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.
MODEL CREATION
To build a model, you may use:
sqw_vaks('gui') displays a dialogue box
sqw_vaks same as above ('gui')
sqw_vaks('KTaO3') use parameters for KTaO3 perovskite
sqw_vaks('BaTiO3') use parameters for BaTiO3 perovskite
sqw_vaks('SrTiO3') use parameters for SrTiO3 perovskite
sqw_vaks([ ... ]) use a 12 values vector as model parameters
sqw_vaks('defaults') selects KTaO3
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]
MODEL EVALUATION
Once created, the model is used as:
value = model(p, qh, qk, ql, w)
value = iData(model, p, qh, qk, ql, w)
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
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)
Version: Nov. 27, 2018
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.