Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-09T06:57:23.855Z Has data issue: false hasContentIssue false

10 - Phase transitions and critical phenomena

Published online by Cambridge University Press:  18 December 2014

João Paulo Casquilho
Affiliation:
Universidade Nova de Lisboa, Portugal
Paulo Ivo Cortez Teixeira
Affiliation:
Instituto Superior de Engenharia de Lisboa, Portugal
Get access

Summary

Introduction

In this chapter we provide a comprehensive and unified treatment of the physical concepts and quantities relevant to phase transitions and critical phenomena. Some of these concepts and quantities have already been discussed in the particular contexts of magnetism (Chapter 7), or liquid crystals (Chapter 9, We conclude the chapter with a brief reference to the application of renormalisation group ideas to critical phenomena. The resulting reconciliation of the predictions of classical theories with experiments and exact or quasi-exact solutions of model systems is a major triumph of twentieth-century physics.

Phases and phase transitions

Thermodynamics habitually deals with equilibrium systems that are uniform on the macroscopic scale – i.e., where the structure, density and composition are the same throughout the bulk of the system, which is many times greater than a single atom or molecule. Because the system is in equilibrium, intensive thermodynamic variables such as the temperature or chemical potential are also spatially uniform. Such a system is said to consist of a single phase – it is a one-phase system. Phases are what used to be called the states of matter. Solids, liquids, gases and plasmas are four commonly occurring phases – they correspond to the four elements of Aristotelian physics: earth, water, air and fire, respectively. There are, however, many other, less easily identified phases, some of which we have already encountered in this book, such as the ferromagnetic, antiferromagnetic, nematic or superconducting phases.

On varying the temperature, pressure and chemical potential(s) of a system, properties such as its structure, density, composition, compressibility, specific heat, etc., in general change smoothly. Yet under certain conditions the changes may be abrupt – some of these properties may exhibit discontinuities, or even divergences, at a phase transition. Phase transitions are among the most spectacular phenomena of nature. Consider, for instance, the phase sequence of water on heating: from ice, an opaque, slippery, rock-like solid; to colourless, incompressible, liquid water, which nevertheless easily flows under gravity; to water vapour, an invisible and very low-density (greenhouse!) gas, hence of ill-defined volume.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrews, T. 1869. The Bakerian Lecture: On the Continuity of the Gaseous and Liquid States of Matter. Phil. Trans. R. Soc. 159, 575–590.CrossRefGoogle Scholar
Binney, J. J., Dowrick, N. J., Fisher, A. J., and Newman, M. E. J. 1993. The Theory of Critical Phenomena. Oxford University Press.Google Scholar
Callen, H. B. 1985, Thermodynamics and an Introduction to Thermostatistics, 2nd edition. Wiley.Google Scholar
Domb, C. 1996. The Critical Point. Taylor and Francis.Google Scholar
Farrell, R. A. 1968. In Fluctuations in Superconductors, ed. by W. S., Goree and F., Chilton. Stanford Research Institute.Google Scholar
Fisher, M. E. 1967. The theory of equilibrium critical phenomena. Rep. Prog. Phys. 30, 615–730.CrossRefGoogle Scholar
Goldenfeld, N. 1992. Lectures on Phase Transitions and the Renormalization Group. Addison-Wesley.Google Scholar
Guggenheim, E. A. 1945. The principle of corresponding states. J. Chem. Phys. 13, 253–261.CrossRefGoogle Scholar
Huang, K. 1987. Statistical Mechanics, 2nd edition. Wiley.Google Scholar
Onsager, L. 1944. Crystal statistics. I. A two-dimensional model with an order–disorder transition. Phys. Rev. 65, 117–149.CrossRefGoogle Scholar
Reif, F. 1985. Statistical and Thermal Physics. McGraw-Hill.Google Scholar
Stanley, H. E. 1971. Introduction to Phase Transitions and Critical Phenomena. Oxford University Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×