12: X-ray Diffraction

Example number 1, Page number 378

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

#Variable declaration
d=0.282;       #lattice spacing(nm)
theta=(8+(35/60))*math.pi/180;     #glancing angle(radian)
n1=1;                  #order

#Calculation
lamda=2*d*math.sin(theta)/n1;    #wavelength of X-rays(nm)
n=2*d/lamda;                     #maximum order of diffraction

#Result
print "wavelength of X-rays is",round(lamda,4),"nm"
print "maximum order of diffraction is",int(n)

wavelength of X-rays is 0.0842 nm
maximum order of diffraction is 6

Example number 2, Page number 378

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=3.209;       #lattice spacing(angstrom)
lamda=1.92;    #wavelength of X-rays(angstrom)
n1=1;                  #order
n2=2;                  #order 

#Calculation
theta1=math.asin(n1*lamda/(2*d))*180/math.pi;    #glancing angle for 1st order(degrees)
theta1d=int(theta1);                             #glancing angle for 1st order(degrees)  
theta1m=(theta1-theta1d)*60;                     #glancing angle for 1st order(minutes)
theta2=math.asin(n2*lamda/(2*d))*180/math.pi;    #glancing angle for 2nd order(degrees)
theta2d=int(theta2);                             #glancing angle for 2nd order(degrees)
theta2m=(theta2-theta2d)*60;                     #glancing angle for 2nd order(minutes)

#Result
print "glancing angle for 1st order is",theta1d,"degrees",int(theta1m),"minutes"
print "glancing angle for 2nd order is",theta2d,"degrees",int(theta2m),"minutes"
print "answers given in the book are wrong"

glancing angle for 1st order is 17 degrees 24 minutes
glancing angle for 2nd order is 36 degrees 44 minutes
answers given in the book are wrong

Example number 4, Page number 379

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=3.05;       #lattice spacing(angstrom)
theta=12*math.pi/180;     #glancing angle(radian)
n=1;                  #order

#Calculation
lamda=2*d*math.sin(theta)/n1;    #wavelength of X-rays(angstrom)

#Result
print "wavelength of X-rays is",round(lamda,3),"angstrom"
print "answer given in the book is wrong"

wavelength of X-rays is 1.268 angstrom
answer given in the book is wrong

Example number 5, Page number 380

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
thetaA=30*math.pi/180;     #glancing angle(radian)
thetaB=60*math.pi/180;     #glancing angle(radian)
n1=1;                  #order
n2=2;                  #order
lamdaB=0.9;            #wavelength of X-rays(angstrom)

#Calculation
lamdaA=2*lamdaB*math.sin(thetaA)/math.sin(thetaB);    #wavelength of line A(angstrom)

#Result
print "wavelength of line A is",round(lamda,3),"angstrom"
print "answer given in the book is wrong"

wavelength of line A is 1.268 angstrom
answer given in the book is wrong

Example number 6, Page number 380

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=2.51;       #lattice spacing(angstrom)
theta=9*math.pi/180;     #glancing angle(radian)
n1=1;                    #order
n2=2;                    #order

#Calculation
lamda=2*d*math.sin(theta)/n1;    #wavelength of X-rays(angstrom)
theta=math.asin(n2*lamda/(2*d))*180/math.pi; #glancing angle for 2nd order(degrees)

#Result
print "wavelength of X-rays is",round(lamda,4),"angstrom"
print "glancing angle for 2nd order is",round(theta,1),"degrees"

wavelength of X-rays is 0.7853 angstrom
glancing angle for 2nd order is 18.2 degrees