model = sqw_acoustopt(p, h,k,l,w, {signal}) : acoutsic/optic dispersion(HKL) with DHO(energy) iFunc/sqw_acoustopt: a 4D S(q,w) with a 3D HKL dispersion with quadratic dependency, and a DHO line shape. This dispersion corresponds with a local description of an excitation, with its minimum around an (H0,K0,L0,E0) point. The model requires to define a direction corresponding with a Slope1 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(E0^2 + Slope^2*(q-HKL0)^2) so that when the dispersion is linear for E0=0 or far from HKL0, else it is quadratic. To define a pure acoustic mode, use (and adjust slopes): sqw_acoustopt(0) % minimum is E0=0 at q=0 To define an optical mode with energy E0 at Q=0, use: sqw_acoustopt([ E0 ]) % minimum is E0 at q=0 To define a mode which has its minimum E0 at a given HKL location, use: sqw_acoustopt([ H K L E0 ]) When creating the Model, the following syntax is possible: sqw_acoustopt(E0) centers the excitation at q=0 with energy E0 sqw_acoustopt([ h k l E0 ]) centers the excitation at q=[H K L] and energy E0 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_acoustopt(5); qh=linspace(0,.5,50);qk=qh; ql=qh'; w=linspace(0.01,10,50); f=iData(s,s.p,qh,qk,ql,w); plot3(log(f(:,1,:,:))); Reference: https://en.wikipedia.org/wiki/Phonon input: p: sqw_acoustopt model parameters (double) p(1) = DC_Hdir1 Slope1 dispersion direction, H [rlu] p(2) = DC_Kdir1 Slope1 dispersion direction, K [rlu] p(3) = DC_Ldir1 Slope1 dispersion direction, L [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 [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 Minimum of the dispersion, H [rlu] p(11)= Ex_K0 Minimum of the dispersion, K [rlu] p(12)= Ex_L0 Minimum of the dispersion, L [rlu] p(13)= Ex_E0_Center Minimum of the dispersion, Energy [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: Aug. 22, 2017 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.

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