import math
#Given Data
H_c0 = 0.0803; # Critical field at absolute zero, Tesla
T_c = 7.19; # Transition temperature of specimen lead, Kelvin
T = 5.0; # Temperature at which destruction of superconductivity is to be found, Kelvin
H_c = H_c0*(1.0-(T/T_c)**2); # Critical field required to destroy superconductivity, Tesla
print"Critical field required to destroy superconductivity = ",round(H_c,4),"T";
import math
#Given Data
H0 = 1970.0; # Critical field at absolute zero, Oe
T_c = 9.25; # Transition temperature of specimen Nb, Kelvin
T = 4.0; # Temperature at which destruction of superconductivity is to be found, Kelvin
H_c = H0*(1.0-(T/T_c)**2); # Limiting magnetic field, Oe
print"Limiting magnetic field of Nb to serve as superconductor = ",round(H_c),"Oe";
import math
#Given Data
T_1 = 14.0; # Temperature, K
T_2 = 13.0; # Temperature, K
H_c1 = 1.4*10**5; # Critical field at T_1, K
H_c2 = 4.2*10**5; # Critical field at T_2, K#As H_c1/H_c2 = (T_c**2-T_1**2)/(T_c**2-T_2**2), solving for T_c
T_c = math.sqrt((H_c2/H_c1*T_1**2 - T_2**2)/2); # The superconducting transition temperature of a specimen, K
print"Transition temperature of a specimen = ",round(T_c,4),"K";
import math
#Given Data
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
E_g = 3.4*10**-4; # Energy gap of aluminium, eV
v_F = 2.02*10**8; # Fermi velocity of aluminium, cm/sec
h_bar = 1.05*10**-34; # Planck's constant
L = h_bar*v_F/(2*E_g*e); # Coherence Length of aluminium, cm
print"The coherence length of aluminium = ","{0:.3e}".format(L),"cm";
import math
#Given Data
h = 6.6*10**-34; # Planck's constant, Js
e = 1.6*10**-19; # Energy eqivalent of 1 eV, eV/J
k = 0.86*10**-4; # Boltzmann constant, eV/K
T_c = 0.56; # Critical temperature for superconducting Zr, K
E_g = 3.52*k*T_c; # Energy gap of aluminium, J
c = 3*10**8; # Speed of light, m/s
lamda = h*c/(E_g*e); # Wavelength of photon required to break a Cooper pair, m
print"The wavelength of photon required to break a Cooper pair = ","{0:.3e}".format(lamda),"m";
import math
#Given Data
Lamda_0 = 390.0; # Penetration depth at absolute zero, angstorm
T_c = 7.0; # Transition temperature of Pb, K
T = 2.0; # Givn temperature, K
Lamda = Lamda_0*(1.0-(T/T_c)**2)**(-1.0/2); # London penetration depth in Pb at 2K, angstorm
print"The London penetration depth in Pb at 2K = ",round(Lamda,4),"angstorm";
print"The London penetration depth at T = T_c becomes Inf";
import math
import numpy
#Given data
M = (199.5, 200.7, 202.0, 203.3); # Isotopic mass of Hg, amu
T_c = (4.185, 4.173, 4.159, 4.146); # Critical temperature of Hg, kelvin
alpha = 0.5; # Trial value of Isotopic exponent
# Accroding to isotopic effect, T_c = K*M**(-alpha), solving for K
K = T_c[1]/M[1]**(-alpha); # Isoptopic coefficent
Tc = numpy.zeros(3);
for i in xrange(len(Tc)):
Tc[i] = K*M[i+1]**(-alpha)
print"Tc[",i,"] = ",round(Tc[i],4);
if T_c[1]-Tc[0]<0.001 and T_c[2]-Tc[1]<0.001 and T_c[3]-Tc[2]<0.001 :
print"The isotopic exponent in Isotopic effect of Hg =",alpha;
import math
#GIven Data
M_1 = 202.0; # Mass of first isotope of mercury, amu
M_2 = 199.0; # Mass of second isotope of mercury, amu
T_c1 = 4.153; # Transition temperature of first isotope of mercury, K
#As T_c1/T_c2 = (M_2/M_1)**1/2, solving for T_c2
T_c2 = math.sqrt(M_1/M_2)*T_c1;
print"The transition temperature of isotope of Hg whose mass number is ",M_2,"=",round(T_c2,4),"K";
import math
#Given Data
alpha = 0.5; # Isotopic exponent of Osmium
T_c = 0.655; # Transition temperature of Osmium, K
M = 190.2; # Mass of Osmium, amu
K = T_c*M**alpha; # K is the constant of proportionality
print"The value of constant of proportionality =",round(K,4);
import math
#Given Data
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J
Theta_D = 96; # Debye temperature, kelvin
N0 = 0.3678; # Density of states at Fermi energy
V = 1.0; # Volume of the material, metre cube
T_c = 1.14*Theta_D*math.exp(-1.0/(N0*V)); # Critical temperature of the material, K
Delta_0 = k*Theta_D/math.sinh(1.0/(N0*V)); # Energy gap at absolute zero, J
print"The transition temperature of a material = ",round(T_c,3),"K";
print"The energy gap of a material = ","{0:.3e}".format(Delta_0/e),"eV";
import math
#Given Data
Theta_D = 350.0; # Debye temperature, kelvin
Lamda = 0.828; # Electron-phonon coupling constant
mu_prime = 0.1373; # Reduced mass of a superconductor, amu
T_c = Theta_D/1.45*math.exp(-1.04*(1+Lamda)/(Lamda-mu_prime*(1+0.62*Lamda))); #Transition temperature of superconductor using McMillan formula,K
print"The transition temperature of the superconductor using McMillan formula = ",round(T_c,3),"K";
import math
#Given Data
Theta_D = 350; # Debye temperature, kelvin
Lamda = 0.641; # Electron-phonon coupling constant
mu_prime = 0.143; # Reduced mass of a superconductor, amu
T_c = Theta_D/1.45*math.exp(-1.04*(1+Lamda)/(Lamda-mu_prime*(1+0.62*Lamda)));#Transition temperature of superconductor using McMillan formula,K
print"The superconducting transition temperature of a superconductor using McMillan formula = ",round(T_c,4),"K";
import math
#Given Data
Theta_D = 490; # Debye temperature, Kelvin
Lamda = 0.8; # wavelength of a superconductor, angstorm
mu_prime = 0.13; # Reduced mass of a superconductor, amu
T_c = Theta_D/1.45*math.exp(-1.04*(1+Lamda)/(Lamda-mu_prime*(1+0.62*Lamda)));
print"The superconducting transition temperature of a borocarbide superconductor =",round(T_c,4),"K";
import math
#Given Data
T_c = 16.5; # Transition temperature of a superconductor, K
Lamda = [0.7, 0.8, 0.9, 1.0] # Electron-phonon coupling constants at different Tc values
Theta_D = 503.0; # Debye temperature, kelvin
mu_prime = 0.13; # Reduced mass of a superconductor, amu
Tc = [0.0, 0.0, 0.0, 0.0];
print"_____________________";
print"Lamda Tc";
print"_____________________";
for i in xrange(len(Lamda)):
Tc[i] = Theta_D/1.45*math.exp(-1.04*(1+Lamda[i])/(Lamda[i]-mu_prime*(1+0.62*Lamda[i])));
if abs(Tc[i] - 16.5) < 1.0 :
best_Lvalue = Lamda[i];
print"",Lamda[i]," ",round(Tc[i],3),"K";
print"_____________________";
print"The best electron-phonon coupling constant should be slightly above ", best_Lvalue;
import math
#Given Data
T_c = 39.4; # Transition temperature of a superconductor, K
Lamda = 1; # Electron-phonon coupling constant for a superconductor
mu_prime= 0.15; # Reduced mass of a superconductor, amu
# As T_c = Theta_D/1.45*exp(-1.04*(1+Lamda)/(Lamda-mu_prime*(1+0.62*Lamda))), solving for Theta_D
Theta_D = T_c*1.45*math.exp(1.04*(1+Lamda)/(Lamda-mu_prime*(1+0.62*Lamda)));
print"The Debye temperature of a BCS superconductor = ",round(Theta_D,3),"K";