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Nathanael A. Fortune edited section_Application_to_Specific_Heat__.tex
over 8 years ago
Commit id: 4a1c9ae1a58792b33a228ae4becae9943f87bffa
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Substituting $g_N = \mathrm{1.5}$ --- the weighted average nuclear g-factor for these two most common Cu isotopes \cite{Leyarovski_1988}--- into Eq.~\ref{eq:CurieConstant} gives a theoretical value $\lambda_{\mathrm{Cu}} = 3.93 \cdot 10^{-12} \textrm{ K}{\textrm{ m}}^3 {\textrm{ mol}}^{-1}$.Experimentally, \cite{Leyarovski_1988} find a value of $\lambda_{\mathrm{Cu}} = 4.03 \cdot 10^{-12} \textrm{ K}{\textrm{ m}}^3 {\textrm{ mol}}^{-1}$ upon fitting Eq.~\ref{eq:SchottkyTail} to their measurements of the specific heat of Cu taken between 0.3 K and 1 K in an applied field of 14 T.
In our Jan 2015 heat capacity run, we used a 0.40 mg sample of $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$. In our July 2015 run, we used a 0.50 mg sample. Assuming a molar mass
$m$ of $832.98 \mathrm{g/mole}$ and 1 Cu atom per mole, the nuclear contribution to the measured heat capacity of $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ is predicted to be
\begin{equation}
\label{eq:NuclearCuContribution}
c = \alpha \frac{H^2}{T^2} \mathrm{\ [J/K]}
\end{equation}
where
$\alpha$ $\alpha = m \frac{{\lambda}_N}{{\mu}_0}$ has units $\left[\frac{\textrm{Joules Kelvin}}{(\textrm{Tesla})^2}\right]$ and values $\alpha_{\textrm{0.4 mg}} = 1.28 \cdot 10^{-9}$ and $\alpha_{\textrm{0.5 mg}} = 1.60 \cdot 10^{-9}$ for the Jan 2015 and July 2015 runs, respectively.