# Chapter 4 : Crystallography¶

### Example 4.3 page no : 82¶

In [1]:
# Variables
r_na = 0.98;			#ionic radius of sodium in angstorm
r_cl = 1.81;			#ionic radius of chlorine in angstorm
n = 4.;     			#in fcc there are 4 Na and 4 Cl ions

# Calculations
a = ((2*r_na)+(2*r_cl));			#latice constant
apf = ((n*(4./3)*3.14*r_na**3)+(n*(4./3)*3.14*r_cl**3))/a**3;

# Results
print "Lattice consmath.tant  =  ",a
print "atomic packing fraction of NaCl having FCC structure  =  %.2f"%apf

Lattice consmath.tant  =   5.58
atomic packing fraction of NaCl having FCC structure  =  0.66


### Example 4.4 pageno : 83¶

In [7]:
import math

# Variables
r = 1.278;			#radius of copper in angstorm

#copper has FCC structure
a = round(4*r/math.sqrt(2),2);			#in angstorm
a1 = a*10**-8;			        #in cm
aw = 63.54;         			#atomic weight of copper
ne = 4.;			            #fcc
na = 6.023*10**23;			    #Avagadro's no.
p = aw*ne/(na*a1**3);			#in g/cm**3

# Results
print "a (in Angstorm)  =  %.2f A"%a
print "Density of Copper (in gm/cm**3) : %.2f"%p

a (in Angstorm)  =  3.61 A
Density of Copper (in gm/cm**3) : 8.97


### Example 4.5 pageno : 84¶

In [13]:
# Variables
w_na = 23.;    			#atomic weight of Na
w_cl = 35.5;			#atomic weight of Cl
w = w_na+w_cl;			#effective no.of atoms in FCC structure
n = 4.;     			#FCC

# Calculations
na = 6.023*10**23;			#Avagadrro's no.
w_4 = w*n/na;			#weight of 4 molecules in gm
p = 2.18;			#density in gm/cm**3
a3 = (w*n)/(na*p)
a = a3**(1./3)
#a = (w_4/p)**(1/3);			#in cm
a1 = a*10**8;			#in angstorm
d = a1/2;

# Results
print "unit cell dimension (in angstorm)  =  %.2f A"%a1
print "Distance between two adjacent atoms (in Angstorm)  =  %.2f A"%d

unit cell dimension (in angstorm)  =  5.63 A
Distance between two adjacent atoms (in Angstorm)  =  2.81 A


### Example 4.6 pageno : 84¶

In [15]:
# Variables
n = 2.;          			#BCC
p = 7.86;	    		    #density in gm/cm**3
aw = 55.85;		        	#atomic weight of iron

# Calculations
na = 6.023*10**23;		            	#Avagadrro's no.
a = ((aw*n)/(na*p))**(1./3);			#in cm
a1 = a*10**8;	                		#in angstorm
r = math.sqrt(3)*a1/4;

# Results
print "unit cell dimension of iron (in angstorm)  =  %.2f A"%a1
print "atomic radius  =  %.3f A"%r

unit cell dimension of iron (in angstorm)  =  2.87 A
atomic radius  =  1.242 A