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ass1: Is this enough for question 1?

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Kees van Kempen
2022-02-17 19:28:59 +01:00
parent 1cb8623412
commit 0ab6e35d2b
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14
sc_elements.py
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@ -70,3 +70,17 @@ fig.savefig('/home/kvkempen/Documents/20212022Q3/Superconductivity/assignments/s
#fig.savefig('/home/kvkempen/Documents/20212022Q3/Superconductivity/assignments/sc_elements.pdf') #fig.savefig('/home/kvkempen/Documents/20212022Q3/Superconductivity/assignments/sc_elements.pdf')
plt.close(fig) plt.close(fig)
##
print(df.corr())
##
# Now we split the data into groups.
elgr1 = ['Nb', 'Tc', 'Pb', 'V', 'Ta', 'Sn', 'In', 'Tl', 'Pa', 'Ga', 'Th', 'Re', 'Al', 'Mn', 'Mo', 'Zn', 'Be', 'Rn', 'Cd']
elgr2 = ['W', 'Li', 'Ru', 'U', 'Hf', 'Ti', 'Zr', 'Lu', 'Am', 'Hg', 'La']
gr1 = df[df['element'].isin(elgr1)]
gr2 = df[df['element'].isin(elgr2)]
print(gr1.corr(), '\n', gr2.corr())

16
superconductivity_assignment1_kvkempen.tex
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@ -56,7 +56,7 @@
\begin{document} \begin{document}
\section{Electron-phonon coupling in elements} \section{Electron-phonon coupling in elements}
Conventional superconductors (sc) are described by considering Cooper pairs: Conventional superconductors are described by considering Cooper pairs:
pairs of electrons mediated by electron-phonon coupling. pairs of electrons mediated by electron-phonon coupling.
This is usually described by BCS theory. This is usually described by BCS theory.
The hypothesis is that stronger electron-phonon coupling results in enhanced critical temperatures for the superconducting phase transition. The hypothesis is that stronger electron-phonon coupling results in enhanced critical temperatures for the superconducting phase transition.
@ -92,6 +92,20 @@ If $|r| = 1$, there is a perfectly linear relation.
The lower $|r|$ is, the less correlated the points are. The lower $|r|$ is, the less correlated the points are.
The sign of $r$ gives the direction of the trend. The sign of $r$ gives the direction of the trend.
This slightly positive value found for the superconducting elements suggests a slightly positive but uncertain correlation. This slightly positive value found for the superconducting elements suggests a slightly positive but uncertain correlation.
As the relation between electron-phonon coupling and resistivity is well-established, it seems reasonable to conclude that there is no unambiguous relation between $T_c$ and $\rho_{300K}$.
There seem to be other factors we are missing in this analysis.
Looking at the plot, however, it would be too easy to conclude there is no relation between these quantities at all.
There do seem to be two branches with approximate linear correlation.
Distinguishing these two groups roughly along the line from the origin under Re, we find $r = 0.69739$ and $r = 0.621341$ respectively above and below the line.
Another missing factor is the comparison to non-superconductor elemental metals.
Although they do not really experience a phase transition to a superconducting state, so they do not have a finite $T_c$ associated to them, they could be plotted having $T_c = 0$.
I chose to exclude them from the plot, as they would only clutter it further, and there is no real relation visible.
Further distinction could be in superconductor type.
Most of the plotted elements are type-I superconductors, but vanadium, for example, is type-II.
Vanadium does, however, behave similar to the rest of the elements.
\section{Exam question electrodynamics in superconductors} \section{Exam question electrodynamics in superconductors}
No idea yet. No idea yet.