model = sqw_vaks(p, h,k,l,w, {signal}) : dispersion(HKL) in perovskites ABX3 with DHO(energy) iFunc/sqw_vaks: a 4D S(q,w) with a HKL dispersion, and a DHO line shape, based on a parameterisation by Vaks, suited for ABX3 perovskite compounds. This parameterisation is based on a quadratic expansion of the Hamiltonian, valid for e.g. |k|<.3 rlu in a cubic crystal and provides energies of TA1,TA2,LA,TO1 and TO2 modes. WARNING: Single intensity and line width parameters are used here. The HKL position is relative to the closest Bragg peak. The acoustic parameters can be related to the elastic constants as: At= (C12+2C44)/rho [meV2/rlu2] Al= C44/rho Aa= (C11-C12-2C44)/rho with rho=density of the crystal [g/cm3] Example: s=sqw_vaks('KTaO3'); qh=linspace(0,.5,50);qk=qh; ql=qh; w=linspace(0.01,10,51); f=iData(s,[],qh,qk,ql,w); scatter3(log(f(:,:,1,:)),'filled'); References: E. Farhi et al, EPJB, 15 (2000) pp 615-623. DOI: 10.1007/s100510051164 A.K. Tagantsev et al, Nature Comm, 4 (2013) 2229. DOI: 10.1038/ncomms3229 V.G. Vaks, Introduction to the Microscopic Theory of Ferroelectrics (Nauka, Moscow, 1973) input: p: sqw_vaks model parameters (double) p(1)=At transverse acoustic [meV2/rlu2] p(2)=Al longitudinal acoustic [meV2/rlu2] p(3)=Aa anisotropic acoustic [meV2/rlu2] p(4)=St soft mode transverse soft optical [meV2/rlu2] p(5)=Sa soft mode anisotropic soft optical [meV2/rlu2] p(6)=Vt transverse acoustic-optical coupling [meV2/rlu2] p(7)=Va anisotropic acoustic-optical coupling [meV2/rlu2] p(8)=w0 soft mode frequency at q=0, depends on temperature [meV] p(9)=Gamma dispersion DHO half-width in energy [meV] p(10)=Temperature of the material [K] p(11)=Amplitude p(12)=Background (constant) or 'KTaO3','BaTiO3','SrTiO3' for predefined settings 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_sine3d sqw_cubic_monoatomic, <a href="matlab:doc(iFunc,'Models')">iFunc:Models</a> (c) E.Farhi, ILL. License: EUPL.