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Merged master into beta-NMR

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Zaher Salman
2018-12-18 10:01:28 +01:00
parent 8207aea183 91e2eca915
commit d1cf374354
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4
doc/html/_sources/index.txt
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@@ -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

338
doc/html/_sources/user-libs.txt
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@@ -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 <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) <non-musr-fit>`.
.. 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) <http://dx.doi.org/10.1103/PhysRevLett.96.147601>`_]:
.. 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) <http://dx.doi.org/10.1007/978-3-642-68756-3_2>`_.
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_1<f_2<f_3`, then
.. index:: Ianiso
.. _Ianiso:
.. math::
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}}},
: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 <Iax>`.
.. 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 <Iax>`.
.. 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 <Ianiso>`. Note that :math:`f_1<f_2<f_3` is not required by the code.
.. index:: PowderLineAsymGss
**Powder average of an anisotropic interaction convoluted with a Gaussian**
::
userFcn libLineProfile PowderLineAsymGss 1 2 3 4
The parameters are:
#. :math:`f_1`
#. :math:`f_1`
#. :math:`f_3` frequencies along the principal axes
#. 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(f)\circledast\left( e^{-\frac{4\ln 2 (f-f_0)^2}{ \sigma^2}} \right)
with :math:`I(f)` defined :ref:`above <Ianiso>`. Note that :math:`f_1<f_2<f_3` is not required by the code.

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doc/html/_sources/user-manual.txt
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@@ -1497,8 +1497,68 @@ The block starts with the *FOURIER* keyword and may contain the following entrie
.. _msr-fourier-block-phase:
**phase**
The initial phase of the input data is given here in degrees. Optionally the phase parameter from the :ref:`FITPARAMETER block <msr-fitparameter-block>` can be given,
*e.g.* par3, which would take the value of parameter number 3.
If a real Fourier shall be plotted, it is necessary to adopt the phases of the different detectors. The number of potentially provided phases can be either **one**, which means that this phase will be applied to *all* Fourier spectra,
or the number of phases have to correspond to the number of runs in the plot block.
Currently there are three options:
#. The phases for each run/detector are given explicitly, *i.e.*
.. code-block:: bash
phase val0 sep val1 sep ... sep valN
where ``val0``, ``val1``, etc. are explicitly given phases (*i.e.* doubles), and ``sep`` is one of the following allowed separators: ``space``, ``,``, ``;``, or ``tab``.
For example
.. code-block:: bash
phase -3.2, 175.9
#. The phases for each run/detector are given as phase parameter from the :ref:`FITPARAMETER block <msr-fitparameter-block>`, *e.g.* par3, which would
take the value of parameter number 3. More explicitly
.. code-block:: bash
phase parX0 sep parX1 sep ... sep parXN
where the same rules applies as for explicit phase values. An example could look like this
.. code-block:: bash
phase par7, par12, par17, par22, par27, par32, par37, par42, par47, par52, par57, par62, par67, par72, par77, par82
One might prefer to express the phases in respect to a reference counter, *e.g.* the forward counter is the reference counter phase (fcp) whereas
the backward counter phase (bcp) is expressed as bcp = fcp + relative_bcp. If the fitting is done along these lines, the phases in the Fourier
block can be expressed the following way
.. code-block:: bash
phase parRX0 sep parX1 sep ... sep parXN
which means that ``X0`` is the reference phase, and all the other phases are relative phases in respect to ``X0``, *i.e.* the absolut phase of
``Xj`` would be the summ of the values of ``parX0`` and ``parXj`` etc. The reference phase in the list is marked by ``parR`` rather than ``par``.
Obviously only *one* reference phase can be defined!
#. Often the phases in the parameter block follow a clear list structure. This allows to write the Fourier phase parameters in a more compact form
.. code-block:: none
phase par(X0, offset, #param)
with ``X0`` the first phase parameter index, ``offset`` being the offset to the next phase parameter, and ``#param`` being the number of phase parameters to be used.
This means that the previous example can be compacted to
.. code-block:: none
phase par(7, 5, 16)
As in the phase parameter list examples before, also here a reference phase with relative phases might be wished. Differently to the phase parameter
list example, the first parameter number will be the reference phase. The compact notation here is
.. code-block:: none
phase parR(X0, offest, #param)
.. index:: fourier-block-range_for_phase_correction
.. _msr-fourier-block-range_for_phase_correction:
@@ -1522,8 +1582,7 @@ Altogether, a possible FOURIER block might look like that:
fourier_power 12
apodization NONE
plot real_and_imag
phase 22.6 # par3
range_for_phase_correction all
phase par5, par8
range 0.0 17.03
.. index:: msr-plot-block