Home > Scripts > Models > Specialized > sqw_linquad.m

DESCRIPTION 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

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. 26, 2018