iData_Sqw2D: moments=moments(sqw, M, T, classical): compute Sqw moments/sum rules (harmonic frequencies)
m = moments(sqw, M, T, classical)
Compute the structure factor (moment 0), recoil energy (moment 1) and the
collective, harmonic and mean energy transfer dispersions.
Input arguments can be given in order, or with name-value pairs, or as a
structure with named fields.
The result is given as an iData array with data sets:
S(q) = \int S(q,w) dw = <S(q,w)> structure factor [moment 0]
Er = \int w*S(q,w) dw = <wS(q,w)> = h2q2/2M recoil energy [moment 1]
Wc = sqrt(2kT*Er/S(q)) collective/isothermal dispersion
Wl harmonic/longitudinal excitation
Wq = 2q*sqrt(kT/S(q)/M) mean energy transfer
M2 = <w2S(q,w)> [moment 2]
M3 = <w3S(q,w)> [moment 3]
M4 = <w4S(q,w)> [moment 4]
Reference:
Helmut Schober, Journal of Neutron Research 17 (2014) pp. 109
Lovesey, Theory of Neutron Scattering from Condensed Matter, Vol 1, p180 eq. 5.38 (w0)
J-P.Hansen and I.R.McDonald, Theory of simple liquids Academic Press New York 2006.
syntax:
m = moments(sqw)
m = moments(sqw, M, T, classical)
m = moments(sqw, 'M', M, 'T', T, 'classical', classical)
input:
sqw: Sqw data set e.g. 2D data set with w as 1st axis (rows, meV), q as 2nd axis (Angs-1).
M: molar weight of the material atom/molecule in [g/mol].
when omitted or empty, it is searched 'weight' or 'mass' is the object.
T: when given, Temperature to use. When not given or empty, the Temperature
is searched in the object. The temperature is in [K]. 1 meV=11.605 K.
classical: 0 for non symmetric S(q,w) [with Bose, from exp.], 1 for symmetric (from MD)
when omitted or empty, this is guessed from the data set when possible
output:
moments=[ sq M1 wc wl wq M2 M3 M4 ] as an iData array
Example: m = moments(iData_Sqw2D('SQW_coh_lGe.nc'), 72.6, 1235); subplot(m);
(c) E.Farhi, ILL. License: EUPL.