Patterned Border Template 2Purdue UniversitySchool of Mechanical EngineeringLecture Topics•The crystal lattice.•The Einstein theory of the heat capacity of crystalline solids.•The Debye theory of the heat capacity of crystalline solids.
Patterned Border Template 3Purdue UniversitySchool of Mechanical EngineeringThe Crystal Lattice•Consider the crystal lattice of a solid as a large number N atoms hooked together by springs:McQuarrie, Statistical Mechanics, 1976
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Patterned Border Template 4Purdue UniversitySchool of Mechanical EngineeringThe Crystal Lattice•The N atoms in the crystal lattice are inherently distinguishable rather than indistinguishable because we can associate each atom with a particular lattice site. Therefore Maxwell-Boltzmann (MB) statistics rather than corrected Maxwell-Boltzmann statistics will apply to the lattice. From our previous discussion of MB and CMB statistics we found:,,!!lnlnlnjNjm MBjjjm MBjjjgWNNgWNNNN(ln)(ln)ln1ln0jjmMBmCMBjjjjjjggdWdWdNdNNN•Differentiating these expressions to find d(lnWm) gives us:2lnlnlnlnjjjjmMBmCMBjjjjjjjgNggWWNNNNgNN,lnlnjm CMBjjjgWNNN