Refinement parameters

Refinement parameters What are the parameters to be determined? atom positional parameters atom thermal motion parameters atom site occupancy parameters background function parameters peak shape parameters unit cell dimensions scale factor(s) sample displacement, sample transparency, zero-shift errors preferred orientation, absorption, porosity, extinction parameters

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 axial divergence

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 axial divergence p1 = –h2 K1/3R R = diffractometer radius p2 = –h2 K2/3R K1,K2 = constants for collimator h = specimen width

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 flat sample

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 flat sample p3 = – a2/K3a = beam divergence K3 = constant

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 specimen transparency

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 specimen transparency p4 = 1/2meffR meff = effective linear absorption coefficient

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 specimen displacement p5 = –2s/R s = displacement

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 zero error

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 p4, p5, &p6 strongly correlated when refined together

Peak shift parameters 2qobs = 2qcalc + D2q where D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 p4, p5, &p6 strongly correlated when refined together When instrument correctly aligned, generally need get only p5

Peak shift parameters D2q= p1/tan 2q + p2/sin 2q + p3/tan q + p4 sin 2q + p5 cos q + p6 In GSAS: where:

Preferred orientation In powder diffractometry, usually assume random orientation For this, need >106 randomly oriented particles

Preferred orientation In powder diffractometry, usually assume random orientation For this, need >106 randomly oriented particles Extremes: diffraction vector plates needles diffraction vector normal cylindrical symmetry

Preferred orientation In powder diffractometry, usually assume random orientation For this, need >106 randomly oriented particles Extremes: diffraction vector plates needles diffraction vector normal cylindrical symmetry S = s - so so s

Preferred orientation In powder diffractometry, usually assume random orientation For this, need >106 randomly oriented particles Extremes: diffraction vector plates needles diffraction vector normal cylindrical symmetry

Preferred orientation March-Dollase function (a la GSAS) plates needles

Preferred orientation March-Dollase function (a la GSAS) plates needles multiplier in intensity equation # symmetrically equivalent reflections

Preferred orientation March-Dollase function (a la GSAS) plates needles multiplier in intensity equation # symmetrically equivalent reflections preferred orientation parameter (refined)

Preferred orientation March-Dollase function (a la GSAS) plates needles multiplier in intensity equation # symmetrically equivalent reflections preferred orientation parameter (refined) angle betwn orientation axis & diffraction vector for hkl

Preferred orientation March-Dollase function (a la GSAS)

Preferred orientation Spherical harmonics (a la GSAS) hkl sample orientation

Preferred orientation Spherical harmonics (a la GSAS) hkl sample orientation harmonic coefficients harmonic functions

Refinement parameters