PHASON ELASTICITY IN EQUILIBRIUM QUASICRYSTAL MODELS

1989 ◽  
Vol 03 (15) ◽  
pp. 1121-1126 ◽  
Author(s):  
LEI-HAN TANG
Keyword(s):  
Free Energy ◽  
High Temperatures ◽  
Elastic Energy ◽  
Thermal Fluctuations ◽  
Zero Temperature ◽  
Long Wavelength ◽  
Random Tiling ◽  
Crystal Model

The phason elasticity of random tiling and quasiperiodic crystal models is discussed. Long-wavelength phasons in the random tiling model are described by a square-gradient free energy of entropic origin. In the quasiperiodic crystal model, thermal fluctuations lead to a transition from the zero temperature singular linear phason elastic energy to a quadratic phason elastic energy at high temperatures.

METASTABLE STATES IN THE HOPFIELD MODEL

1990 ◽  
Vol 04 (01) ◽  
pp. 143-150 ◽  
Author(s):  
CLAUDIO PROCESI ◽  
BRUNELLO TIROZZI
Keyword(s):  
Free Energy ◽  
Finite Number ◽  
Thermodynamic Limit ◽  
Metastable States ◽  
Hopfield Model ◽  
Zero Temperature

We describe the properties of the free energy of the Hopfield model with a finite number of patterns and describe its dynamic at zero temperature in the space of overlaps in the thermodynamic limit.

MODEL FOR OXYGEN ABSORPTION AND STRUCTURAL PHASE TRANSITION IN YBa2Cu3O7−y

1988 ◽  
Vol 02 (08) ◽  
pp. 1017-1023
Author(s):  
C. VAREA ◽  
A. ROBLEDO
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Elastic Energy ◽  
Structural Transition ◽  
Lattice Gas ◽  
Structural Phase ◽  
External Source ◽  
Oxygen Absorption ◽  
Low Oxygen ◽  
Oxygen Oxygen

We reproduce, quantitatively, the observed dependence with temperature and O 2 partial pressure of the ordering of oxygen and the concommitant structural transition in YBa 2 Cu 3 O 7−y by means of a layered oxygen lattice gas model in equilibrium with an external source of O 2. The free energy considers, in addition to Cu -mediated oxygen-oxygen interactions, the elastic energy of the crystal. Depending on the coupling between these two terms the transition may turn into 1st order and further ordering along the Cu-O chains may appear for low oxygen content.

Disordering of MgAl2O4 spinel from first principles

2000 ◽  
Vol 64 (2) ◽  
pp. 311-317 ◽  
Author(s):  
M. C. Warren ◽  
M. T. Dove ◽  
S. A. T. Redfern
Keyword(s):  
Free Energy ◽  
Electronic Structure ◽  
First Principles ◽  
Large Scale ◽  
Experimental Measurements ◽  
Zero Temperature ◽  
Macroscopic Models ◽  
Tetrahedral Sites ◽  
Degree Of Order ◽  
Good Agreement

AbstractAt high temperature, MgAl2O4 spinel is stabilized by disorder of Mg and Al between octahedral and tetrahedral sites. This behaviour has been measured up to 1700 K in recent neutron experiments, but the extrapolation of subsequently fitted thermodynamic models is not reliable. First principles simulation of the electronic structure of such minerals can in principle accurately predict disorder, but would require unfeasibly large computing resources. We have instead parameterized on-site and short-ranged cluster potentials using a small number of electronic structure simulations at zero temperature. These potentials were then used in large-scale statistical simulations at finite temperatures to predict disordering thermodynamics beyond the range of experimental measurements. Within the temperature range of the experiment, good agreement is obtained for the degree of order. The entropy and free energy are calculated and compared to those from macroscopic models.

scholarly journals An Asymmetric Mechanism in a Symmetric Molecular Machine

2020 ◽  
Author(s):  
Florian Blanc ◽  
Marco Cecchini
Keyword(s):  
Free Energy ◽  
Large Scale ◽  
Technological Development ◽  
Thermal Fluctuations ◽  
Free Energy Calculations ◽  
Molecular Machine ◽  
Free Energy Surface ◽  
Promising Area ◽  
Sequential Mechanism ◽  
External Stimuli

The design of molecular architectures exhibiting functional motions is a promising area for disruptive technological development. Towards this goal, rotaxanes and catenanes, which undergo relative motions of their sub-units in response to external stimuli, are prime candidates. Here, we report on the computational analysis of the contraction/extension of a bistable [c2]-daisy chain rotaxane. Using free energy calculations and transition path optimizations, we explore the free energy landscape governing the functional motions of a prototypical molecular machine with atomic resolution.<br>The calculations reveal a sequential mechanism for contraction/extension in which the asynchronous gliding of each ring is preferred over the concerted movement suggested by chemical intuition. Analysis of the underlying free energy surface indicates that dissymmetric gliding is favored because it entails crossings of much smaller barriers.<br>Our findings illustrate an important design principle for molecular machines, namely that efficient exploitation of thermal fluctuations may be realized by breaking down the large-scale functional motions into smaller steps.

Thermal fluctuations in a realistic ionic-crystal model

2022 ◽  
Vol 586 ◽  
pp. 126463
Author(s):  
Fabrizio Gangemi ◽  
Roberto Gangemi ◽  
Andrea Carati ◽  
Luigi Galgani
Keyword(s):  
Ionic Crystal ◽  
Thermal Fluctuations ◽  
Crystal Model

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.

CoSi and CoSi2 Phase Formation on Bulk and Soi Si Substrates

1993 ◽  
Vol 320 ◽  
Author(s):  
S. L. Hsia ◽  
T. Y. Tan ◽  
P. L. Smith ◽  
G. E. Mcguire
Keyword(s):  
Free Energy ◽  
Energy Release ◽  
Gibbs Free Energy ◽  
High Temperatures ◽  
Phase Formation ◽  
Energy Reduction ◽  
Formation Temperature ◽  
Si Substrates ◽  
Two Phases ◽  
Source Materials

ABSTRACTWe have studied the CoSi and CoSi2 phase formation sequence in (001) bulk and SOI Si wafers, using Co/Ti bimetallic layers as source materials which are suitable for growing epitaxial CoSi2 films on (001) Si. In bulk Si, co-formation of polycrystalline CoSi and epitaxial CoSi2 phases at T>500°C have been observed. These phases form respectively at the metal and Si sides of the film. For very long times and/or at high temperatures, only epitaxial CoSi2 is observed, e.g., for samples annealed at 560°C for 30 min or at 900°C for 10 s. When using (001) SOI Si with inexhaustible Co supply, only polycrystalline CoSi has been formed for a 900°C 10 s annealing, which is in contrast to the bulk Si results. This phenomenon is understood on the basis of Gibbs free energy reduction in forming the two phases. In the CoSi2 formation temperature range, Gibbs free energy release in forming CoSi2 is only ∼10% more than that of forming CoSi. Consequently, after all Si atoms have been consumed, the formation of CoSi becomes energetically more favorable, since the free energy reduction due to formation of 2x mole of CoSi is much larger than that due to formation of lx mole of CoSi2, where x is the SOI Si mole number.

scholarly journals A novel representation for the free energy in string theory at non-zero temperature

1993 ◽  
Vol 394 (2) ◽  
pp. 423-442 ◽  
Author(s):  
A.A. Bytsenko ◽  
E. Elizalde ◽  
S.D. Odintsov ◽  
S. Zerbini
Keyword(s):  
Free Energy ◽  
String Theory ◽  
Zero Temperature
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