diff --git a/sc_elements.py b/sc_elements.py index b99d613..1a39fdc 100755 --- a/sc_elements.py +++ b/sc_elements.py @@ -70,3 +70,17 @@ fig.savefig('/home/kvkempen/Documents/20212022Q3/Superconductivity/assignments/s #fig.savefig('/home/kvkempen/Documents/20212022Q3/Superconductivity/assignments/sc_elements.pdf') 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()) diff --git a/superconductivity_assignment1_kvkempen.tex b/superconductivity_assignment1_kvkempen.tex index 449e39d..9172137 100755 --- a/superconductivity_assignment1_kvkempen.tex +++ b/superconductivity_assignment1_kvkempen.tex @@ -56,7 +56,7 @@ \begin{document} \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. 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. @@ -92,6 +92,20 @@ If $|r| = 1$, there is a perfectly linear relation. The lower $|r|$ is, the less correlated the points are. 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. +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} No idea yet.