# Chapter 21 : Diffusion of Solids¶

### Example 21.1 pageno : 577¶

In :
# Variables
c_cu = 2.*10**13;			#concentration of copper in /m**3
c_al = 4.*10**6;			#concn of copper on other side of Al in /m**3

# Calculations
t = 3.*10**-3;		    	#thickness in m
z = (c_cu-c_al)/t;			#z = dm/dx,concentration graient
jx = 10.**21;		    	#outward flux of copperv atoms in /sq m/sec
d = -jx/z;			        #diffusivity in sq m/sec

# Results
print "Diffusivity (in sq m/sec)  =  %.2e m**2/s"%d

Diffusivity (in sq m/sec)  =  -1.50e+05 m**2/s


### Example 21.2 pageno : 583¶

In :
import math

c_n = 12.;			#nitrogen concentration in kg/m**3
t = 6.*10**-3;			#thickness in m

# Calculations
z = (c_n-0)/t;			#concentration gradient in kg/m**4
d0 = 5.*10**-7;			#in sqm/sec
q = 75.*10**3;			#in j/mol
r = 8.314;			#in J/mol/K
t = 400.;			#in K
dx = d0*math.exp(-q/(r*t));			#diffusivity in sqm/sec
jx = dx * 2*10**-3;			#rate of flow of nitrogen in kg/sqm/sec

# Results
print "concentration gradient (in kg/m4)  =  %.0e"%z
print "Diffusivity (in sqm/sec)  =  %.3e m**2/s"%dx
print "Rate at which nitrogen escapes (in kg/sqm/sec)  =  %.3e kg/m**2/s"%jx

concentration gradient (in kg/m4)  =  2e+03
Diffusivity (in sqm/sec)  =  8.028e-17 m**2/s
Rate at which nitrogen escapes (in kg/sqm/sec)  =  1.606e-19 kg/m**2/s


### Example 21.4 pageno : 585¶

In :
import math

# variables
z = 8.;			#ratio of diffusion in silicon at 1350 C and 1100 C
x = math.log(z);

# calculations
q = x/(1.35*10**-5);			#activation energy for silver diffusion in J/mol
q1 = q/1000.;	        		#in kJ/mol

# results
print "Activation Energy in Silver diffusion (in kJ/mol)  =  %d kJ/mol"%q1

Activation Energy in Silver diffusion (in kJ/mol)  =  154 kJ/mol