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appendix_SCO_exc.tex
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appendix_SCO_exc.tex
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\chapter{Sample Excitation Condition in SCO Literature}
\label{ap: sco-exc}
In Section~\ref{sec: SCO-photo-4}, high sample excitation condition is suggested
as a possible explanation for the apparent conflict between the results
described by authors using different experimental techniques.
Table~\ref{tab: SCO-exc} contains a tabulation of the values of some key parameters
from some select works from SCO literature.
For reference, an extended version is included herein.
%
The peak fluence~$f$ and peak intensity~$I$ of the pump-laser pulse
are defined as
%
\begin{equation}
\begin{aligned}
f & = 4 \ln(2) \frac{E}{\unslant[-.2]\pi w^2} \\
I & = \frac{f}{\tau}
\end{aligned}
\end{equation}
%
where $\lambda, E, \tau, w$ are the centre wavelength, pulse energy,
pulse duration~(FWHM), and beamwidth~(FWHM) on the sample.
%
From the Beer-Lambert law,
the excitation fraction $\eta_\text{exc}$ as a function of optical path length~$l$
is given by
%
\begin{equation}
\begin{aligned}
\eta_\text{exc}(l) & = \frac{f}{h c / \lambda}
\frac{\Phi}{c_\text{abs} N_\text{A} l} \left( 1 - 10^{-l/L_\text{exc}}\right)
\end{aligned}
\end{equation}
%
where $L_\text{exc} = 1/(\epsilon_\text{abs} c_\text{abs})$ and
$h c / \lambda$ are the excitation depth and photon energy of the pump pulse.
$\epsilon_\text{abs}$, $c_\text{abs}$, $\Phi \approx 1$ are
the sample excitation depth, molar absorption coefficient, molar concentration,
and quantum yield of the excitation;
$N_\text{A} \approx 6.022 \times 10^{23}$~mol$^{-1}$ is the Avogadro constant.
%
At the surface of the sample,
%
\begin{equation}
\begin{aligned}
\eta_\text{exc}^0 & = \lim \limits_{l \to 0} \eta_\text{exc}(l) \\
& = \frac{f}{h c / \lambda}
\frac{\Phi}{c_\text{abs} N_\text{A}}
\lim \limits_{l \to 0} \frac{1 - 10^{-l/L_\text{exc}}}{l} \\
& = \frac{f}{h c / \lambda} \frac{\Phi}{c_\text{abs} N_\text{A}}
\frac{\ln(10)}{L_\text{exc}}
\end{aligned}
\end{equation}
% Tables:
\begin{table}[htp!]
\centering
{\renewcommand*{\arraystretch}{1.5}
\begin{tabular}{ C{1cm} C{2cm} C{2.65cm} C{2.75cm} C{1cm} }
\toprule
\multirow{2}{*}{Work} & \multirow{2}{*}{Technique}
& \multirow{2}{*}{
\begin{minipage}[c]{2.5cm} \centering Peak Fluence (mJ/cm$^2$) \end{minipage}}
& \multirow{2}{*}{
\begin{minipage}[c]{2.6cm} \centering Peak Intensity (GW/cm$^2$) \end{minipage}}
& \multirow{2}{*}{$\eta_\text{exc}^0$} \\
& & & & \\
\midrule
\cite{Lorenc2009} & TR-XRD & 15 & 150 & ? \\
\cite{Collet2012a} & TR-XRD & 15 & ? & ? \\
\cite{Collet2012b} & TR-XRD & 15 & 150 & ? \\
\cite{Lorenc2012} & TR-XRD & 10 & 91 & ? \\
\cite{Marino2015} & TR-XRD & 0.7 & ? & ? \\
\cite{Bertoni2016b} & TR-XRD & 4 & ? & ? \\
\cite{Freyer2013} & TR-XRD & 32 & 800 & ? \\
\bottomrule
\end{tabular}
}
\caption{Sample excitation condition for works in SCO literature (part~1).}
\label{tab: SCO-exc-app-1}
\end{table}
% Abbreviation: TR-XRD = time-resolved X-ray diffraction.
\begin{table}[htp!]
\centering
{\renewcommand*{\arraystretch}{1.5}
\begin{tabular}{ C{1cm} C{2cm} C{2.65cm} C{2.75cm} C{1cm} }
\toprule
\multirow{2}{*}{Work} & \multirow{2}{*}{Technique}
& \multirow{2}{*}{
\begin{minipage}[c]{2.5cm} \centering Peak Fluence (mJ/cm$^2$) \end{minipage}}
& \multirow{2}{*}{
\begin{minipage}[c]{2.6cm} \centering Peak Intensity (GW/cm$^2$) \end{minipage}}
& \multirow{2}{*}{$\eta_\text{exc}^0$} \\
& & & & \\
\midrule
\cite{Monat2000} & TA & 0.6 & ? & 0.01 \\
\cite{Smeigh2008} & FSRS & ? & ? & ? \\
\cite{Gawelda2007a} & FLUPS & 2.8 & 70.6 & 0.06 \\
\cite{Gawelda2007a} & TA & 80 & 2724.9 & 1.9 \\
\cite{Consani2009} & TA & 38.1 & 846.7 & 1.2 \\
\cite{Aubock2015} & UV TA & 0.7 & 18.2 & 0.01 \\
\cite{Aubock2015} & Vis TA & 2.2 & 54.7 & 0.07 \\
\cite{Tribollet2011} & TA & ? & ? & ? \\
\cite{Galle2013} & TA & ? & ? & ? \\
\cite{Moisan2008} & TA & 4 & 40 & ? \\
\cite{Lorenc2009} & TA & 15 & 150 & ? \\
\cite{Tissot2011} & TA & 1 & 7 & ? \\
\cite{Collet2012a} & TA & 10 & 222 & ? \\
\cite{Bertoni2012} & TA & 4.5 & 64 & ? \\
\cite{Kaszub2013} & TA & 25 & 500 & ? \\
\cite{Marino2014} & TA & 11 & 220 & ? \\
\cite{Bertoni2016a} & TA & ? & ? & ? \\
\cite{Bertoni2016b} & TA & 4 & ? & ? \\
\cite{Marino2015} & TA & 1.4 & ? & ? \\
\cite{Marino2016} & TA & 40 & 1000 & 4.6 \\
\cite{Parpiiev2017} & TR & 0.35 & 2.2 & 0.02 \\
\cite{Zerdane2017} & TA & 0.4 & 5.7 & ? \\
\cite{Zerdane2017} & TA & 0.42 & 5.9 & ? \\
\cite{Moguilevski2016} & PES & 17.6 & 293 & 1.4 \\
\bottomrule
\end{tabular}
}
\caption{Sample excitation condition for works in SCO literature (part~2).}
\label{tab: SCO-exc-app-2}
\end{table}
% Abbreviations: FLUPS = fluorescence up-conversion spectroscopy,
% TA = transient absorption, TR = transient reflectivity, PES = photoemission spectrocopy.
\begin{table}[htp!]
\centering
{\renewcommand*{\arraystretch}{1.5}
\begin{tabular}{ C{1cm} C{2cm} C{2.65cm} C{2.75cm} C{1cm} }
\toprule
\multirow{2}{*}{Work} & \multirow{2}{*}{Technique}
& \multirow{2}{*}{
\begin{minipage}[c]{2.5cm} \centering Peak Fluence (mJ/cm$^2$) \end{minipage}}
& \multirow{2}{*}{
\begin{minipage}[c]{2.6cm} \centering Peak Intensity (GW/cm$^2$) \end{minipage}}
& \multirow{2}{*}{$\eta_\text{exc}^0$} \\
& & & & \\
\midrule
\cite{Khalil2006} & XAS & 123.6 & 1235.6 & 4.76 \\
\cite{Gawelda2007b} & XAS & 180 & 1800 & 4.2 \\
\cite{Sato2009} & XAS & 245.1 & 1634 & 7.6 \\
\cite{Bressler2009} & XAS & ? & ? & ? \\
\cite{Vanko2010} & XES & 294 & 2942 & 6.8 \\
\cite{Huse2010} & XAS & 15.7 & 224 & 2.20 \\
\cite{Huse2011} & XAS & 3 & 43 & 0.4 \\
\cite{Lima2011} & XAS & 13--400 & 1.3--40 & 1--32 \\
\cite{Haldrup2012} & XXX & 19.6 & 1.96 & 1.6 \\
\cite{Vanko2013} & XES & 8.2 & 29 & 0.6 \\
\cite{Lemke2013} & XAS & 567.3 & 11346 & 13.10 \\
\cite{Cammarata2014} & XAS & 1.8 & 36 & ? \\
\cite{Zhang2014} & XES & 120 & 1714 & 9.4 \\
\cite{Canton2014} & XAS & ? & ? & ? \\
\cite{XZhang2015} & XAS & 100 & 20 & 12 \\
\cite{Vanko2015} & XES & 19.6 & 1.96 & 2.4 \\
\cite{Marino2016} & XAS & 50 & 1000 & 5.8 \\
\cite{VanKuiken2016} & XAS & 4.2 & 42 & 0.1 \\
\cite{Haldrup2016} & XX & 785 & 15700 & 18 \\
\cite{Biasin2016} & XDS & 275 & 3922 & 2.1 \\
\cite{Lemke2017} & XAS & 220 & 4400 & 17.51 \\
\cite{March2017} & XES & 30 & 3 & 3.7 \\
\cite{Zhang2017} & XES & 0.1 & 1.7 & 0.003 \\
\cite{Kjaer2017} & XES & 0.1 & 2.1 & 0.004 \\
\bottomrule
\end{tabular}
}
\caption{Sample excitation condition for works in SCO literature (part~3).}
\label{tab: SCO-exc-app-3}
\end{table}
% XAS = X-ray absorption spectroscopy,
% XES = X-ray emission spectroscopy, XDS = X-ray diffuse scattering,