1 1Phasetransitions
Changes ofphase are ofgreatinterest, notleastbecause oftheir surprise value. In this
chapter we examinehow statisticalphysics canbe usedtohelp our understandingof
some phase transitions.1 1.1 Types ofphase transition
As mentionedearlier under our comments about theheliumliquids (sections 8.3 and
9.2) phase transitions are commonly classified into ‘orders’. In terms of the Gibbs
free energyG(G=U−TS+PVisthe appropriatefree energy sincePandTare
fixedinthephase change), afirst-order transition occurs where theGsurfaces forthe
two phases cross. The stable phase is the one with minimumG(compare the previous
chapter’sdiscussion ofminimumFatfixedVandT), so that thereisajumpinthe
firstderivatives ofG(i.e.SandV)atthe transition. Hence ‘first-order’. Furthermore
supercooling and superheating effects can occur in a first-order transition, since the
system canforatimebedriven alongthe unstable(higher)branchoftheGsurface
(Fig. 11.1).
However,this isnotto be the topic of this chapter. Rather we shall be discussing
second-order transitions. Here thechangesinGatthe transition are muchmoregentle.
As the temperature is lowered, the system as it were eases itselfgraduallyinto a new
phase which grows out of the first one. There is no superheating or supercooling; it
isjust that theGsurfacehasasingularityat the transition. Thesingularityin a true
second-ordertransitionis suchthatSandVare continuous,but the second derivatives
ofGjump. Hence there is no latent heat (= change inS), but there is a jump inC
(sincedS/dTchanges). Exact second-order transitions are rarein practice, thebest
example beingthe transition to superconductivityof a metal in zero applied magnetic
field. However, there are common examples of phase transitions which are close to
second-order, namelythe‘lambda transitions’,likethatinliquid^4 He (section 9.2).
Other instances include transitions to ferromagnetism from paramagnetism, many
transitions toferroelectricity andsome structuralphase transitionsfrom one solid
phase to another.
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