Next Article in Journal
Nonequilibrium Thermodynamics and Entropy Production in Simulation of Electrical Tree Growth
Previous Article in Journal
Numerical Performance of Thermodynamic Behavior of Shipping-Container Architecture
Proceedings

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

Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
Author to whom correspondence should be addressed.
Presented at the 5th International Electronic Conference on Entropy and Its Applications, 18–30 November 2019; Available online: https://ecea-5.sciforum.net/.
Proceedings 2020, 46(1), 23; https://doi.org/10.3390/ecea-5-06677
Published: 17 November 2019
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.
MDPI and ACS Style

Gorham, C.S.; Laughlin, D.E. A New Perspective on the Kauzmann Entropy Paradox: A Crystal/Glass Critical Point in Four- and Three-Dimensions. Proceedings 2020, 46, 23. https://doi.org/10.3390/ecea-5-06677

AMA Style

Gorham CS, Laughlin DE. A New Perspective on the Kauzmann Entropy Paradox: A Crystal/Glass Critical Point in Four- and Three-Dimensions. Proceedings. 2020; 46(1):23. https://doi.org/10.3390/ecea-5-06677

Chicago/Turabian Style

Gorham, Caroline S., and David E. Laughlin 2020. "A New Perspective on the Kauzmann Entropy Paradox: A Crystal/Glass Critical Point in Four- and Three-Dimensions" Proceedings 46, no. 1: 23. https://doi.org/10.3390/ecea-5-06677

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop