scholarly journals A New Perspective on the Kauzmann Entropy Paradox: A Crystal/Glass Critical Point in Four- and Three-Dimensions

Proceedings ◽  
2019 ◽  
Vol 46 (1) ◽  
pp. 23
Author(s):  
Caroline Gorham ◽  
David Laughlin
Keyword(s):  
Critical Point ◽  
Order Parameter ◽  
Orientational Order ◽  
Configurational Entropy ◽  
Three Dimensions ◽  
Crystalline Solid ◽  
Crystal Glass ◽  
First Order ◽  
Kauzmann Temperature ◽  
New Perspective

In this article, a new perspective on the Kauzmann point is presented. The “ideal glass transition” that occurs at the Kauzmann temperature is the point at which the configurational entropy of an undercooled metastable liquid equals that of its crystalline counterpart. We model solidifying liquids by using a quaternion orientational order parameter and find that the Kauzmann point is a critical point that exists to separate crystalline and non-crystalline solid states. We identify the Kauzmann point as a first-order critical point, and suggest that it belongs to quaternion ordered systems that exist in four- or three-dimensions. This “Kauzmann critical point” can be considered to be a higher-dimensional analogue to the superfluid-to-Mott insulator quantum phase transition that occurs in two- and one-dimensional complex ordered systems. Such critical points are driven by tuning a non-thermal frustration parameter, and result due to characteristic softening of a `Higgs’ type mode that corresponds to amplitude fluctuations of the order parameter. The first-order nature of the finite temperature Kauzmann critical point is a consequence of the discrete change of the topology of the ground state manifold of the quaternion order parameter field that applies to crystalline and non-crystalline solids.

scholarly journals Observation of an apparent first-order glass transition in ultrafragile Pt–Cu–P bulk metallic glasses

2020 ◽  
Vol 117 (6) ◽  
pp. 2779-2787 ◽  
Author(s):  
Jong H. Na ◽  
Sydney L. Corona ◽  
Andrew Hoff ◽  
William L. Johnson
Keyword(s):  
Glass Transition ◽  
Configurational Entropy ◽  
Freezing Temperature ◽  
Thin Wall ◽  
First Order ◽  
Cu Content ◽  
Kauzmann Temperature ◽  
Entropy Of Fusion ◽  
Glass Forming ◽  
Third Law Of Thermodynamics

An experimental study of the configurational thermodynamics for a series of near-eutectic Pt80-xCuxP20 bulk metallic glass-forming alloys is reported where 14 < x < 27. The undercooled liquid alloys exhibit very high fragility that increases as x decreases, resulting in an increasingly sharp glass transition. With decreasing x, the extrapolated Kauzmann temperature of the liquid, TK, becomes indistinguishable from the conventionally defined glass transition temperature, Tg. For x < 17, the observed liquid configurational enthalpy vs. T displays a marked discontinuous drop or latent heat at a well-defined freezing temperature, Tgm. The entropy drop for this first-order liquid/glass transition is approximately two-thirds of the entropy of fusion of the crystallized eutectic alloy. Below Tgm, the configurational entropy of the frozen glass continues to fall rapidly, approaching that of the crystallized eutectic solid in the low T limit. The so-called Kauzmann paradox, with negative liquid entropy (vs. the crystalline state), is averted and the liquid configurational entropy appears to comply with the third law of thermodynamics. Despite their ultrafragile character, the liquids at x = 14 and 16 are bulk glass formers, yielding fully glassy rods up to 2- and 3-mm diameter on water quenching in thin-wall silica tubes. The low Cu content alloys are definitive examples of glasses that exhibit first-order melting.

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.

Nematic/Smectic-A Transition (NSA), Location of Tri Critical Point (TCP) in nO.m Series – A Birefringence Study

2010 ◽  
Vol 65 (4) ◽  
pp. 335-341 ◽  
Author(s):  
Venkata G.K. M. Pisipati ◽  
Divi Madhavi Latha ◽  
Boddapati T. P. Madhav ◽  
Potapragada V. Datta Prasad
Keyword(s):  
Critical Point ◽  
Homologous Series ◽  
Order Parameter ◽  
Second Order ◽  
The Body ◽  
Order Transition ◽  
Refractive Indices ◽  
First Order ◽  
Smectic A ◽  
Second Order Transition

The tri critical point (TCP), where the second-order transition transforms to first order has been located in nO.m homologous series. The order parameter has been estimated from the birefringence δn, from the refractive indices and from birefringence data available in literature and from those obtained at our laboratory on a number of nO.m compounds. The compounds in the nO.m series exhibit both second and first-order nematic/smectic-A (NSA) transition depending on the McMillan ratio (TNA/TIN) which in turn depends on the nematic and smectic-A thermal ranges. The data presented are compared with the body of the data available on this homologous series obtained with other techniques.

scholarly journals Priestley duality for MV-algebras and beyond

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wesley Fussner ◽  
Mai Gehrke ◽  
Samuel J. van Gool ◽  
Vincenzo Marra
Keyword(s):  
Large Class ◽  
Order Conditions ◽  
Enriched Environment ◽  
Priestley Duality ◽  
Distributive Lattices ◽  
First Order ◽  
Dual Spaces ◽  
Binary Operations ◽  
New Perspective ◽  
Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

scholarly journals Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers

Polymers ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1262
Author(s):  
Mikhail A. Osipov ◽  
Maxim V. Gorkunov ◽  
Alexander A. Antonov
Keyword(s):  
Liquid Crystal ◽  
Order Parameter ◽  
Density Functional ◽  
Diblock Copolymers ◽  
Microphase Separation ◽  
Hexagonal Phase ◽  
Orientational Order ◽  
Order Parameters ◽  
Copolymer Composition ◽  
Rigid Rod

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.

Laser-Induced Pretransitional Ordering And Nonlinear Optical Properties Of Rigid-Rod Polymer Suspensions

1993 ◽  
Vol 328 ◽  
Author(s):  
Boris E. Vugmeister ◽  
Michelle S. Malcuit ◽  
John C. Kralik ◽  
Colleen Stevens
Keyword(s):  
Phase Transition ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Orientational Order ◽  
Critical Value ◽  
Orientational Relaxation ◽  
First Order ◽  
First Order Phase Transition ◽  
Rigid Rod ◽  
First Order Phase

ABSTRACTWe investigate the pretransitional behavior in laser-induced alignment of rigid rod-like polytetraflouroethylene (PTFE) suspensions. Using a laser-induced birefringence experiment, we measure both the orientational order parameter and the orientational relaxation time. We find that both increase as the volume fraction of colloidal particles approaches the critical value for the isotropic-nematic phase transition. Experimental results are compared with theory which takes into account the possibility of a first-order phase transition induced by a laser electric field.

scholarly journals 3D subduction dynamics: A first-order parameter of the transition from copper- to gold-rich deposits in the eastern Mediterranean region

2018 ◽  
Vol 94 ◽  
pp. 118-135 ◽  
Author(s):  
Armel Menant ◽  
Laurent Jolivet ◽  
Johann Tuduri ◽  
Christelle Loiselet ◽  
Guillaume Bertrand ◽  
...  
Keyword(s):  
Order Parameter ◽  
Mediterranean Region ◽  
Eastern Mediterranean ◽  
Eastern Mediterranean Region ◽  
First Order

scholarly journals Order parameter fluctuations at a buried quantum critical point

2012 ◽  
Vol 109 (19) ◽  
pp. 7224-7229 ◽  
Author(s):  
Y. Feng ◽  
J. Wang ◽  
R. Jaramillo ◽  
J. van Wezel ◽  
S. Haravifard ◽  
...  
Keyword(s):  
Critical Point ◽  
Order Parameter ◽  
Quantum Critical Point ◽  
Quantum Critical
Sign in / Sign up

Export Citation Format

Share Document