Wavelength λ₁

wavelength_1 · \(\lambda_1\) · Å · refinable

The wavelength of the main line; with d it sets each Bragg angle.

\(\lambda_1 = 2 d_{hkl} \sin\theta_{hkl}\)

Equation as printed in: FullProf_Manual.pdf, p. 75. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Wavelength λ₂

wavelength_2 · \(\lambda_2\) · Å · refinable

The wavelength of the second line of a doublet (Kα2); equal to λ1 for one line.

\(\lambda_2 = 2 d_{hkl} \sin\theta_{hkl,2}\)

Equation as printed in: FullProf_Manual.pdf, p. 75. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Intensity ratio λ₂/λ₁

wavelength_ratio · \(R_{21}\) · 1 · refinable

The intensity of the λ2 line relative to λ1; each reflection is added a second time at λ2 with this weight.

\(y_i \mathrel{+}= R_{21}\, I_h\, \Omega(2\theta_i - 2\theta_{h,2})\)

Equation as printed in: FullProf_Manual.pdf, p. 75. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Monochromator polarisation

monochromator_polarisation · \(C_{\mathrm{thm}} = \cos^2 2\theta_M\) · 1 · refinable

The polarisation by a monochromator at Bragg angle \(\theta\)_M, in the X-ray Lorentz–polarisation factor.

\(L_p = \frac{1 - K + K\, C_{\mathrm{thm}} \cos^2 2\theta}{2 \sin^2\theta \cos\theta}\)

Equation as printed in: FullProf_Manual.pdf, p. 53. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

FullProf computes twice eq. 3.26 for X-rays with K = ½ (L033); the default is eq. 3.26 (Convention::lorentz_polarisation), and the import doubles each structure phase's scale, exactly (L047, L050). The papers of manuals/papers/ do not set Lp.

Polarisation fraction

polarisation_fraction · \(K\) · 1 · refinable

The polarised fraction of a synchrotron beam (Ilo = 3), or the perfect-crystal fraction in flat-plate transmission (Ilo = 2).

\(L_p = \frac{1 - K + K\, C_{\mathrm{thm}} \cos^2 2\theta}{2 \sin^2\theta \cos\theta}\)

Equation as printed in: FullProf_Manual.pdf, p. 53. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Ilo = 3 and Cthm = 0 (no monochromator) FullProf takes C_thm as 1, cos\(^{2}\)2\(\theta\)_M of no deflection: FullProf's joint run prbaco (BM16, K = 0.1) is met so to rms 6·\(10^{-3}\), where 1 − K alone leaves every peak at 0.90 of FullProf's (runs/prbaco/prbaco_calc_1.prf, L322). Ilo = 3 with Cthm ≠ 0 is not checked.

Instrument resolution

instrument_resolution · \(U_i, V_i, W_i, X_i, Y_i, Z_i\) · deg\(^{2}\) (U, V, W), deg (X, Y, Z) · read, not refined

The instrument's Gaussian and Lorentzian widths, from a resolution file; added to the sample's.

\(H_{G,i}^2 = (U_i \tan\theta + V_i)\tan\theta + W_i,\quad H_{L,i} = X_i \tan\theta + \frac{Y_i}{\cos\theta} + Z_i\)

Equation as printed in: FullProf_Manual.pdf, p. 70. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

A TOF pattern's resolution file (Res = 5, 6; P05) gives instead Zero, Dtt1, Dtt2, Hodges' terms, \(\sigma\), \(\gamma\), α, β (ZD2TOF, ZD2TOT, SIGMA, GAMMA, ALFBE, ALFBT, TWOTH), added to the bank's and the phases' values (docs/TOF_FullProf.pdf): tof::Instrument.

TOF bank angle 2θ

tof_bank_two_theta · \(2\theta_B\) · deg · read, not refined

The detector bank's scattering angle; it sets the Lorentz factor, the wavelength of each reflection and the absorption.

\(I_h \propto d_h^4 \sin\theta_B,\quad \lambda_h = 2 d_h \sin\theta_B\)

Equation as printed in: FullProf_Manual.pdf, p. 82. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The d\(^{4}\) sin \(\theta\)_B Lorentz factor against FullProf's intensities: 0.9531/0.9533 (arg_si, 144.8°), 0.9997 (CeO2, 90°), 0.9943 (lamn_pol, 29.0°) (L341).

Zero shift

zero_shift · \(2\theta_0\) · deg 2\(\theta\) · refinable

The offset of the detector's angle reading, added to every peak position.

\(2\theta_h = 2\arcsin\frac{\lambda}{2 d_h} + 2\theta_0 + S_c \cos\theta + S_s \sin 2\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 56 · FullProf_Manual.pdf, p. 82. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

In a TOF pattern the zero is a time, T₀ in µs, on line 14 (p. 82): T_h = T₀ + Dtt1 d + Dtt2 d\(^{2}\) + Dtt_1overd/d (P05, tof_dtt1).

Sample displacement

sample_displacement · \(S_c = -2s/R\) · deg 2\(\theta\) · refinable

The shift from a sample surface displaced by s from the goniometer axis (Bragg–Brentano), radius R.

\(\Delta 2\theta = -\frac{2s}{R}\cos\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 56. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Sample transparency

sample_transparency · \(S_s = 1/(2\mu R)\) · deg 2\(\theta\) · refinable

The shift from the beam's penetration into a thick absorbing sample of linear absorption μ (Bragg–Brentano).

\(\Delta 2\theta = \frac{1}{2\mu R}\sin 2\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 56. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

TOF Dtt1 (DIFC)

tof_dtt1 · \(D_1\) · µs/Å · refinable

The time of flight per Å of d-spacing: the bank's flight path and angle in one constant.

\(T_h = T_0 + D_1 d_h + D_2 d_h^2 + \frac{D_{-1}}{d_h}\)

Equation as printed in: FullProf_Manual.pdf, p. 82. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The position's form: FullProf's .prf ticks follow it with Dtt_1overd; its .hkl and .out print Dtt1·d alone for Npr = 9 (L341).

TOF Dtt2 (DIFA)

tof_dtt2 · \(D_2\) · µs/Ų · refinable

The quadratic term of the time of flight in d.

\(T_h = T_0 + D_1 d_h + D_2 d_h^2 + \frac{D_{-1}}{d_h}\)

Equation as printed in: FullProf_Manual.pdf, p. 82. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

TOF Dtt_1overd (DIFB)

tof_dtt_1overd · \(D_{-1}\) · µs·Å · refinable

The term of the time of flight in 1/d.

\(T_h = T_0 + D_1 d_h + D_2 d_h^2 + \frac{D_{-1}}{d_h}\)

Equation as printed in: FullProf_Manual.pdf, p. 82. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

TOF thermal zero

tof_thermal_zero · \(T_{0t}\) · µs · refinable

The zero of the thermal neutrons' time of flight (Hodges).

\(T_h = n\,(T_0 + D_1 d_h) + (1 - n)\left(T_{0t} + D_{1t} d_h - \frac{D_{2t}}{d_h}\right),\quad n = \tfrac{1}{2}\operatorname{erfc}\!\left(w\,(x_c - d_h^{-1})\right)\)

Equation as printed in: FullProf_Manual.pdf, pp. 84–85. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

T to 0.003 µs against the .out of gabriela's 1288 reflections (L341).

TOF thermal Dtt1

tof_thermal_dtt1 · \(D_{1t}\) · µs/Å · refinable

The thermal neutrons' time of flight per Å.

\(T_h = n\,(T_0 + D_1 d_h) + (1 - n)\left(T_{0t} + D_{1t} d_h - \frac{D_{2t}}{d_h}\right),\quad n = \tfrac{1}{2}\operatorname{erfc}\!\left(w\,(x_c - d_h^{-1})\right)\)

Equation as printed in: FullProf_Manual.pdf, pp. 84–85. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

T to 0.003 µs against the .out of gabriela's 1288 reflections (L341).

TOF thermal Dtt2

tof_thermal_dtt2 · \(D_{2t}\) · µs·Å · refinable

The thermal neutrons' term in 1/d, subtracted.

\(T_h = n\,(T_0 + D_1 d_h) + (1 - n)\left(T_{0t} + D_{1t} d_h - \frac{D_{2t}}{d_h}\right),\quad n = \tfrac{1}{2}\operatorname{erfc}\!\left(w\,(x_c - d_h^{-1})\right)\)

Equation as printed in: FullProf_Manual.pdf, pp. 84–85. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

T to 0.003 µs against the .out of gabriela's 1288 reflections (L341).

TOF crossover

tof_crossover · \(x_c\) · Å⁻¹ · refinable

The 1/d at which the epithermal and thermal times of flight cross.

\(T_h = n\,(T_0 + D_1 d_h) + (1 - n)\left(T_{0t} + D_{1t} d_h - \frac{D_{2t}}{d_h}\right),\quad n = \tfrac{1}{2}\operatorname{erfc}\!\left(w\,(x_c - d_h^{-1})\right)\)

Equation as printed in: FullProf_Manual.pdf, pp. 84–85. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

T to 0.003 µs against the .out of gabriela's 1288 reflections (L341).

TOF crossover width

tof_crossover_width · \(w\) · Å · refinable

How sharply the epithermal time of flight gives way to the thermal one.

\(T_h = n\,(T_0 + D_1 d_h) + (1 - n)\left(T_{0t} + D_{1t} d_h - \frac{D_{2t}}{d_h}\right),\quad n = \tfrac{1}{2}\operatorname{erfc}\!\left(w\,(x_c - d_h^{-1})\right)\)

Equation as printed in: FullProf_Manual.pdf, pp. 84–85. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

T to 0.003 µs against the .out of gabriela's 1288 reflections (L341).

Caglioti U

caglioti_u · \(U\) · deg\(^{2}\) · refinable

The tan\(^{2}\)\(\theta\) term of the squared Gaussian width; with a resolution file, the sample's Gaussian strain.

\(H_G^2 = (U \tan\theta + V)\tan\theta + W + \frac{I_G}{\cos^2\theta}\)

Equation as printed in: Caglioti_Paoletti_Ricci_1958.pdf, pp. 224–225 · Thompson_Cox_Hastings_1987.pdf, p. 81 · FullProf_Manual.pdf, p. 45 · FullProf_Manual.pdf, p. 49 · Microstructural_effects.pdf, p. 4. Paper: G. Caglioti, A. Paoletti & F. P. Ricci (1958). Choice of collimators for a crystal spectrometer for neutron diffraction. Nucl. Instrum. 3, 223–228. doi:10.1016/0369-643X(58)90029-X

Caglioti's eq. 11 (p. 225) gives the squared Gaussian FWHM as a quadratic in a = tan \(\theta\) / tan \(\theta\)_M (eq. 5, p. 224); the names U, V, W are Rietveld's (1969), as Thompson, Cox & Hastings (eq. 4, p. 81) write it. No departure: the same in the default and in FullProf.

Caglioti V

caglioti_v · \(V\) · deg\(^{2}\) · refinable

The tanθ term of the squared Gaussian width.

\(H_G^2 = (U \tan\theta + V)\tan\theta + W + \frac{I_G}{\cos^2\theta}\)

Equation as printed in: Caglioti_Paoletti_Ricci_1958.pdf, pp. 224–225 · Thompson_Cox_Hastings_1987.pdf, p. 81 · FullProf_Manual.pdf, p. 45 · FullProf_Manual.pdf, p. 49. Paper: G. Caglioti, A. Paoletti & F. P. Ricci (1958). Choice of collimators for a crystal spectrometer for neutron diffraction. Nucl. Instrum. 3, 223–228. doi:10.1016/0369-643X(58)90029-X

Caglioti W

caglioti_w · \(W\) · deg\(^{2}\) · refinable

The constant term of the squared Gaussian width.

\(H_G^2 = (U \tan\theta + V)\tan\theta + W + \frac{I_G}{\cos^2\theta}\)

Equation as printed in: Caglioti_Paoletti_Ricci_1958.pdf, pp. 224–225 · Thompson_Cox_Hastings_1987.pdf, p. 81 · FullProf_Manual.pdf, p. 45 · FullProf_Manual.pdf, p. 49. Paper: G. Caglioti, A. Paoletti & F. P. Ricci (1958). Choice of collimators for a crystal spectrometer for neutron diffraction. Nucl. Instrum. 3, 223–228. doi:10.1016/0369-643X(58)90029-X

Gaussian size broadening

gaussian_size · \(I_G\) · deg\(^{2}\) · refinable

The Gaussian size broadening of the phase, the 1/cos\(^{2}\)\(\theta\) term of the squared Gaussian width.

\(H_{G,\mathrm{size}} = \frac{\sqrt{I_G}}{\cos\theta}\)

Equation as printed in: FullProf_Manual.pdf, p. 49 · Microstructural_effects.pdf, p. 4. Paper: J. Rodríguez-Carvajal. Study of micro-structural effects by powder diffraction using the program FullProf. Laboratoire Léon Brillouin (manuals/fullprof/docs/Microstructural_effects.pdf)

Lorentzian strain broadening

lorentzian_strain · \(X\) · deg · refinable

The tanθ term of the Lorentzian width of the TCH profile: the phase's Lorentzian strain.

\(H_L = X \tan\theta + \frac{Y}{\cos\theta}\)

Equation as printed in: Microstructural_effects.pdf, p. 4 · FullProf_Manual.pdf, p. 49 · Thompson_Cox_Hastings_1987.pdf, p. 80. Paper: J. Rodríguez-Carvajal. Study of micro-structural effects by powder diffraction using the program FullProf. Laboratoire Léon Brillouin (manuals/fullprof/docs/Microstructural_effects.pdf)

Thompson, Cox & Hastings have only the size term X/cos \(\theta\) (their X, eq. 8b, p. 82); FullProf's X tan \(\theta\) is the microstructure paper's Lorentzian strain (eq. 19, p. 4). The TCH (H, η) of eqs. 2–3 (p. 80) combine H_G and H_L. FullProf counts its peak window without X tan \(\theta\) (L035) and takes one more low point when X ≠ 0 (L042): Convention::peak_window, kept on import (no exact translation, L050).

Lorentzian size broadening

lorentzian_size · \(Y\) · deg · refinable

The 1/cosθ term of the Lorentzian width of the TCH profile: the phase's Lorentzian (Scherrer) size.

\(H_L = X \tan\theta + \frac{Y}{\cos\theta},\qquad D = \frac{\lambda}{\beta^{*}\cos\theta}\)

Equation as printed in: Thompson_Cox_Hastings_1987.pdf, pp. 80–82 · FullProf_Manual.pdf, p. 49 · Microstructural_effects.pdf, p. 4. Paper: P. Thompson, D. E. Cox & J. B. Hastings (1987). Rietveld refinement of Debye–Scherrer synchrotron X-ray data from Al2O3. J. Appl. Cryst. 20, 79–83. doi:10.1107/S0021889887087090

Thompson, Cox & Hastings's X (F_L = X/cos \(\theta\), eq. 8b, p. 82) is FullProf's Y; GSAS-II also calls it X. No departure.

Anisotropic strain, quartic form

quartic_strain · \(S_{HKL}\) · \(10^{-8}\) Å⁻⁴ · refinable

The coefficients of Stephens' quartic form in hkl, the variance of 1/d\(^{2}\) over the crystallites: a strain broadening that depends on the reflection.

\(\sigma^2(M_{hkl}) = 10^{-8}\sum_{H+K+L=4} S_{HKL}\,h^H k^K l^L,\quad D_{ST} = \sqrt{8\ln 2}\,\frac{180}{\pi}\,\frac{\sigma(M_{hkl})}{M_{hkl}},\quad H_G^2 \mathrel{+}= [(1-\xi)D_{ST}]^2\tan^2\theta,\quad H_L \mathrel{+}= \xi D_{ST}\tan\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 22 · FullProf_Manual.pdf, p. 121 · NdNi_LTOa_calc1.mic. Paper: J. Rodríguez-Carvajal. Study of micro-structural effects by powder diffraction using the program FullProf. Laboratoire Léon Brillouin (manuals/fullprof/docs/Microstructural_effects.pdf)

Stephens' paper (J. Appl. Cryst. 32, 281, 1999) is not in the repository: the form, its factor \(10^{-8}\) and the split by ξ are as the manual (pp. 22, 121) and the .mic header state them, checked on FullProf's run of \(\mathrm{Nd_{2}NiO_{4}}\) (fullprof_anisotropic_strain, L211). FullProf's own forms of the trigonal, hexagonal and cubic classes and of −1 (the manual lists S_301 twice, p. 119) are not read yet; its strain model 8 (Str = 0, hexagonal, p. 29) is, as S_400 = Saa\(^{2}\), S_004 = Scc\(^{2}\), S_112 = 2 Saa Scc Cac, checked on its joint run scor_rxn (L322).

Anisotropic strain, Lorentzian share

quartic_strain_lorentzian · \(\xi\) · 1 · refinable

The share of the anisotropic strain's width taken by the Lorentzian part of the TCH profile; the rest is Gaussian.

\(H_G^2 \mathrel{+}= [(1-\xi)D_{ST}]^2\tan^2\theta,\quad H_L \mathrel{+}= \xi D_{ST}\tan\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 22 · FullProf_Manual.pdf, p. 121 · NdNi_LTOa_calc1.mic. Paper: J. Rodríguez-Carvajal. Study of micro-structural effects by powder diffraction using the program FullProf. Laboratoire Léon Brillouin (manuals/fullprof/docs/Microstructural_effects.pdf)

As the .mic header writes it (lines 36–38): the Gaussian strain (U + [(1 − ξ)D_ST]²) tan\(^{2}\)\(\theta\), the Lorentzian (X + ξ D_ST) tan \(\theta\).

Anisotropic size by shape

shape_size · \(S_Z\) · 1 · refinable

The Lorentzian size broadening of crystallites of a shape: platelets (|cos φ|), needles (sin φ), φ the angle between the scattering vector and the platelets' normal or the needles' axis; or the antiphase domains of \(\mathrm{Cu_{3}Au}\), broadening the reflections whose h, k, l are not all of one parity.

\(H_L \mathrel{+}= \frac{360}{\pi^2}\,10^{-3}\,\lambda\, S_Z\, g(\mathbf{h})/\cos\theta,\quad g = |\cos\varphi|,\ \sin\varphi\ \text{or}\ 1\)

Equation as printed in: FullProf_Manual.pdf, p. 23 · FullProf_Manual.pdf, p. 24 · prba10k_calc.out · pdfinal_calc.out. Paper: J. Rodríguez-Carvajal. Study of micro-structural effects by powder diffraction using the program FullProf. Laboratoire Léon Brillouin (manuals/fullprof/docs/Microstructural_effects.pdf)

k_s = (360/π²) λ \(10^{-3}\) as the manual gives it for the quadratic form of size (p. 23); the needles' sin φ and the platelets' |cos φ| as on p. 24. FullProf's vector is taken as a direction [u v w] of the crystal; prba10k's [0 0 1] in a tetragonal cell cannot tell it from a reciprocal one (L267).

Pseudo-Voigt η₀

pv_eta0 · \(\eta_0\) · 1 · refinable

The Lorentzian fraction of the pseudo-Voigt profile (Npr = 5) at 2\(\theta\) = 0.

\(\Omega = \eta L + (1-\eta) G,\quad \eta = \eta_0 + X\, 2\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 44 · FullProf_Manual.pdf, p. 45. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Pseudo-Voigt η slope

pv_eta_slope · \(X_\eta\) · 1/deg · refinable

The linear change of the pseudo-Voigt mixing η with 2\(\theta\) (Npr = 5); the same .pcr field as the TCH's X.

\(\eta = \eta_0 + X_\eta\, 2\theta\)

Equation as printed in: FullProf_Manual.pdf, p. 45. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

TOF σ₀

tof_sigma0 · \(\sigma_0\) · µs\(^{2}\) · refinable

A term of the variance of the Gaussian part of a TOF peak.

\(\sigma_h^2 = \sigma_0 + \sigma_1 d_h^2 + \sigma_2 d_h^4 + \sigma_Q d_h,\quad H_G = \sqrt{8 \ln 2\, \sigma_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

HwG of FullProf's .out met (L341).

TOF σ₁

tof_sigma1 · \(\sigma_1\) · µs\(^{2}\)/Ų · refinable

A term of the variance of the Gaussian part of a TOF peak.

\(\sigma_h^2 = \sigma_0 + \sigma_1 d_h^2 + \sigma_2 d_h^4 + \sigma_Q d_h,\quad H_G = \sqrt{8 \ln 2\, \sigma_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

HwG of FullProf's .out met (L341).

TOF σ₂

tof_sigma2 · \(\sigma_2\) · µs\(^{2}\)/Å⁴ · refinable

A term of the variance of the Gaussian part of a TOF peak.

\(\sigma_h^2 = \sigma_0 + \sigma_1 d_h^2 + \sigma_2 d_h^4 + \sigma_Q d_h,\quad H_G = \sqrt{8 \ln 2\, \sigma_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

HwG of FullProf's .out met (L341).

TOF σ_Q

tof_sigma_q · \(\sigma_Q\) · µs\(^{2}\)/Å · refinable

A term of the variance of the Gaussian part of a TOF peak.

\(\sigma_h^2 = \sigma_0 + \sigma_1 d_h^2 + \sigma_2 d_h^4 + \sigma_Q d_h,\quad H_G = \sqrt{8 \ln 2\, \sigma_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

\(\sigma\)_Q·d as GSAS-II's sig-q, believed: alum's 0.001 is below the print of FullProf's .out (L341).

TOF γ₀

tof_gamma0 · \(\gamma_0\) · µs · refinable

A term of the FWHM of the Lorentzian part of a TOF peak.

\(H_{L,h} = \gamma_0 + \gamma_1 d_h + \gamma_2 d_h^2\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

H and η from H_G and H_L by the Thompson–Cox–Hastings relations: FullProf's Hw and ETA met (L341).

TOF γ₁

tof_gamma1 · \(\gamma_1\) · µs/Å · refinable

A term of the FWHM of the Lorentzian part of a TOF peak.

\(H_{L,h} = \gamma_0 + \gamma_1 d_h + \gamma_2 d_h^2\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

H and η from H_G and H_L by the Thompson–Cox–Hastings relations: FullProf's Hw and ETA met (L341).

TOF γ₂

tof_gamma2 · \(\gamma_2\) · µs/Ų · refinable

A term of the FWHM of the Lorentzian part of a TOF peak.

\(H_{L,h} = \gamma_0 + \gamma_1 d_h + \gamma_2 d_h^2\)

Equation as printed in: FullProf_Manual.pdf, p. 111. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

H and η from H_G and H_L by the Thompson–Cox–Hastings relations: FullProf's Hw and ETA met (L341).

Bérar–Baldinozzi asymmetry

berar_baldinozzi · \(P_1, P_2, P_3, P_4\) · 1 · refinable

The four coefficients of the empirical asymmetry multiplier, below AsyLim.

\(A(u) = 1 + \frac{P_1 F_a(u) + P_2 F_b(u)}{\tan\theta_h} + \frac{P_3 F_a(u) + P_4 F_b(u)}{\tan 2\theta_h},\ u = \frac{2\theta_h - 2\theta}{H},\ F_a = 2u e^{-u^2},\ F_b = (8u^3 - 12u) e^{-u^2}\)

Equation as printed in: Berar_Baldinozzi_1993.pdf, pp. 128–129 · FullProf_Manual.pdf, p. 54. Paper: J.-F. Bérar & G. Baldinozzi (1993). Modeling of line-shape asymmetry in powder diffraction. J. Appl. Cryst. 26, 128–129. doi:10.1107/S0021889892009725

The paper's u is positive on the low-angle side (eqs. 1–3, p. 128), as FullProf computes it; the manual's eq. 3.29 prints the opposite sign. FullProf's F_b = (4u\(^{2}\) − 3)F_a is the paper's + 3F_a (L035): Convention::berar_baldinozzi; a .pcr's (P1, P2, P3, P4) are imported as (P1 + 3P2, P2, P3 + 3P4, P4), exactly (L050).

Axial divergence S/L

axial_divergence_s_l · \(S/L\) · 1 · refinable

The sample half-height S over the goniometer radius L, in the Finger–Cox–Jephcoat axial-divergence profile.

\(2\phi_{\min} = \arccos\left(\cos 2\theta \sqrt{\left(\tfrac{H+S}{L}\right)^2 + 1}\right),\quad 2\phi_{\mathrm{infl}} = \arccos\left(\cos 2\theta \sqrt{\left(\tfrac{H-S}{L}\right)^2 + 1}\right)\)

Equation as printed in: Finger_Cox_Jephcoat_1994.pdf, pp. 893–895 · FullProf_Manual.pdf, p. 69 · FullProf_Manual.pdf, p. 112. Paper: L. W. Finger, D. E. Cox & A. P. Jephcoat (1994). A correction for powder diffraction peak asymmetry due to axial divergence. J. Appl. Cryst. 27, 892–900. doi:10.1107/S0021889894004218

FullProf (CrysFML's Prof_Val, lines 1289–1294) reads a pair with D_L < 0.0002 as (H/L + S/L, H/L − S/L), so S_L alone means S/L = H/L = S_L/2; the default takes the paper's S/L and H/L as given (Convention::axial_divergence), and a .pcr's pair is imported through profile::fullprof_axial, exactly (L050).

Axial divergence H/L

axial_divergence_d_l · \(D/L\) · 1 · refinable

The detector half-opening H over the goniometer radius L (FCJ's H/L), in the Finger–Cox–Jephcoat profile.

\(2\phi_{\min} = \arccos\left(\cos 2\theta \sqrt{\left(\tfrac{H+S}{L}\right)^2 + 1}\right),\quad 2\phi_{\mathrm{infl}} = \arccos\left(\cos 2\theta \sqrt{\left(\tfrac{H-S}{L}\right)^2 + 1}\right)\)

Equation as printed in: Finger_Cox_Jephcoat_1994.pdf, pp. 893–895 · FullProf_Manual.pdf, p. 69 · FullProf_Manual.pdf, p. 112. Paper: L. W. Finger, D. E. Cox & A. P. Jephcoat (1994). A correction for powder diffraction peak asymmetry due to axial divergence. J. Appl. Cryst. 27, 892–900. doi:10.1107/S0021889894004218

FullProf (CrysFML's Prof_Val, lines 1289–1294) reads a pair with D_L < 0.0002 as (H/L + S/L, H/L − S/L), so S_L alone means S/L = H/L = S_L/2; the default takes the paper's S/L and H/L as given (Convention::axial_divergence), and a .pcr's pair is imported through profile::fullprof_axial, exactly (L050).

TOF α₀

tof_alpha0 · \(\alpha_0\) · µs\(^{-1}\) · refinable

The constant of the rise of a TOF peak (its leading exponential).

\(\alpha_h = \alpha_0 + \frac{\alpha_1}{d_h} + \frac{\alpha_Q}{\sqrt{d_h}},\quad \beta_h = \beta_0 + \frac{\beta_1}{d_h^4} + \frac{\beta_Q}{d_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 112 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Npr = 10 α₀ + α₁ d is a time (µs) mixed with the thermal one as 1/α (the 2003 document's Panel 10); α_Q, β_Q found from alum's .out to its six digits (L341).

TOF α₁

tof_alpha1 · \(\alpha_1\) · µs\(^{-1}\)·Å · refinable

The 1/d term of the rise of a TOF peak.

\(\alpha_h = \alpha_0 + \frac{\alpha_1}{d_h} + \frac{\alpha_Q}{\sqrt{d_h}},\quad \beta_h = \beta_0 + \frac{\beta_1}{d_h^4} + \frac{\beta_Q}{d_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 112 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Npr = 10 α₀ + α₁ d is a time (µs) mixed with the thermal one as 1/α (the 2003 document's Panel 10); α_Q, β_Q found from alum's .out to its six digits (L341).

TOF α_Q

tof_alpha_q · \(\alpha_Q\) · µs\(^{-1}\)·Å^½ · refinable

The 1/√d term of the rise of a TOF peak.

\(\alpha_h = \alpha_0 + \frac{\alpha_1}{d_h} + \frac{\alpha_Q}{\sqrt{d_h}},\quad \beta_h = \beta_0 + \frac{\beta_1}{d_h^4} + \frac{\beta_Q}{d_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 112 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Npr = 10 α₀ + α₁ d is a time (µs) mixed with the thermal one as 1/α (the 2003 document's Panel 10); α_Q, β_Q found from alum's .out to its six digits (L341).

TOF β₀

tof_beta0 · \(\beta_0\) · µs\(^{-1}\) · refinable

The constant of the decay of a TOF peak (its trailing exponential).

\(\alpha_h = \alpha_0 + \frac{\alpha_1}{d_h} + \frac{\alpha_Q}{\sqrt{d_h}},\quad \beta_h = \beta_0 + \frac{\beta_1}{d_h^4} + \frac{\beta_Q}{d_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 112 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Npr = 10 α₀ + α₁ d is a time (µs) mixed with the thermal one as 1/α (the 2003 document's Panel 10); α_Q, β_Q found from alum's .out to its six digits (L341).

TOF β₁

tof_beta1 · \(\beta_1\) · µs\(^{-1}\)·Å⁴ · refinable

The 1/d\(^{4}\) term of the decay of a TOF peak.

\(\alpha_h = \alpha_0 + \frac{\alpha_1}{d_h} + \frac{\alpha_Q}{\sqrt{d_h}},\quad \beta_h = \beta_0 + \frac{\beta_1}{d_h^4} + \frac{\beta_Q}{d_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 112 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Npr = 10 α₀ + α₁ d is a time (µs) mixed with the thermal one as 1/α (the 2003 document's Panel 10); α_Q, β_Q found from alum's .out to its six digits (L341).

TOF β_Q

tof_beta_q · \(\beta_Q\) · µs\(^{-1}\)·Å² · refinable

The 1/d\(^{2}\) term of the decay of a TOF peak.

\(\alpha_h = \alpha_0 + \frac{\alpha_1}{d_h} + \frac{\alpha_Q}{\sqrt{d_h}},\quad \beta_h = \beta_0 + \frac{\beta_1}{d_h^4} + \frac{\beta_Q}{d_h^2}\)

Equation as printed in: FullProf_Manual.pdf, p. 112 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

With Npr = 10 α₀ + α₁ d is a time (µs) mixed with the thermal one as 1/α (the 2003 document's Panel 10); α_Q, β_Q found from alum's .out to its six digits (L341).

TOF thermal α₀

tof_alpha0_thermal · \(\alpha_{0t}\) · µs · refinable

A term of the thermal neutrons' rise or decay time (Hodges), mixed with the epithermal one by the crossover.

\(\frac{1}{\alpha_h} = n\,(\alpha_0 + \alpha_1 d_h) + (1 - n)\left(\alpha_{0t} - \frac{\alpha_{1t}}{d_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 113 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The 2003 document's form, 1/α mixed; the manual (p. 112) mixes α itself. FullProf's .out follows the document, to six digits (L341).

TOF thermal β₀

tof_beta0_thermal · \(\beta_{0t}\) · µs · refinable

A term of the thermal neutrons' rise or decay time (Hodges), mixed with the epithermal one by the crossover.

\(\frac{1}{\alpha_h} = n\,(\alpha_0 + \alpha_1 d_h) + (1 - n)\left(\alpha_{0t} - \frac{\alpha_{1t}}{d_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 113 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The 2003 document's form, 1/α mixed; the manual (p. 112) mixes α itself. FullProf's .out follows the document, to six digits (L341).

TOF thermal α₁

tof_alpha1_thermal · \(\alpha_{1t}\) · µs·Å · refinable

A term of the thermal neutrons' rise or decay time (Hodges), mixed with the epithermal one by the crossover.

\(\frac{1}{\alpha_h} = n\,(\alpha_0 + \alpha_1 d_h) + (1 - n)\left(\alpha_{0t} - \frac{\alpha_{1t}}{d_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 113 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The 2003 document's form, 1/α mixed; the manual (p. 112) mixes α itself. FullProf's .out follows the document, to six digits (L341).

TOF thermal β₁

tof_beta1_thermal · \(\beta_{1t}\) · µs·Å · refinable

A term of the thermal neutrons' rise or decay time (Hodges), mixed with the epithermal one by the crossover.

\(\frac{1}{\alpha_h} = n\,(\alpha_0 + \alpha_1 d_h) + (1 - n)\left(\alpha_{0t} - \frac{\alpha_{1t}}{d_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 113 · TOF_FullProf.pdf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The 2003 document's form, 1/α mixed; the manual (p. 112) mixes α itself. FullProf's .out follows the document, to six digits (L341).

Absorption μR

absorption_mur · \(\mu R\) · 1 · refinable

Linear absorption times the radius of a cylindrical sample (or μt of a flat plate in transmission).

\(T_h = \exp\{-(1.7133 - 0.0368 \sin^2\theta)\mu R + (0.0927 + 0.375 \sin^2\theta)(\mu R)^2\}\)

Equation as printed in: FullProf_Manual.pdf, p. 55. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Micro-absorption P₀

microabsorption_p0 · \(P_0\) · 1 · refinable

The constant part of the loss of intensity by surface roughness in Bragg–Brentano geometry.

\(S_r(h) = 1 - P(h),\quad P(h) = P_0 + C_p\,\frac{\tau}{\sin\theta_h}\left(1 - \frac{\tau}{\sin\theta_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 55 · FullProf_Manual.pdf, p. 84. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Micro-absorption Cp

microabsorption_cp · \(C_p\) · 1 · refinable

The amplitude of the angle-dependent loss of intensity by surface roughness in Bragg–Brentano geometry.

\(P(h) = P_0 + C_p\,\frac{\tau}{\sin\theta_h}\left(1 - \frac{\tau}{\sin\theta_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 55 · FullProf_Manual.pdf, p. 84. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Micro-absorption τ

microabsorption_tau · \(\tau\) · 1 · refinable

The roughness parameter of the angle-dependent loss of intensity in Bragg–Brentano geometry, in units of sin \(\theta\).

\(P(h) = P_0 + C_p\,\frac{\tau}{\sin\theta_h}\left(1 - \frac{\tau}{\sin\theta_h}\right)\)

Equation as printed in: FullProf_Manual.pdf, p. 55 · FullProf_Manual.pdf, p. 84. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Preferred orientation G₁

po_g1 · \(G_1\) · 1 · refinable

The preferred-orientation strength: March's ratio r (Nor = 1, 1 = none) or the exponential coefficient (Nor = 0, 0 = none).

\(P_h = \frac{1}{m}\sum_{i=1}^{m} \left[G_2 + (1 - G_2)\left((G_1\cos\alpha_i)^2 + \frac{\sin^2\alpha_i}{G_1}\right)^{-3/2}\right]\ (\text{March}),\quad G_2 + (1-G_2)\, e^{-G_1 \alpha_i^2}\ (\text{exponential})\)

Equation as printed in: Dollase_1986.pdf, p. 268 · March_1932.pdf, p. 291 · FullProf_Manual.pdf, p. 54 · FullProf_Manual.pdf, p. 55. Paper: W. A. Dollase (1986). Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Cryst. 19, 267–272. doi:10.1107/S0021889886089458

Dollase sums P over the m symmetry-equivalent planes (eq. 4, p. 268), as FullProf (L042) and GSAS-II (GSASIIstrMath.py lines 3066–3078) do. March–Dollase is Dollase's Table 1, no. 6, the axial case of March (p. 291): the same in FullProf. The exponential is Dollase's no. 5, b + (1 − b)exp(−Gα²); FullProf's eq. 3.31 writes exp(+G1 α²): Convention::preferred_orientation, and a .pcr's Pref1 with Nor = 0 is imported as −Pref1, exactly (L050).

Preferred orientation G₂

po_g2 · \(G_2\) · 1 · refinable

The fraction of the sample without preferred orientation.

\(P_h = G_2 + (1 - G_2)\left[(G_1\cos\alpha_h)^2 + \frac{\sin^2\alpha_h}{G_1}\right]^{-3/2}\)

Equation as printed in: Dollase_1986.pdf, p. 268 · FullProf_Manual.pdf, p. 55. Paper: W. A. Dollase (1986). Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Cryst. 19, 267–272. doi:10.1107/S0021889886089458

Preferred-orientation axis

po_direction · \(\mathbf{h}_{\mathrm{PO}}\) · reciprocal-lattice components · read, not refined

The preferred-orientation axis; α_h is the angle between it and the scattering vector.

\(\cos\alpha_h = \frac{\mathbf{h}^{T} G^{*} \mathbf{h}_{\mathrm{PO}}}{|\mathbf{h}|\,|\mathbf{h}_{\mathrm{PO}}|}\)

Equation as printed in: FullProf_Manual.pdf, p. 54. Paper: W. A. Dollase (1986). Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Cryst. 19, 267–272. doi:10.1107/S0021889886089458

March ratio of a preferred-orientation axis

po_axis_ratio · \(r_j\) · 1 · refinable

March's ratio r_j of axis j of a phase textured along several axes: the crystallites with that axis are distributed about the sample's axis by March's density, below 1 for plates, above 1 for needles, 1 for none.

\(P_h = \frac{1}{m}\sum_{i=1}^{m} \sum_j f_j\, \left(r_j^2\cos^2\rho_{ij} + \frac{\sin^2\rho_{ij}}{r_j}\right)^{-3/2}\)

Equation as printed in: Dollase_1986.pdf, p. 268 · March_1932.pdf, p. 291 · Fullprof_News_2003.htm L310–340 · yb_nor2.out L440–445. Paper: W. A. Dollase (1986). Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Cryst. 19, 267–272. doi:10.1107/S0021889886089458

ρ_ij is the angle between axis j and the sample's axis for the i-th of the m reflections equivalent to h: its angle α to h in reflection (Nor = 2, FullProf's G2 does not enter: yb_nor2_g2 has yb_nor2's CORR, L360); in an anvil cell with the beam along the force (Nor = 3), averaged over the cone cos ρ = cos α cos ψ + sin α sin ψ cos φ, ψ = 90° − \(\theta\) (Wright et al. 1996, believed: FullProf's yb_nor3 CORR is up to 3.6 % below it, L360).

Fraction of a preferred-orientation axis

po_axis_fraction · \(f_j\) · 1 · refinable

The fraction f_j of a phase's crystallites oriented about axis j; the fractions sum to 1, and the last is 1 minus the others.

\(f_n = 1 - \sum_{j<n} f_j\)

Equation as printed in: Fullprof_News_2003.htm L310–320

Steps of the anvil cell's texture integration

po_axis_steps · \(N_\varphi\) · steps · read, not refined

For an anvil cell with the beam along the force: the steps over the azimuth φ of each axis's cone about the scattering vector; 0 for a flat sample in reflection.

\(\bar D_j = \frac{1}{N_\varphi}\sum_{k=1}^{N_\varphi} D\!\left(r_j, \cos\alpha\cos\psi + \sin\alpha\sin\psi\cos\varphi_k\right),\ \varphi_k = \pi\frac{k - 1/2}{N_\varphi}\)

Equation as printed in: Fullprof_News_2003.htm L326–340 · Fullprof_News_2003.htm L408–412

The form is believed (Wright, Nelmes, Belmonte & McMahon 1996, eqs. 4–6, which the News names; the paper is not in manuals/papers): FullProf's yb_nor3 CORR is up to 3.6 % below it, frozen in test texture and listed for Josu (L360).

TOF extinction

tof_extinction · \(E_x\) · Å⁴/(\(10^{-12}\) cm)² · refinable

Sabine's extinction of a powder in a TOF pattern.

\(x = E_x \left(\frac{\lambda_h F_h}{V}\right)^2,\quad E_h = E_L \cos^2\theta_B + E_B \sin^2\theta_B,\quad E_B = (1 + x)^{-1/2}\)

Equation as printed in: FullProf_Manual.pdf, p. 110. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Sabine, Von Dreele & Jørgensen (1988), as GSAS: x/(E_x F\(^{2}\) λ²) = 1/V\(^{2}\) on every reflection of arg_si_ext10 and ext100 (L341). E_L = 1 − x/2 + x\(^{2}\)/4 − 5x\(^{3}\)/48 + 7x\(^{4}\)/192 for x \(\le 1\), √(2/πx)(1 − 1/8x − 3/128x\(^{2}\) − 15/1024x\(^{3}\)) above.

TOF absorption

tof_absorption · \(A_1\) · Å⁻¹ · refinable

The sample's absorption per Å of wavelength in a TOF pattern, by the bank's absorption function.

\(x = A_1 \lambda_h:\ \frac{1 - e^{-2x}}{2x}\ \text{(flat plate)},\ e^{-(1.7133 - 0.0368 s^2) x + (0.0927 + 0.375 s^2) x^2}\ \text{(cylinder)},\ e^{-x}\)

Equation as printed in: FullProf_Manual.pdf, p. 113 · FullProf_Manual.pdf, p. 76. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Each function found from FullProf's CORR (arg_si_abs1, _calc, _abs3: to six digits, 8·\(10^{-6}\) for the cylinder); the manual's Iabscor 3 is e^{−cλ²}, FullProf's e^{−x} (L341). ABS2 is refused: FullProf's two runs with it stopped (L334).

Background points

background_points · \(b(2\theta_k)\) · counts · refinable

Background heights at chosen angles, interpolated linearly between them.

\(b_i = b_k + (b_{k+1} - b_k)\frac{2\theta_i - 2\theta_k}{2\theta_{k+1} - 2\theta_k}\)

Equation as printed in: FullProf_Manual.pdf, p. 45 · FullProf_Manual.pdf, p. 78. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Background polynomial

background_polynomial · \(B_m\) · counts · refinable

The coefficients of a polynomial background in (2\(\theta\)/Bkpos − 1).

\(b_i = \sum_{m=0}^{11} B_m \left(\frac{2\theta_i}{\mathrm{BKPOS}} - 1\right)^m\)

Equation as printed in: FullProf_Manual.pdf, pp. 45–46. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Background origin

background_origin · \(\mathrm{BKPOS}\) · deg 2\(\theta\) · read, not refined

The origin of the polynomial background.

\(b_i = \sum_{m} B_m \left(\frac{2\theta_i}{\mathrm{BKPOS}} - 1\right)^m\)

Equation as printed in: FullProf_Manual.pdf, p. 46 · FullProf_Manual.pdf, p. 75. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Background Chebyshev series

background_chebyshev · \(c_m\) · counts · refinable

The coefficients of a Chebyshev series over the data range (Nba = −5; not in the 2001 manual, since June 2011).

\(b_i = \sum_{m=0}^{23} c_m T_m(x_i),\quad x_i = 2\frac{2\theta_i - 2\theta_{\min}}{2\theta_{\max} - 2\theta_{\min}} - 1\)

Equation as printed in: FullProf_News_2011.htm L129–137 · Cocus-asym.pcr L25–33

Background Fourier series

background_fourier · \(B_j\) · counts · refinable

The coefficients of a Fourier cosine series in 2\(\theta\) (Nba = −4).

\(b_i = \sum_{j=0}^{11} B_j \cos(j\, 2\theta_i)\)

Equation as printed in: FullProf_Manual.pdf, pp. 45–46 · Fullprof_News_2001.htm L513–554. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Background Debye-like amplitude

background_debye_amplitude · \(A_j\) · counts · refinable

The amplitude of a Debye-like term of the background: the diffuse scattering of a pair of atoms at distance r_j in an amorphous part or a liquid (FullProf's Nba = −1).

\(b_i = \sum_m B_m \left(\frac{2\theta_i}{\mathrm{BKPOS}} - 1\right)^m + \sum_j A_j \frac{\sin(Q_i r_j)}{Q_i r_j},\quad Q_i = \frac{4\pi\sin\theta_i}{\lambda_1}\)

Equation as printed in: FullProf_Manual.pdf, p. 45 · nac_3t2_calc.prf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Background Debye-like distance

background_debye_distance · \(r_j\) · Å · refinable

The distance of a Debye-like term of the background, the separation of the pair of atoms whose diffuse scattering it is.

\(A_j \frac{\sin(Q_i r_j)}{Q_i r_j}\)

Equation as printed in: FullProf_Manual.pdf, p. 45 · nac_3t2_calc.prf. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Background inverse powers

background_inverse_power · \(c_j\) · counts·deg^j · refinable

The coefficients of 1/2\(\theta\), 1/2\(\theta\)² and 1/2\(\theta\)³ added to a polynomial of nine coefficients (FullProf's Nba = −3), for the steep background at low angles.

\(b_i = \sum_{m=0}^{8} B_m \left(\frac{2\theta_i}{\mathrm{BKPOS}} - 1\right)^m + \sum_{j=1}^{3} c_j (2\theta_i)^{-j}\)

Equation as printed in: Fullprof_News_2003.htm L963 · y2o3_poly12_b10.prf · y2o3_poly12_b12.prf

Background profile coefficient

background_profile · \(k_n\) · 1 · refinable

The coefficient of a background profile read from a file (an empty holder's pattern, a calculated thermal diffuse scattering), added to the background function.

\(b_i = f(2\theta_i) + \sum_n k_n\, P_n(2\theta_i)\)

Equation as printed in: Fullprof_News_2003.htm L1149–1153 · y2o3_more2_two.out

Background file scale b₁

background_file_scale · \(b_1\) · 1 · refinable

The factor on a background read from a file (FullProf's Nba = 1); FullProf reads 0 as 1.

\(b_i = b_1\,B\left[(1 + b_3)\,2\theta_i + b_4\right] + b_2\)

Equation as printed in: FullProf_Manual.pdf, p. 46 · y2o3_bac_b3b4.out

Background file offset b₂

background_file_offset · \(b_2\) · counts · refinable

A constant added to a background read from a file (Nba = 1).

\(b_i = b_1\,B\left[(1 + b_3)\,2\theta_i + b_4\right] + b_2\)

Equation as printed in: FullProf_Manual.pdf, p. 46 · y2o3_bac_b3b4.out

Background file stretch b₃

background_file_stretch · \(b_3\) · 1 · refinable

The stretch of the angle a background read from a file is read at, (1 + b₃)2\(\theta\) (Nba = 1).

\(b_i = b_1\,B\left[(1 + b_3)\,2\theta_i + b_4\right] + b_2\)

Equation as printed in: FullProf_Manual.pdf, p. 46 · y2o3_bac_b3b4.out

Background file shift b₄

background_file_shift · \(b_4\) · deg · refinable

The shift of the angle a background read from a file is read at, (1 + b₃)2\(\theta\) + b₄ (Nba = 1).

\(b_i = b_1\,B\left[(1 + b_3)\,2\theta_i + b_4\right] + b_2\)

Equation as printed in: FullProf_Manual.pdf, p. 46 · y2o3_bac_b3b4.out

Scale factor

scale_factor · \(S_\phi\) · arbitrary · refinable

The factor that brings the phase's calculated intensities to the observed counts.

\(y_{ci} = \sum_\phi S_\phi \sum_h I_{\phi h}\, \Omega(2\theta_i - 2\theta_{\phi h}) + b_i\)

Equation as printed in: FullProf_Manual.pdf, p. 41. Paper: H. M. Rietveld (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71. doi:10.1107/S0021889869006558

A .pcr's X-ray scale is doubled on import (Ilo = 0, 1, 4): FullProf's Lp is twice the manual's eq. 3.26 (L047, L050).

Phase mass factor ATZ

qpa_atz · \(ATZ_\phi\) · g/mol · read, not refined

The phase's mass per cell over its absorption contrast, which turns its scale factor into a weight fraction.

\(ATZ_\phi = \frac{Z_\phi M_\phi f_\phi^2}{t_\phi},\quad W_\phi = \frac{S_\phi\, ATZ_\phi V_\phi / t_\phi}{\sum_\psi S_\psi\, ATZ_\psi V_\psi / t_\psi}\)

Equation as printed in: FullProf_Manual.pdf, p. 91 · FullProf_Manual.pdf, p. 31. Paper: R. J. Hill & C. J. Howard (1987). Quantitative phase analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Cryst. 20, 467–474

The core divides by the Brindley coefficient once more, as the manual's p. 31 writes W; every phase of the material has t = 1, so whether FullProf's ATZ already holds t is not checked.

Brindley coefficient

brindley_coefficient · \(t_\phi\) · 1 · read, not refined

Brindley's particle absorption contrast factor of the phase, for microabsorption in quantitative analysis.

\(t_\phi = \frac{1}{V_\phi}\int \exp\{-(\mu_\phi - \bar\mu)x\}\, dV_\phi\)

Equation as printed in: FullProf_Manual.pdf, p. 31. Paper: R. J. Hill & C. J. Howard (1987). Quantitative phase analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Cryst. 20, 467–474

Overall displacement B

overall_b · \(B_{\mathrm{ov}}\) · Ų · refinable

An isotropic displacement common to all atoms of the phase, applied to the intensities.

\(I_h \propto |F_h|^2 \exp(-2 B_{\mathrm{ov}} s^2),\quad s = \frac{\sin\theta}{\lambda}\)

Equation as printed in: FullProf_Manual.pdf, p. 58. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Cell a

cell_a · \(a\) · Å · refinable

The length of the first cell edge.

\(\frac{1}{d_{hkl}^2} = \mathbf{h}^{T} G^{*} \mathbf{h}\)

Equation as printed in: FullProf_Manual.pdf, p. 107. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Cell b

cell_b · \(b\) · Å · refinable

The length of the second cell edge.

\(\frac{1}{d_{hkl}^2} = \mathbf{h}^{T} G^{*} \mathbf{h}\)

Equation as printed in: FullProf_Manual.pdf, p. 107. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Cell c

cell_c · \(c\) · Å · refinable

The length of the third cell edge.

\(\frac{1}{d_{hkl}^2} = \mathbf{h}^{T} G^{*} \mathbf{h}\)

Equation as printed in: FullProf_Manual.pdf, p. 107. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Cell α

cell_alpha · \(\alpha\) · deg · refinable

The angle between the b and c edges.

\(\frac{1}{d_{hkl}^2} = \mathbf{h}^{T} G^{*} \mathbf{h}\)

Equation as printed in: FullProf_Manual.pdf, p. 107. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Cell β

cell_beta · \(\beta\) · deg · refinable

The angle between the a and c edges.

\(\frac{1}{d_{hkl}^2} = \mathbf{h}^{T} G^{*} \mathbf{h}\)

Equation as printed in: FullProf_Manual.pdf, p. 107. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Cell γ

cell_gamma · \(\gamma\) · deg · refinable

The angle between the a and b edges.

\(\frac{1}{d_{hkl}^2} = \mathbf{h}^{T} G^{*} \mathbf{h}\)

Equation as printed in: FullProf_Manual.pdf, p. 107. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Atom position

atom_position · \(x_j, y_j, z_j\) · fraction of the cell edge · refinable

The fractional coordinates of an atom; the structure factor sums over its images by the space group.

\(F_h = \sum_j f_j\, \mathrm{Occ}_j\, T_j \sum_{s} \exp\{2\pi i\, \mathbf{h}\cdot(R_s \mathbf{x}_j + \mathbf{t}_s)\}\)

Equation as printed in: FullProf_Manual.pdf, p. 41 · FullProf_Manual.pdf, p. 100. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Isotropic displacement B

atom_biso · \(B_j\) · Ų · refinable

The isotropic displacement (Debye–Waller) parameter of an atom; B = 8π²U.

\(T_j = \exp(-B_j s^2),\quad s = \frac{\sin\theta}{\lambda}\)

Equation as printed in: FullProf_Manual.pdf, p. 100. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Occupancy

atom_occupancy · \(\mathrm{Occ}_j\) · 1 · refinable

FullProf's occupancy: the chemical occupancy times the site's multiplicity over the general position's.

\(\mathrm{Occ}_j = o_j\, \frac{m_j}{M}\)

Equation as printed in: FullProf_Manual.pdf, p. 100. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Anisotropic displacement β

atom_betas · \(\beta_{11} \dots \beta_{23}\) · 1 · refinable

The anisotropic displacement of an atom, as FullProf's betas.

\(T_j = \exp\{-(\beta_{11}h^2 + \beta_{22}k^2 + \beta_{33}l^2 + 2\beta_{12}hk + 2\beta_{13}hl + 2\beta_{23}kl)\}\)

Equation as printed in: FullProf_Manual.pdf, p. 100. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Symmetry-mode amplitude

mode_amplitude · \(Q_m\) · Å · refinable

The amplitude of a symmetry-adapted distortion mode: the atoms sit at the reference (parent) structure's positions plus Σ_m Q_m c_m V_m, refined in place of the coordinates (R29); the modes of one irrep make its amplitude A = √(Σ Q\(^{2}\)) and polarisation vector Q/A.

\(\mathbf{r}_j = \mathbf{r}^0_j + \sum_m Q_m\, c_m\, \mathbf{V}_{mj},\qquad A_{\Gamma} = \Big(\sum_{m \in \Gamma} Q_m^2\Big)^{1/2}\)

Equation as printed in: FullProf-Tutorial-Symmetry-Modes.pdf, p. 4 · nb5132.md L255. Paper: J. Rodríguez-Carvajal, notes on symmetry modes in FullProf (fp2k.inf, 29 August 2008 – 20 May 2010), reproduced in the tutorial 'AMPLIMODES and FullProf: symmetry modes crystallography' (manuals/fullprof/7-FullProf-Tutorial-SymmetryModes/FullProf-Tutorial-Symmetry-Modes.pdf)

Rigid group origin

rigid_origin · \(X_0, Y_0, Z_0\) · fraction of the cell edge · refinable

Where a rigid group's own frame sits in the cell: its atoms are r_C = R(\(\theta\), φ, \(\chi\)) r_m + M X_0 in the crystal's Cartesian frame (x ∥ a, z ∥ c*); refined in place of the atoms' coordinates (P41). A satellite group's origin is its parent's atom N1.

\(\mathbf{x}_j = \mathbf{X}_0 + M^{-1} R(\theta,\phi,\chi)\, \mathbf{r}^{m}_j\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 8 · FullProf_Manual.pdf, p. 34. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

Rigid group orientation

rigid_orientation · \(\theta, \phi, \chi\) · deg · refinable

The Euler angles that turn a rigid group's own frame into the crystal's: R = R_z(φ) R_y(\(\theta\)) R_z(\(\chi\)). A satellite's \(\theta\) and φ are those of its bond from its parent; its \(\chi\) is its own.

\(R(\theta,\phi,\chi) = R_z(\phi)\, R_y(\theta)\, R_z(\chi)\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 8 · FullProf_Manual.pdf, p. 34. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

Rigid group internal length

rigid_length · \(r, \rho, d, x_m, y_m, z_m\) · Å · refinable

A length among a group atom's internal coordinates: the radius of spherical coordinates, ρ and z of cylindrical ones, x, y, z of Cartesian ones, the distance to N1 of a Z-matrix.

\(\mathbf{r}^{m} = r(\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)\ \text{(spherical)},\ (\rho\cos\phi, \rho\sin\phi, z)\ \text{(cylindrical)}\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 5 · FullProf-Restraints-RigidBodies.pdf, p. 6. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

Rigid group internal angle

rigid_angle · \(\theta_m, \phi_m, \alpha, \tau\) · deg · refinable

An angle among a group atom's internal coordinates: \(\theta\) and φ of spherical ones, φ of cylindrical ones, the bond angle to N2 and the torsion to N3 of a Z-matrix (FullProf's sense, the opposite of IUPAC's; the third atom on the +y side of the xy plane).

\(\text{Z-matrix: } |\mathbf{r}_j - \mathbf{r}_{N1}| = d,\ \angle(N2, N1, j) = \alpha,\ \text{torsion}(N3, N2, N1, j) = -\tau\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 6 · FullProf-Restraints-RigidBodies.pdf, p. 11. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

TLS translation tensor

rigid_tls_t · \(T_{ij}\) · Ų · refinable

The rigid group's translational displacement (Schomaker & Trueblood 1968): T11 T22 T33 T12 T13 T23 in the crystal's Cartesian frame (x along a, z along c*); with L and S it gives every atom of the group and of its satellites an anisotropic U (L367).

\(U = T + A L A^{T} + A S + S^{T} A^{T},\ A = \begin{pmatrix} 0 & z & -y \\ -z & 0 & x \\ y & -x & 0 \end{pmatrix},\ \beta = 2\pi^2 M^{-1} U M^{-T}\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 8 · FullProf_Manual.pdf, p. 38. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

TLS libration tensor

rigid_tls_l · \(L_{ij}\) · rad\(^{2}\) · refinable

The rigid group's libration about its centre: L11 L22 L33 L12 L13 L23 in the crystal's Cartesian frame, in rad\(^{2}\) as FullProf's .pcr holds them (its .out prints deg\(^{2}\), as the results file does).

\(U = T + A L A^{T} + A S + S^{T} A^{T}\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 8 · FullProf_Manual.pdf, p. 38. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

TLS screw tensor

rigid_tls_s · \(S_{ij}\) · Å·rad · refinable

The correlation of the group's translation and libration: S11 S22 S33 S12 S13 S23, then S21 S31 S32 (S is not symmetric); its trace is not determined by the data, so one of S11, S22, S33 is tied to the others (urea's s22 = −s11). FullProf's .out prints Å·deg, as the results file does.

\(U = T + A L A^{T} + A S + S^{T} A^{T}\)

Equation as printed in: FullProf-Restraints-RigidBodies.pdf, p. 8 · FullProf_Manual.pdf, p. 38. Paper: J. Rodríguez-Carvajal, restraints and rigid bodies in FullProf (manuals/fullprof/docs/FullProf-Restraints-RigidBodies.pdf), after V. Rodríguez's STRMOD, 'General Rigid-Body-Constraints/TLS Subroutine' (FullProf's manual, pp. 32–36)

Symmetry-mode polarisation vector

mode_vector · \(\mathbf{V}_{mj}\) · fraction of the cell edge · read, not refined

The displacement of atom j in mode m, fixed by group theory (AMPLIMODES); normalised so that its squares over the distorted structure's primitive cell make 1 Ų in the reference (parent) metric, so amplitudes scale with that metric.

\(\sum_{j \in \text{primitive cell}} \mathbf{V}_{mj}^{T} G_0\, \mathbf{V}_{nj} = \delta_{mn}\ \text{Å}^2\)

Equation as printed in: nb5132.md L255. Paper: D. Orobengoa, C. Capillas, M. I. Aroyo & J. M. Perez-Mato (2009). AMPLIMODES: symmetry-mode analysis on the Bilbao Crystallographic Server. J. Appl. Cryst. 42, 820–833

Reflection intensity

reflection_intensity · \(I_h\) · counts · refinable

The integrated intensity of a reflection given directly, with no structure: extracted at each cycle by Le Bail's partition (profile matching, Jbt = 2), or refined by least squares with the cell and profile in a Pawley fit (P36), reflections that coincide for every cell the crystal system allows tied with equal |F|² (I_h in proportion to the multiplicity).

\(y_{ci} = \sum_h I_h\, \Omega(2\theta_i - 2\theta_h) + b_i\)

Equation as printed in: FullProf_Manual.pdf, p. 14 · FullProf_Manual.pdf, p. 15. Paper: G. S. Pawley (1981). Unit-cell refinement from powder diffraction scans. J. Appl. Cryst. 14, 357–361. doi:10.1107/S0021889881009618

TOF range end

tof_max · \(T_{\max}\) · µs · read, not refined

The pattern's last time of flight, the period of the Fourier background.

\(b_i = \sum_j B_j \cos\frac{j \pi T_i}{T_{\max}}\)

Equation as printed in: FullProf_Manual.pdf, p. 76. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

FullProf's Fourier background in TOF: C = T_max/π, where the manual (p. 47) writes C = T_max; arg_si_calc.prf's background met to its print, 0.03 (L341).

Peak window

peak_window · \(W_{dt}\) · FWHM · read, not refined

The half-range over which a peak is calculated, in units of its FWHM; beyond it the profile is zero.

\(\Omega(x) = 0 \quad\text{for}\quad |x| > W_{dt}\, H\)

Equation as printed in: FullProf_Manual.pdf, p. 75. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

The default calculates each peak to ±Wdt·H and tapers it to zero by \(\pm\)1.25·Wdt·H, so that \(\chi^2\) is continuous as widths and positions change (L058; FullProf cuts it at the edge: Convention::window_edge). FullProf counts the window without X tan \(\theta\) for TCH and takes one more low point when X ≠ 0 (L035, L042): Convention::peak_window. No exact translation: a .pcr keeps FullProf's window on import (L050); switching it to the default moves \(\chi^2\) by up to 6.2% on the FullProf runs (YVO3, with the tapered edge, L058).

Asymmetry limit

asymmetry_limit · \(2\theta_{\mathrm{asym}}\) · deg 2\(\theta\) · read, not refined

The angle below which the asymmetry corrections are applied.

\(A(z) \text{ and } \Omega_{\mathrm{FCJ}} \text{ for } 2\theta_h < 2\theta_{\mathrm{asym}}\)

Equation as printed in: FullProf_Manual.pdf, p. 75. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

Excluded regions

excluded_regions · \([2\theta_a, 2\theta_b]\) · deg 2\(\theta\) · read, not refined

Ranges of the pattern left out of the calculation and of the agreement factors.

\(y_{ci} = b_i \quad\text{for}\quad 2\theta_a \le 2\theta_i \le 2\theta_b\)

Equation as printed in: FullProf_Manual.pdf, p. 78. Paper: J. Rodríguez-Carvajal (2001). An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, CEA-CNRS (manuals/fullprof/FullProf_Manual.pdf)

FullProf also leaves out a point whose step reaches into a region (L033): Convention::excluded_points. On import with the data, each run of points FullProf leaves out becomes a region from its first to its last point, exactly (L050).