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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="#supeconducting-gap-integrals-to-calculate-1-lambda-2-vs-t">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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<div class="section" id="documentation-of-user-libs-user-functions">
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<span id="user-libs"></span><span id="index-0"></span><h1>Documentation of user libs (user functions)<a class="headerlink" href="#documentation-of-user-libs-user-functions" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="meissner-profiles-vortex-lattice-related-functions-bmw-libs">
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<span id="bmw-libs"></span><span id="index-1"></span><h2>Meissner-Profiles / Vortex-Lattice related functions (BMW libs)<a class="headerlink" href="#meissner-profiles-vortex-lattice-related-functions-bmw-libs" title="Permalink to this headline">¶</a></h2>
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<div class="section" id="libfitpofb">
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<span id="index-2"></span><h3>libFitPofB<a class="headerlink" href="#libfitpofb" title="Permalink to this headline">¶</a></h3>
|
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<div class="section" id="introduction">
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<h4>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h4>
|
||||
|
||||
<section id="documentation-of-user-libs-user-functions">
|
||||
<span id="user-libs"></span><span id="index-0"></span><h1>Documentation of user libs (user functions)<a class="headerlink" href="#documentation-of-user-libs-user-functions" title="Link to this heading"></a></h1>
|
||||
<section id="meissner-profiles-vortex-lattice-related-functions-bmw-libs">
|
||||
<span id="bmw-libs"></span><span id="index-1"></span><h2>Meissner-Profiles / Vortex-Lattice related functions (BMW libs)<a class="headerlink" href="#meissner-profiles-vortex-lattice-related-functions-bmw-libs" title="Link to this heading"></a></h2>
|
||||
<section id="libfitpofb">
|
||||
<span id="index-2"></span><h3>libFitPofB<a class="headerlink" href="#libfitpofb" title="Link to this heading"></a></h3>
|
||||
<section id="introduction">
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<h4>Introduction<a class="headerlink" href="#introduction" title="Link to this heading"></a></h4>
|
||||
<p><code class="docutils literal notranslate"><span class="pre">libFitPofB</span></code> 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>. The classes contained in this
|
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library generally implement calculations of one-dimensional static magnetic field distributions
|
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@@ -211,13 +133,13 @@ low-energy μSR (see <a class="reference external" href="https://www.psi.ch/smus
|
||||
In the following the basic usage of the library in <code class="docutils literal notranslate"><span class="pre">musrfit</span></code> is explained—the calculations by themselves are only
|
||||
outlined. For further information please refer to the original literature and/or the source code of the implementation.</p>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<p class="last">In order to supply certain information needed for the calculations but not suited to be stored in the <code class="docutils literal notranslate"><span class="pre">musrfit</span></code>
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>In order to supply certain information needed for the calculations but not suited to be stored in the <code class="docutils literal notranslate"><span class="pre">musrfit</span></code>
|
||||
msr files an <code class="docutils literal notranslate"><span class="pre">XML</span></code> configuration file in the working directory is used. For details, see below.</p>
|
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</div>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<p class="last">The implementations in this library heavily rely on <a class="reference external" href="http://fftw.org/">FFTW3</a>. In principle, it always checks what
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>The implementations in this library heavily rely on <a class="reference external" href="http://fftw.org/">FFTW3</a>. In principle, it always checks what
|
||||
is the best way to do efficient Fourier transforms for a given machine before the transforms are actually done. If
|
||||
repeatedly Fourier transforms of the same (sizable) length should be done, it might be worth storing the once
|
||||
obtained information in an external file and just load it the next time this information is needed
|
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@@ -225,8 +147,8 @@ obtained information in an external file and just load it the next time this inf
|
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file has to be specified in the <code class="docutils literal notranslate"><span class="pre">XML</span></code> file.</p>
|
||||
</div>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<p class="last">The model functions described in the following do generally <em>not behave nicely</em> in conjunction with <code class="docutils literal notranslate"><span class="pre">MINUIT</span></code>
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>The model functions described in the following do generally <em>not behave nicely</em> in conjunction with <code class="docutils literal notranslate"><span class="pre">MINUIT</span></code>
|
||||
function minimizations (or maximizations). The analysis process at the moment in most cases involves some
|
||||
tedious trial-and-error procedure, where the displayed MINUIT information as always deserves attention.
|
||||
This is especially true if small effects should be analyzed (<em>e.g.</em> small diamagnetic shifts in superconductors).
|
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@@ -234,15 +156,15 @@ The parameter uncertainty in many cases has to be estimated independently. Due t
|
||||
the use of the fit option of <code class="docutils literal notranslate"><span class="pre">msr2data</span></code> <em>cannot</em> be advised.</p>
|
||||
</div>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<p class="last">If these classes still prove useful and results obtained through them are part of scientific publications,
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>If these classes still prove useful and results obtained through them are part of scientific publications,
|
||||
an acknowledgment of the use of the library is appreciated.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="le-mgrsr">
|
||||
<h4>LE-μSR<a class="headerlink" href="#le-mgrsr" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="section" id="one-dimensional-london-model-for-the-meissner-state-of-isotropic-superconductors">
|
||||
<span id="index-3"></span><h5>One-dimensional London model for the Meissner state of isotropic superconductors<a class="headerlink" href="#one-dimensional-london-model-for-the-meissner-state-of-isotropic-superconductors" title="Permalink to this headline">¶</a></h5>
|
||||
</section>
|
||||
<section id="le-mgrsr">
|
||||
<h4>LE-μSR<a class="headerlink" href="#le-mgrsr" title="Link to this heading"></a></h4>
|
||||
<section id="one-dimensional-london-model-for-the-meissner-state-of-isotropic-superconductors">
|
||||
<span id="index-3"></span><h5>One-dimensional London model for the Meissner state of isotropic superconductors<a class="headerlink" href="#one-dimensional-london-model-for-the-meissner-state-of-isotropic-superconductors" title="Link to this heading"></a></h5>
|
||||
<p>The models for analyzing LE-μSR data assume the magnetic induction <span class="math notranslate nohighlight">\(B(z)\)</span> to vary only in the
|
||||
dimension parallel to the momentum of the incident muons. In such a case the magnetic field distribution is given by</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
@@ -267,11 +189,11 @@ of a <code class="docutils literal notranslate"><span class="pre">musrfit</span>
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</li>
|
||||
<li>applied field (G)</li>
|
||||
<li>thickness of the dead layer (nm)</li>
|
||||
<li>magnetic field penetration depth (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</p></li>
|
||||
<li><p>applied field (G)</p></li>
|
||||
<li><p>thickness of the dead layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth (nm)</p></li>
|
||||
</ol>
|
||||
<p id="index-5"><strong>Superconducting thin film (one layer)</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libFitPofB</span> <span class="n">TLondon1D1L</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span><span class="p">]</span>
|
||||
@@ -279,17 +201,17 @@ of a <code class="docutils literal notranslate"><span class="pre">musrfit</span>
|
||||
</div>
|
||||
<p>The mandatory parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</li>
|
||||
<li>applied field (G)</li>
|
||||
<li>thickness of the dead layer (nm)</li>
|
||||
<li>thickness of the actually superconducting layer (nm)</li>
|
||||
<li>magnetic field penetration depth (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</p></li>
|
||||
<li><p>applied field (G)</p></li>
|
||||
<li><p>thickness of the dead layer (nm)</p></li>
|
||||
<li><p>thickness of the actually superconducting layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth (nm)</p></li>
|
||||
</ol>
|
||||
<p>The optional parameters are:</p>
|
||||
<ol class="loweralpha simple">
|
||||
<li>fraction f<sub>1</sub> of muons in the thin film contributing to the signal (0 ≤ f<sub>1</sub> ≤ 1)</li>
|
||||
<li>fraction f<sub>s</sub> of muons in the substrate contributing to the signal (0 ≤ f<sub>s</sub> ≤ 1)</li>
|
||||
<li><p>fraction f<sub>1</sub> of muons in the thin film contributing to the signal (0 ≤ f<sub>1</sub> ≤ 1)</p></li>
|
||||
<li><p>fraction f<sub>s</sub> of muons in the substrate contributing to the signal (0 ≤ f<sub>s</sub> ≤ 1)</p></li>
|
||||
</ol>
|
||||
<p id="index-6"><strong>Superconducting thin-film bilayer heterostructure</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libFitPofB</span> <span class="n">TLondon1D2L</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span>
|
||||
@@ -297,20 +219,20 @@ of a <code class="docutils literal notranslate"><span class="pre">musrfit</span>
|
||||
</div>
|
||||
<p>The mandatory parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</li>
|
||||
<li>applied field (G)</li>
|
||||
<li>thickness of the dead layer (nm)</li>
|
||||
<li>thickness of the actually superconducting first layer (nm)</li>
|
||||
<li>thickness of the actually superconducting second layer (nm)</li>
|
||||
<li>magnetic field penetration depth of the first layer (nm)</li>
|
||||
<li>magnetic field penetration depth of the second layer (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</p></li>
|
||||
<li><p>applied field (G)</p></li>
|
||||
<li><p>thickness of the dead layer (nm)</p></li>
|
||||
<li><p>thickness of the actually superconducting first layer (nm)</p></li>
|
||||
<li><p>thickness of the actually superconducting second layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth of the first layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth of the second layer (nm)</p></li>
|
||||
</ol>
|
||||
<p>The optional parameters are:</p>
|
||||
<ol class="loweralpha simple">
|
||||
<li>fraction f<sub>1</sub> of muons in the dead and first layer contributing to the signal (0 ≤ f<sub>1</sub> ≤ 1)</li>
|
||||
<li>fraction f<sub>2</sub> of muons in the second layer contributing to the signal (0 ≤ f<sub>2</sub> ≤ 1)</li>
|
||||
<li>fraction f<sub>s</sub> of muons in the substrate contributing to the signal (0 ≤ f<sub>s</sub> ≤ 1)</li>
|
||||
<li><p>fraction f<sub>1</sub> of muons in the dead and first layer contributing to the signal (0 ≤ f<sub>1</sub> ≤ 1)</p></li>
|
||||
<li><p>fraction f<sub>2</sub> of muons in the second layer contributing to the signal (0 ≤ f<sub>2</sub> ≤ 1)</p></li>
|
||||
<li><p>fraction f<sub>s</sub> of muons in the substrate contributing to the signal (0 ≤ f<sub>s</sub> ≤ 1)</p></li>
|
||||
</ol>
|
||||
<p id="index-7"><strong>Superconducting thin-film trilayer heterostructure</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libFitPofB</span> <span class="n">TLondon1D3L</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span> <span class="mi">10</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span>
|
||||
@@ -318,30 +240,30 @@ of a <code class="docutils literal notranslate"><span class="pre">musrfit</span>
|
||||
</div>
|
||||
<p>The mandatory parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</li>
|
||||
<li>applied field (G)</li>
|
||||
<li>thickness of the dead layer (nm)</li>
|
||||
<li>thickness of the actually superconducting first layer (nm)</li>
|
||||
<li>thickness of the actually superconducting second layer (nm)</li>
|
||||
<li>thickness of the actually superconducting third layer (nm)</li>
|
||||
<li>magnetic field penetration depth of the first layer (nm)</li>
|
||||
<li>magnetic field penetration depth of the second layer (nm)</li>
|
||||
<li>magnetic field penetration depth of the third layer (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>muon implantation energy as specified in the <a class="reference internal" href="#bmwlibs-xml"><span class="std std-ref">XML startup</span></a> file (keV)</p></li>
|
||||
<li><p>applied field (G)</p></li>
|
||||
<li><p>thickness of the dead layer (nm)</p></li>
|
||||
<li><p>thickness of the actually superconducting first layer (nm)</p></li>
|
||||
<li><p>thickness of the actually superconducting second layer (nm)</p></li>
|
||||
<li><p>thickness of the actually superconducting third layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth of the first layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth of the second layer (nm)</p></li>
|
||||
<li><p>magnetic field penetration depth of the third layer (nm)</p></li>
|
||||
</ol>
|
||||
<p>The optional parameters are:</p>
|
||||
<ol class="loweralpha simple">
|
||||
<li>fraction f<sub>1</sub> of muons in the dead and first layer contributing to the signal (0 ≤ f<sub>1</sub> ≤ 1)</li>
|
||||
<li>fraction f<sub>2</sub> of muons in the second layer contributing to the signal (0 ≤ f<sub>2</sub> ≤ 1)</li>
|
||||
<li>fraction f<sub>3</sub> of muons in the third layer contributing to the signal (0 ≤ f<sub>3</sub> ≤ 1)</li>
|
||||
<li>fraction f<sub>s</sub> of muons in the substrate contributing to the signal (0 ≤ f<sub>s</sub> ≤ 1)</li>
|
||||
<li><p>fraction f<sub>1</sub> of muons in the dead and first layer contributing to the signal (0 ≤ f<sub>1</sub> ≤ 1)</p></li>
|
||||
<li><p>fraction f<sub>2</sub> of muons in the second layer contributing to the signal (0 ≤ f<sub>2</sub> ≤ 1)</p></li>
|
||||
<li><p>fraction f<sub>3</sub> of muons in the third layer contributing to the signal (0 ≤ f<sub>3</sub> ≤ 1)</p></li>
|
||||
<li><p>fraction f<sub>s</sub> of muons in the substrate contributing to the signal (0 ≤ f<sub>s</sub> ≤ 1)</p></li>
|
||||
</ol>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="bulk-mgrsr">
|
||||
<h4>Bulk μSR<a class="headerlink" href="#bulk-mgrsr" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="section" id="field-distributions-in-the-mixed-state-of-isotropic-superconductors">
|
||||
<span id="index-8"></span><h5>Field distributions in the mixed state of isotropic superconductors<a class="headerlink" href="#field-distributions-in-the-mixed-state-of-isotropic-superconductors" title="Permalink to this headline">¶</a></h5>
|
||||
</section>
|
||||
</section>
|
||||
<section id="bulk-mgrsr">
|
||||
<h4>Bulk μSR<a class="headerlink" href="#bulk-mgrsr" title="Link to this heading"></a></h4>
|
||||
<section id="field-distributions-in-the-mixed-state-of-isotropic-superconductors">
|
||||
<span id="index-8"></span><h5>Field distributions in the mixed state of isotropic superconductors<a class="headerlink" href="#field-distributions-in-the-mixed-state-of-isotropic-superconductors" title="Link to this heading"></a></h5>
|
||||
<p>When investigating superconductors in the mixed state by means of conventional μSR a
|
||||
two-dimensional flux-line lattice is probed randomly by the muons. The spatial field
|
||||
distributions within such an ordered lattice are modeled using the Fourier series</p>
|
||||
@@ -375,10 +297,10 @@ The muon-spin depolarization functions finally are calculated using the followin
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>mean magnetic induction (G)</li>
|
||||
<li>magnetic penetration depth (nm)</li>
|
||||
<li>Ginzburg-Landau coherence length (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>mean magnetic induction (G)</p></li>
|
||||
<li><p>magnetic penetration depth (nm)</p></li>
|
||||
<li><p>Ginzburg-Landau coherence length (nm)</p></li>
|
||||
</ol>
|
||||
<p id="index-10"><strong>2D triangular vortex lattice, modified London model</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libFitPofB</span> <span class="n">TBulkTriVortexML</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||
@@ -386,10 +308,10 @@ The muon-spin depolarization functions finally are calculated using the followin
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>mean magnetic induction (G)</li>
|
||||
<li>magnetic penetration depth (nm)</li>
|
||||
<li>Ginzburg-Landau coherence length (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>mean magnetic induction (G)</p></li>
|
||||
<li><p>magnetic penetration depth (nm)</p></li>
|
||||
<li><p>Ginzburg-Landau coherence length (nm)</p></li>
|
||||
</ol>
|
||||
<p id="index-11"><strong>2D triangular vortex lattice, analytic Ginzburg-Landau model</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libFitPofB</span> <span class="n">TBulkTriVortexAGL</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||
@@ -397,10 +319,10 @@ The muon-spin depolarization functions finally are calculated using the followin
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>mean magnetic induction (G)</li>
|
||||
<li>magnetic penetration depth (nm)</li>
|
||||
<li>Ginzburg-Landau coherence length (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>mean magnetic induction (G)</p></li>
|
||||
<li><p>magnetic penetration depth (nm)</p></li>
|
||||
<li><p>Ginzburg-Landau coherence length (nm)</p></li>
|
||||
</ol>
|
||||
<p id="index-12"><strong>2D triangular vortex lattice, numerical Ginzburg-Landau model</strong></p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">userFcn</span> <span class="n">libFitPofB</span> <span class="n">TBulkTriVortexNGL</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||
@@ -408,14 +330,14 @@ The muon-spin depolarization functions finally are calculated using the followin
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>phase (deg)</li>
|
||||
<li>mean magnetic induction (G)</li>
|
||||
<li>magnetic penetration depth (nm)</li>
|
||||
<li>Ginzburg-Landau coherence length (nm)</li>
|
||||
<li><p>phase (deg)</p></li>
|
||||
<li><p>mean magnetic induction (G)</p></li>
|
||||
<li><p>magnetic penetration depth (nm)</p></li>
|
||||
<li><p>Ginzburg-Landau coherence length (nm)</p></li>
|
||||
</ol>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<p class="last">In order to improve the convergence of <code class="docutils literal notranslate"><span class="pre">MIGRAD</span></code> it has proven useful to use the log-likelihood
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>In order to improve the convergence of <code class="docutils literal notranslate"><span class="pre">MIGRAD</span></code> it has proven useful to use the log-likelihood
|
||||
maximization instead of the <span class="math notranslate nohighlight">\(\chi^2\)</span> minimization routines and to choose sufficiently large
|
||||
initial steps for the parameters. Calling <code class="docutils literal notranslate"><span class="pre">MINOS</span></code> in conjunction with these functions is futile.</p>
|
||||
</div>
|
||||
@@ -428,47 +350,44 @@ initial steps for the parameters. Calling <code class="docutils literal notransl
|
||||
<span class="n">SAVE</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="the-xml-startup-file">
|
||||
<span id="bmwlibs-xml"></span><span id="index-13"></span><h4>The XML startup file<a class="headerlink" href="#the-xml-startup-file" title="Permalink to this headline">¶</a></h4>
|
||||
</section>
|
||||
</section>
|
||||
<section id="the-xml-startup-file">
|
||||
<span id="bmwlibs-xml"></span><span id="index-13"></span><h4>The XML startup file<a class="headerlink" href="#the-xml-startup-file" title="Link to this heading"></a></h4>
|
||||
<p><code class="docutils literal notranslate"><span class="pre">BMW_startup.xml</span></code> is a configuration file located in the working directory. In this file some settings
|
||||
like the time and field resolution of the calculations as well as the present muon implantation profiles
|
||||
for a LE-μSR analysis have to be defined. The following XML tags are allowed to define settings:</p>
|
||||
<dl class="docutils">
|
||||
<dt><strong><debug>ONE_OR_ZERO</debug></strong></dt>
|
||||
<dd>activate the debugging output of the settings read from the XML file by setting 1, deactivate it with 0.</dd>
|
||||
<dt><strong><wisdom>PATH_TO_FILE</wisdom></strong></dt>
|
||||
<dd>specify the <code class="docutils literal notranslate"><span class="pre">PATH_TO_FILE</span></code> to an <a class="reference external" href="http://fftw.org/fftw3_doc/Wisdom.html#Wisdom">FFTW3 wisdom file</a>
|
||||
that should be used; if the <code class="docutils literal notranslate"><span class="pre">PATH_TO_FILE</span></code> is invalid, no <code class="docutils literal notranslate"><span class="pre">FFTW3</span></code> wisdom will be used.</dd>
|
||||
<dt><strong><delta_t>ResT</delta_t></strong></dt>
|
||||
<dd>set the time resolution <code class="docutils literal notranslate"><span class="pre">ResT</span></code> for the calculated depolarization function in microseconds.</dd>
|
||||
<dt><strong><delta_B>ResB</delta_B></strong></dt>
|
||||
<dd>set the field resolution <code class="docutils literal notranslate"><span class="pre">ResB</span></code> for the calculated field distribution in Gauss.</dd>
|
||||
<dt><strong><VortexLattice></VortexLattice></strong></dt>
|
||||
<dd><p class="first">set the parameters used for the calculation of the spatial field distribution of a vortex lattice.</p>
|
||||
<dl class="last docutils">
|
||||
<dt><strong><N_VortexGrid>N</N_VortexGrid></strong></dt>
|
||||
<dd>specify the number of points <strong>N</strong> (in each of the two dimensions) for which the fields within the
|
||||
vortex lattice are calculated (inside a <strong><VortexLattice></strong> environment)</dd>
|
||||
<dl>
|
||||
<dt><strong><debug>ONE_OR_ZERO</debug></strong></dt><dd><p>activate the debugging output of the settings read from the XML file by setting 1, deactivate it with 0.</p>
|
||||
</dd>
|
||||
<dt><strong><wisdom>PATH_TO_FILE</wisdom></strong></dt><dd><p>specify the <code class="docutils literal notranslate"><span class="pre">PATH_TO_FILE</span></code> to an <a class="reference external" href="http://fftw.org/fftw3_doc/Wisdom.html#Wisdom">FFTW3 wisdom file</a>
|
||||
that should be used; if the <code class="docutils literal notranslate"><span class="pre">PATH_TO_FILE</span></code> is invalid, no <code class="docutils literal notranslate"><span class="pre">FFTW3</span></code> wisdom will be used.</p>
|
||||
</dd>
|
||||
<dt><strong><delta_t>ResT</delta_t></strong></dt><dd><p>set the time resolution <code class="docutils literal notranslate"><span class="pre">ResT</span></code> for the calculated depolarization function in microseconds.</p>
|
||||
</dd>
|
||||
<dt><strong><delta_B>ResB</delta_B></strong></dt><dd><p>set the field resolution <code class="docutils literal notranslate"><span class="pre">ResB</span></code> for the calculated field distribution in Gauss.</p>
|
||||
</dd>
|
||||
<dt><strong><VortexLattice></VortexLattice></strong></dt><dd><p>set the parameters used for the calculation of the spatial field distribution of a vortex lattice.</p>
|
||||
<dl class="simple">
|
||||
<dt><strong><N_VortexGrid>N</N_VortexGrid></strong></dt><dd><p>specify the number of points <strong>N</strong> (in each of the two dimensions) for which the fields within the
|
||||
vortex lattice are calculated (inside a <strong><VortexLattice></strong> environment)</p>
|
||||
</dd>
|
||||
</dl>
|
||||
</dd>
|
||||
<dt><strong><LEM></LEM></strong></dt>
|
||||
<dd><p class="first">set the parameters used for the calculation of LE-μSR field distributions</p>
|
||||
<dl class="last docutils">
|
||||
<dt><strong><data_path>DATA_PATH_PREFIX</data_path></strong></dt>
|
||||
<dd>specify the <code class="docutils literal notranslate"><span class="pre">DATA_PATH_PREFIX</span></code> to the <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> implantation profiles (inside a <strong><LEM></strong> environment)</dd>
|
||||
<dt><strong><N_theory>N_THEORY</N_theory></strong></dt>
|
||||
<dd>specify the number of points <strong>N_THEORY</strong> for which <em>B(z)</em> is calculated (inside a <strong><LEM></strong> environment)
|
||||
The specification of this number is not needed if the calculation of the inverse of <em>B(z)</em> is implemented!</dd>
|
||||
<dt><strong><energy_list></energy_list></strong></dt>
|
||||
<dd><p class="first">set the energies for which <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> implantation profiles are available (inside a <strong><LEM></strong> environment)</p>
|
||||
<dl class="last docutils">
|
||||
<dt><strong><energy_label>LABEL</energy_label></strong></dt>
|
||||
<dd>specify the <strong>LABEL</strong> within the file name of a available <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> <code class="docutils literal notranslate"><span class="pre">RGE</span></code> file (inside a <strong><energy_list></strong> environment)
|
||||
The expected name of the <code class="docutils literal notranslate"><span class="pre">RGE</span></code> file will be: <code class="docutils literal notranslate"><span class="pre">DATA_PATH_PREFIX</span> <span class="pre">+</span> <span class="pre">LABEL</span> <span class="pre">+</span> <span class="pre">.rge</span></code></dd>
|
||||
<dt><strong><energy>E</energy></strong></dt>
|
||||
<dd>specify the muon energy <em>E</em> (in keV) belonging to the <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> <code class="docutils literal notranslate"><span class="pre">RGE</span></code> file given above (inside a <strong><energy_list></strong> environment)</dd>
|
||||
<dt><strong><LEM></LEM></strong></dt><dd><p>set the parameters used for the calculation of LE-μSR field distributions</p>
|
||||
<dl>
|
||||
<dt><strong><data_path>DATA_PATH_PREFIX</data_path></strong></dt><dd><p>specify the <code class="docutils literal notranslate"><span class="pre">DATA_PATH_PREFIX</span></code> to the <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> implantation profiles (inside a <strong><LEM></strong> environment)</p>
|
||||
</dd>
|
||||
<dt><strong><N_theory>N_THEORY</N_theory></strong></dt><dd><p>specify the number of points <strong>N_THEORY</strong> for which <em>B(z)</em> is calculated (inside a <strong><LEM></strong> environment)
|
||||
The specification of this number is not needed if the calculation of the inverse of <em>B(z)</em> is implemented!</p>
|
||||
</dd>
|
||||
<dt><strong><energy_list></energy_list></strong></dt><dd><p>set the energies for which <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> implantation profiles are available (inside a <strong><LEM></strong> environment)</p>
|
||||
<dl class="simple">
|
||||
<dt><strong><energy_label>LABEL</energy_label></strong></dt><dd><p>specify the <strong>LABEL</strong> within the file name of a available <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> <code class="docutils literal notranslate"><span class="pre">RGE</span></code> file (inside a <strong><energy_list></strong> environment)
|
||||
The expected name of the <code class="docutils literal notranslate"><span class="pre">RGE</span></code> file will be: <code class="docutils literal notranslate"><span class="pre">DATA_PATH_PREFIX</span> <span class="pre">+</span> <span class="pre">LABEL</span> <span class="pre">+</span> <span class="pre">.rge</span></code></p>
|
||||
</dd>
|
||||
<dt><strong><energy>E</energy></strong></dt><dd><p>specify the muon energy <em>E</em> (in keV) belonging to the <code class="docutils literal notranslate"><span class="pre">TRIM.SP</span></code> <code class="docutils literal notranslate"><span class="pre">RGE</span></code> file given above (inside a <strong><energy_list></strong> environment)</p>
|
||||
</dd>
|
||||
</dl>
|
||||
</dd>
|
||||
</dl>
|
||||
@@ -477,43 +396,43 @@ The expected name of the <code class="docutils literal notranslate"><span class=
|
||||
<p>An example XML file looks as follows:</p>
|
||||
<div class="highlight-xml notranslate"><div class="highlight"><pre><span></span><span class="cp"><?xml version="1.0" encoding="UTF-8"?></span>
|
||||
<span class="nt"><BMW></span>
|
||||
<span class="nt"><debug></span>0<span class="nt"></debug></span>
|
||||
<span class="nt"><wisdom></span>/home/user/WordsOfWisdom.dat<span class="nt"></wisdom></span>
|
||||
<span class="nt"><delta_t></span>0.01<span class="nt"></delta_t></span>
|
||||
<span class="nt"><delta_B></span>0.5<span class="nt"></delta_B></span>
|
||||
<span class="nt"><VortexLattice></span>
|
||||
<span class="nt"><N_VortexGrid></span>1024<span class="nt"></N_VortexGrid></span>
|
||||
<span class="nt"></VortexLattice></span>
|
||||
<span class="nt"><LEM></span>
|
||||
<span class="nt"><data_path></span>/home/user/TrimSP/some-sample-<span class="nt"></data_path></span>
|
||||
<span class="nt"><N_theory></span>5000<span class="nt"></N_theory></span>
|
||||
<span class="nt"><energy_list></span>
|
||||
<span class="nt"><energy_label></span>02_0<span class="nt"></energy_label></span>
|
||||
<span class="nt"><energy></span>2.0<span class="nt"></energy></span>
|
||||
<span class="nt"><energy_label></span>03_0<span class="nt"></energy_label></span>
|
||||
<span class="nt"><energy></span>3.0<span class="nt"></energy></span>
|
||||
<span class="nt"><energy_label></span>03_6<span class="nt"></energy_label></span>
|
||||
<span class="nt"><energy></span>3.6<span class="nt"></energy></span>
|
||||
<span class="nt"><energy_label></span>05_0<span class="nt"></energy_label></span>
|
||||
<span class="nt"><energy></span>5.0<span class="nt"></energy></span>
|
||||
<span class="nt"><energy_label></span>05_3<span class="nt"></energy_label></span>
|
||||
<span class="nt"><energy></span>5.3<span class="nt"></energy></span>
|
||||
<span class="nt"></energy_list></span>
|
||||
<span class="nt"></LEM></span>
|
||||
<span class="w"> </span><span class="nt"><debug></span>0<span class="nt"></debug></span>
|
||||
<span class="w"> </span><span class="nt"><wisdom></span>/home/user/WordsOfWisdom.dat<span class="nt"></wisdom></span>
|
||||
<span class="w"> </span><span class="nt"><delta_t></span>0.01<span class="nt"></delta_t></span>
|
||||
<span class="w"> </span><span class="nt"><delta_B></span>0.5<span class="nt"></delta_B></span>
|
||||
<span class="w"> </span><span class="nt"><VortexLattice></span>
|
||||
<span class="w"> </span><span class="nt"><N_VortexGrid></span>1024<span class="nt"></N_VortexGrid></span>
|
||||
<span class="w"> </span><span class="nt"></VortexLattice></span>
|
||||
<span class="w"> </span><span class="nt"><LEM></span>
|
||||
<span class="w"> </span><span class="nt"><data_path></span>/home/user/TrimSP/some-sample-<span class="nt"></data_path></span>
|
||||
<span class="w"> </span><span class="nt"><N_theory></span>5000<span class="nt"></N_theory></span>
|
||||
<span class="w"> </span><span class="nt"><energy_list></span>
|
||||
<span class="w"> </span><span class="nt"><energy_label></span>02_0<span class="nt"></energy_label></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>2.0<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy_label></span>03_0<span class="nt"></energy_label></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>3.0<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy_label></span>03_6<span class="nt"></energy_label></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>3.6<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy_label></span>05_0<span class="nt"></energy_label></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>5.0<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy_label></span>05_3<span class="nt"></energy_label></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>5.3<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"></energy_list></span>
|
||||
<span class="w"> </span><span class="nt"></LEM></span>
|
||||
<span class="nt"></BMW></span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="supeconducting-gap-integrals-to-calculate-vs">
|
||||
<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>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
<section id="supeconducting-gap-integrals-to-calculate-1-lambda-2-vs-t">
|
||||
<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-1-lambda-2-vs-t" title="Link to this heading"></a></h2>
|
||||
<p>The details about the various superconducting gap-integrals are found in the
|
||||
pdf-file <strong>GapIntegrals.pdf</strong> which can be found in the musrfit source under
|
||||
<code class="docutils literal notranslate"><span class="pre"><musrfit-dir>/src/external/libGapIntegrals/</span></code>.</p>
|
||||
</div>
|
||||
<div class="section" id="nonlocal-superconductivity-related-meissner-screening-functions-as-libs">
|
||||
<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>
|
||||
</section>
|
||||
<section id="nonlocal-superconductivity-related-meissner-screening-functions-as-libs">
|
||||
<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="Link to this heading"></a></h2>
|
||||
<p>This library allows to calculate the magnetic field profile <span class="math notranslate nohighlight">\(B(z)\)</span> for nonlocal superconductors.
|
||||
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>
|
||||
<p>The provided function calculates the muon spin polarization</p>
|
||||
@@ -526,45 +445,45 @@ The corresponding user function is called as</p>
|
||||
</div>
|
||||
<p>with the parameters</p>
|
||||
<ol class="arabic simple">
|
||||
<li>implantation energy in (keV).</li>
|
||||
<li>reduced temperature <span class="math notranslate nohighlight">\(t=T/T_c\)</span>.</li>
|
||||
<li>thickness in (nm).</li>
|
||||
<li>electron mean path, <span class="math notranslate nohighlight">\(\ell\)</span> in (nm).</li>
|
||||
<li>superconducting coherence length, <span class="math notranslate nohighlight">\(\xi\)</span> in (nm).</li>
|
||||
<li>London penetration length, <span class="math notranslate nohighlight">\(\lambda_{\rm L}\)</span> in (nm).</li>
|
||||
<li>external magnetic field strength in (G).</li>
|
||||
<li>the effective detector phase, <span class="math notranslate nohighlight">\(\varphi\)</span> in <span class="math notranslate nohighlight">\((^\circ)\)</span>.</li>
|
||||
<li>a “dead layer” thickness in (nm).</li>
|
||||
<li><p>implantation energy in (keV).</p></li>
|
||||
<li><p>reduced temperature <span class="math notranslate nohighlight">\(t=T/T_c\)</span>.</p></li>
|
||||
<li><p>thickness in (nm).</p></li>
|
||||
<li><p>electron mean path, <span class="math notranslate nohighlight">\(\ell\)</span> in (nm).</p></li>
|
||||
<li><p>superconducting coherence length, <span class="math notranslate nohighlight">\(\xi\)</span> in (nm).</p></li>
|
||||
<li><p>London penetration length, <span class="math notranslate nohighlight">\(\lambda_{\rm L}\)</span> in (nm).</p></li>
|
||||
<li><p>external magnetic field strength in (G).</p></li>
|
||||
<li><p>the effective detector phase, <span class="math notranslate nohighlight">\(\varphi\)</span> in <span class="math notranslate nohighlight">\((^\circ)\)</span>.</p></li>
|
||||
<li><p>a “dead layer” thickness in (nm).</p></li>
|
||||
</ol>
|
||||
<p>Typically this function needs to be multiplied by a Gaussian in order to take into account: nuclear dipole broadening, partial trapped flux, etc.</p>
|
||||
<p>In order to find the muon stopping profile, <span class="math notranslate nohighlight">\(n(z,E)\)</span>, needed for the calculation, the library needs to find the corresponding trimsp
|
||||
rge-files (muon stoppping profiles). For this the library reads at start-up the following xml-file (example):</p>
|
||||
<div class="highlight-xml notranslate"><div class="highlight"><pre><span></span><span class="cp"><?xml version="1.0" encoding="UTF-8"?></span>
|
||||
<span class="nt"><nonlocal</span> <span class="na">xmlns=</span><span class="s">"http://nemu.web.psi.ch/musrfit/nonlocal"</span><span class="nt">></span>
|
||||
<span class="nt"><comment></span>
|
||||
nonlocal_startup.xml
|
||||
<span class="nt"></comment></span>
|
||||
<span class="nt"><nonlocal_par></span>
|
||||
<span class="nt"><fourier_points></span>262144<span class="nt"></fourier_points></span>
|
||||
<span class="nt"></nonlocal_par></span>
|
||||
<span class="nt"><trim_sp></span>
|
||||
<span class="nt"><data_path></span>./profiles/<span class="nt"></data_path></span>
|
||||
<span class="nt"><rge_fln_pre></span>Sn_E<span class="nt"></rge_fln_pre></span>
|
||||
<span class="nt"><energy_list></span>
|
||||
<span class="nt"><energy></span>1000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>2000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>4000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>6000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>8000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>10000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>12000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>14100<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>18000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>22000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>25000<span class="nt"></energy></span>
|
||||
<span class="nt"><energy></span>27300<span class="nt"></energy></span>
|
||||
<span class="nt"></energy_list></span>
|
||||
<span class="nt"></trim_sp></span>
|
||||
<span class="nt"><nonlocal</span><span class="w"> </span><span class="na">xmlns=</span><span class="s">"http://nemu.web.psi.ch/musrfit/nonlocal"</span><span class="nt">></span>
|
||||
<span class="w"> </span><span class="nt"><comment></span>
|
||||
<span class="w"> </span>nonlocal_startup.xml
|
||||
<span class="w"> </span><span class="nt"></comment></span>
|
||||
<span class="w"> </span><span class="nt"><nonlocal_par></span>
|
||||
<span class="w"> </span><span class="nt"><fourier_points></span>262144<span class="nt"></fourier_points></span>
|
||||
<span class="w"> </span><span class="nt"></nonlocal_par></span>
|
||||
<span class="w"> </span><span class="nt"><trim_sp></span>
|
||||
<span class="w"> </span><span class="nt"><data_path></span>./profiles/<span class="nt"></data_path></span>
|
||||
<span class="w"> </span><span class="nt"><rge_fln_pre></span>Sn_E<span class="nt"></rge_fln_pre></span>
|
||||
<span class="w"> </span><span class="nt"><energy_list></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>1000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>2000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>4000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>6000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>8000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>10000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>12000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>14100<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>18000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>22000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>25000<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"><energy></span>27300<span class="nt"></energy></span>
|
||||
<span class="w"> </span><span class="nt"></energy_list></span>
|
||||
<span class="w"> </span><span class="nt"></trim_sp></span>
|
||||
<span class="nt"></nonlocal></span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -574,9 +493,9 @@ contains all the information needed to load the proper muon stopping profiles. <
|
||||
muon stopping profile for an energy of <span class="math notranslate nohighlight">\(E=1000\)</span> (eV).</p>
|
||||
<p>The name of the xml-file has to be <code class="docutils literal notranslate"><span class="pre">nonlocal_startup.xml</span></code> and needs to be placed in the directory where the analysis takes place, i.e.
|
||||
in the directory of all the msr-files.</p>
|
||||
</div>
|
||||
<div class="section" id="depth-resolved-information-as-libs">
|
||||
<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>
|
||||
</section>
|
||||
<section id="depth-resolved-information-as-libs">
|
||||
<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="Link to this heading"></a></h2>
|
||||
<p>A method to extract depth-resolved information from the implantation energy dependence of the experimental parameters in a low-energy
|
||||
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>
|
||||
<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.
|
||||
@@ -590,8 +509,8 @@ Hence the measured property as function of energy is</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[f(E) = \sum_{i=1}^N p_{i}(E) \cdot f_i.\]</div>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<p class="last">Currently it is recommended to read in the data in ASCII or DAT 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>
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>Currently it is recommended to read in the data in ASCII or DAT 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>
|
||||
</div>
|
||||
<p>The user library for the depth profile analysis looks for a <strong>3 layer material</strong>, assuming one is looking for the diamagnetic fraction, like</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1">###############################################################</span>
|
||||
@@ -612,33 +531,33 @@ Hence the measured property as function of energy is</p>
|
||||
<p>In order to find the muon stopping profile, <span class="math notranslate nohighlight">\(n(z,E)\)</span>, needed for the calculation, the library needs to find the corresponding trimsp
|
||||
rge-files (muon stoppping profiles). For this the library reads at start-up the following xml-file (example):</p>
|
||||
<div class="highlight-xml notranslate"><div class="highlight"><pre><span></span><span class="cp"><?xml version="1.0" encoding="UTF-8"?></span>
|
||||
<span class="nt"><depthProf</span> <span class="na">xmlns=</span><span class="s">"http://nemu.web.psi.ch/musrfit/depthProf"</span><span class="nt">></span>
|
||||
<span class="nt"><comment></span>
|
||||
TrimSp information
|
||||
<span class="nt"></comment></span>
|
||||
<span class="nt"><trim_sp></span>
|
||||
<span class="nt"><data_path></span>./TRIMSP/<span class="nt"></data_path></span>
|
||||
<span class="nt"><rge_fln_pre></span>SiO2_70nm2.0_30nm2.2_SiC_E<span class="nt"></rge_fln_pre></span>
|
||||
<span class="nt"><energy_vect</span> <span class="na">start=</span><span class="s">"1000"</span> <span class="na">stop=</span><span class="s">"22000"</span> <span class="na">step=</span><span class="s">"1000"</span><span class="nt">/></span>
|
||||
<span class="nt"></trim_sp></span>
|
||||
<span class="nt"><depthProf</span><span class="w"> </span><span class="na">xmlns=</span><span class="s">"http://nemu.web.psi.ch/musrfit/depthProf"</span><span class="nt">></span>
|
||||
<span class="w"> </span><span class="nt"><comment></span>
|
||||
<span class="w"> </span>TrimSp<span class="w"> </span>information
|
||||
<span class="w"> </span><span class="nt"></comment></span>
|
||||
<span class="w"> </span><span class="nt"><trim_sp></span>
|
||||
<span class="w"> </span><span class="nt"><data_path></span>./TRIMSP/<span class="nt"></data_path></span>
|
||||
<span class="w"> </span><span class="nt"><rge_fln_pre></span>SiO2_70nm2.0_30nm2.2_SiC_E<span class="nt"></rge_fln_pre></span>
|
||||
<span class="w"> </span><span class="nt"><energy_vect</span><span class="w"> </span><span class="na">start=</span><span class="s">"1000"</span><span class="w"> </span><span class="na">stop=</span><span class="s">"22000"</span><span class="w"> </span><span class="na">step=</span><span class="s">"1000"</span><span class="nt">/></span>
|
||||
<span class="w"> </span><span class="nt"></trim_sp></span>
|
||||
<span class="nt"></depthProf></span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="functions-to-analyze-bgr-nmr-data-bnmr-libs">
|
||||
<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>
|
||||
</section>
|
||||
<section id="functions-to-analyze-bgr-nmr-data-bnmr-libs">
|
||||
<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="Link to this heading"></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>
|
||||
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>
|
||||
<ul class="simple">
|
||||
<li><code class="docutils literal notranslate"><span class="pre">libBNMR</span></code> contains functions to fit spin lattice relaxation (SLR) data.</li>
|
||||
<li><code class="docutils literal notranslate"><span class="pre">libLineProfile</span></code> contains functions to fit resonance lineshapes.</li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">libBNMR</span></code> contains functions to fit spin lattice relaxation (SLR) data.</p></li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">libLineProfile</span></code> contains functions to fit resonance lineshapes.</p></li>
|
||||
</ul>
|
||||
<div class="admonition note">
|
||||
<p class="first admonition-title">Note</p>
|
||||
<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>
|
||||
<p class="admonition-title">Note</p>
|
||||
<p>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>
|
||||
</div>
|
||||
<div class="section" id="libbnmr">
|
||||
<span id="index-18"></span><h3>libBNMR<a class="headerlink" href="#libbnmr" title="Permalink to this headline">¶</a></h3>
|
||||
<section id="libbnmr">
|
||||
<span id="index-18"></span><h3>libBNMR<a class="headerlink" href="#libbnmr" title="Link to this heading"></a></h3>
|
||||
<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.
|
||||
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>
|
||||
<div class="math notranslate nohighlight" id="slr">
|
||||
@@ -647,8 +566,8 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
|
||||
\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,
|
||||
\end{matrix}\right.\end{split}\]</div>
|
||||
<p>where <span class="math notranslate nohighlight">\(\tau_{\mathrm{Li}}=1.21\)</span>s is the <span class="math notranslate nohighlight">\(^8\)</span>Li lifetime.</p>
|
||||
<div class="section" id="functions">
|
||||
<h4>Functions<a class="headerlink" href="#functions" title="Permalink to this headline">¶</a></h4>
|
||||
<section id="functions">
|
||||
<h4>Functions<a class="headerlink" href="#functions" title="Link to this heading"></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-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>
|
||||
@@ -656,8 +575,8 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>pulse length <span class="math notranslate nohighlight">\(t_0\)</span> (s)</li>
|
||||
<li>relaxation rate <span class="math notranslate nohighlight">\(\lambda\)</span> (s<span class="math notranslate nohighlight">\(^{-1}\)</span>)</li>
|
||||
<li><p>pulse length <span class="math notranslate nohighlight">\(t_0\)</span> (s)</p></li>
|
||||
<li><p>relaxation rate <span class="math notranslate nohighlight">\(\lambda\)</span> (s<span class="math notranslate nohighlight">\(^{-1}\)</span>)</p></li>
|
||||
</ol>
|
||||
<p>This function implements <span class="math notranslate nohighlight">\(f(t)=e^{-\lambda t}\)</span>.</p>
|
||||
<p id="index-21"><strong>Stretched exponential relaxation</strong></p>
|
||||
@@ -666,15 +585,15 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>pulse length <span class="math notranslate nohighlight">\(t_0\)</span> (s)</li>
|
||||
<li>relaxation rate <span class="math notranslate nohighlight">\(\lambda\)</span> (s<span class="math notranslate nohighlight">\(^{-1}\)</span>)</li>
|
||||
<li>stretching exponent <span class="math notranslate nohighlight">\(\beta\)</span></li>
|
||||
<li><p>pulse length <span class="math notranslate nohighlight">\(t_0\)</span> (s)</p></li>
|
||||
<li><p>relaxation rate <span class="math notranslate nohighlight">\(\lambda\)</span> (s<span class="math notranslate nohighlight">\(^{-1}\)</span>)</p></li>
|
||||
<li><p>stretching exponent <span class="math notranslate nohighlight">\(\beta\)</span></p></li>
|
||||
</ol>
|
||||
<p>This function implements <span class="math notranslate nohighlight">\(f(t)=e^{-(\lambda t)^{\beta}}\)</span>.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="liblineprofile">
|
||||
<span id="index-22"></span><h3>libLineProfile<a class="headerlink" href="#liblineprofile" title="Permalink to this headline">¶</a></h3>
|
||||
</section>
|
||||
</section>
|
||||
<section id="liblineprofile">
|
||||
<span id="index-22"></span><h3>libLineProfile<a class="headerlink" href="#liblineprofile" title="Link to this heading"></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.
|
||||
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>
|
||||
@@ -699,8 +618,8 @@ m&=\left\{\begin{matrix}
|
||||
\\
|
||||
K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\end{split}\]</div>
|
||||
<p><span class="math notranslate nohighlight">\(K(m)\)</span> is the complete elliptic integral of the first kind.</p>
|
||||
<div class="section" id="id1">
|
||||
<h4>Functions<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h4>
|
||||
<section id="id1">
|
||||
<h4>Functions<a class="headerlink" href="#id1" title="Link to this heading"></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-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>
|
||||
@@ -708,8 +627,8 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></li>
|
||||
<li>FWHM of the line <span class="math notranslate nohighlight">\(\sigma\)</span></li>
|
||||
<li><p>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></p></li>
|
||||
<li><p>FWHM of the line <span class="math notranslate nohighlight">\(\sigma\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is 1.</div>
|
||||
@@ -723,8 +642,8 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></li>
|
||||
<li>FWHM of the line <span class="math notranslate nohighlight">\(w\)</span></li>
|
||||
<li><p>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></p></li>
|
||||
<li><p>FWHM of the line <span class="math notranslate nohighlight">\(w\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is 1.</div>
|
||||
@@ -738,8 +657,8 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></li>
|
||||
<li>FWHM of the line <span class="math notranslate nohighlight">\(w\)</span></li>
|
||||
<li><p>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></p></li>
|
||||
<li><p>FWHM of the line <span class="math notranslate nohighlight">\(w\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is 1.</div>
|
||||
@@ -753,9 +672,9 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></li>
|
||||
<li>width of the line <span class="math notranslate nohighlight">\(w\)</span></li>
|
||||
<li>skewness parameter <span class="math notranslate nohighlight">\(a\)</span></li>
|
||||
<li><p>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></p></li>
|
||||
<li><p>width of the line <span class="math notranslate nohighlight">\(w\)</span></p></li>
|
||||
<li><p>skewness parameter <span class="math notranslate nohighlight">\(a\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is 1.</div>
|
||||
@@ -769,9 +688,9 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></li>
|
||||
<li>width left of the center <span class="math notranslate nohighlight">\(w_1\)</span></li>
|
||||
<li>width right of the center <span class="math notranslate nohighlight">\(w_2\)</span></li>
|
||||
<li><p>center of the line <span class="math notranslate nohighlight">\(f_0\)</span></p></li>
|
||||
<li><p>width left of the center <span class="math notranslate nohighlight">\(w_1\)</span></p></li>
|
||||
<li><p>width right of the center <span class="math notranslate nohighlight">\(w_2\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is 1.</div>
|
||||
@@ -785,9 +704,9 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>frequency for the field oriented paralell to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></li>
|
||||
<li>frequency for the field oriented perpendicular to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></li>
|
||||
<li>FWHM of the Lorentzian <span class="math notranslate nohighlight">\(w\)</span></li>
|
||||
<li><p>frequency for the field oriented paralell to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></p></li>
|
||||
<li><p>frequency for the field oriented perpendicular to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></p></li>
|
||||
<li><p>FWHM of the Lorentzian <span class="math notranslate nohighlight">\(w\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is <span class="math notranslate nohighlight">\(\sim\)</span>1.</div>
|
||||
@@ -802,9 +721,9 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>frequency for the field oriented paralell to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></li>
|
||||
<li>frequency for the field oriented perpendicular to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></li>
|
||||
<li>FWHM of the Gaussian <span class="math notranslate nohighlight">\(\sigma\)</span></li>
|
||||
<li><p>frequency for the field oriented paralell to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></p></li>
|
||||
<li><p>frequency for the field oriented perpendicular to the symmetry axis <span class="math notranslate nohighlight">\(f_\parallel\)</span></p></li>
|
||||
<li><p>FWHM of the Gaussian <span class="math notranslate nohighlight">\(\sigma\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is <span class="math notranslate nohighlight">\(\sim\)</span>1.</div>
|
||||
@@ -819,10 +738,10 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li><span class="math notranslate nohighlight">\(f_1\)</span></li>
|
||||
<li><span class="math notranslate nohighlight">\(f_1\)</span></li>
|
||||
<li><span class="math notranslate nohighlight">\(f_3\)</span> frequencies along the principal axes</li>
|
||||
<li>FWHM of the Lorentzian <span class="math notranslate nohighlight">\(w\)</span></li>
|
||||
<li><p><span class="math notranslate nohighlight">\(f_1\)</span></p></li>
|
||||
<li><p><span class="math notranslate nohighlight">\(f_1\)</span></p></li>
|
||||
<li><p><span class="math notranslate nohighlight">\(f_3\)</span> frequencies along the principal axes</p></li>
|
||||
<li><p>FWHM of the Lorentzian <span class="math notranslate nohighlight">\(w\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is <span class="math notranslate nohighlight">\(\sim\)</span>1.</div>
|
||||
@@ -837,10 +756,10 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
</div>
|
||||
<p>The parameters are:</p>
|
||||
<ol class="arabic simple">
|
||||
<li><span class="math notranslate nohighlight">\(f_1\)</span></li>
|
||||
<li><span class="math notranslate nohighlight">\(f_1\)</span></li>
|
||||
<li><span class="math notranslate nohighlight">\(f_3\)</span> frequencies along the principal axes</li>
|
||||
<li>FWHM of the Gaussian <span class="math notranslate nohighlight">\(\sigma\)</span></li>
|
||||
<li><p><span class="math notranslate nohighlight">\(f_1\)</span></p></li>
|
||||
<li><p><span class="math notranslate nohighlight">\(f_1\)</span></p></li>
|
||||
<li><p><span class="math notranslate nohighlight">\(f_3\)</span> frequencies along the principal axes</p></li>
|
||||
<li><p>FWHM of the Gaussian <span class="math notranslate nohighlight">\(\sigma\)</span></p></li>
|
||||
</ol>
|
||||
<div class="line-block">
|
||||
<div class="line">The height of the peak is <span class="math notranslate nohighlight">\(\sim\)</span>1.</div>
|
||||
@@ -849,75 +768,38 @@ K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
|
||||
<div class="math notranslate nohighlight">
|
||||
\[A(f)= I(f)\circledast\left( e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} \right)\]</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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
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|
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||||
|
||||
<div role="contentinfo">
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||||
<p>
|
||||
© Copyright 2023, Andreas Suter.
|
||||
Last updated on Jun 24, 2024.
|
||||
|
||||
</p>
|
||||
<p>© Copyright 2025, Andreas Suter.
|
||||
<span class="lastupdated">Last updated on Jun 06, 2025.
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