702 



BELL SYSTEM TECHNICAL JOURNAL 



but a diatomic molecule. Suppose Fig. 24 gives the dependence of 

 the energy of a molecule upon the internuclear distance. Suppose the 

 molecule is given vibrational energy corresponding to E on the figure. 



ao 



LATTICE CONSTANT 



60 

 TEMPERATURE 



Fig. 24 — The theory of thermal expansion. The asymmetry of the curve for 

 the energy of a crystal versus the lattice constant is responsible for the thermal 

 expansion. 



Then the nuclei will vibrate between positions h and c on the figure. 

 Since c lies more to the right of the equilibrium position than h does to 

 the left, the mean distance of separation, a, lies to the right of ao. 

 Increasing the vibrational energy to E' increases the mean separation 

 to a'. This shows that the asymmetry of the potential curve results in 

 a continuous increase in mean internuclear separation with increasing 

 energy of vibration. A crystal is, in a sense, an assemblage of diatomic 

 molecules, each pair of nearest neighbors having a potential energy 

 curve like that of Fig. 24, and its expansion is explained in the same 

 way. 



The theory outlined above can be made quantitative. From it we 

 obtain the interesting result that the thermal expansion coefficient is 

 proportional to the specific heat. This is a rather natural result: 

 we have seen that the total expansion is proportional to the thermal 

 energy; hence the rate of expansion with increasing temperature, i.e. 

 the thermal expansion coefficient, should be proportional to the rate of 

 increase in thermal energy with increasing temperature, i.e. to the 

 specific heat. The relationship embodying this statement is known 

 as Griineisen's law and is expressed by the equation 



a = 7-p.CF, 



(10) 



where a is the volume coefficient of thermal expansion (three times the 

 linear coefficient) , K is the compressibility, V the volume of one gram 



