Verified Commit 710fb517 authored by Tobias WEBER's avatar Tobias WEBER
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parent 6fc5ca57
......@@ -171,7 +171,7 @@ which corresponds to scattering on the $\left(002\right)$ Bragg reflection of hi
pyrolithic graphite (HOPG) \cite[p. 250]{Shirane2002}, which is one of the standard crystals used as a
monochromator or analyser in a TAS instrument.
Finally, the check boxes named ``scattering senses'' control the sign of the scattering angles.
If the box is checked, a positive angle corresponds to a counterclockwise sense, i.e. corresponding
If the box is checked, a positive angle corresponds to a counter-clockwise sense, i.e. corresponding
to the usual mathematical definition, and alternatively to a clockwise sense when unchecked.
From the standpoint of the physics to be studied in the sample, these signs have no influence
in practice. They do, however, strongly affect the resolution of the instrument \cite{Eckold2014} \cite[p. 260]{Shirane2002}
......
......@@ -183,7 +183,10 @@ in Ref. \cite[pp. 55-93]{Shirane2002}.
from the monochromator crystal (M), picking out a single wavelength $\lambda_i$ and wavevector $\underline{k}_i$.
The monochromatic beam is next scattered on the sample (S) at an angle $2\theta_S$, defining a wavevector $\underline{k}_f$.
The magnitude of $\underline{k}_f$ and thus $\lambda_f$ is determined by Bragg-scattering on the analyser crystal (A).
The momentum and energy transfers are given by Eqs. \ref{eq:Q} and \ref{eq:E}, respectively. }
The momentum and energy transfers are given by Eqs. \ref{eq:Q} and \ref{eq:E}, respectively.
The figure was inspired by Ref. \cite[p. 72, Fig. 3.8]{Shirane2002}, which is a more detailed version of the same figure,
and is similar to Ref. \cite[p. 10, Fig. 2.1]{PhDWeber}.
}
\label{fig:spectroscopy}
\end{figure}
......@@ -197,7 +200,9 @@ in Ref. \cite[pp. 55-93]{Shirane2002}.
In addition to the theoretical layout shown in Fig. \ref{fig:spectroscopy},
an optional beryllium filter removing unwanted high energy neutrons \cite[pp. 78-84]{Shirane2002}
is also visible in this picture.
This picture is reproduced from the supplementary information of Ref. \cite{skxpaper}.}
This picture is reproduced from the supplementary information of Ref. \cite{skxpaper}.
Similar figures, albeit showing different instruments, have been published in my PhD
thesis \cite[pp. 13-14]{PhDWeber}. }
\label{fig:thales}
\end{figure}
......
......@@ -16,9 +16,10 @@ in the control programs of triple-axis instruments, among them \textit{NOMAD} \c
or \textit{NICOS} \cite{web_NICOS}, but are also employed in virtual instrument simulators like \textit{vTAS} \cite{vTAS2013} or
\textit{McStas} \cite{McStas2020}, as well as in data analysis software like \textit{Mantid} \cite{Arnold2014}.
Note that this chapter has already been published in the manual of the software from Ref. \cite{Takin2021}
and is furthermore based on an earlier version of the same text and derivations from my (physics) PhD thesis
\cite[pp. 139-143]{PhDWeber}. Originally, these formula were re-derived with the aid of the source
Note that this chapter has already been published in the manual of the software from Ref. \cite{Takin2021},
as well as in my (physics) PhD thesis \cite[pp. 139-143]{PhDWeber},
where the latter featured an earlier version of the same text, figures, and derivations.
Originally, these formula were re-derived with the aid of the source
code of \textit{McStas'} \textit{templateTAS} virtual instrument \cite{web_mcstas_templateTAS, McStas2020}.
......@@ -300,7 +301,9 @@ Here, the two wavevectors enclose the scattering angle $2 \theta_S$.
\includegraphics[width = 0.75 \textwidth]{figures/tas_triangle}
\end{center}
\caption[TAS layout and scattering triangle.]{
Triple-axis layout (left) and corresponding scattering triangle (right). \label{fig:scattering_triangle}}
Triple-axis layout (left) and corresponding scattering triangle (right).
Figures inspired by Ref. \cite[p. 72, Fig. 3.8]{Shirane2002} and \cite[p. 15, Fig. 1.6]{Shirane2002}, respectively.
\label{fig:scattering_triangle}}
\end{figure}
We can calculate $2 \theta_S$ via the cosine theorem \cite[pp. 694-695]{Arens2015}, i.e.
......@@ -319,7 +322,7 @@ by forming the scalar product of $\left| Q \right>$ with itself \cite[p. 11]{Shi
\boxed{ 2 \theta_S \ =\ \sigma_s \cdot \arccos \left( \frac{k_i^2 + k_f^2 - Q^2}{2 k_i k_f} \right). }
\end{equation}
As we could scatter in either clockwise or counterclockwise direction, $2 \theta_S$ can be positive or negative.
As we could scatter in either clockwise or counter-clockwise direction, $2 \theta_S$ can be positive or negative.
The sign of $2 \theta_S$ is given by the sample scattering sense $\sigma_s = \pm 1$.
......@@ -328,11 +331,11 @@ The sign of $2 \theta_S$ is given by the sample scattering sense $\sigma_s = \pm
The final and most complicated angle to determine is the sample rotation $\Theta_S$.
It is given by the angle of the incoming wavevector $\left| k_i \right>$ to an (arbitrary) direction
$\left| a \right>$ which is known from sample orientation, this is usually a Bragg peak.
$\left| a \right>$ which is known from sample orientation, this is usually a Bragg peak \cite[p. 87]{Shirane2002}.
If we were to explicitly use the $U$ matrix here, this vector would be one of its rows.
The situation is shown in the right panel of Fig. \ref{fig:scattering_triangle}.
We split $\Theta_S$ into the angle $\psi$ between $\left| k_i \right>$ and $\left| Q \right>$
and the angle $\xi$ between $\left| k_i \right>$ and $\left| a \right>$:
and the angle $\xi$ between $\left| Q \right>$ and $\left| a \right>$:
\begin{equation} \boxed{ \Theta_S \ =\ 180^{\circ} - \left( \psi + \xi \right).} \end{equation}
......
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