Critical Exponent β and Rectilinear Diameter of the Binary-Liquid System Carbon Disulfide + Nitromethane

The system CS2 + CH3NO2 shows β=0.315±0.004 over 10-6<ε=|T-Tc| / Tc<2�10-1 with no indication of a classical value ½ even far away from Tc. The diameter shows a curvature and is of the form �c+b ε+fε7 / 8exp(-gεh).

Critical Exponent β and Rectilinear Diameter of the Binary-Liquid System Carbon Disulfide + Nitromethane

The system CS2 + CH3NO2 shows β=0.315±0.004 over 10-6<ε=|T-Tc| / Tc<2-10-1 with no indication of a classical value ½ even far away from Tc. The diameter shows a curvature and is of the form - c+b ε+fε7 / 8exp(-gεh).

A High Pressure Study of the Phase Diagram and the Critical Exponent β of Binary Liquid Systems

The pressure dependence of critical parameters xc, Tc, and β have been analysed in four systems namely cyclohexane + acetic anhydride, n-heptane + acetic anhydride, methanol + n-heptane, and carbon disulphide + acetonitrile. The separation temperature was found to increase linearly with pressure the value of dTc/dP being 28 mK, 11 mK, 22 mK, and 25 mK respectively. These are in fair agreement with earlier measurements available for two systems. For the methanol + n-heptane system dTc/dP is apparently not consistent with the value predicted from the specific heat and thermal expansion data.Die Druckabhängigkeit der kritischen Parameter xc, Tc und β ist in den vier Systemen Cyclohexan + Essigsäureanhydrid, n-Heptan + Essigsäureanhydrid, Methanol + n-Heptan und Schwefelkohlenstoff + Acetonitril analysiert worden. Es wurde gefunden, daß die kritische Temperatur linear mit dem Druck ansteigt. Die Werte für dTc/dP betragen 28 mK, 11 mK, 22 mK und 25 mK. Sie sind in guter überein-stimmung mit früheren Messungen an zweien dieser Systeme. Für Methanol + n-Heptan stimmt der Wert für dT/dP offensichtlich nicht mit Werten, die mit Hilfe von Daten für die spezifische Wärme und die thermische Ausdehnung vorhergesagt wurden, überein.

Critical exponent of the electrical conductivity in the paracoherence region of a thin film of YBa2Cu3O7?x

Critical exponent of the electrical conductivity in the paracoherence region (gamma) of the high temperature superconductor YBa2Cu3O7-x (YBCO) has been estimated for high quality thin film on ZrO2 substrate prepared by high pressure oxygen sputtering. High energy ion irradiation was carried out using 100 MeV O-16(7+) ions at liquid nitrogen to see the effects of disorder on the value of the exponent. The critical exponent from a value of about 2 to 1.62 upon irradiation. Studies were also carried film to see the effect of ageing and annealing.

Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

The critical behavior of osmotic susceptibility in an aqueous electrolyte mixture 1-propanol (1P)+water (W)+potassium chloride is reported. This mixture exhibits re-entrant phase transitions and has a nearly parabolic critical line with its apex representing a double critical point (DCP). The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths (by varying t) in the one-phase region. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the TL far away from the DCP, the effective susceptibility exponent γeff as a function of t displays a nonmonotonic crossover from its single limit three-dimensional (3D)-Ising value ( ∼ 1.24) toward its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value toward its nearly doubled mean-field value with increase in t. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend toward shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover to the mean-field limit extends well beyond t>10−2 for the TL’s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques. As far as the critical behavior in complex or associating mixtures with special critical points (like the DCP) is concerned, our results indicate that the influence of the DCP on the critical behavior must be taken into account not only on the renormalization of the critical exponent but also on the range of the Ising regime, which can shrink with decrease in the influence of the DCP and with the extent of structuring in the system. The utility of the field variable tUL in analyzing re-entrant phase transitions is demonstrated. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value toward a value slightly lower than its nonasymptotic mean-field value of 1. This behavior in the nonasymptotic, high tUL region is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values, as foreseen earlier in micellar systems.

Crossover from Ising to mean-field critical behavior in an aqueous electrolyte solution

The near-critical behavior of the susceptibility deduced from light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide has been determined. The measurements have been performed in the one-phase region near the lower consolute points of samples with different concentrations of sodium bromide. A crossover from Ising asymptotic behavior to mean-field behavior has been observed. As the concentration of sodium bromide increases, the crossover becomes more pronounced, and the crossover temperature shifts closer to the critical temperature. The data are well described by a model that contains two independent crossover parameters. The crossover of the susceptibility critical exponent γ from its Ising value γ=1.24 to the mean-field value γ=1 is sharp and nonmonotonic. We conclude that there exists an additional length scale in the system due to the presence of the electrolyte which competes with the correlation length of the concentration fluctuations. An analogy with crossover phenomena in polymer solutions and a possible connection with multicritical phenomena is discussed.

Liquid-liquid critical phenomena. The coexistence curve of n-heptane-acetic anhydride

The coexistence curve of the binary liquid mixture n-heptane-acetic anhydride has been determined by the observation of the transition temperatures of 76 samples over the range of compositions. The functional form of the difference in order parameter, in terms of either the mole fraction or the volume fraction, is consistent with theoretical predictions invoking the concept of universality at critical points. The average value of the order parameter, the diameter of the coexistence curve, shows an anomaly which can be described by either an exponent 1 - a, as predicted by various theories (where a is the critical exponent of the specific heat), or by an exponent 20 (where P is the coexistence curve exponent), as expected when the order parameter used is not the one the diameter of which diverges asymptotically as 1 - a.

Effect of disorder on the exponent in the coherence region in high temperature superconductors

Effect of disorder on the electrical resistance near the superconducting transition temperature in the paracoherence region of high temperature YBa2CU3O7-delta (YBCO) thin film superconductor is reported. For this, c-axis oriented YBa2Cu3O7-delta thin films having superconducting transition width varying between 0.27 K and 6 K were deposited using laser ablation and high pressure oxygen sputtering techniques. Disorder in these films was further created by using 100 MeV oxygen and 200 MeV silver ions with varying fluences. It is observed that the critical exponent in the paracoherence region for films with high transition temperature and small transition width is in agreement with the theoretically predicted value (gamma = 1.33) and is not affected by disorder, while for films with lower transition temperature and larger transition width the value of exponent is much larger as compared to that theoretically predicted and it varies from sample to sample and usually changes with disorder induced by radiation. This difference in the behaviour of the exponent has been explained on the basis of differences in the strength of weak links and the transition between temperatures T. and T, is interpreted as a percolation like transition with disorder. (c) 2006 Elsevier B.V. All rights reserved.

Electrical and Dielectric Behaviour at the Critical Point of Binary Liquids: Acetonitrile + Cyclohexane

The electrical capacitance and resistance of the binary liquid mixture cyclohexane + acetonitrile are measured in the one phase and two phase regions at spot frequencies between 5 kHz and 100 kHz. This sample has a very low gravity affected (∼0.6 mK) region. In one phase region the capacitance data show a sharp, ∼0.7% increase above background within 0.5 degrees of Tc whereas the resistance has a smooth increase of ∼1.5% above background in a (T−Tc) range of 4 degrees. Two phase values of capacitance and resistance from the coexisting phases are used to determine the critical parameters Tc (critical temperature), Rc (resistance at Tc) and Cc (capacitance at Tc). A precise knowledge of these parameters reduces the uncertainty on the critical exponent 0 for C and R. The one phase capacitance data fit to an (1 - α) exponent in a limited temperature range of 0.2 degrees. Resistance data strongly support an (1 - α) exponent over the entire 5 degree range.

Methyl ethyl ketone plus water plus secondary butyl alcohol: A potential system for the exploration of a quadruple critical point

We report preliminary experiments on the ternary-liquid mixture, methyl ethyl ketone (MEK)+water (W)+secondary butyl alcohol (sBA)-a promising system for the realization of the quadruple critical point (QCP). The unusual tunnel-shaped phase diagram shown by this system is characterized and visualized by us in the form of a prismatic phase diagram. Light-scattering experiments reveal that (MEK+W+sBA) shows near three-dimensional-Ising type of critical behavior near the lower critical solution temperatures, with the susceptibility exponent (gamma) in the range of 1.217 <=gamma <= 1.246. The correlation length amplitudes (xi(o)) and the critical exponent (nu) of the correlation length (xi) are in the ranges of 3.536 <=xi(o)<= 4.611 A and 0.619 <=nu <= 0.633, respectively. An analysis in terms of the effective susceptibility exponent (gamma(eff)) shows that the critical behavior is of the Ising type for MEK concentrations in the ranges of 0.1000 <= X <= 0.1250 and X >= 0.3000. But, for the intermediate range of 0.1750 <= X < 0.3000, the system shows a tendency towards mean-field type of critical behavior. The advantages of the system (MEK+W+sBA) over the system (3-methylpyridine+water+heavy water+potassium Iodide) for the realization of a QCP are outlined.

Critical resistivity in impurity doped binary liquid mixtures

The electrical resistance of the critical binary liquid system C6H12+(CH3CO)2O is measured both in the pure form and when the system is doped with small amounts (≈ 100 ppm) of H2O impurities. Near Tc, the resistance varies as dR/dT = A1+A2 (T-Tc)-b with b ≈ 0.35. Neither the critical exponent b nor the amplitude ratio A1/A2 are affected by the impurities. A sign reversal of dR/dT is noticed at high temperatures T much greater-than Tc.

Critical phenomena in electrical resistance of binary liquids: A study of the frequency dependence

The electrical resistance is measured in two binary liquid systems CS2 + CH3NO2 and n-C7H16 + CH3OH in the critical region as a function of frequency from 10 Hz to 100 kHz. The critical exponent b ≈ 0.35 in the singularity of dR/dT α (T - Tc)−b near Tc has no appreciable dependence upon the frequency. Thus any contribution from dielectric dispersion to the critical resistivity is not appreciable. The universal behaviour of the dR/dT anomaly does not seem to be followed in binary liquid systems.

Observation of the doubling of critical exponents in reentrant phase transitions

Electrical resistance (R) measurements are reported for ternary mixtures of 3-methylpyridine, water and heavy water as a function of temperature (T) and heavy water content in total water. These mixtures exhibit a limited two-phase region marked by a loop size (ΔT) that goes to zero as the double critical point (DCP) is approached. The measurements scanned the ΔT range 1.010°C less-than-or-equals, slant ΔT less-than-or-equals, slant 77.5°C. The critical exponent (θ), which signifies the divergence of ∂R/∂T, doubles within our experimental uncertainties as the DCP is reached very closely.

Intrinsically limited critical temperatures of highly doped Ga1-xMnxAs thin films

Ga1-xMnxAs films with exceptionally high saturation magnetizations of approximate to 100 emu/cm(3) corresponding to effective Mn concentrations of x(eff)approximate to 0.10 still have a Curie temperature T-C smaller than 195 K contradicting mean-field predictions. The analysis of the critical exponent beta of the remnant magnetization-beta = 0.407(5)-in the framework of the models for disordered/amorphous ferromagnets suggests that this limit on T-C is intrinsic and due to the short range of the ferromagnetic interactions resulting from the small mean-free path of the holes. This result questions the perspective of room-temperature ferromagnetism in highly doped GaMnAs.