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SassenaFFT v1¶

Summary ¶

Performs complex Fast Fourier Transform of intermediate scattering function

Properties ¶

Name	Direction	Type	Default	Description
InputWorkspace	InOut	WorkspaceGroup	Mandatory	The name of the input group workspace
FFTonlyRealPart	Input	boolean	False	Do we FFT only the real part of I(Q,t)? (optional, default is False)
DetailedBalance	Input	boolean	False	Do we apply detailed balance condition? (optional, default is False)
Temp	Input	number	300	Multiply structure factor by exp(E/(2*kT)

The Sassena application generates intermediate scattering factors from molecular dynamics trajectories. This algorithm reads Sassena output and stores all data in workspaces of type Workspace2D, grouped under a single WorkspaceGroup. It is implied that the time unit is one picosecond.

Sassena output files are in HDF5 format, and can be made up of the following datasets: qvectors, fq, fq0, fq2, and fqt

The group workspace should contain workspaces _fqt.Re and _fqt.Im containing the real and imaginary parts of the intermediate structure factor, respectively. This algorithm will take both and perform FFT v1, storing the real part of the transform in workspace _fqw and placing this workspace under the input group workspace. Assuming the time unit to be one picosecond, the resulting energies will be in units of one micro-eV.

The Schofield correction (P. Schofield, Phys. Rev. Letters 4(5), 239 (1960)) is optionally applied to the resulting dynamic structure factor to reinstate the detailed balance condition \(S(Q,\omega)=e^{\beta \hbar \omega}S(-Q,-\omega)\).

Details ¶

Parameter FFTonlyRealPart ¶

Setting parameter FFTonlyRealPart to true will produce a transform on only the real part of I(Q,t). This is convenient if we know that I(Q,t) should be real but a residual imaginary part was left in a Sassena calculation due to finite orientational average in Q-space.

Below are plots after application of SassenaFFT to \(I(Q,t) = e^{-t^2/(2\sigma^2)} + i\cdot t \cdot e^{-t^2/(2\sigma^2)}\) with \(\sigma=1ps\). Real an imaginary parts are shown in panels (a) and (b). Note that \(I(Q,t)*=I(Q,-t)\). If only \(Re[I(Q,t)]\) is transformed, the result is another Gaussian: \(\sqrt{2\pi}\cdot e^{-E^2/(2\sigma'^2)}\) with \(\sigma'=4136/(2\pi \sigma)\) in units of \(\mu\)eV (panel (c)). If I(Q,t) is transformed, the result is a modulated Gaussian: \((1+\sigma' E)\sqrt{2\pi}\cdot e^{-E^2/(2\sigma'^2)}\)(panel (d)).

Usage ¶

Example - Load a Sassena file, Fourier transform it, and do a fit of S(Q,E):

ws = LoadSassena("loadSassenaExample.h5", TimeUnit=1.0)
SassenaFFT(ws, FFTonlyRealPart=1, Temp=1000, DetailedBalance=1)

print('workspaces instantiated:  {}'.format(', '.join(ws.getNames())))

sqt = ws[3] # S(Q,E)
# I(Q,t) is a Gaussian, thus S(Q,E) is a Gaussian too (at high temperatures)
# Let's fit it to a Gaussian. We start with an initial guess
intensity = 100.0
center = 0.0
sigma = 0.01    #in meV
startX = -0.1   #in meV
endX = 0.1
myFunc = 'name=Gaussian,Height={0},PeakCentre={1},Sigma={2}'.format(intensity,center,sigma)

# Call the Fit algorithm and perform the fit
fit_output = Fit(Function=myFunc, InputWorkspace=sqt, WorkspaceIndex=0,
                 StartX = startX, EndX=endX, Output='fit')
paramTable = fit_output.OutputParameters  # table containing the optimal fit parameters
fitWorkspace = fit_output.OutputWorkspace

print("The fit was: " + str(fit_output.OutputStatus))
print("Fitted Height value is: {:.1f}".format(paramTable.column(1)[0]))
print("Fitted centre value is: {:.1f}".format(abs(paramTable.column(1)[1])))
print("Fitted sigma value is: {:.4f}".format(paramTable.column(1)[2]))
# fitWorkspace contains the data, the calculated and the difference patterns
print("Number of spectra in fitWorkspace is: " +  str(fitWorkspace.getNumberHistograms()))

Output:

workspaces instantiated:  ws_qvectors, ws_fqt.Re, ws_fqt.Im, ws_sqw
The fit was: success
Fitted Height value is: 250.7
Fitted centre value is: 0.0
Fitted sigma value is: 0.0066
Number of spectra in fitWorkspace is: 3

Categories: AlgorithmIndex | Arithmetic\FFT