update of the documentation.
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>Documentation of user libs (user functions) — musrfit 1.9.1 documentation</title>
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<title>Documentation of user libs (user functions) — musrfit 1.9.3 documentation</title>
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@ -30,7 +30,9 @@
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<link rel="index" title="Index" href="genindex.html" />
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<link rel="search" title="Search" href="search.html" />
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<link rel="next" title="Setting up musrfit on Different Platforms" href="setup-standard.html" />
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<link rel="prev" title="User manual" href="user-manual.html" />
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<link rel="prev" title="User manual" href="user-manual.html" />
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<link href="_static/style.css" rel="stylesheet" type="text/css">
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<script src="_static/js/modernizr.min.js"></script>
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@ -98,6 +100,7 @@
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</li>
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</ul>
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</li>
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<li class="toctree-l2"><a class="reference internal" href="#supeconducting-gap-integrals-to-calculate-vs">Supeconducting Gap-Integrals to calculate <span class="math notranslate nohighlight">\(1/\lambda^2\)</span> vs <span class="math notranslate nohighlight">\(T\)</span></a></li>
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<li class="toctree-l2"><a class="reference internal" href="#nonlocal-superconductivity-related-meissner-screening-functions-as-libs">Nonlocal superconductivity related Meissner screening functions (AS libs)</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#depth-resolved-information-as-libs">Depth resolved information (AS libs)</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#functions-to-analyze-bgr-nmr-data-bnmr-libs">Functions to analyze β-NMR data (BNMR libs)</a><ul>
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@ -503,8 +506,14 @@ The expected name of the <code class="docutils literal notranslate"><span class=
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</div>
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</div>
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</div>
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<div class="section" id="supeconducting-gap-integrals-to-calculate-vs">
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<span id="gap-integral-libs"></span><span id="index-14"></span><h2>Supeconducting Gap-Integrals to calculate <span class="math notranslate nohighlight">\(1/\lambda^2\)</span> vs <span class="math notranslate nohighlight">\(T\)</span><a class="headerlink" href="#supeconducting-gap-integrals-to-calculate-vs" title="Permalink to this headline">¶</a></h2>
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<p>The details about the various superconducting gap-integrals are found in the
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pdf-file <strong>GapIntegrals.pdf</strong> which can be found in the musrfit source under
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<code class="docutils literal notranslate"><span class="pre"><musrfit-dir>/src/external/libGapIntegrals/</span></code>.</p>
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</div>
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<div class="section" id="nonlocal-superconductivity-related-meissner-screening-functions-as-libs">
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<span id="nonlocal-libs"></span><span id="index-14"></span><h2>Nonlocal superconductivity related Meissner screening functions (AS libs)<a class="headerlink" href="#nonlocal-superconductivity-related-meissner-screening-functions-as-libs" title="Permalink to this headline">¶</a></h2>
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<span id="nonlocal-libs"></span><span id="index-15"></span><h2>Nonlocal superconductivity related Meissner screening functions (AS libs)<a class="headerlink" href="#nonlocal-superconductivity-related-meissner-screening-functions-as-libs" title="Permalink to this headline">¶</a></h2>
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<p>This library allows to calculate the magnetic field profile <span class="math notranslate nohighlight">\(B(z)\)</span> for nonlocal superconductors.
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For details see <a class="reference external" href="http://dx.doi.org/10.1103/PhysRevLett.95.197201">A. Suter, et al., PRB 72, 024506 (2005)</a>, and references therein.</p>
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<p>The provided function calculates the muon spin polarization</p>
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@ -567,7 +576,7 @@ muon stopping profile for an energy of <span class="math notranslate nohighlight
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in the directory of all the msr-files.</p>
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</div>
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<div class="section" id="depth-resolved-information-as-libs">
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<span id="depthprof-lib"></span><span id="index-15"></span><h2>Depth resolved information (AS libs)<a class="headerlink" href="#depth-resolved-information-as-libs" title="Permalink to this headline">¶</a></h2>
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<span id="depthprof-lib"></span><span id="index-16"></span><h2>Depth resolved information (AS libs)<a class="headerlink" href="#depth-resolved-information-as-libs" title="Permalink to this headline">¶</a></h2>
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<p>A method to extract depth-resolved information from the implantation energy dependence of the experimental parameters in a low-energy
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muon spin spectroscopy experiment. For details see <a class="reference external" href="https://doi.org/10.1063/1.5126529">A. F. A. Simões, et al. Review of Scientific Instruments. 2020; 91(2): 023906 (7 pp.)</a>.</p>
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<p>If you have a layered material (e.g. <span class="math notranslate nohighlight">\(N\)</span> layers), properties like the asymmetry might depend on the layer in which the muons are stopped.
|
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@ -617,7 +626,7 @@ rge-files (muon stoppping profiles). For this the library reads at start-up the
|
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</div>
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</div>
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<div class="section" id="functions-to-analyze-bgr-nmr-data-bnmr-libs">
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||||
<span id="bnmr-libs"></span><span id="index-16"></span><h2>Functions to analyze β-NMR data (BNMR libs)<a class="headerlink" href="#functions-to-analyze-bgr-nmr-data-bnmr-libs" title="Permalink to this headline">¶</a></h2>
|
||||
<span id="bnmr-libs"></span><span id="index-17"></span><h2>Functions to analyze β-NMR data (BNMR libs)<a class="headerlink" href="#functions-to-analyze-bgr-nmr-data-bnmr-libs" title="Permalink to this headline">¶</a></h2>
|
||||
<p>This is a collection of <code class="docutils literal notranslate"><span class="pre">C++</span></code> classes using the <code class="docutils literal notranslate"><span class="pre">musrfit</span></code> <a class="reference internal" href="user-manual.html#id38"><span class="std std-ref">user-functions</span></a>
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interface in order to facilitate the usage in conjunction with <code class="docutils literal notranslate"><span class="pre">musrfit</span></code>. It consists of two libraries:</p>
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<ul class="simple">
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@ -629,11 +638,11 @@ interface in order to facilitate the usage in conjunction with <code class="docu
|
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<p class="last">Currently it is recommended to read in the data in ASCII format as a non-μSR fit <a class="reference internal" href="user-manual.html#non-musr-fit"><span class="std std-ref">(fit type 8)</span></a>.</p>
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</div>
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<div class="section" id="libbnmr">
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<span id="index-17"></span><h3>libBNMR<a class="headerlink" href="#libbnmr" title="Permalink to this headline">¶</a></h3>
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<span id="index-18"></span><h3>libBNMR<a class="headerlink" href="#libbnmr" title="Permalink to this headline">¶</a></h3>
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<p>In β-NMR the SLR is usually measured by implanting a pulse of <span class="math notranslate nohighlight">\(^8\)</span>Li with a length <span class="math notranslate nohighlight">\(t_0\)</span> into the sample.
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The asymmetry is measured both during the pulse and afterwards. For a a general spin relaxation function <span class="math notranslate nohighlight">\(f(t)\)</span> the time evolution of the asymmetry is then given by [<a class="reference external" href="http://dx.doi.org/10.1103/PhysRevLett.96.147601">Z. Salman, et al., PRL 96, 147601 (2006)</a>]:</p>
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<div class="math notranslate nohighlight" id="slr">
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<span id="index-18"></span>\[\begin{split}P(t) = \left\{\begin{matrix}
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<span id="index-19"></span>\[\begin{split}P(t) = \left\{\begin{matrix}
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\frac{\int_0^t e^{-(t-t')/\tau_{\mathrm{Li}}}f(t-t')dt'}{\int_0^t e^{-t'/\tau_{\mathrm{Li}}}dt' } & t\leq t_0\\[6pt]
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||||
\frac{\int_0^{t_0}e^{-(t_0-t')/\tau_{\mathrm{Li}}}f(t-t')dt'}{\int_0^{t_0}e^{-t'/\tau_{\mathrm{Li}}}dt'} & t> t_0,
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\end{matrix}\right.\end{split}\]</div>
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@ -641,7 +650,7 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
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<div class="section" id="functions">
|
||||
<h4>Functions<a class="headerlink" href="#functions" title="Permalink to this headline">¶</a></h4>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">libBNMR</span></code> library currently contains the following functions:</p>
|
||||
<p id="index-19"><strong>Exponential relaxation</strong></p>
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||||
<p id="index-20"><strong>Exponential relaxation</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libBNMR</span> <span class="n">ExpRlx</span> <span class="mi">1</span> <span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
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||||
@ -651,7 +660,7 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
|
||||
<li>relaxation rate <span class="math notranslate nohighlight">\(\lambda\)</span> (s<span class="math notranslate nohighlight">\(^{-1}\)</span>)</li>
|
||||
</ol>
|
||||
<p>This function implements <span class="math notranslate nohighlight">\(f(t)=e^{-\lambda t}\)</span>.</p>
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||||
<p id="index-20"><strong>Stretched exponential relaxation</strong></p>
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||||
<p id="index-21"><strong>Stretched exponential relaxation</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libBNMR</span> <span class="n">SExpRlx</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
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||||
@ -665,19 +674,19 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
|
||||
</div>
|
||||
</div>
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||||
<div class="section" id="liblineprofile">
|
||||
<span id="index-21"></span><h3>libLineProfile<a class="headerlink" href="#liblineprofile" title="Permalink to this headline">¶</a></h3>
|
||||
<span id="index-22"></span><h3>libLineProfile<a class="headerlink" href="#liblineprofile" title="Permalink to this headline">¶</a></h3>
|
||||
<p>In addition to some simple line shapes <code class="docutils literal notranslate"><span class="pre">libLineProfile</span></code> contains functions to fit chemical shift anisotropies in the powder average.
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||||
Their functional form can be found in <a class="reference external" href="http://dx.doi.org/10.1007/978-3-642-68756-3_2">M. Mehring, Principles of High Resolution NMR in Solids (Springer 1983)</a>.</p>
|
||||
<p>For an axially symmetric interaction it is given by:</p>
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||||
<div class="math notranslate nohighlight" id="iax">
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||||
<span id="index-22"></span>\[\begin{split}I_{\mathrm ax}(f)=\left\{\begin{matrix} \frac{1}{2\sqrt{(f_\parallel-f_\perp)(f-f_\perp)}}& f\in(f_\perp,f_\parallel)\cup(f_\parallel,f_\perp)\\[6pt] 0 & \text{otherwise}\end{matrix} \right.\end{split}\]</div>
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||||
<span id="index-23"></span>\[\begin{split}I_{\mathrm ax}(f)=\left\{\begin{matrix} \frac{1}{2\sqrt{(f_\parallel-f_\perp)(f-f_\perp)}}& f\in(f_\perp,f_\parallel)\cup(f_\parallel,f_\perp)\\[6pt] 0 & \text{otherwise}\end{matrix} \right.\end{split}\]</div>
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||||
<p>where <span class="math notranslate nohighlight">\(f_\parallel\)</span> and <span class="math notranslate nohighlight">\(f_\perp\)</span> are the frequencies that would be observed if the field is oriented paralell or perpendicular to the symmetry axis, respectively.</p>
|
||||
<div class="line-block">
|
||||
<div class="line">In case of a completely anisotropic interaction, the powder average can be described by the frequencies along the three principle axis <span class="math notranslate nohighlight">\(f_1,f_2,f_3\)</span>.</div>
|
||||
<div class="line">Assume without loss of generality that <span class="math notranslate nohighlight">\(f_1<f_2<f_3\)</span>, then</div>
|
||||
</div>
|
||||
<div class="math notranslate nohighlight" id="ianiso">
|
||||
<span id="index-23"></span>\[\begin{split}I(f)&=\left\{\begin{matrix}
|
||||
<span id="index-24"></span>\[\begin{split}I(f)&=\left\{\begin{matrix}
|
||||
\frac{K(m)}{\pi\sqrt{(f-f_1)(f_3-f_2)}},& f_3\geq f>f_2 \\[9pt]
|
||||
\frac{K(m)}{\pi\sqrt{(f_3-f)(f_2-f_1)}},& f_2>f\geq f_1\\[9pt]
|
||||
0 & \text{otherwise}
|
||||
@ -693,7 +702,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<div class="section" id="id1">
|
||||
<h4>Functions<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h4>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">libLineProfile</span></code> library currently contains the following functions:</p>
|
||||
<p id="index-24"><strong>Gaussian</strong></p>
|
||||
<p id="index-25"><strong>Gaussian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">LineGauss</span> <span class="mi">1</span> <span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -708,7 +717,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)=e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}}\]</div>
|
||||
<p id="index-25"><strong>Lorentzian</strong></p>
|
||||
<p id="index-26"><strong>Lorentzian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">LineLorentzian</span> <span class="mi">1</span> <span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -723,7 +732,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)= \frac{w^2}{4(f-f_0)^2+w^2}\]</div>
|
||||
<p id="index-26"><strong>Laplacian</strong></p>
|
||||
<p id="index-27"><strong>Laplacian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">LineLaplace</span> <span class="mi">1</span> <span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -738,7 +747,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)=e^{-2\ln 2 \left|\frac{f-f_0}{w}\right|}\]</div>
|
||||
<p id="index-27"><strong>Skewed Lorentzian</strong></p>
|
||||
<p id="index-28"><strong>Skewed Lorentzian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">LineSkewLorentzian</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -754,7 +763,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)= \frac{w w_a}{4(f-f_0)^2+w_a^2}, \quad w_a=\frac{2w}{1+e^{a(f-f_0)}}\]</div>
|
||||
<p id="index-28"><strong>Skewed Lorentzian 2</strong></p>
|
||||
<p id="index-29"><strong>Skewed Lorentzian 2</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">LineSkewLorentzian2</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -770,7 +779,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}A(f)= \left\{\begin{matrix}\frac{{w_1}^2}{4{(f-f_0)}^2+{w_1}^2},&f\leq f_0\\[9pt] \frac{{w_2}^2}{4{(f-f_0)}^2+{w_2}^2},&f>f_0\end{matrix}\right.\end{split}\]</div>
|
||||
<p id="index-29"><strong>Powder average of an axially symmetric interaction convoluted with a Lorentzian</strong></p>
|
||||
<p id="index-30"><strong>Powder average of an axially symmetric interaction convoluted with a Lorentzian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">PowderLineAxialLor</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -787,7 +796,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)= I_{\mathrm ax}(f)\circledast\left( \frac{w^2}{4f^2+w^2} \right)\]</div>
|
||||
<p>with <span class="math notranslate nohighlight">\(I_{\mathrm ax}(f)\)</span> defined <a class="reference internal" href="#iax"><span class="std std-ref">above</span></a>.</p>
|
||||
<p id="index-30"><strong>Powder average of an axially symmetric interaction convoluted with a Gaussian</strong></p>
|
||||
<p id="index-31"><strong>Powder average of an axially symmetric interaction convoluted with a Gaussian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">PowderLineAxialGss</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -804,7 +813,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)= I_{\mathrm ax}(f)\circledast\left( e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} \right)\]</div>
|
||||
<p>with <span class="math notranslate nohighlight">\(I_{\mathrm ax}(f)\)</span> defined <a class="reference internal" href="#iax"><span class="std std-ref">above</span></a>.</p>
|
||||
<p id="index-31"><strong>Powder average of an anisotropic interaction convoluted with a Lorentzian</strong></p>
|
||||
<p id="index-32"><strong>Powder average of an anisotropic interaction convoluted with a Lorentzian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">PowderLineAsymLor</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -822,7 +831,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)= I(f)\circledast\left( \frac{w^2}{4f^2+w^2} \right)\]</div>
|
||||
<p>with <span class="math notranslate nohighlight">\(I(f)\)</span> defined <a class="reference internal" href="#ianiso"><span class="std std-ref">above</span></a>. Note that <span class="math notranslate nohighlight">\(f_1<f_2<f_3\)</span> is not required by the code.</p>
|
||||
<p id="index-32"><strong>Powder average of an anisotropic interaction convoluted with a Gaussian</strong></p>
|
||||
<p id="index-33"><strong>Powder average of an anisotropic interaction convoluted with a Gaussian</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libLineProfile</span> <span class="n">PowderLineAsymGss</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -866,7 +875,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<div role="contentinfo">
|
||||
<p>
|
||||
© Copyright 2023, Andreas Suter.
|
||||
Last updated on Aug 17, 2023.
|
||||
Last updated on Apr 23, 2024.
|
||||
|
||||
</p>
|
||||
</div>
|
||||
@ -888,7 +897,7 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<script type="text/javascript">
|
||||
var DOCUMENTATION_OPTIONS = {
|
||||
URL_ROOT:'./',
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VERSION:'1.9.1',
|
||||
VERSION:'1.9.3',
|
||||
LANGUAGE:'None',
|
||||
COLLAPSE_INDEX:false,
|
||||
FILE_SUFFIX:'.html',
|
||||
|
||||
Reference in New Issue
Block a user