

In [1]:

    
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit  # import the curve fitting function
%matplotlib inline

DATA!



In [2]:

    
#Current in Pico Amps
#T157

FST157 = np.loadtxt('FS1_T157.csv');
Voltage_FST157 = np.array([FST157[i][0] for i in np.arange(len(FST157))])
Current_FST157 = np.array([FST157[i][1] for i in np.arange(len(FST157))])*1e12

Min6to9T157 = np.loadtxt('Min6to9T157.csv');
Voltage_Min6to9T157 = np.array([Min6to9T157[i][0] for i in np.arange(len(Min6to9T157))])
Current_Min6to9T157 = np.array([Min6to9T157[i][1] for i in np.arange(len(Min6to9T157))])*1e12

Min11to14T157 = np.loadtxt('Min11to14T157.csv');
Voltage_Min11to14T157= np.array([Min11to14T157[i][0] for i in np.arange(len(Min11to14T157))])
Current_Min11to14T157 = np.array([Min11to14T157[i][1] for i in np.arange(len(Min11to14T157))])*1e12

Min16to19T157 = np.loadtxt('Min16to19T157.csv');
Voltage_Min16to19T157= np.array([Min16to19T157[i][0] for i in np.arange(len(Min16to19T157))])
Current_Min16to19T157 = np.array([Min16to19T157[i][1] for i in np.arange(len(Min16to19T157))])*1e12

Min21to24T157 = np.loadtxt('Min21to24T157.csv');
Voltage_Min21to24T157= np.array([Min21to24T157[i][0] for i in np.arange(len(Min21to24T157))])
Current_Min21to24T157 = np.array([Min21to24T157[i][1] for i in np.arange(len(Min21to24T157))])*1e12

Min24to29T157 = np.loadtxt('Min24to29T157.csv');
Voltage_Min24to29T157= np.array([Min24to29T157[i][0] for i in np.arange(len(Min24to29T157))])
Current_Min24to29T157 = np.array([Min24to29T157[i][1] for i in np.arange(len(Min24to29T157))])*1e12

Min31to34T157 = np.loadtxt('Min31to34T157.csv');
Voltage_Min31to34T157= np.array([Min31to34T157[i][0] for i in np.arange(len(Min31to34T157))])
Current_Min31to34T157 = np.array([Min31to34T157[i][1] for i in np.arange(len(Min31to34T157))])*1e12

Min36to39T157 = np.loadtxt('Min36to39T157.csv');
Voltage_Min36to39T157= np.array([Min36to39T157[i][0] for i in np.arange(len(Min36to39T157))])
Current_Min36to39T157 = np.array([Min36to39T157[i][1] for i in np.arange(len(Min36to39T157))])*1e12

Min37to40T157 = np.loadtxt('Min37to40T157.csv');
Voltage_Min37to40T157= np.array([Min37to40T157[i][0] for i in np.arange(len(Min37to40T157))])
Current_Min37to40T157 = np.array([Min37to40T157[i][1] for i in np.arange(len(Min37to40T157))])*1e12



In [3]:

    
#Current in Pico Amps
#T186

FST186 = np.loadtxt('FS1_T186.csv');
Voltage_FST186 = np.array([FST186[i][0] for i in np.arange(len(FST186))])
Current_FST186 = np.array([FST186[i][1] for i in np.arange(len(FST186))])*1e12

Min11to14T186 = np.loadtxt('Min11to14T186.csv');
Voltage_Min11to14T186 = np.array([Min11to14T186[i][0] for i in np.arange(len(Min11to14T186))])
Current_Min11to14T186 = np.array([Min11to14T186[i][1] for i in np.arange(len(Min11to14T186))])*1e12

Min16to19T186= np.loadtxt('Min16to19T186.csv');
Voltage_Min16to19T186= np.array([Min16to19T186[i][0] for i in np.arange(len(Min16to19T186))])
Current_Min16to19T186 = np.array([Min16to19T186[i][1] for i in np.arange(len(Min16to19T186))])*1e12

Min21to24T186 = np.loadtxt('Min21to24T186.csv');
Voltage_Min21to24T186= np.array([Min21to24T186[i][0] for i in np.arange(len(Min21to24T186))])
Current_Min21to24T186 = np.array([Min21to24T186[i][1] for i in np.arange(len(Min21to24T186))])*1e12

Min25to28T186 = np.loadtxt('Min25to28T186.csv');
Voltage_Min25to28T186= np.array([Min25to28T186[i][0] for i in np.arange(len(Min25to28T186))])
Current_Min25to28T186 = np.array([Min25to28T186[i][1] for i in np.arange(len(Min25to28T186))])*1e12

Min31to34T186 = np.loadtxt('Min31to34T186.csv');
Voltage_Min31to34T186= np.array([Min31to34T186[i][0] for i in np.arange(len(Min31to34T186))])
Current_Min31to34T186 = np.array([Min31to34T186[i][1] for i in np.arange(len(Min31to34T186))])*1e12

Min36to39T186 = np.loadtxt('Min36to39T186.csv');
Voltage_Min36to39T186= np.array([Min36to39T186[i][0] for i in np.arange(len(Min36to39T186))])
Current_Min36to39T186 = np.array([Min36to39T186[i][1] for i in np.arange(len(Min36to39T186))])*1e12

430 K



In [4]:

    
plt.figure(figsize=(10,6))
plt.xticks(size = 15);
plt.yticks(size = 15);

plt.scatter(Voltage_FST157,Current_FST157,marker='.');
plt.xlim(0,40);
plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);
plt.savefig('IV430K.png')

Individual Dips

First Dip



In [5]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(6.75,8.25) 

plsq, pcov = curve_fit(myfun, Voltage_Min6to9T157[80:220], Current_Min6to9T157[80:220], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min
    


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min6to9T157[80:220],Current_Min6to9T157[80:220],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(6.7,8.3);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(7,9.1, '$V_{min} = %.1f \pm %.1f$ V' % (V_min, dV) ,size=20)

plt.legend(loc='best');

Second Dip



In [6]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(12.05,13.05) 

plsq, pcov = curve_fit(myfun, Voltage_Min11to14T157[110:200], Current_Min11to14T157[110:200], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min11to14T157[110:200],Current_Min11to14T157[110:200],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(12.05,13.05);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(12.1,20.1, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)

plt.legend(loc='best');

Dip Three



In [7]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(17.2,17.85) 

plsq, pcov = curve_fit(myfun, Voltage_Min16to19T157[62:90], Current_Min16to19T157[62:90], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min16to19T157[62:90],Current_Min16to19T157[62:90],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(17.2,17.85);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(17.25,32, '$V_{min} = %.1f \pm %.1f$ V' % (minima(b,c), np.sqrt((eb/b)**2 + (ec/c)**2)*minima(b,c)) ,size=20)

plt.legend(loc='best');

Dip Four



In [8]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(22.15,23.25) 

plsq, pcov = curve_fit(myfun, Voltage_Min21to24T157[60:110], Current_Min21to24T157[60:110], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min21to24T157[60:110],Current_Min21to24T157[60:110],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(22.15,23.25);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(22.4,64, '$V_{min} = %.1f \pm %.1f$ V' % (minima(b,c), np.sqrt((eb/b)**2 + (ec/c)**2)*minima(b,c)) ,size=20)

plt.legend(loc='best');

Fifth Dip



In [9]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(27.39,28.2) 

plsq, pcov = curve_fit(myfun, Voltage_Min24to29T157[70:110], Current_Min24to29T157[70:110], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min24to29T157[70:110],Current_Min24to29T157[70:110],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(27.39,28.2);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(27.6,96, '$V_{min} = %.1f \pm %.1f$ V' % (minima(b,c), np.sqrt((eb/b)**2 + (ec/c)**2)*minima(b,c)) ,size=20)

plt.legend(loc='best');

Dip 6



In [10]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(32.5,33.81) 

plsq, pcov = curve_fit(myfun, Voltage_Min31to34T157[80:125], Current_Min31to34T157[80:125], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min31to34T157[80:125],Current_Min31to34T157[80:125],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(32.5,33.6);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(32.6,155, '$V_{min} = %.1f \pm %.1f$ V' % (minima(b,c), np.sqrt((eb/b)**2 + (ec/c)**2)*minima(b,c)) ,size=20)

plt.legend(loc='best');

Dip 7



In [11]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(37.95,38.65) 

plsq, pcov = curve_fit(myfun, Voltage_Min37to40T157[95:165], Current_Min37to40T157[95:165], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min37to40T157[95:165],Current_Min37to40T157[95:165],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(37.95,38.65);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(38.1,191, '$V_{min} = %.1f \pm %.1f$ V' % (minima(b,c), np.sqrt((eb/b)**2 + (ec/c)**2)*minima(b,c)) ,size=20)

plt.legend(loc='best');

T = 459 K



In [12]:

    
plt.figure(figsize=(10,6))
plt.xticks(size = 15);
plt.yticks(size = 15);

plt.scatter(Voltage_FST186,Current_FST186,marker='.');
plt.xlim(0,41);
plt.ylim(0,155);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);
plt.savefig('IV459K.png')

Individual Dips

Dip One



In [13]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(7,10) 

plsq, pcov = curve_fit(myfun, Voltage_FST186[70:100], Current_FST186[70:100], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_FST186[70:100],Current_FST186[70:100],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(7,10);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(7.5,10, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)

plt.legend(loc='best');

Dip Two



In [14]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(11.65,14.1) 

plsq, pcov = curve_fit(myfun, Voltage_Min11to14T186[30:250], Current_Min11to14T186[30:250], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min11to14T186[30:250],Current_Min11to14T186[30:250],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(11.65,14.1);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(12.5,20, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)

plt.legend(loc='best');

Third Dip



In [15]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(16.55,18.45) 

plsq, pcov = curve_fit(myfun, Voltage_Min16to19T186[65:240], Current_Min16to19T186[65:240], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min16to19T186[65:240],Current_Min16to19T186[65:240],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(16.55,18.45);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(17,30, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)

plt.legend(loc='best');

Dip Four



In [16]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(21.45,23.15) 

plsq, pcov = curve_fit(myfun, Voltage_Min21to24T186[50:210], Current_Min21to24T186[50:210], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min21to24T186[50:210],Current_Min21to24T186[50:210],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(21.45,23.15);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(21.8,40, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)

plt.legend(loc='best');

Dip Five



In [17]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(26.25,28.05) 

plsq, pcov = curve_fit(myfun, Voltage_Min25to28T186[80:250], Current_Min25to28T186[80:250], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min25to28T186[80:250],Current_Min25to28T186[80:250],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(26.25,28.05);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(26.8,55, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)
plt.legend(loc='best');

Dip Six



In [18]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(31.2,32.9) 

plsq, pcov = curve_fit(myfun, Voltage_Min31to34T186[30:180], Current_Min31to34T186[30:180], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min31to34T186[30:180],Current_Min31to34T186[30:180],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(31.2,32.9);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(31.5,65, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)
plt.legend(loc='best');

Dip 7



In [19]:

    
def myfun(V,a,b,c):
    ans =  a + b*V + c*V**2
    return ans

p0 = [0.5,0.5,0.5] #guess

xspace = np.linspace(36.25,37.85) 

plsq, pcov = curve_fit(myfun, Voltage_Min36to39T186[30:180], Current_Min36to39T186[30:180], p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
a = plsq[0]
ea = np.sqrt(pcov[0,0])

b = plsq[1]
eb = np.sqrt(pcov[1,1])

c = plsq[2]
ec = np.sqrt(pcov[2,2])


def minima(b,c):
    return -b/(2*c)

V_min = minima(b,c)

dV = np.sqrt((eb/b)**2 + (ec/c)**2)*V_min


yfit = myfun(xspace,plsq[0],plsq[1],plsq[2])  # use fit results for a, b, c

plt.figure(figsize=(10,6));


plt.scatter(Voltage_Min36to39T186[30:180],Current_Min36to39T186[30:180],marker='.',label='Data');
plt.xticks(size = 15);
plt.yticks(size = 15);
plt.xlim(36.25,37.85);
#plt.ylim(0,400);
plt.xlabel('Accelerating Voltage (V)',size=20);
plt.ylabel('Current (pA)',size=20);

plt.plot(xspace,yfit,label='Fit');
plt.text(36.5,85, '$V_{min} = %.1f \pm %.1f$ V' % (V_min,dV) ,size=20)
plt.legend(loc='best');

Together



In [20]:

    
f, axarr = plt.subplots(1, 2,figsize=(8,3));

axarr[0].scatter(Voltage_FST157,Current_FST157,marker='.');
axarr[0].set_xlabel('Accelerating Voltage (V)');
axarr[0].set_ylabel('Current Signal (pA)');
axarr[0].set_xlim(0,41);
axarr[0].set_ylim(0,375);
axarr[0].text(3,300,'T = 430 K');

axarr[1].scatter(Voltage_FST186,Current_FST186,marker='.');
axarr[1].set_xlabel('Accelerating Voltage (V)');
#axarr[1].set_ylabel('Current Signal (pA)');
axarr[1].set_xlim(0,41);
axarr[1].set_ylim(0,150);
axarr[1].text(3,117,'T = 459 K');


# Fine-tune figure; hide x ticks for top plots and y ticks for right plots
f.tight_layout()
#plt.setp([a.get_xticklabels() for a in axarr[0, :]], visible=False);
#plt.setp([a.get_yticklabels() for a in axarr[:, 1]], visible=False);
plt.savefig('BothIV.png')

Contact Potential and First Excitation Energy

The contact potential is independent of the accelerating voltage, so its presence is of equal strength for all dips. Naively we would expect, the dip energy when divided by the dip number to provide the excitation energy. But this is actually E_dip = n*E_ex + E_con



In [21]:

    
EDip430 = np.array([7.5,12.5,17.5,22.7,27.9,33.1,38.3])
dEDip430 = np.array([0.2,0.4,0.8,0.6,0.7,0.9,1.4])

EDip459 = np.array([7.8,12.9,17.5,22.2,27.1,32,37.1])
dEDip459 = np.array([1.6,0.3,0.5,0.6,0.7,1,0.6])

n = np.array([1,2,3,4,5,6,7])



In [30]:

    
def myfun(n,EHg,EContact):
    ans =  n*EHg + EContact
    return ans

p0 = [0.5,0.5] #guess

xspace = np.linspace(1,7) 

plsq, pcov = curve_fit(myfun, n, EDip430, p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
EHg430 = plsq[0]
eEHg430 = np.sqrt(pcov[0,0])

EContact430 = plsq[1]
eEContact430 = np.sqrt(pcov[1,1])

yfit430 = myfun(xspace,plsq[0],plsq[1])  # use fit results for a, b, c



In [38]:

    
def myfun(n,EHg,EContact):
    ans =  n*EHg + EContact
    return ans

p0 = [0.5,0.5] #guess

xspace = np.linspace(1,7) 

plsq, pcov = curve_fit(myfun, n, EDip459, p0)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
EHg459 = plsq[0]
eEHg459 = np.sqrt(pcov[0,0])

EContact459 = plsq[1]
eEContact459 = np.sqrt(pcov[1,1])

yfit459 = myfun(xspace,plsq[0],plsq[1])  # use fit results for a, b, c



In [51]:

    
f, axarr = plt.subplots(1, 2,figsize=(8,3));

axarr[0].scatter(n,EDip430,marker='.',label='T = 430 K');
axarr[0].errorbar(n,EDip430,yerr =dEDip430,fmt='none');
axarr[0].plot(xspace,yfit430,label='Fit')
axarr[0].legend(loc='best')


axarr[0].set_xlabel('$n$',size=20);
axarr[0].set_ylabel('$K_n$',size=20);

axarr[0].text(4.1,15,'$E_{Hg} = %.2f \pm %.2f$ eV' % (EHg430,eEHg430));
axarr[0].text(4.1,10,'$E_{Contact} = %.2f \pm %.2f$ eV' % (EContact430,eEContact430));

axarr[1].scatter(n,EDip459,marker='.',label='T = 459 K');
axarr[1].errorbar(n,EDip459,yerr =dEDip459,fmt='none');
axarr[1].set_xlabel('$n$',size=20);

axarr[1].text(4.1,10,'$E_{Hg} = %.2f \pm %.2f$ eV' % (EHg459,eEHg459));
axarr[1].text(4.1,5,'$E_{Contact} = %.2f \pm %.2f$ eV' % (EContact459,eEContact459));

axarr[1].plot(xspace,yfit459,label='Fit')
axarr[1].legend(loc='best')

#axarr[1].text(1,35,'T = 459 K');


# Fine-tune figure; hide x ticks for top plots and y ticks for right plots
f.tight_layout()
#plt.setp([a.get_xticklabels() for a in axarr[0, :]], visible=False);
#plt.setp([a.get_yticklabels() for a in axarr[:, 1]], visible=False);
plt.savefig('ContactPotential.png')

Part 2



In [ ]:

    
EDip430 = np.array([7.5,12.5,17.5,22.7,27.9,33.1,38.3])
dEDip430 = np.array([0.2,0.4,0.8,0.6,0.7,0.9,1.4])

EDip459 = np.array([7.8,12.9,17.5,22.2,27.1,32,37.1])
dEDip459 = np.array([1.6,0.3,0.5,0.6,0.7,1,0.6])

n = np.array([1,2,3,4,5,6,7])



In [72]:

    
DeltaE430 = np.array([EDip430[i] - EDip430[i-1] for i in np.arange(1,7)])
eDeltaE430 = np.array([np.sqrt(dEDip430[i]**2 + dEDip430[i-1]**2) for i in np.arange(1,7)])

DeltaE459 = np.array([EDip459[i] - EDip459[i-1] for i in np.arange(1,7)])
eDeltaE459 = np.array([np.sqrt(dEDip459[i]**2 + dEDip459[i-1]**2) for i in np.arange(1,7)])

n = np.array([2,3,4,5,6,7])



In [96]:

    
def myfun(n,yl,EHg):
    ans =  (1+yl*(2*n-1))*EHg
    return ans

p0 = [0.5,0.5] #guess

xspace = np.linspace(2,7) 

plsq, pcov = curve_fit(myfun, n, DeltaE430, p0,sigma = eDeltaE430)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
yl430  = plsq[0]
eyl430 = np.sqrt(pcov[0,0])

EHg430 = plsq[1]
eHg430 = np.sqrt(pcov[1,1])

yfit430 = myfun(xspace,plsq[0],plsq[1])  # use fit results for a, b, c



In [94]:

    
def myfun(n,yl,EHg):
    ans =  (1+yl*(2*n-1))*EHg
    return ans

p0 = [0.5,0.5] #guess

xspace = np.linspace(2,7) 

plsq, pcov = curve_fit(myfun, n, DeltaE459, p0,sigma = eDeltaE459)  # curve fit returns p and covariance matrix
# these give the parameters and the uncertainties
yl459  = plsq[0]
eyl459 = np.sqrt(pcov[0,0])

EHg459 = plsq[1]
eHg459 = np.sqrt(pcov[1,1])

yfit459 = myfun(xspace,plsq[0],plsq[1])  # use fit results for a, b, c



In [98]:

    
f, axarr = plt.subplots(1, 2,figsize=(10,4));

axarr[0].scatter(n,DeltaE430,marker='.',label='T = 430 K');
axarr[0].errorbar(n,DeltaE430,yerr = eDeltaE430,fmt='none');
axarr[0].plot(xspace,yfit430,label='Fit')
axarr[0].legend(loc='best')


axarr[0].set_xlabel('$n$',size=20);
axarr[0].set_ylabel('$\Delta K_n$',size=20);

axarr[0].text(2.3,3.3,'$E_{Hg} = %.2f \pm %.2f$ eV' % (EHg430,eEHg430),size='20');

axarr[1].scatter(n,DeltaE459,marker='.',label='T = 459 K');
axarr[1].errorbar(n,DeltaE459,yerr = eDeltaE459,fmt='none');

axarr[1].set_xlabel('$n$',size=20);

axarr[1].text(2.5,3.2,'$E_{Hg} = %.2f \pm %.2f$ eV' % (EHg459,eEHg459),size='20');

axarr[1].plot(xspace,yfit459,label='Fit')
axarr[1].legend(loc='best')

#axarr[1].text(1,35,'T = 459 K');


# Fine-tune figure; hide x ticks for top plots and y ticks for right plots
f.tight_layout()
#plt.setp([a.get_xticklabels() for a in axarr[0, :]], visible=False);
#plt.setp([a.get_yticklabels() for a in axarr[:, 1]], visible=False);
plt.savefig('End.png')



In [100]:

    
f, axarr = plt.subplots(1, 2,figsize=(10,4));

axarr[0].scatter(n,DeltaE430,marker='.',label='T = 430 K');
#axarr[0].errorbar(n,DeltaE430,yerr = eDeltaE430,fmt='none');
#axarr[0].plot(xspace,yfit430,label='Fit')
axarr[0].legend(loc='best')


axarr[0].set_xlabel('$n$',size=20);
axarr[0].set_ylabel('$\Delta K_n$',size=20);

#axarr[0].text(2.3,3.3,'$E_{Hg} = %.2f \pm %.2f$ eV' % (EHg430,eEHg430),size='20');

axarr[1].scatter(n,DeltaE459,marker='.',label='T = 459 K');
#axarr[1].errorbar(n,DeltaE459,yerr = eDeltaE459,fmt='none');

axarr[1].set_xlabel('$n$',size=20);

#axarr[1].text(2.5,3.2,'$E_{Hg} = %.2f \pm %.2f$ eV' % (EHg459,eEHg459),size='20');

#axarr[1].plot(xspace,yfit459,label='Fit')
axarr[1].legend(loc='best')

#axarr[1].text(1,35,'T = 459 K');


# Fine-tune figure; hide x ticks for top plots and y ticks for right plots
f.tight_layout()
#plt.setp([a.get_xticklabels() for a in axarr[0, :]], visible=False);
#plt.setp([a.get_yticklabels() for a in axarr[:, 1]], visible=False);
plt.savefig('End2.png')



In [ ]: