Chapter 19: Superconductivity

Example 19.1, Page 19.13

In [1]:
# Given 
T_c = 7.2 # critical temperature in K
T = 5.1 # temperature in K
lambda_ = 380 # penetration depth at 0 K in A

#Calculations
lamda = lambda_ * (1 - (T / T_c)**4)**(-1./2)

#Result
print "Penetration depth is %.2f A"%lamda

Penetration depth is 439.30 A

Example 19.2, Page 19.13

In [2]:
from math import *

# Given 
Hc1 = 1.41e5 # first critical field at 14.1K
Hc2 = 4.205e5 # second critical field at 12.9K 
T1 = 14.11 # temperature in K
T2 = 12.9 # temperature in K 
T = 4.2 # temperature in K
lambda_ = 380 # penetration depth at 0 K in A

#Calculations
Tc = sqrt((Hc2*T1**2 - Hc1*T2**2) / (Hc2 - Hc1))
H_ = Hc1 / (1 - (T1 / Tc)**2)
Hc = H_ * (1 - (T/Tc)**2)

#Result
print "Transition temperature is %.2f K\nCritical field at temperate at 4.2 k is %.2e A/m"%(Tc,Hc)

Transition temperature is 14.68 K
Critical field at temperate at 4.2 k is 1.69e+06 A/m

Example 19.3, Page 19.14

In [3]:
from math import *

# Given 
d = 1e-3 # diameter of wire in m
T1 = 4.2 # temperature in K
T2 = 7.18 # temperature in K
H_ = 6.51e4 # critical magnetic field at 0 K

#Calculations
r = d / 2
Hc = H_ * (1 - (T1 / T2)**2)
Jc = (2 * pi * r * Hc) / (pi * r**2)

#Result
print "Critical current density is %.3e A/m^2"%Jc

Critical current density is 1.713e+08 A/m^2

Example 19.4, Page 19.15

In [4]:
 
# Given 
w = 199.5 # isotopic mass of Hg
Tc = 4.186 # critical temperature in K 
w_ = 203.4 # increased isotope mass of Hg

#Calculations
Tc_ = Tc * (w / w_)**(1./2)

#Result
print "Critical temperature is %.4f K"%Tc_

Critical temperature is 4.1457 K

Example 19.5, Page 19.15

In [5]:
 
# Given 
T_c = 4.2 # critical temperature in K
T = 2.9 # temperature in K
lamda = 57 # penetration depth at 2.9 K in nm

#Calculations
lambda_ = lamda * (1 - (T / T_c)**4)**(1./2)

#Result
print "Penetration depth at 0 K is %.2f nm"%lambda_

Penetration depth at 0 K is 50.10 nm

Example 19.6, Page 19.15

In [6]:
 
# Given
T1 = 2.18 # temperature in first case in K
lambda1 = 16 # penetration depth at 2.18 K in nm
T2 = 8.1 # temperature in second case in K
lambda2 = 96 # penetration depth at 8.1 K in nm

#Calculations
Tc = (((lambda2**2 * T2**4) - (T1**4 * lambda1**2)) / (lambda2**2 - lambda1**2))**(1./4)

#Result
print "Critical temperature is %.2f K"%Tc

Critical temperature is 8.16 K

Example 19.7, Page 19.16

In [7]:
 
# Given 
w = 26.91 # isotopic mass of superconducting sample
Tc = 1.19 # first critical temperature in K 
w_ = 32.13 # increased isotope mass of superconducting sample

#Calculations
Tc_ = Tc * (w / w_)**(1./2)

#Result
print "Critical temperature is %.3f K"%Tc_

Critical temperature is 1.089 K

Example 19.8, Page 19.16

In [8]:
 
# Given 
k = 1.38e-23 # Boltzmann's constant in J/K
h = 6.62e-34 # Planck constant in J sec
Tc = 4.2 # critical temperature of Hg in K
c = 3e8 # speed of light in m/sec 

#Calculations
E = 3 * k * Tc
lamda = h * c / E

#Result
print "Energy gap is %.2e eV\nWavelength of photon is %.2e m"%(E/1.6e-19,lamda)

Energy gap is 1.09e-03 eV
Wavelength of photon is 1.14e-03 m