diff --git a/doc/html/_sources/index.txt b/doc/html/_sources/index.txt index 8ac278b4..b4ed7d2f 100644 --- a/doc/html/_sources/index.txt +++ b/doc/html/_sources/index.txt @@ -3,8 +3,8 @@ You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. -Welcome to musrfit documentation! -================================= +Welcome to the musrfit documentation! +===================================== .. toctree:: :maxdepth: 2 diff --git a/doc/html/_sources/user-libs.txt b/doc/html/_sources/user-libs.txt index 97a9b762..91388440 100644 --- a/doc/html/_sources/user-libs.txt +++ b/doc/html/_sources/user-libs.txt @@ -407,3 +407,341 @@ Nonlocal superconductivity related Meissner screening functions (AS libs) ------------------------------------------------------------------------- To be written yet ... + +.. index:: BNMR-libs +.. _BNMR-libs: + +Functions to analyze |bgr|-NMR data (BNMR libs) +------------------------------------------------------------------------- + +This is a collection of ``C++`` classes using the ``musrfit`` :ref:`user-functions ` +interface in order to facilitate the usage in conjunction with ``musrfit``. It consists of two libraries: + +* ``libBNMR`` contains functions to fit spin lattice relaxation (SLR) data. +* ``libLineProfile`` contains functions to fit resonance lineshapes. + + +.. note:: + + Currently it is recommended to read in the data in ASCII format as a non-|mgr|\SR fit :ref:`(fit type 8) `. + +.. index:: libBNMR + +libBNMR +++++++++++ + +In |bgr|-NMR the SLR is usually measured by implanting a pulse of :math:`^8`\ Li with a length :math:`t_0` into the sample. +The asymmetry is measured both during the pulse and afterwards. For a a general spin relaxation function :math:`f(t)` the time evolution of the asymmetry is then given by [`Z. Salman, et al., PRL 96, 147601 (2006) `_]: + + + +.. index:: SLR +.. _SLR: + +.. math:: + P(t) = \left\{\begin{matrix} + \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] + \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. + +where :math:`\tau_{\mathrm{Li}}=1.21`\ s is the :math:`^8`\ Li lifetime. + + +Functions +^^^^^^^^^^^^ +The ``libLineProfile`` library currently contains the following functions: + + + + +.. index:: ExpRlx + +**Exponential relaxation** + +:: + + userFcn libBNMR ExpRlx 1 2 + +The parameters are: + +#. pulse length :math:`t_0` (ms) +#. relaxation rate :math:`\sigma` (ms\ :math:`^{-1}`\ ) + +This function implements :math:`f(t)=e^{-\sigma t}`. + +.. index:: SExpRlx + +**Stretched exponential relaxation** + +:: + + userFcn libBNMR SExpRlx 1 2 3 + +The parameters are: + +#. pulse length :math:`t_0` (ms) +#. relaxation rate :math:`\sigma` (ms\ :math:`^{-1}`\ ) +#. stretching exponent :math:`\beta` + +This function implements :math:`f(t)=e^{-(\sigma t)^{\beta}}`. + + + +.. index:: libLineProfile + +libLineProfile ++++++++++++++++++ +In addition to some simple line shapes ``libLineProfile`` contains functions to fit chemical shift anisotropies in the powder average. +Their functional form can be found in `M. Mehring, Principles of High Resolution NMR in Solids (Springer 1983) `_. + +For an axially symmetric interaction it is given by: + +.. index:: Iax +.. _Iax: + +.. math:: + + 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. + +where :math:`f_\parallel` and :math:`f_\perp` are the frequencies that would be observed if the field is oriented paralell or perpendicular to the symmetry axis, respectively. + + +| In case of a completely anisotropic interaction, the powder average can be described by the frequencies along the three principle axis :math:`f_1,f_2,f_3`. +| Assume without loss of generality that :math:`f_1f_2 \\[9pt] + \frac{K(m)}{\pi\sqrt{(f_3-f)(f_2-f_1)}},& f_2>f\geq f_1\\[9pt] + 0 & \text{otherwise} + \end{matrix} \right. \\ + \\ + m&=\left\{\begin{matrix} + \frac{(f_2-f_1)(f_3-f)}{(f_3-f_2)(f-f_1)},& f_3\geq f>f_2 \\[6pt] + \frac{(f-f_1)(f_3-f_2)}{(f_3-f)(f_2-f_1)},& f_2>f\geq f_1\\[6pt] + \end{matrix} \right. \\ + \\ + K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}}, + + +:math:`K(m)` is the complete elliptic integral of the first kind. + + + +Functions +^^^^^^^^^^^^ +The ``libLineProfile`` library currently contains the following functions: + + + + +.. index:: LineGauss + +**Gaussian** + +:: + + userFcn libLineProfile LineGauss 1 2 + +The parameters are: + +#. center of the line :math:`f_0` +#. FWHM of the line :math:`\sigma` + +| The height of the peak is 1. +| The functional form is given by + +.. math:: + A(f)=e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} + + +.. index:: LineLorentzian + +**Lorentzian** + +:: + + userFcn libLineProfile LineLorentzian 1 2 + +The parameters are: + +#. center of the line :math:`f_0` +#. FWHM of the line :math:`w` + +| The height of the peak is 1. +| The functional form is given by + +.. math:: + A(f)= \frac{w^2}{4(f-f_0)^2+w^2} + + +.. index:: LineLaplace + +**Laplacian** + +:: + + userFcn libLineProfile LineLaplace 1 2 + +The parameters are: + +#. center of the line :math:`f_0` +#. FWHM of the line :math:`w` + +| The height of the peak is 1. +| The functional form is given by + +.. math:: + A(f)=e^{-2\ln 2 \left|\frac{f-f_0}{w}\right|} + + + +.. index:: LineSkewLorentzian + +**Skewed Lorentzian** + +:: + + userFcn libLineProfile LineSkewLorentzian 1 2 3 + +The parameters are: + +#. center of the line :math:`f_0` +#. width of the line :math:`w` +#. skewness parameter :math:`a` + +| The height of the peak is 1. +| The functional form is given by + +.. math:: + 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)}} + + + +.. index:: LineSkewLorentzian2 + +**Skewed Lorentzian 2** + +:: + + userFcn libLineProfile LineSkewLorentzian2 1 2 3 + +The parameters are: + +#. center of the line :math:`f_0` +#. width left of the center :math:`w_1` +#. width right of the center :math:`w_2` + +| The height of the peak is 1. +| The functional form is given by + +.. math:: + 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. + + + +.. index:: PowderLineAxialLor + + +**Powder average of an axially symmetric interaction convoluted with a Lorentzian** + +:: + + userFcn libLineProfile PowderLineAxialLor 1 2 3 + +The parameters are: + +#. frequency for the field oriented paralell to the symmetry axis :math:`f_\parallel` +#. frequency for the field oriented perpendicular to the symmetry axis :math:`f_\parallel` +#. FWHM of the Lorentzian :math:`w` + +| The height of the peak is :math:`\sim`\ 1. +| The functional form is given by + +.. math:: + A(f)= I_{\mathrm ax}(f)\circledast\left( \frac{w^2}{4f^2+w^2} \right) + +with :math:`I_{\mathrm ax}(f)` defined :ref:`above `. + + + +.. index:: PowderLineAxialGss + + +**Powder average of an axially symmetric interaction convoluted with a Gaussian** + +:: + + userFcn libLineProfile PowderLineAxialGss 1 2 3 + +The parameters are: + +#. frequency for the field oriented paralell to the symmetry axis :math:`f_\parallel` +#. frequency for the field oriented perpendicular to the symmetry axis :math:`f_\parallel` +#. FWHM of the Gaussian :math:`\sigma` + +| The height of the peak is :math:`\sim`\ 1. +| The functional form is given by + +.. math:: + A(f)= I_{\mathrm ax}(f)\circledast\left( e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} \right) + +with :math:`I_{\mathrm ax}(f)` defined :ref:`above `. + + + +.. index:: PowderLineAsymLor + + +**Powder average of an anisotropic interaction convoluted with a Lorentzian** + +:: + + userFcn libLineProfile PowderLineAsymLor 1 2 3 4 + +The parameters are: + +#. :math:`f_1` +#. :math:`f_1` +#. :math:`f_3` frequencies along the principal axes +#. FWHM of the Lorentzian :math:`w` + +| The height of the peak is :math:`\sim`\ 1. +| The functional form is given by + +.. math:: + A(f)= I(f)\circledast\left( \frac{w^2}{4f^2+w^2} \right) + +with :math:`I(f)` defined :ref:`above `. Note that :math:`f_1`. Note that :math:`f_1 diff --git a/doc/html/any2many.html b/doc/html/any2many.html index 996df599..020a38ea 100644 --- a/doc/html/any2many.html +++ b/doc/html/any2many.html @@ -107,7 +107,7 @@ For a detailed description see © Copyright 2018, Andreas Suter. - Last updated on Jul 03, 2018. + Last updated on Aug 23, 2018. Created using Sphinx 1.2.3. diff --git a/doc/html/bugtracking.html b/doc/html/bugtracking.html index 1e78f2c8..fd6f2b1b 100644 --- a/doc/html/bugtracking.html +++ b/doc/html/bugtracking.html @@ -98,7 +98,7 @@ or send an e-mail to A. Suter at PSI.

diff --git a/doc/html/cite.html b/doc/html/cite.html index dd3581ca..d1359e1c 100644 --- a/doc/html/cite.html +++ b/doc/html/cite.html @@ -26,7 +26,7 @@ - + diff --git a/doc/html/index.html b/doc/html/index.html index 6367b69e..8cf5959f 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -6,7 +6,7 @@ - Welcome to musrfit documentation! — musrfit 1.4.0 documentation + Welcome to the musrfit documentation! — musrfit 1.4.0 documentation @@ -46,8 +46,8 @@
-
-

Welcome to musrfit documentation!

+
+

Welcome to the musrfit documentation!

diff --git a/doc/html/mupp.html b/doc/html/mupp.html index 253d96b3..cb9579e1 100644 --- a/doc/html/mupp.html +++ b/doc/html/mupp.html @@ -257,7 +257,7 @@ SCRIPT COMMANDS:
diff --git a/doc/html/musr-root.html b/doc/html/musr-root.html index 37fd0913..d1547866 100644 --- a/doc/html/musr-root.html +++ b/doc/html/musr-root.html @@ -928,7 +928,7 @@ the entry has been added. The last token, diff --git a/doc/html/musredit.html b/doc/html/musredit.html index 46314eb7..fc7e6388 100644 --- a/doc/html/musredit.html +++ b/doc/html/musredit.html @@ -555,7 +555,7 @@ the corresponding fit parameter value, except the phases where the step will be
diff --git a/doc/html/objects.inv b/doc/html/objects.inv index 94b55d05..4ce8549a 100644 Binary files a/doc/html/objects.inv and b/doc/html/objects.inv differ diff --git a/doc/html/search.html b/doc/html/search.html index acf648fc..26f95593 100644 --- a/doc/html/search.html +++ b/doc/html/search.html @@ -94,7 +94,7 @@
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\ No newline at end of file diff --git a/doc/html/setup-dks.html b/doc/html/setup-dks.html index 0c5498f3..03859bcc 100644 --- a/doc/html/setup-dks.html +++ b/doc/html/setup-dks.html @@ -359,7 +359,7 @@ The only thing you need DKS diff --git a/doc/html/setup-standard.html b/doc/html/setup-standard.html index fee3faaf..6fa19e78 100644 --- a/doc/html/setup-standard.html +++ b/doc/html/setup-standard.html @@ -1486,7 +1486,7 @@ $ musrview test-histo-ROOT-NPP.msr
diff --git a/doc/html/tutorial.html b/doc/html/tutorial.html index dd91f84c..0adb9796 100644 --- a/doc/html/tutorial.html +++ b/doc/html/tutorial.html @@ -448,7 +448,7 @@ For a complete description please refer to the manuals of © Copyright 2018, Andreas Suter. - Last updated on Jul 03, 2018. + Last updated on Aug 23, 2018. Created using Sphinx 1.2.3. diff --git a/doc/html/user-libs.html b/doc/html/user-libs.html index 6b42bb37..c3975e98 100644 --- a/doc/html/user-libs.html +++ b/doc/html/user-libs.html @@ -370,6 +370,233 @@ The expected name of the RGENonlocal superconductivity related Meissner screening functions (AS libs)

To be written yet ...

+
+

Functions to analyze β-NMR data (BNMR libs)

+

This is a collection of C++ classes using the musrfit user-functions +interface in order to facilitate the usage in conjunction with musrfit. It consists of two libraries:

+
    +
  • libBNMR contains functions to fit spin lattice relaxation (SLR) data.
  • +
  • libLineProfile contains functions to fit resonance lineshapes.
  • +
+
+

Note

+

Currently it is recommended to read in the data in ASCII format as a non-μSR fit (fit type 8).

+
+
+

libBNMR

+

In β-NMR the SLR is usually measured by implanting a pulse of \(^8\)Li with a length \(t_0\) into the sample. +The asymmetry is measured both during the pulse and afterwards. For a a general spin relaxation function \(f(t)\) the time evolution of the asymmetry is then given by [Z. Salman, et al., PRL 96, 147601 (2006)]:

+
+\[\begin{split}P(t) = \left\{\begin{matrix} +\frac{\int_0^t e^{-(t-t')/\tau_{\mathrm{Li}}}f(t-t')dt'}{\int_0^t e^{-t'/\tau_{\mathrm{Li}}}dt' } & t\leq t_0\\[6pt] +\frac{\int_0^{t_0}e^{-(t_0-t')/\tau_{\mathrm{Li}}}f(t-t')dt'}{\int_0^{t_0}e^{-t'/\tau_{\mathrm{Li}}}dt'} & t> t_0, +\end{matrix}\right.\end{split}\]
+

where \(\tau_{\mathrm{Li}}=1.21\)s is the \(^8\)Li lifetime.

+
+

Functions

+

The libLineProfile library currently contains the following functions:

+

Exponential relaxation

+
userFcn libBNMR ExpRlx 1 2
+
+
+

The parameters are:

+
    +
  1. pulse length \(t_0\) (ms)
  2. +
  3. relaxation rate \(\sigma\) (ms\(^{-1}\))
  4. +
+

This function implements \(f(t)=e^{-\sigma t}\).

+

Stretched exponential relaxation

+
userFcn libBNMR SExpRlx 1 2 3
+
+
+

The parameters are:

+
    +
  1. pulse length \(t_0\) (ms)
  2. +
  3. relaxation rate \(\sigma\) (ms\(^{-1}\))
  4. +
  5. stretching exponent \(\beta\)
  6. +
+

This function implements \(f(t)=e^{-(\sigma t)^{\beta}}\).

+
+
+
+

libLineProfile

+

In addition to some simple line shapes libLineProfile contains functions to fit chemical shift anisotropies in the powder average. +Their functional form can be found in M. Mehring, Principles of High Resolution NMR in Solids (Springer 1983).

+

For an axially symmetric interaction it is given by:

+
+\[\begin{split}I_{\mathrm ax}(f)=\left\{\begin{matrix} \frac{1}{2\sqrt{(f_\parallel-f_\perp)(f-f_\perp)}}& f\in(f_\perp,f_\parallel)\cup(f_\parallel,f_\perp)\\[6pt] 0 & \text{otherwise}\end{matrix} \right.\end{split}\]
+

where \(f_\parallel\) and \(f_\perp\) are the frequencies that would be observed if the field is oriented paralell or perpendicular to the symmetry axis, respectively.

+
+
In case of a completely anisotropic interaction, the powder average can be described by the frequencies along the three principle axis \(f_1,f_2,f_3\).
+
Assume without loss of generality that \(f_1<f_2<f_3\), then
+
+
+\[\begin{split}I(f)&=\left\{\begin{matrix} + \frac{K(m)}{\pi\sqrt{(f-f_1)(f_3-f_2)}},& f_3\geq f>f_2 \\[9pt] + \frac{K(m)}{\pi\sqrt{(f_3-f)(f_2-f_1)}},& f_2>f\geq f_1\\[9pt] + 0 & \text{otherwise} +\end{matrix} \right. \\ + \\ +m&=\left\{\begin{matrix} + \frac{(f_2-f_1)(f_3-f)}{(f_3-f_2)(f-f_1)},& f_3\geq f>f_2 \\[6pt] + \frac{(f-f_1)(f_3-f_2)}{(f_3-f)(f_2-f_1)},& f_2>f\geq f_1\\[6pt] +\end{matrix} \right. \\ + \\ +K(m)&=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\end{split}\]
+

\(K(m)\) is the complete elliptic integral of the first kind.

+
+

Functions

+

The libLineProfile library currently contains the following functions:

+

Gaussian

+
userFcn  libLineProfile LineGauss 1 2
+
+
+

The parameters are:

+
    +
  1. center of the line \(f_0\)
  2. +
  3. FWHM of the line \(\sigma\)
  4. +
+
+
The height of the peak is 1.
+
The functional form is given by
+
+
+\[A(f)=e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}}\]
+

Lorentzian

+
userFcn  libLineProfile LineLorentzian 1 2
+
+
+

The parameters are:

+
    +
  1. center of the line \(f_0\)
  2. +
  3. FWHM of the line \(w\)
  4. +
+
+
The height of the peak is 1.
+
The functional form is given by
+
+
+\[A(f)= \frac{w^2}{4(f-f_0)^2+w^2}\]
+

Laplacian

+
userFcn  libLineProfile LineLaplace 1 2
+
+
+

The parameters are:

+
    +
  1. center of the line \(f_0\)
  2. +
  3. FWHM of the line \(w\)
  4. +
+
+
The height of the peak is 1.
+
The functional form is given by
+
+
+\[A(f)=e^{-2\ln 2 \left|\frac{f-f_0}{w}\right|}\]
+

Skewed Lorentzian

+
userFcn  libLineProfile LineSkewLorentzian 1 2 3
+
+
+

The parameters are:

+
    +
  1. center of the line \(f_0\)
  2. +
  3. width of the line \(w\)
  4. +
  5. skewness parameter \(a\)
  6. +
+
+
The height of the peak is 1.
+
The functional form is given by
+
+
+\[A(f)= \frac{w w_a}{4(f-f_0)^2+w_a^2}, \quad w_a=\frac{2w}{1+e^{a(f-f_0)}}\]
+

Skewed Lorentzian 2

+
userFcn  libLineProfile LineSkewLorentzian2 1 2 3
+
+
+

The parameters are:

+
    +
  1. center of the line \(f_0\)
  2. +
  3. width left of the center \(w_1\)
  4. +
  5. width right of the center \(w_2\)
  6. +
+
+
The height of the peak is 1.
+
The functional form is given by
+
+
+\[\begin{split}A(f)= \left\{\begin{matrix}\frac{{w_1}^2}{4{(f-f_0)}^2+{w_1}^2},&f\leq f_0\\[9pt] \frac{{w_2}^2}{4{(f-f_0)}^2+{w_2}^2},&f>f_0\end{matrix}\right.\end{split}\]
+

Powder average of an axially symmetric interaction convoluted with a Lorentzian

+
userFcn  libLineProfile PowderLineAxialLor 1 2 3
+
+
+

The parameters are:

+
    +
  1. frequency for the field oriented paralell to the symmetry axis \(f_\parallel\)
  2. +
  3. frequency for the field oriented perpendicular to the symmetry axis \(f_\parallel\)
  4. +
  5. FWHM of the Lorentzian \(w\)
  6. +
+
+
The height of the peak is \(\sim\)1.
+
The functional form is given by
+
+
+\[A(f)= I_{\mathrm ax}(f)\circledast\left( \frac{w^2}{4f^2+w^2} \right)\]
+

with \(I_{\mathrm ax}(f)\) defined above.

+

Powder average of an axially symmetric interaction convoluted with a Gaussian

+
userFcn  libLineProfile PowderLineAxialGss 1 2 3
+
+
+

The parameters are:

+
    +
  1. frequency for the field oriented paralell to the symmetry axis \(f_\parallel\)
  2. +
  3. frequency for the field oriented perpendicular to the symmetry axis \(f_\parallel\)
  4. +
  5. FWHM of the Gaussian \(\sigma\)
  6. +
+
+
The height of the peak is \(\sim\)1.
+
The functional form is given by
+
+
+\[A(f)= I_{\mathrm ax}(f)\circledast\left( e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} \right)\]
+

with \(I_{\mathrm ax}(f)\) defined above.

+

Powder average of an anisotropic interaction convoluted with a Lorentzian

+
userFcn  libLineProfile PowderLineAsymLor 1 2 3 4
+
+
+

The parameters are:

+
    +
  1. \(f_1\)
  2. +
  3. \(f_1\)
  4. +
  5. \(f_3\) frequencies along the principal axes
  6. +
  7. FWHM of the Lorentzian \(w\)
  8. +
+
+
The height of the peak is \(\sim\)1.
+
The functional form is given by
+
+
+\[A(f)= I(f)\circledast\left( \frac{w^2}{4f^2+w^2} \right)\]
+

with \(I(f)\) defined above. Note that \(f_1<f_2<f_3\) is not required by the code.

+

Powder average of an anisotropic interaction convoluted with a Gaussian

+
userFcn  libLineProfile PowderLineAsymGss 1 2 3 4
+
+
+

The parameters are:

+
    +
  1. \(f_1\)
  2. +
  3. \(f_1\)
  4. +
  5. \(f_3\) frequencies along the principal axes
  6. +
  7. FWHM of the Gaussian \(\sigma\)
  8. +
+
+
The height of the peak is \(\sim\)1.
+
The functional form is given by
+
+
+\[A(f)= I(f)\circledast\left( e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} \right)\]
+

with \(I(f)\) defined above. Note that \(f_1<f_2<f_3\) is not required by the code.

+
+
+
@@ -386,6 +613,11 @@ The expected name of the RGE
  • Nonlocal superconductivity related Meissner screening functions (AS libs)
  • +
  • Functions to analyze β-NMR data (BNMR libs) +
  • @@ -435,7 +667,7 @@ The expected name of the RGE diff --git a/doc/html/user-manual.html b/doc/html/user-manual.html index 2811f5c9..a99d33d1 100644 --- a/doc/html/user-manual.html +++ b/doc/html/user-manual.html @@ -2162,7 +2162,7 @@ In case this cannot be ensured, the parallelization can be disabled by ̵