing transition in the lattice-gas model

In the lattice-gas model, condensation of a gas to its liquid phase is identified as the long range ordering transition in the equivalent Ising model. The same model has a second percolation transition at a lower temperature, which is identified here as the freezing transition of the liquid to its solid phase. It predicts that the mass diffusion in a liquid should decay near the freezing point T_F ≈ (T ? T_F)^t?β, where t is the conductivity exponent and β is the percolation probability exponent.     

The liquid-vapour phase transition in fluid mercury

The paper discusses recent experimental results in the liquid-vapour critical region of metals which show that the existence of the metal-non-metal transition noticeably influences the electronic, thermodynamic, structural and interfacial features of the fluid. The main emphasis is on surface-induced phenomena. Reflectivity experiments on mercury against an optically transparent sapphire window close to the vapour-liquid coexistence curve reveal clearly the existence of a prewetting transition of mercury on the sapphire substrate. The transition line, which terminates at high temperatures at a prewetting critical temperature T _pwc lying below the bulk critical temperature T _c and at low temperatures at the wetting transition temperature T _w lies close to the bulk vapour-liquid coexistence curve.     

Temperature dependence of the rotational life times in solid H2

We have studied the temperature dependence of the nuclear transverse and longitudinal relaxation times in solid H₂ for ortho concentrations 10^-3 < X < 10^-2 between 0.4 K and the triple point, 13.9 K. We find a striking temperature dependence in T₂ over the whole temperature range. This new effect is ascribed to a coupling between molecular rotation and lattice vibrations, which is brought into evidence by the narrow width of the spectral density of the rotational fluctuations at low X.     

Theoretical analysis of the effect of temperature dependence of Auger coefficient on the turn-on time delay of uncooled semiconductor laser diodes

In this paper, a novel interpretation of the effect of Auger recombination coefficient (C) on the turn-on time delay (t_on) of semiconductor laser diodes (SLDs) is presented. To the date, the well-known conclusion is that the main effect of C is to decrease t_on. This is because the earlier studies were based on less physical assumptions. Contrarily, we show that the general effect of C is to increase t_on. This conclusion is supported by including the effect of temperature of operation (T) on t_on of uncooled SLDs. Advanced analytical model is presented to determine t_on analytically and in term of nonradiative (A), radiative (B) and C recombination coefficients. The derived model can be applied to bulk and multiple quantum-well (MQW) long-wavelength SLDs at any value of temperature of operation degree (T) within the range 25-85 °C. The temperature dependence of t_on is calculated according to the temperature dependences of C and threshold carrier density (N_th). The temperature dependence of the latter is calculated according to the temperature dependence of laser cavity parameters and not by the well-known Parkovian relationship. Numerical and analytical results show that t_on increases as T increases due to increasing of N_th and C which its effect dominates at high temperature degrees. In addition, we show that the effect of temperature dependence of t_on in MQW SLD is smaller than the bulk one. Moreover, MQW SLD needs a lower injection current than the bulk one to achieve the same value of t_on.     

Phase transition in V1+xTe2 (0.04⩽x⩽0.11)

1T-V_1+xTe₂ was synthesized in a composition range of 0.04?x?0.11. The reversible first order transition was observed by DTA (DSC), powder X-ray diffraction, magnetic susceptibility (χ), and d.c. electrical resistivity (?) measurements. Transition temperature (T_t is 474 K for V_1.04Te₂, and decreases with increasing x. Heat of transition, ΔH was estimated to be as high as 500 cal mol^?1 from the endothermical peak in DSC. The expansion of the c-axis is observed at T_t. χ exhibits a jump at T_t, showing the paramagnetic temperature dependence both below and above T_t. ? measurements show the metallic-like behavior with a slight decrease at T_t. Preliminary electron diffraction examination suggests the formation of a super-structure below T_t.     

Verwey transition in spin polarization of field-emitted electrons from 〈1 1 0〉-oriented single crystal magnetite whisker

We measured temperature dependence of a spin polarization of field-emitted electrons from a single-crystalline magnetite (Fe₃O₄) whisker with 〈1 1 0〉 orientation. The spin polarization of emitted electrons began to increase above 130 K corresponding to the temperature of Verwey point (T_v). The increase is considered as reflection of the change of the spin state near the Fermi level due to the Verwey transition. Our experimental results support a localization of t_2g orbital electrons below the Verwey point and a model of charge ordering for magnetite.     

Mössbauer investigations of the surface state of hexagonal ferrites Sr-M near the curie point

The temperature dependence of the parameters of the hyperfine interaction in the surface layers and in the bulk of macroscopic crystals of hexagonal ferrites of the type Sr-M (SrFe₁₂O₁₉) is investigated by the method of simultaneous gamma-, x-ray, and electron Mössbauer spectroscopy. It is shown experimentally that the transition of an ≈ 200 nm thick surface layer of macroscopic ferromagnets to the paramagnetic state occurs at a temperature 3° below the Curie point (T _c) for the bulk of the crystal. It was established that the transition temperatureT _c(L) of a thin layer localized at a depthL from the surface of the crystal increases away from the surface and reaches the valueT _c at the lower (away from the surface) boundary of the so-called “critical” surface layer. A nonuniform state in which the bulk region of the crystal is magnetically ordered while the surface region is disordered is observed nearT _N.     

The kinetics of the photolysis of thin films of lead iodide

The kinetics of the photolysis of thin films of PbI₂ have been followed using a quartz crystal microbalance method. Rate as a function of temperature, light intensity and wavelength has been determined. The influence of grain size and gaseous ambient has also been investigated. Three ranges of kinetics were identified. Initial; associated with nucleation and surface chemical reactions. Intermediate; associated with photolysis without the intervention of optically absorbing product, gives $\text{(}\text{?θ}\text{?t}\text{)}{}_{\mathrm{T}}\text{,λ,I ∝ T}$. Terminal; attenuation due to lead particles, gives $\text{(}\text{?θ}\text{?t}\text{)}{}_{\mathrm{T}}\text{,λ,I ∝ t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$.Results show that iodine is generated at the solid/vacuum interface and lead is generated in the bulk. Photolysis is described by phenomenological equations involving bulk and surface recombination of hole/electron pairs plus photolysis. A mechanism is proposed in which the rate determining step is anion vacancy diffusion from the surface, the activation energy for photolysis and anion vacancy diffusion being the same.     

Studies of the surface magnetic state of the Sr-M hexagonal ferrites near the phase transition at the Curie temperature

A study is reported of the temperature dependences of the hyperfine (HF) interaction parameters in a ～200-nm thick surface layer and in the bulk of macroscopic hexagonal ferrite crystals of the Sr-M type (SrFe₁₂O₁₉ and SrFe_10.2Al_1.8O₁₉). The method used for the measurements is Mössbauer spectroscopy with simultaneous detection of gamma quanta, characteristic x-ray emission, and electrons, which permits direct comparison of the HF parameters in the bulk and the near-surface layers of a sample. As follows from the experimentally determined temperature dependences of the effective magnetic fields, the fields at the nuclei of the iron ions located in a ～200-nm thick near-surface layer decrease with increasing temperature faster than those of the ions in the bulk. The transition to paramagnetic state in a ～200-nm thick surface layer was found to occur 3° below the bulk Curie temperature. This offers the first experimental evidence for the transition to paramagnetic state in a surface layer of macroscopic ferromagnets to take place below the Curie temperature T _c for the bulk of the crystal. It has been established that the transition temperature T _c (L) of a thin layer at a depth L from the surface of a crystal increases as one moves away from the surface to reach T _c at the inner boundary of the surface layer called critical. In the vicinity of T _c one observes a nonuniform state, with the crystal being magnetically ordered in the bulk but disordered on the surface. The experimental data obtained were used to construct a phase diagram of surface and bulk states for macroscopic magnets near the Curie (or Néel) temperature.     

Pressure-induced magnetic transition in MnRhAs

The magnetic properties of a Fe₂P-type intermetallic compound MnRhAs have been investigated under high pressure up to 8.0 GPa by AC susceptibility measurement. Initially, both the antiferromagnetic (AF(I)) to the canted state magnetic transition temperature T_t and the canted state to another antiferromagnetic one (AF(II)) transition temperature T_C increase with compression. At 4.0 GPa, however, T_t decreases abruptly, while the increasing rate of T_C becomes larger above this pressure. A pressure-induced magnetic phase transition was seen at around this pressure when T_t and T_C are plotted in the pressure–temperature phase diagram. The transition from the antiferromagnetic to the ferromagnetic state observed below 160 K with increasing pressure is not frequently observed.     

Coexistence of color superconductivity and chiral symmetry breaking within the NJL model

The phase diagram for quark matter is investigated within a simple Nambu-Jona-Lasinio model without vector correlations. It is found that the phase structure in the temperature-density plane depends sensitively on the parametrization of the model. We present two schemes of parametrization of the model where, within the first one, a first-order phase transition from a phase with broken chiral symmetry to a color superconducting phase for temperatures below the triple point at T _t = 55 MeV occurs, whereas for the second one a second-order phase transition for temperatures below T _t = 7 MeV is found. In the latter case, there is also a coexistence phase of broken chiral symmetry with color superconductivity, which is a new finding within this class of models. Possible consequences for the phenomenology of the QCD phase transition at high baryon densities are discussed. Received: 3 January 2003 / Accepted: 21 February 2003 / Published online: 24 April 2003     

Thermodynamic Study of Formamidinium Lead Iodide (CH5N2PbI3) from 5 to 357 K

In the present study, the molar heat capacity of solid formamidinium lead iodide (CH₅N₂PbI₃) was measured over the temperature range from 5 to 357 K using a precise automated adiabatic calorimeter. In the above temperature interval, three distinct phase transitions were found in ranges from 49 to 56 K, from 110 to 178 K, and from 264 to 277 K. The standard thermodynamic functions of the studied perovskite, namely the heat capacity C°_p(T), enthalpy [H⁰(T) − H⁰(0)], entropy S⁰(T), and [G°(T) − H°(0)]/T, were calculated for the temperature range from 0 to 345 K based on the experimental data. Herein, the results are discussed and compared with those available in the literature as measured by nonclassical methods.     

Neutron diffraction determination of the magnetic phases of FeCl2·2H2O

The metamagnetic behaviour of FeCl₂·2H₂O has been determined. At T = 4.2 K the reflections of the antiferromagnetic zero-field-phase dissapear, when a magnetic field of H₁ = 39 kG is applied along the direction of sublattice magnetization. There is evidence for a ferrimagnetic phase with a unit cell in which the a axis is tripled. At H₂ = 46 kG this phase vanishes, and the magnetically saturated configuration is reached. As the temperature is increased, the three phases meet at a triple point at T_T = 11.7K and H_T = 42.0 kG.     

Magnetic states of the surface and bulk of ferrites near a phase transition at the Curie temperature

Investigations of the magnetic state of a surface layer ~200 nm thick and of the bulk in macroscopic ferrite crystals of the type Ba-M (BaFe₁₂O₁₉) are performed in the phase transition region around the Curie temperature (T _c). The method of simultaneous gamma, x-ray, and electron Mössbauer spectroscopy, which made it possible to compare directly the phase states of the surface and bulk of the sample, is used for the measurements. It is observed experimentally that in BaFe₁₂O₁₉ the transition of a surface layer ~200 nm thick to the paramagnetic state occurs at temperatures below T _c. It is established that the transition temperature T _c(L) of a thin layer localized at depth L from the surface of the crystal increases with distance from the surface and reaches the value T _c at the lower boundary of the “critical” surface layer. Therefore, near T _c a nonuniform state in which the crystal is magnetically ordered in the bulk but disordered at the surface is observed. A phase diagram of the states of the surface and of the bulk of macroscopic magnets near the Curie (or Néel) point is proposed on the basis of all the experimental results obtained in the present work as well as previously published results.