model = sqw_linquad(p, h,k,l,w, {signal}) : linear-quadratic dispersion(HKL) with DHO(energy)
iFunc/sqw_linquad: a 4D S(q,w) with a 3D HKL dispersion with linear or
quadratic dependency, and a DHO line shape.
This dispersion corresponds with a local description of an excitation,
centered around an (H0,K0,L0,E0) point.
The model requires to define a direction corresponding with a Slope1 linear
dependency as well as a second direction. An ortho-normal coordinate basis
is then derived. All HKL coordinates are in rlu, and energies are in meV.
The dispersion has the form:
w(q) = sqrt[(Slope1*(q-HKL0) + E0)^2 + Slope^2*(q-HKL0)^2]
so that when the dispersion is linear arount [HKL0 E0], else it is
quadratic.
To define a mode which has its minimum E0 at a given HKL location, use:
sqw_linquad([ H K L E0 ])
this can be used to get a linear dispersion.
You can of course tune other parameters once the model object has been created.
WARNING: Single intensity and line width parameters are used here.
To model more than one branch, just add these models together.
Example:
s=sqw_linquad([.25 0 0 5]); qh=linspace(0,.5,50);qk=qh; ql=qh'; w=linspace(0.01,20,50);
f=iData(s,s.p,qh,qk,ql,w); plot3(log(f(:,1,:,:)));
Reference: https://en.wikipedia.org/wiki/Phonon
input: p: sqw_linquad model parameters (double)
p(1) = DC_Hdir1 Slope1 dispersion direction, H (linear) [rlu]
p(2) = DC_Kdir1 Slope1 dispersion direction, K (linear) [rlu]
p(3) = DC_Ldir1 Slope1 dispersion direction, L (linear) [rlu]
p(4) = DC_Hdir2 Slope2 dispersion direction, H (transverse) [rlu]
p(5) = DC_Kdir2 Slope2 dispersion direction, K (transverse) [rlu]
p(6) = DC_Ldir2 Slope2 dispersion direction, L (transverse) [rlu]
p(7) = DC_Slope1 Dispersion slope along 1st axis (linear) [meV/rlu]
p(8) = DC_Slope2 Dispersion slope along 2nd axis (transverse) [meV/rlu]
p(9) = DC_Slope3 Dispersion slope along 3rd axis (vertical) [meV/rlu]
p(10)= Ex_H0 Excitation location, H [rlu]
p(11)= Ex_K0 Excitation location, K [rlu]
p(12)= Ex_L0 Excitation location, L [rlu]
p(13)= Ex_E0_Center Excitation energy center [meV]
p(14)= DHO_Amplitude
p(15)= DHO_Damping Excitation damping, half-width [meV]
p(16)= DHO_Temperature Temperature [K]
p(17)= Background
or p='guess'
qh: axis along QH in rlu (row,double)
qk: axis along QK in rlu (column,double)
ql: axis along QL in rlu (page,double)
w: axis along energy in meV (double)
signal: when values are given, a guess of the parameters is performed (double)
output: signal: model value
Version: Nov. 27, 2018
See also iData, iFunc/fits, iFunc/plot, gauss, sqw_phonons, sqw_cubic_monoatomic, sqw_vaks
<a href="matlab:doc(iFunc,'Models')">iFunc:Models</a>
(c) E.Farhi, ILL. License: EUPL.