Chapter 10 : Crystallography and Crystal Imperfections

Example number 1 , Page number 178

In [1]:
#importing module
import math
from __future__ import division

#Variable declaration
rho=10.6              #density of material
n=4                   #No. of atoms/cell
A=108                 #Atomic weigth
No=6.023*10**23       #Avagadro's No.

#Calculations
a=((n*A)/(No*rho))**(1/3)/10**-8

#Result
print"lattice parameter a= %1.3f*10**-8 cm"  %a

lattice parameter a= 4.075*10**-8 cm

Example number 2 , Page number 179

In [2]:
#importing module
import math
from __future__ import division

#Variable declaration
rho=7.86*10**3        #density of material
n=2                   #No. of atoms/cell
A=55.85               #Atomic weigth
No=6.023*10**26       #Avagadro's No.

#Calculations
a=((n*A)/(No*rho))**(1/3)/10**-10

#Result
print"lattice parameter a= %1.2f*10**-10 m" %a

lattice parameter a= 2.87*10**-10 m

Example number 3 , Page number 179

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

#Variable declaration
M=58.5                #formula weigth
rho=2180              #density of material
n=4                   #No. of atoms/cell              
No=6.02*10**26        #Avagadro's No.

#Calculations
a=((n*M)/(No*rho))**(1/3)/10**-10/2

#Result
print"Distance between like atoms a= %1.3f*10**-10 m" %(2*a)
print"Distance between adjacent atoms a/2= %1.2f*10**-10 m" %a

Distance between like atoms a= 5.628*10**-10 m
Distance between adjacent atoms a/2= 2.81*10**-10 m

Example number 4 , Page number 179

In [4]:
#importing module
import math
from __future__ import division

#Variable declaration
M=58.45               #formula weigth
rho=2.17*10**3        #density of material
n=4                   #No. of atoms/cell              
No=6*10**26           #Avagadro's No.

#Calculations
a=((n*M)/(No*rho))**(1/3)/10**-10

#Result
print"Lattice constant a= %1.2f*10**-10 m" %a

Lattice constant a= 5.64*10**-10 m

Example number 5 , Page number 180

In [5]:
#importing module
import math
from __future__ import division

#Variable declaration
r=1.278               #atomic weigth              
No=6.02*10**26        #Avagadro's No.

#Calculations
a=2*math.sqrt(2)*r

#Result
print"Lattice constant a= %1.3f" %a,"Armstrong"

Lattice constant a= 3.615 Armstrong

Example number 6 , Page number 180

In [9]:
#importing module
import math
from __future__ import division

#Variable declaration
r=1.278               #atomic weigth              
N0=6.02*10**23        #Avagadro's No.
no=4                  #No. of atoms/cell
A=63.54               #Atomic weigth

#Calculations
a=2*math.sqrt(2)*r
rho=(no*A)/(N0*a**3)/10**-24

#Result
print"Density of the material= %1.2f" %rho,"gm/cc"

Density of the material= 8.94 gm/cc

Example number 7 , Page number 180

In [7]:
#importing module
import math
from __future__ import division

#Variable declaration
x=2                    #x intercept  
y=3                    #y intercept
z=3                    #z intercept

#Calculations          
rx=(1/x)*6             #reciprocal of x intercept
ry=(1/y)*6             #reciprocal of y intercept
rz=(1/z)*6             #reciprocal of z intercept

#Result
print"Miller indices are (",rx,",",ry,",",rz,")"

Miller indices are ( 3.0 , 2.0 , 2.0 )

Example number 8 , Page number 181

In [8]:
#importing module
import math
from __future__ import division

#Variable declaration
h=1
k=1
l=2
a=b=2.5
c=2.6

#Calculations          
d=((h**2/a**2)+(k**2/b**2)+(l**2/c**2))**(-0.5)

#Result
print"inter-planar spacing d= %1.2f" %d,"Armstrong"

inter-planar spacing d= 1.05 Armstrong