AppendixE 197(Hint:Disorder now occursinthe arrangementbothofthe vacancies andofthe
interstitial atoms.)
Chapter 11
1 Estimate the strengthoftheeffectiveinteractionfield(11.2)in a strongferromagnet
such as iron(TTTC= 1 043 K). You may assume that iron is a spin-^12 solid,with
μ=μB.Thisis not accurate,butitwillgive an order ofmagnitude.
2 Estimate thetypicalorderingtemperaturefor a nuclear spin-^12 solid.Assume that all
the nuclei have a momentμN,that they are separated by 0.3 nm and that the inter-
actions arisefrom themagneticdipoleinfluence ofabout eight nearest neighbours.
(Don’t tryto be too accurate!)
3 In the case of beta-brass (section 11.4) show that, in the mean field approximation,
the structuralcontribution to theinternalenergymaybewritten as
U=UUU 0 − 2 Nm^2 VwhereUUU 0 = 2 N(VVVCuCu+VVVZnZn+ 2 VVVCuZn),andV=VVVCuCu+VVVZnZn− 2 VVVCuZn.
Hence derive an expression for the ordering temperature in terms of the bond energy
differenceV.(Hint:Workout the number ofeachtype ofbondas afunction ofthe
orderparameterm,assumingthat the occupation ofeachsiteis uncorrelatedwith
its neighbours – the mean field assumption.)Chapter 12
1 Verifythat (12.4)leadstotheFDdistribution, as statedin section 12.1.2.
2 (a) If the atoms were interacting with a gas consisting of real (massive) bosons,
what equations should replace (12.4) in order for the BE distribution to follow?
(b) Repeat (a)for an MBgasleadingto theMBdistribution.
3 Verify thatZZA = ZN, for an assembly ofN localized particles, using the
multinomial theorem method. (See note 5 after (12.7).)
Chapter 13
1 Work through the derivations of (13. 5 ) and (13.6), the basic ideas in the use of the
grandcanonicalensemble.
2 As outlinedin section 13.3.3, use (13.13) toderive theheat capacityCVofanideal
gas which is (i) monatomic, (ii) diatomic. Express the result in terms of theN
rather thanμ(compare (13.14)).
3 Consider thechemicalreaction 2H 2 +O 2 2 H 2 O.Writingsubscripts 1forH 2 ,
2 forO 2 and 3 forH 2 O, show that (i) the corresponding result to (13.22) is 2μ 1 +
μ 2 = 2 μ 3 and(ii)thelaw ofmass action (compare (13.24))for the reactionis
N 12 NNN 2 /NNN 32 =K(V,T).