238 lines
14 KiB
HTML
238 lines
14 KiB
HTML
<!DOCTYPE html><html lang="en">
|
|
|
|
<!-- Mirrored from intranet.psi.ch/MUSR/LibZFRelaxation?cover=print by HTTrack Website Copier/3.x [XR&CO'2010], Thu, 28 Apr 2016 07:39:33 GMT -->
|
|
<!-- Added by HTTrack --><meta http-equiv="content-type" content="text/html;charset=utf-8"><!-- /Added by HTTrack -->
|
|
<head>
|
|
<link rel="stylesheet" href="../pub/System/HeadlinesPlugin/style.css" type="text/css" media="all" />
|
|
<title> MUSR :: LibZFRelaxation</title>
|
|
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
|
|
<meta charset="utf-8" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1.5, user-scalable=yes" />
|
|
<meta name="mobile-web-app-capable" content="yes" />
|
|
<meta name="mobile-web-app-status-bar-style" content="black-translucent" />
|
|
<meta name="apple-mobile-web-app-capable" content="yes" />
|
|
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" />
|
|
<link rel="icon" href="../pub/Main/WebPreferences/favicon.ico" type="image/x-icon" />
|
|
<link rel="shortcut icon" href="../pub/Main/WebPreferences/favicon.ico" type="image/x-icon" />
|
|
<link rel="alternate" href="https://intranet.psi.ch/wiki/bin/edit/MUSR/LibZFRelaxation?t=1461829164" type="application/x-wiki" title="edit LibZFRelaxation" />
|
|
<meta name="TEXT_NUM_TOPICS" content="Number of topics:" />
|
|
<meta name="TEXT_MODIFY_SEARCH" content="Modify search" />
|
|
<meta name="robots" content="noindex" /><link rel="alternate" type="application/rss+xml" title="RSS Feed" href="WebRsshtml.html" />
|
|
<base /><!--[if IE]></base><![endif]--><link class='head SMILIESPLUGIN' rel='stylesheet' href='../pub/System/SmiliesPlugin/smilies.css' type='text/css' media='all' /><!--SMILIESPLUGIN-->
|
|
<link class='head JQUERYPLUGIN::COMMENT' rel='stylesheet' href='../pub/System/CommentPlugin/commentf5b6.css?version=3.0' type='text/css' media='all' /><!--JQUERYPLUGIN::COMMENT-->
|
|
<link class='head CLASSIFICATIONPLUGIN::CSS' rel="stylesheet" href="../pub/System/ClassificationPlugin/styles.css" media="all" /><!--CLASSIFICATIONPLUGIN::CSS-->
|
|
<link class='head FOOTNOTEPLUGIN_LINKCSS' rel="stylesheet" href="../pub/System/FootNotePlugin/styles.css" type="text/css" media="all" /><!--FOOTNOTEPLUGIN_LINKCSS--><link rel='stylesheet' href='../pub/System/SkinTemplates/base.css' media='all' type='text/css' />
|
|
<style type="text/css" media="all">
|
|
@import url('../pub/System/PatternSkinTheme/layout.css');
|
|
@import url('../pub/System/PatternSkinTheme2009/style.css');
|
|
@import url('../pub/System/PatternSkinTheme2009/colors.css');
|
|
</style>
|
|
<link rel='stylesheet' href='../pub/System/PatternSkinTheme2009/column_left.css' media='all' type='text/css' />
|
|
<link rel='stylesheet' href='../pub/System/PatternSkinTheme2009/variant_twiki.css' media='all' type='text/css' /><style type="text/css" media="all">
|
|
/* Styles that are set using variables */
|
|
.patternBookView .foswikiTopRow,
|
|
.patternWebIndicator,
|
|
.patternWebIndicator a {
|
|
background-color:#D0D0D0;
|
|
}
|
|
#patternTopBarContents { background-image:url(../pub/System/PatternSkin/header5.gif); background-repeat:repeat-x;}
|
|
#patternTopBarContents { background-color:#ffffff;}
|
|
.patternBookView {
|
|
border-color:#D0D0D0;
|
|
}
|
|
.patternPreviewPage #patternMain {
|
|
/* uncomment to set the preview image */
|
|
/*background-image:url("/pub/System/PreviewBackground/preview2bg.gif");*/
|
|
}
|
|
</style>
|
|
<style type="text/css" media="all">
|
|
@import url("../pub/System/PsiSkin/psicolors.css");
|
|
@import url("../pub/System/PsiSkin/psistyle.css");
|
|
.foswikiTopic {overflow: hidden;}
|
|
</style>
|
|
|
|
|
|
|
|
<link rel='stylesheet' href='../pub/System/PatternSkin/print.css' media='all' type='text/css' />
|
|
<!--[if IE 7 ]><style type="text/css" media="screen">
|
|
.foswikiAttachments,
|
|
.foswikiForm,
|
|
.foswikiHelp,
|
|
.foswikiPreviewArea,
|
|
.patternPreviewPage .foswikiForm,
|
|
.patternSigLine,
|
|
.patternToolBar,
|
|
.patternTop,
|
|
.patternTopicAction,
|
|
#patternSideBarContents .patternLeftBarPersonal,
|
|
#patternSideBarContents h2,
|
|
#patternSideBarContents li,
|
|
#patternTopBarButtons ul {
|
|
height:1%;
|
|
}
|
|
#patternSideBarContents .patternLeftBarPersonal {
|
|
width:100%;
|
|
}
|
|
.foswikiFormStep {
|
|
height:100%;
|
|
}
|
|
#foswikiLogin {
|
|
margin-left: 25%;
|
|
margin-right: 25%;
|
|
}
|
|
#foswikiLogin .foswikiFormSteps {
|
|
width:auto;
|
|
}
|
|
#foswikiLogin input[type="text"],
|
|
#foswikiLogin input[type="password"] {
|
|
width: auto;
|
|
}
|
|
.patternShadow {
|
|
border:10px solid #fff;
|
|
margin-top:10px;
|
|
margin-bottom:10px;
|
|
border:2px solid #ccc;
|
|
}
|
|
</style><![endif]-->
|
|
<!--[if lte IE 9]>
|
|
|
|
<![endif]-->
|
|
<!--[if gt IE 9]><!-->
|
|
|
|
<!--<![endif]-->
|
|
<!--JQUERYPLUGIN-->
|
|
<!--JQUERYPLUGIN::MIGRATE-->
|
|
<!--JQUERYPLUGIN::LIVEQUERY-->
|
|
<!--JQUERYPLUGIN::FOSWIKI-->
|
|
<!--JavascriptFiles/foswikiString-->
|
|
<!--JavascriptFiles/foswikiPref-->
|
|
<!--JQUERYPLUGIN::COMMENT-->
|
|
<!--JQUERYPLUGIN::METADATA-->
|
|
<!--JavascriptFiles/foswikiForm-->
|
|
<!--JQUERYPLUGIN::FOSWIKI::PREFERENCES-->
|
|
<!--PatternSkin/pattern-->
|
|
|
|
<!--JQUERYPLUGIN::CHILI--><link class='head FOOTNOTEPLUGIN_LINKCSS' rel="stylesheet" href="../pub/System/FootNotePlugin/styles.css" type="text/css" media="all" /><!--FOOTNOTEPLUGIN_LINKCSS-->
|
|
</head>
|
|
<body class="foswikiNoJs patternViewPage patternPrintPage">
|
|
<span id="PageTop"></span><div class="foswikiPage"><div id="patternScreen">
|
|
<div id="patternPageShadow">
|
|
<div id="patternPage">
|
|
<div id="patternOuter" class="clear">
|
|
<div id="patternFloatWrap">
|
|
<div id="patternMain">
|
|
<div id="patternMainContents">
|
|
<div class="patternContent"><div class="foswikiTopic">
|
|
<span id="TopIc"></span>
|
|
<h1 id="libZFRelaxation"> libZFRelaxation </h1>
|
|
<div class="foswikiToc" id="foswikiTOC"> <ul>
|
|
<li> <a href="LibZFRelaxation.html#libZFRelaxation"> libZFRelaxation </a>
|
|
</li> <li> <a href="LibZFRelaxation.html#A_1_Introduction"> 1 Introduction </a>
|
|
</li> <li> <a href="LibZFRelaxation.html#A_2_Isotropic_static_Gaussian_broadened_randomly_oriented_internal_fields"> 2 Isotropic static Gaussian broadened randomly oriented internal fields </a>
|
|
</li> <li> <a href="LibZFRelaxation.html#A_3_Isotropic_static_Lorentzian_broadened_randomly_oriented_internal_fields"> 3 Isotropic static Lorentzian broadened randomly oriented internal fields </a>
|
|
</li> <li> <a href="LibZFRelaxation.html#A_4_Static_Gaussian_distributed_fields_with_uniaxial_anisotropy"> 4 Static Gaussian distributed fields with uniaxial anisotropy </a>
|
|
</li></ul>
|
|
</div>
|
|
<span id="IntroDuction"></span>
|
|
<h1 id="A_1_Introduction"> 1 Introduction </h1>
|
|
<p></p>
|
|
<code>libZFRelaxation</code> is a collection of <code>C++</code> classes using the <code><a href="MusrFit.html">musrfit</a></code> <code><a href="MusrFit.html#UserFunctions1">user-function interface</a></code> in order to facilitate the usage in conjunction with <code>musrfit</code>. The classes contained in this library implement the calculation of some additional zero-field μSR relaxation functions which are not built-in into <code>musrfit</code>.
|
|
<p></p>
|
|
In the following the use of the implemented functions is shortly introduced—for details on the applicability and derivation of these functions please refer to the original publications.
|
|
<p></p>
|
|
If these classes prove useful and results obtained through them are part of scientific publications,
|
|
an acknowledgement of the use of the library is appreciated.
|
|
<p></p>
|
|
<h1 id="A_2_Isotropic_static_Gaussian_broadened_randomly_oriented_internal_fields"> 2 Isotropic static Gaussian broadened randomly oriented internal fields </h1>
|
|
<p></p>
|
|
E. I. Kornilov and V. Yu. Pomjakushin, Phys. Lett. A <b>153</b>, 364–367 (1991), doi: <a href="http://dx.doi.org/10.1016/0375-9601(91)90959-C">10.1016/0375-9601(91)90959-C</a>
|
|
<p></p>
|
|
<p style="text-align:center">
|
|
<img alt="\mathcal{P}(t) = \left(1-\alpha\right)\exp\left(-\frac{\sigma_{\mathrm{L}}^2t^2}{2}\right)+\alpha\left(\cos\left(2\pi\nu t\right)-\frac{\sigma_{\mathrm{T}}^2t}{2\pi\nu}\sin\left(2\pi\nu t\right)\right)\exp\left(-\frac{\sigma_{\mathrm{T}}^2t^2}{2}\right)" class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_fca91646b118061038b53ada5563c17c.png" title="ZFMagGss" />
|
|
</p>
|
|
<p></p>
|
|
<code>musrfit</code> THEORY-block line: <pre>
|
|
userFcn libZFRelaxation ZFMagGss 1 2 3 4
|
|
</pre>
|
|
The parameters are: <ol>
|
|
<li> the precessing fraction α (= 2/3 in the article),
|
|
</li> <li> the "internal frequency" ν (MHz),
|
|
</li> <li> the "transverse depolarization rate" σ<sub>T</sub> (μs<sup>-1</sup>),
|
|
</li> <li> the "longitudinal depolarization rate" σ<sub>L</sub> (μs<sup>-1</sup>) (= 0 in the article).
|
|
</li></ol>
|
|
<p></p>
|
|
<h1 id="A_3_Isotropic_static_Lorentzian_broadened_randomly_oriented_internal_fields"> 3 Isotropic static Lorentzian broadened randomly oriented internal fields </h1>
|
|
<p></p>
|
|
M. I. Larkin, Y. Fudamoto, I. M. Gat, A. Kinkhabwala, K. M. Kojima, G. M. Luke, J. Merrin, B. Nachumi, Y. J. Uemura, M. Azuma, T. Saito, and M. Takano, Physica B <b>289–290</b>, 153–156 (2000), doi: <a href="http://dx.doi.org/10.1016/S0921-4526(00)00337-9"">10.1016/S0921-4526(00)00337-9</a>
|
|
<p></p>
|
|
<p style="text-align:center">
|
|
<img alt="\mathcal{P}(t) = \left(1-\alpha\right)\exp\left(-a_{\mathrm{L}}t\right) + \alpha\left(\cos\left(2\pi\nu t\right)-\frac{a_{\mathrm{T}}}{2\pi\nu}\sin\left(2\pi\nu t\right)\right)\exp\left(-a_{\mathrm{T}}t\right)" class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_975f948b57199037b2b8bfb5e986b6a9.png" title="ZFMagExp" />
|
|
</p>
|
|
<p></p>
|
|
<code>musrfit</code> THEORY-block line: <pre>
|
|
userFcn libZFRelaxation ZFMagExp 1 2 3 4
|
|
</pre>
|
|
The parameters are: <ol>
|
|
<li> the precessing fraction α (= 2/3 in the article),
|
|
</li> <li> the "internal frequency" ν (MHz),
|
|
</li> <li> the "transverse depolarization rate" a<sub>T</sub> (μs<sup>-1</sup>),
|
|
</li> <li> the "longitudinal depolarization rate" a<sub>L</sub> (μs<sup>-1</sup>) (= 0 in the article).
|
|
</li></ol>
|
|
<p></p>
|
|
<h1 id="A_4_Static_Gaussian_distributed_fields_with_uniaxial_anisotropy"> 4 Static Gaussian distributed fields with uniaxial anisotropy </h1>
|
|
<p></p>
|
|
G. Solt, Hyperfine Interactions <b>96</b>, 167–175 (1995), doi: <a href="http://dx.doi.org/10.1007/BF02066280">10.1007/BF02066280</a>
|
|
<p></p>
|
|
<p style="text-align:center">
|
|
<img alt="\mathcal{P}(t) = \frac{1}{2}\sin^2\Theta + \left(\frac{3}{2}\cos^2\Theta-\frac{1}{2}\right)f_1\left(\epsilon\right) + \sin^2\Theta f_2(\epsilon, \sigma_1, t) + \left(\frac{3}{2}\cos^2\Theta-\frac{1}{2}\right)f_3\left(\epsilon, \sigma_1, t\right)," class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_4611c56f1556464dd8a6eaabbe070c05.png" title="UniaxialStatGssKT" />
|
|
</p>
|
|
where
|
|
<p style="text-align:center">
|
|
<img alt="\epsilon = \left(\frac{\sigma_1}{\sigma_3}\right)^2-1,\quad p(x) = 1+\epsilon x^2," class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_2b4a75902dcb0b8de5a662656d3b9066.png" title="epsilon_p(x)" />
|
|
</p>
|
|
<p style="text-align:center">
|
|
<img alt="f_1\left(\epsilon\right) = 1 - \frac{\sqrt{1+\epsilon}}{\epsilon}\left(\sqrt{1+\epsilon}-\left\lbrace \begin{matrix} \left(\mathrm{asinh}\sqrt{\epsilon}\right)/\sqrt{\epsilon} \\ \left(\arcsin\sqrt{-\epsilon}\right)/\sqrt{-\epsilon} \end{matrix} \right\rbrace\right),\:\mathrm{for}\,\bigg\lbrace\begin{matrix}\epsilon > 0 \\ \epsilon < 0\end{matrix}\,," class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_5100b245762fc5c6dee8db3b05032a18.png" title="f1" />
|
|
</p>
|
|
<p style="text-align:center">
|
|
<img alt="f_2\left(\epsilon, \sigma_1, t\right) = \sqrt{1+\epsilon}\int_0^1\mathrm{d}x\left(\frac{1}{p(x)^{3/2}}-\frac{\gamma_{\mu}^2\sigma_1^2t^2}{p(x)^{5/2}}\right)\exp\left(-\frac{\gamma_{\mu}^2\sigma_1^2t^2}{2\,p(x)}\right)," class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_0a70ac778f3ffbf2c93d46b23559d371.png" title="f2" />
|
|
</p>
|
|
and
|
|
<p style="text-align:center">
|
|
<img alt="f_3\left(\epsilon, \sigma_1, t\right) = \sqrt{1+\epsilon}\int_0^1\mathrm{d}x\left(1-x^2\right)\left(\frac{1}{p(x)^{3/2}}-\frac{\gamma_{\mu}^2\sigma_1^2t^2}{p(x)^{5/2}}\right)\exp\left(-\frac{\gamma_{\mu}^2\sigma_1^2t^2}{2\,p(x)}\right)." class="mmpImage" src="../pub/MUSR/LibZFRelaxation/_MathModePlugin_52c5f826fb399ae721887c5fb4e31de0.png" title="f3" />
|
|
</p>
|
|
<p></p>
|
|
<code>musrfit</code> THEORY-block line: <pre>
|
|
userFcn libZFRelaxation UniaxialStatGssKT 1 2 3
|
|
</pre>
|
|
The parameters are: <ol>
|
|
<li> σ<sub>1</sub> (μs<sup>-1</sup>),
|
|
</li> <li> σ<sub>3</sub> (μs<sup>-1</sup>),
|
|
</li> <li> Θ (°).
|
|
</li></ol>
|
|
<p></p>
|
|
-- <a href="http://www.fsf.org/register_form?referrer=8369">BMW</a> & <a href="http://www.psi.ch/low-energy-muons/people">AS</a></div>
|
|
<p></p>
|
|
<p></p>
|
|
</div>
|
|
<div class="patternInfo">This topic: MUSR<span class='foswikiSeparator'> > </span><a class="foswikiCurrentWebHomeLink" href="WebHome.html">WebHome</a> > <a href="MusrFit.html">MusrFit</a> > <a href="BmwLibs.html">BmwLibs</a><span class='foswikiSeparator'> > </span>LibZFRelaxation <br />
|
|
Topic revision: <span class='patternRevInfo'>03 Jul 2015, suter_a</span></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div><div id="patternBottomBar"><div id="patternBottomBarContents"><div id="patternWebBottomBar"><span class="foswikiRight"> <a href="http://foswiki.org/"><img src="../pub/System/ProjectLogos/foswiki-badge.png" alt="This site is powered by Foswiki" title="This site is powered by Foswiki" /></a></span>Copyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors. <br /> Ideas, requests, problems regarding PSI Wiki? <a href='mailto:thomas.buecklers@psi.ch?subject=PSI Wiki %20Feedback%20on%20MUSR.LibZFRelaxation'>Send feedback</a></div></div></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div></div><!-- /endWrap -->
|
|
<p></p>
|
|
<!-- Piwik -->
|
|
|
|
<noscript><p><img src="../piwik/piwikf832.gif?idsite=7" style="border:0" alt=""></p></noscript>
|
|
<!-- End Piwik Tag -->
|
|
|
|
|
|
</body>
|
|
|
|
<!-- Mirrored from intranet.psi.ch/MUSR/LibZFRelaxation?cover=print by HTTrack Website Copier/3.x [XR&CO'2010], Thu, 28 Apr 2016 07:39:36 GMT -->
|
|
<!-- Added by HTTrack --><meta http-equiv="content-type" content="text/html;charset=utf-8"><!-- /Added by HTTrack -->
|
|
</html> |