11: Crystal Structure

Example number 1, Page number 357

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

#Variable declaration  
a=1/2;
b=1/3;
c=1/4;     #intercepts along the three axes

#Calculations
def lcm(x, y):
    if x > y:
        greater = x
    else:
        greater = y
    while(True):
        if((greater % x == 0) and (greater % y == 0)):
            lcm = greater
            break
        greater += 1
        
    return lcm

z=lcm(1/a,1/b);
lcm=lcm(z,1/c);
h=a*lcm;
k=b*lcm;
l=c*lcm;      #miller indices of plane

#Result
print "miller indices of plane are (",int(h),int(k),int(l),")"

miller indices of plane are ( 6 4 3 )

Example number 2, Page number 357

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

#Variable declaration  
a=1/2;
b=1/3;
x=float("inf");
c=1/x;     #intercepts along the three axes

#Calculations
def lcm(x, y):
    if x > y:
        greater = x
    else:
        greater = y
    while(True):
        if((greater % x == 0) and (greater % y == 0)):
            lcm = greater
            break
        greater += 1
        
    return lcm

lcm=lcm(1/a,1/b);
h=a*lcm;
k=b*lcm;
l=c*lcm;      #miller indices of plane

#Result
print "miller indices of plane are (",int(h),int(k),int(l),")"

miller indices of plane are ( 3 2 0 )

Example number 3, Page number 358

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

#Variable declaration  
a=1/1;
b=1/2;
c=1/3;     #intercepts along the three axes

#Calculations
def lcm(x, y):
    if x > y:
        greater = x
    else:
        greater = y
    while(True):
        if((greater % x == 0) and (greater % y == 0)):
            lcm = greater
            break
        greater += 1
        
    return lcm

z=lcm(1/a,1/b);
lcm=lcm(z,1/c);
h=a*lcm;
k=b*lcm;
l=c*lcm;      #miller indices of plane

#Result
print "miller indices of plane are (",int(h),int(k),int(l),")"

miller indices of plane are ( 6 3 2 )

Example number 4, Page number 359

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

#Variable declaration  
a=1.1;
b=1.2;
c=1.3;     #intercepts along the three axes(angstrom)
h=2;
k=3;
l=4;       #miller indices of plane

#Calculations
l1=a*h/h;
l2=b*h/k;    #corresponding intercept on Y-axis(angstrom)
l3=c*h/l;    #corresponding intercept on Z-axis(angstrom)

#Result
print "corresponding intercept on Y-axis and Z-axis are",l2,"angstrom and",l3,"angstrom"

corresponding intercept on Y-axis and Z-axis are 0.8 angstrom and 0.65 angstrom

Example number 5, Page number 360

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

#Variable declaration  
a=1/1;
b=-1/3;
c=1/2;     #intercepts along the three axes

#Calculations
def lcm(x, y):
    if x > y:
        greater = x
    else:
        greater = y
    while(True):
        if((greater % x == 0) and (greater % y == 0)):
            lcm = greater
            break
        greater += 1
        
    return lcm

z=lcm(1/a,1/b);
lcm=lcm(z,1/c);
h=a*lcm;
k=b*lcm;
l=c*lcm;      #miller indices of plane

#Result
print "miller indices of plane are (",int(h),int(k),int(l),")"

miller indices of plane are ( 6 -2 3 )

Example number 6, Page number 360

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration    
n=4;        #number of molecules per unit cell
M=63.5;     #molecular weight
N=6.02*10**26;     #avagadro number(kg mol-1)
rho=8.96*10**3;    #density(kg/m**3)

#Calculations
a=(n*M/(rho*N))**(1/3);     #lattice constant(m)
a=round(a*10**10,2);        #lattice constant(angstrom) 
d=a/math.sqrt(2);           #distance between two nearest copper atoms(angstrom)

#Result
print "lattice constant is",a,"angstrom"
print "distance between two nearest copper atoms is",round(d,2),"angstrom"

lattice constant is 3.61 angstrom
distance between two nearest copper atoms is 2.55 angstrom

Example number 7, Page number 361

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

#Variable declaration    
n=2;        #number of molecules per unit cell
M=55.85;     #molecular weight
N=6.02*10**26;     #avagadro number(kg mol-1)
rho=7860;          #density(kg/m**3)

#Calculations
a=(n*M/(rho*N))**(1/3);     #lattice constant(m)

#Result
print "lattice constant is",round(a*10**10,4),"angstrom"

lattice constant is 2.8687 angstrom