Critical line near the zero-density critical point of the Kosterlitz-Thouless transition

1997 ◽  
Vol 87 (3-4) ◽  
pp. 891-895 ◽  
Author(s):  
A. Alastuey ◽  
F. Cornu
Keyword(s):  
Critical Point ◽  
Critical Line ◽  
Zero Density

Scaling Near the Critical Point in Mixture

2005 ◽  
Author(s):  
Eldred H. Chimowitz
Keyword(s):  
Critical Point ◽  
Binary Systems ◽  
Critical Line ◽  
Phase Region ◽  
Unique Point ◽  
Pure Fluid ◽  
High Volatility ◽  
Two Phases ◽  
The One ◽  
Dew Line

The critical point of mixtures requires a more intricate set of conditions to hold than those at a pure-fluid critical point. In contrast to the pure-fluid case, in which the critical point occurs at a unique point, mixtures have additional thermodynamic degrees of freedom. They, therefore, possess a critical line which defines a locus of critical points for the mixture. At each point along this locus, the mixture exhibits a critical point with its own composition, temperature, and pressure. In this chapter we investigate the critical behavior of binary mixtures, since higher-order systems do not bring significant new considerations beyond those found in binaries. We deal first with mixtures at finite compositions along the critical locus, followed by consideration of the technologically important case involving dilute mixtures near the solvent’s critical point. Before taking up this discussion, however, we briefly describe some of the main topographic features of the critical line of systems of significant interest: those for which nonvolatile solutes are dissolved in a solvent near its critical point. The critical line divides the P–T plane into two distinctive regions. The area above the line is a one-phase region, while below this line, phase transitions can occur. For example, a mixture of overall composition xc will have a loop associated with it, like the one shown in figure 4.1, which just touches the critical line of the mixture at a unique point. The leg of the curve to the “left” of the critical point is referred to as the bubble line; while that to the right is termed the dew line. Phase equilibrium occurs between two phases at the point where the bubble line at one composition intersects the dew line; this requires two loops to be drawn of the sort shown in figure 4.1. A question naturally arises as to whether or not all binary systems exhibit continuous critical lines like that shown. In particular we are interested in the situation involving a nonvolatile solute dissolved in a supercritical fluid of high volatility.

Investigation of the Phase Equilibria in the System Neon-Xenon Using a Diamond-Anvil System

1983 ◽  
Vol 22 ◽  
Author(s):  
J.A. Schouten ◽  
L.C. Van Den Bergh ◽  
N.J. Trappeniers
Keyword(s):  
Critical Temperature ◽  
Critical Point ◽  
Double Point ◽  
Critical Line ◽  
Solid Phase ◽  
Volatile Component ◽  
The Other ◽  
Temperature Minimum ◽  
Ideal System ◽  
Diamond Anvil

The critical line of a nearly ideal binary system generally moves from the critical point of one of the components directly to the critical point of the other component (curve 1 Fig. 1). In a less ideal system, however, the behaviour is quite different. In some cases the curves move from the critical point of the less volatile component (component 2) to lower temperatures and higher pressures (curve 2) and rise again to higher temperatures via a temperature minimum, the critical double point. In other systems, the critical temperature increases continuously from the critical point of the less volatile component when the pressure is increased (curve 3). We assume here that the critical line is not interrupted by the appearance of a solid phase.

scholarly journals Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
L. S. Campana ◽  
A. Cavallo ◽  
L. De Cesare ◽  
U. Esposito ◽  
A. Naddeo
Keyword(s):  
Low Temperature ◽  
Critical Point ◽  
Longitudinal Magnetic Field ◽  
Critical Line ◽  
Heisenberg Ferromagnet ◽  
Zero Temperature ◽  
Many Body ◽  
The One ◽  
Quantum Counterpart ◽  
Shift Exponent

We explore the low-temperature thermodynamic properties and crossovers of ad-dimensional classical planar Heisenberg ferromagnet in a longitudinal magnetic field close to its field-induced zero-temperature critical point by employing the two-time Green’s function formalism in classical statistical mechanics. By means of a classical Callen-like method for the magnetization and the Tyablikov-like decoupling procedure, we obtain, for anyd, a low-temperature critical scenario which is quite similar to the one found for the quantum counterpart. Remarkably, ford>2the discrimination between the two cases is found to be related to the different values of the shift exponent which governs the behavior of the critical line in the vicinity of the zero-temperature critical point. The observation of different values of the shift-exponent and of the related critical exponents along thermodynamic paths within the typical V-shaped region in the phase diagram may be interpreted as a signature of emerging quantum critical fluctuations.

scholarly journals Baryon Clustering at the critical line and near the hypothetical critical point

2019 ◽  
Vol 982 ◽  
pp. 831-834 ◽  
Author(s):  
Edward Shuryak ◽  
Juan Torres-Rincon
Keyword(s):  
Critical Point ◽  
Critical Line

Investigations of the Nature of Critical Line Very Close to a Double Critical Point

1991 ◽  
Vol 95 (1) ◽  
pp. 12-14 ◽  
Author(s):  
T. Narayanan ◽  
B. V. Prafulla ◽  
A. Kumar ◽  
E. S. R. Gopal
Keyword(s):  
Critical Point ◽  
Critical Line ◽  
Double Critical Point

The Critical Point Drying Method Applied to Scanning Electron Microscopy of L-929 Cells

1970 ◽  
Vol 28 ◽  
pp. 278-279
Author(s):  
Charles TurnbiLL ◽  
Delbert E. Philpott
Keyword(s):  
Electron Microscopy ◽  
Carbon Dioxide ◽  
Surface Tension ◽  
Critical Point ◽  
Freeze Drying ◽  
Attractive Alternative ◽  
Crystal Formation ◽  
Critical Point Drying ◽  
Time Required ◽  
Scanning Electron

The advent of the scanning electron microscope (SCEM) has renewed interest in preparing specimens by avoiding the forces of surface tension. The present method of freeze drying by Boyde and Barger (1969) and Small and Marszalek (1969) does prevent surface tension but ice crystal formation and time required for pumping out the specimen to dryness has discouraged us. We believe an attractive alternative to freeze drying is the critical point method originated by Anderson (1951; for electron microscopy. He avoided surface tension effects during drying by first exchanging the specimen water with alcohol, amy L acetate and then with carbon dioxide. He then selected a specific temperature (36.5°C) and pressure (72 Atm.) at which carbon dioxide would pass from the liquid to the gaseous phase without the effect of surface tension This combination of temperature and, pressure is known as the "critical point" of the Liquid.

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