# Crystal Physics¶

## Example number 5.1, Page number 149¶

In :
#To calculate the Miller indices

#Calculation
#The plane has intercepts a,2b,3c along 3 crystal axes
#lattice points are r = pa+qb+sc
#therefore p = 1 q = 2 s = 3
#miller indices are [1/p,1/q,1/s]

#Result
print "lattice points are p = 1 q = 2 s = 3"
print "miller indices are [1/p,1/q,1/s] or [1,1/2,1/3] or [6,3,2]"

lattice points are p = 1 q = 2 s = 3
miller indices are [1/p,1/q,1/s] or [1,1/2,1/3] or [6,3,2]


## Example number 5.2, Page number 150¶

In :
#To calculate the density of Si

#importing modules
import math

#Variable declaration
n = 8;          #number of atoms per cell
a = 5.43*10**-8;       #lattice constant(cm)
w = 28.1;              #atomic weight(gm)

#Calculation
ac = n/(a**3);         #atomic concentration(atoms/cm**3)
d = ac*w/N;            #density of Si(g/cm**3)
d=math.ceil(d*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "density of Si is",d,"g/cm**3"

density of Si is 2.333 g/cm**3


## Example number 5.3, Page number 151¶

In :
#To calculate the surface density of atoms

#importing modules
import math
from __future__ import division

#Variable declaration
a = 5;       #lattice constant(Angstrom)

#Calculation
a = a*10**-10;         #lattice constant(m)
#to calculate the planar concentration, only equilateral triangular region is considered of length a*math.sqrt(2) and height a*math.sqrt(3/2)
l = a*math.sqrt(2);           #length of face diagonal(m)
h = a*math.sqrt(3/2);         #height of triangle(m)
A = l*h/2;                    #area of shaded portion(m**2)
#every atom at the corner contributes 1/6 to this area.
n111 = (3/6)*(1/A);           #planar concentration(atoms/m**2)

#Result
print "surface density of atoms is",n111,"atoms/m**2"

surface density of atoms is 2.30940107676e+18 atoms/m**2


## Example number 5.4, Page number 152¶

In :
#To calculate the spacing of planes

#importing modules
import math

#Variable declaration
a = 4.049;       #lattice constant(Angstrom)
h = 2;
k = 2;
l = 0;           #miller indices of(2 2 0)

#Calculation
d = a/math.sqrt(h**2+k**2+l**2);        #spacing of planes(Angstrom)
d=math.ceil(d*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "spacing of planes is",d,"Angstrom"

spacing of planes is 1.432 Angstrom


## Example number 5.5, Page number 152¶

In :
#To calculate the size of unit cell

#importing modules
import math

#Variable declaration
d110 = 2.03;       #distance between planes(Angstrom)
h = 1;
k = 1;
l = 0;           #miller indices of(1 1 0)

#Calculation
a = d110*math.sqrt(h**2+k**2+l**2);        #size of unit cell(Angstrom)
a=math.ceil(a*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "size of unit cell is",a,"Angstrom"

size of unit cell is 2.871 Angstrom


## Example number 5.6, Page number 152¶

In :
#To calculate the spacing of planes

#importing modules
import math

#Variable declaration
a = 5.64;       #lattice constant(Angstrom)
h1 = 1;
k1 = 0;
l1 = 0;           #miller indices of(1 0 0)
h2 = 1;
k2 = 1;
l2 = 0;           #miller indices of(1 1 0)
h3 = 1;
k3 = 1;
l3 = 1;           #miller indices of(1 1 1)

#Calculation
d100 = a/math.sqrt(h1**2+k1**2+l1**2);        #spacing of planes(Angstrom)
d110 = a/math.sqrt(h2**2+k2**2+l2**2);        #spacing of planes(Angstrom)
d111 = a/math.sqrt(h3**2+k3**2+l3**2);        #spacing of planes(Angstrom)
d111=math.ceil(d111*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "spacing of plane  is",d100,"Angstrom"
print "spacing of plane  is",round(d110),"Angstrom"
print "spacing of plane  is",d111,"Angstrom"

spacing of plane  is 5.64 Angstrom
spacing of plane  is 4.0 Angstrom
spacing of plane  is 3.26 Angstrom


## Example number 5.7, Page number 153¶

In :
#To calculate the volume of unit cell

#importing modules
import math

#Variable declaration
r = 1.605;         #radius of atom(Angstrom)

#Calculation
r = r*10**-10;      #radius of atom(m)
a = 2*r;        #size of unit cell(m)
c = a*math.sqrt(8/3);
V = 3*math.sqrt(3)*a**2*c/2;       #volume of unit cell(m**3)

#Result
print "volume of unit cell is",V,"m**3"

volume of unit cell is 1.40330266432e-28 m**3

In [ ]: