First order quantum correction to the free energy of simple liquids

Pramana ◽  
1985 ◽  
Vol 25 (3) ◽  
pp. 335-340
Author(s):  
S K Datta
Keyword(s):  
Free Energy ◽  
Quantum Correction ◽  
Simple Liquids ◽  
First Order

Second virial coefficients of water beyond the conventional first-order quantum correction

2005 ◽  
Vol 405 (1-3) ◽  
pp. 203-207 ◽  
Author(s):  
Raúl A. Bustos Marún ◽  
Eduardo A. Coronado ◽  
Juan C. Ferrero
Keyword(s):  
Quantum Correction ◽  
Virial Coefficients ◽  
Second Virial Coefficients ◽  
First Order

TEMPERATURE DEPENDENCE OF SURFACE TENSION OF LIQUID CRYSTALS AT THE PHASE TRANSITION

1995 ◽  
Vol 09 (03n04) ◽  
pp. 237-242 ◽  
Author(s):  
R. MOLDOVAN ◽  
M. TINTARU ◽  
T. BEICA ◽  
S. FRUNZA ◽  
D. N. STOENESCU
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Surface Tension ◽  
Free Energy ◽  
Surface Layer ◽  
Order Parameter ◽  
Unit Area ◽  
Negative Slope ◽  
First Order ◽  
First Order Transition

The surface tension is calculated as the excess of the free energy per unit area, due to the presence of a surface layer, using Landau–de Gennes expansions, in the hypothesis of a first order transition in the bulk and taking into account the dependence of the surface free energy from the surface tilt angle. The surface order parameter is calculated and surface-ordered phase above the phase transition temperature has been found. A variety of calculated surface tension versus temperature curves with a jump at the phase transition, with positive or negative slope, well describing the experimental data from literature, have been attained.

scholarly journals EFFECTS OF STRAIN COUPLING AND MARGINAL DIMENSIONALITY IN THE NATURE OF PHASE TRANSITION IN QUANTUM PARAELECTRICS

2013 ◽  
Vol 27 (08) ◽  
pp. 1350028 ◽  
Author(s):  
NABYENDU DAS
Keyword(s):  
Free Energy ◽  
Critical Point ◽  
Finite Temperature ◽  
Order Parameter ◽  
Quantum Critical Point ◽  
Order Transition ◽  
Zero Temperature ◽  
First Order ◽  
Quantum Paraelectrics ◽  
First Order Transition

Here a recently observed weak first order transition in doped SrTiO 3 [Taniguchi, Itoh and Yagi, Phys. Rev. Lett.99, 017602 (2007)] is argued to be a consequence of the coupling between strain and order parameter fluctuations. Starting with a semi-microscopic action, and using renormalization group equations for vertices, we write the free energy of such a system. This fluctuation renormalized free energy is then used to discuss the possibility of first order transition at zero temperature as well as at finite temperature. An asymptotic analysis predicts small but a finite discontinuity in the order parameter near a mean field quantum critical point at zero temperature. In case of finite temperature transition, near quantum critical point such a possibility is found to be extremely weak. Results are in accord with some experimental findings on quantum paraelectrics such as SrTiO 3 and KTaO 3.

CHARACTERISTIC TEMPERATURES OF FIRST-ORDER FERROELECTRIC PHASE TRANSITION: EFFECTIVE FIELD APPROACH

2012 ◽  
Vol 02 (02) ◽  
pp. 1241007 ◽  
Author(s):  
C. L. WANG ◽  
C. ARAGÓ ◽  
M. I. MARQUÉS
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Ferroelectric Phase ◽  
Effective Field ◽  
Static Properties ◽  
Field Approach ◽  
First Order ◽  
Characteristic Temperatures ◽  
Ferroelectric Phase Transitions

The explicit expression of Helmholtz free energy has been obtained from the equation of state from effective field approach. From the Helmholtz free energy, four characteristic temperatures describing a first-order ferroelectric phase transitions have been determined. The physical meaning of coefficients in Landau-type free energy has been revealed by comparison with the expanding Helmholtz function. Temperature dependence of polarization under different bias, and hysteresis loops at different temperatures are presented and discussed. These results provide the basic understandings of the static properties of first-order ferroelectric phase transitions.

scholarly journals On the existence of thermodynamically stable rigid solids

2018 ◽  
Vol 115 (19) ◽  
pp. E4322-E4329 ◽  
Author(s):  
Parswa Nath ◽  
Saswati Ganguly ◽  
Jürgen Horbach ◽  
Peter Sollich ◽  
Smarajit Karmakar ◽  
...  
Keyword(s):  
Free Energy ◽  
Strain Rate ◽  
Elastic Limit ◽  
Finite Strain ◽  
Free Energy Barrier ◽  
First Order ◽  
Simulation Techniques ◽  
Collective Processes ◽  
First Order Phase ◽  
Shape Changes

Customarily, crystalline solids are defined to be rigid since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the metastable state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable when an external field, which penalizes particle rearrangements, is switched on. This produces a line of first-order phase transitions in the field–strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

Effect of Preferential Solvation on the Kinetics and Thermodynamics of Oxidation of Anilines by Nicotinium Dichromate

2005 ◽  
Vol 60 (10) ◽  
pp. 1105-1111 ◽  
Author(s):  
Durvas S. Bhuvaneshwari ◽  
Kuppanagounder P. Elango
Keyword(s):  
Free Energy ◽  
Preferential Solvation ◽  
Zero Order ◽  
Substituted Anilines ◽  
Isokinetic Relationship ◽  
Solvent Interactions ◽  
Activation Free Energy ◽  
First Order ◽  
Linear Free Energy ◽  
Energy Relationships

The nicotinium dichromate (NDC) oxidation of anilines, in varying mole fractions of benzene/2- methylpropan-2-ol mixtures, in the presence of p-toluenesulfonic acid (TsOH) is first order in NDC and TsOH and zero order with respect to anilines in the concentration range investigated. The NDC oxidation of 15 meta- and para-substituted anilines complies with the isokinetic relationship but not to any of the linear free energy relationships. The activation free energy data failed to correlate with macroscopic solvent parameters such as εr and ENT. Correlation of ΔG# with Kamlet-Taft solvatochromic parameters (α, β , π*) suggests that the specific solute-solvent-solvent interactions play a major role in governing the reactivity.

Effect of Strain on Barium Titanate Epitaxial Films

2013 ◽  
Vol 547 ◽  
pp. 139-144
Author(s):  
Lye Hock Ong ◽  
A.M. Alrub ◽  
Khian Hooi Chew
Keyword(s):  
Thin Films ◽  
Phase Transition ◽  
Free Energy ◽  
Epitaxial Films ◽  
Ferroelectric Films ◽  
Eighth Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Highly Strained ◽  
First Order Phase

Landau-Ginzburg free energy expression with the normalized coefficients is used to elucidate the phase transition properties of strained ferroelectric films. In particular, we investigate the need to include higher order free energy terms for epitaxial strained BaTiO3 thin films. Our study reveals that the inclusion of eighth-order expression into the free energy is crucial in determining the phase transition of highly-strained BaTiO3 epitaxial films normally grown on thick cubic substrates. The phase transition is found to be second order but the unstrained film undergoes the first order phase transition. On the order hand, the calculation based on the usual sixth-order Landau-Ginzburg expression show that the films have no phase transition, which is contrary to the experimental observations.

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