11: Lattice dynamics

Example number 11.1, Page number 238

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;    #planck's constant(Js)
k=1.38*10**-23;   #boltzmann constant(J/K)
thetaD=350;    #temperature for Cu(K)
theetaD=550;   #temperature for Si(K)

#Calculation
newDCu=k*thetaD/h;   #highest possible frequency for Cu(per sec)
newDSi=k*theetaD/h;  #highest possible frequency for Si(per sec)

#Result
print "highest possible frequency for Cu is",round(newDCu/10**11,3),"*10**11 per sec"
print "highest possible frequency for Si is",round(newDSi/10**11,2),"*10**11 per sec"

highest possible frequency for Cu is 72.895 *10**11 per sec
highest possible frequency for Si is 114.55 *10**11 per sec

Example number 11.2, Page number 238

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;    #planck's constant(Js)
k=1.38*10**-23;   #boltzmann constant(J/K)
N=6.02*10**26;   #avagadro number(k/mole)
T=10;   #temperature(K)
thetaD=105;   #debye temperature(K)

#Calculation
C=(12/5)*(math.pi**4)*N*k*(T/thetaD)**3;   #specific heat of lead(J/K kmol)
newD=k*thetaD/h;    #highest frequency(per sec)

#Result
print "specific heat of lead is",round(C,1),"J/K kmol"
print "answer varies due to rounding off errors"
print "highest frequency is",round(newD/10**11,2),"*10**11 per sec"

specific heat of lead is 1677.7 J/K kmol
answer varies due to rounding off errors
highest frequency is 21.87 *10**11 per sec