Einstein temperature h@o k2Og hoo eir g 0:=ka G,=3x,号 for the majority of solids (ee-12 0。=100K~300K 6×4.18 5×4.18 24×4.18 是3×418 G2×4.18 1×4.18 00.10.20.30.40.50.60.70.80.91.0 XCH003013 T/O Diamond 0E=1320K
Einstein temperature B E k 0 = / 2 / 2 ( 1) 3 ( ) − = T T E V B E E e e T C Nk for the majority of solids Diamond
hightcmperature ho<1k,0e=h@02<T kgT 1 (er-12 e-。y号 C≡3Nkg consistent with the experimental results lowteperwture @>1k9e=h0, 0>T kgT er1C=3,2 xperimental Cy=AT3
CV 3NkB B E 0 k = high temperature consistent with the experimental results low temperature k T B V B B e k T C Nk 0 0 2 3 ( ) − = B E 0 k = Experimental
Despite its success in reproducing the approach of Cy->0 as T >0,the Einstein model is clearly deficient at very low T.What might be wrong with the assumptions it makes? 3N independent oscillators,all with frequency o Discrete allowed energies: En=nhon=0,l,2,. ● At high T the small spacing between the energy levels is irrelevant. At sufficiently low temperature,the energy level separation is much bigger than kBT. Eventually all the oscillators are "frozen"in the ground state.Increasing T a little does not change this,i.e.it does not change the energy
• At high T the small spacing between the energy levels is irrelevant. • At sufficiently low temperature, the energy level separation is much bigger than kBT. • Eventually all the oscillators are “frozen” in the ground state. Increasing T a little does not change this, i.e. it does not change the energy. Despite its success in reproducing the approach of CV → 0 as T → 0, the Einstein model is clearly deficient at very low T. What might be wrong with the assumptions it makes? • 3N independent oscillators, all with frequency • Discrete allowed energies: E = n n = 0,1, 2, . n