Parameter map

This page lists every parameter rietx can refine, grouped by what it does to the pattern.

Every parameter has a name made of parts joined by dots. phases.0.cell.a is lattice parameter a of the first phase, counting from 0, and instrument.zero_shift is the instrument’s zero shift. A * in a name matches any run of characters, dots included, so phases.*.cell.a is lattice parameter a of every phase and phases.0.* is every parameter of the first phase. The tables write names this way, and a refinement plan uses the same names to say which parameters to refine.

Each row gives the parameter’s unit, its default and a typical range to check a refined value against. A parameter with no default takes its value from the structure or instrument you load.

Cell and structure

These are the parameters a CIF holds. They set where each reflection falls and how strong it is.

Cell

The space group ties the lattice parameters together. A cubic phase refines one length, and an angle the symmetry fixes is locked.

Name	Parameter	Unit	Default	Typical
phases.*.cell.a phases.*.cell.b phases.*.cell.c	Lattice parameter a, b, c	Å		3-40 Å for an inorganic phase; refined shifts are 10-1000 ppm
phases.*.cell.alpha phases.*.cell.beta phases.*.cell.gamma	Lattice parameter α, β, γ	deg		90° or 120° when symmetry fixes it; 80-100° for a monoclinic β

Lattice parameter a, b, c

A lattice parameter that gives the length of a unit-cell axis. It sets every reflection position through the lattice metric. A powder pattern determines it better than any other parameter, and a systematic position error corrupts it first. An edge that the space-group setting ties to another (b to a in a tetragonal cell) is held and follows its source.

Lattice parameter α, β, γ

A lattice parameter that gives the angle between two cell axes. The space-group setting fixes some angles at 90° or 120°. Those angles are locked and cannot be freed. A monoclinic cell frees only its unique-axis angle.

Atoms

An atom’s coordinates x, y and z refine within its site symmetry. rietx refines the directions the site lets the atom move, the dof parameters, and x, y and z follow from them. A general position has three such directions, a special position fewer, and a fixed point none. GSAS-II applies the same restriction behind its X refine flag, and in FullProf you tie the coordinates with codewords. Anisotropic displacement parameters work the same way: the adp parameters refine, and u11 to u23 follow from them.

Name	Parameter	Unit	Default	Typical
phases.*.atoms.*.x phases.*.atoms.*.y phases.*.atoms.*.z	Fractional coordinate			0 to 1
phases.*.atoms.*.dof.*	Atom position shift			0 to 1, in the same units as the coordinate it drives
phases.*.atoms.*.occ	Site occupancy		1.0	0 to 1; above 1 when a mixed site declared as its lighter species refines site scattering
phases.*.atoms.*.biso	Isotropic displacement parameter	Ų	0.5	0.2-2 Ų for an inorganic framework at room temperature
phases.*.atoms.*.u11 phases.*.atoms.*.u22 phases.*.atoms.*.u33 phases.*.atoms.*.u12 phases.*.atoms.*.u13 phases.*.atoms.*.u23	Anisotropic displacement component	Ų		0.005-0.05 Ų on the diagonal; off-diagonal components are smaller
phases.*.atoms.*.adp.*	Anisotropic displacement parameter	Ų		0.005-0.05 Ų

Fractional coordinate

An atom’s position along a cell axis, as a fraction of the lattice parameter along that axis. You do not refine it directly. rietx ties x, y and z to the shifts that the site symmetry allows, so editing a position means editing the dof.k entries it follows. An atom on a fully fixed special position has no free direction, and its coordinates are locked.

Atom position shift

One direction in which an atom on its Wyckoff site is free to move. GSAS-II and FullProf refine x, y and z under constraints that hold an atom on its special position. rietx refines only the directions that the site symmetry leaves free, so the site symmetry holds exactly. The coordinates x, y and z are tied to these directions. Each value is a step from where the fit began. A site with no free direction produces no dof entry, and its coordinates are locked. Free these parameters with phases.*.atoms.*.dof.*. In a polar space group, Phase.floating_origin = "hold" holds, for each direction in which the origin floats, the first atom shift along it that moves the origin, and the row says so. "centroid" holds nothing and restrains a data-weighted centroid of the sites instead, so every shift keeps an esd.

Site occupancy

The fraction of the site occupied by this species. It is close to degenerate with the displacement parameter of the site, because both reduce the scattered intensity. X-rays have little power to separate the two. Refine one or the other unless the data reach high Q. Constrain occupancies that must sum to 1 with a user tie. The default lower bound is 0, and there is no default upper bound. A refined value above 1 raises OCCUPANCY_ABOVE_ONE.

Isotropic displacement parameter

The isotropic B of the atom, related to the mean-square displacement by B = 8π²·Uiso. It damps intensity as exp(−B·sin²θ/λ²), so the high-angle data determine it, and a too-flexible background biases it first. A negative B is unphysical. A refined B above about 5 Ų for a heavy atom usually points to an absorption or background error and not to a real displacement. There is no default bound. A negative B reports BISO_NEGATIVE, and one past the melting estimate of the phase reports BISO_UNUSUALLY_LARGE. A stage holds B where the fitted range cannot separate it from the scale of the phase (SCALE_B_INSEPARABLE). Give the parameter a min or max to bound it yourself.

Anisotropic displacement component

One component of the anisotropic displacement tensor U^ij, as stored in the CIF, in Ų. Like the coordinates, it is tied to other entries. The refined quantities are the adp.k entries, which span the tensors that the site symmetry allows. rietx refuses a tensor outside that set.

Anisotropic displacement parameter

One allowed component of the anisotropic displacement tensor on this Wyckoff site. Unlike an atom’s position shift, it is absolute. The tensor is the sum of the refined values times basis tensors that the site symmetry allows, so the site symmetry holds exactly. Positive-definiteness couples all six components, so it cannot be a bound. A tensor that loses it raises ADP_NOT_POSITIVE_DEFINITE, because the Debye-Waller factor then diverges at high Q. Free these parameters with phases.*.atoms.*.adp.*, alongside the biso pattern that every displacement stage carries.

Magnetic moments

A magnetic site carries a moment. It refines along the directions the magnetic symmetry allows, as a coordinate does.

Name	Parameter	Unit	Default	Typical
phases.*.atoms.*.moment.crystalaxis_*	Magnetic moment component	μB		1-5 μB for a 3d ion, up to 10 μB for a rare earth
phases.*.atoms.*.moment.dof*	Magnetic moment parameter			1-5 μB for the modulus. The angles are unbounded while a stage solves. They are reported with μ ≥ 0, the polar angle in [0, π] and the azimuth in (−π, π]

Magnetic moment component

One crystal-axis component of this site’s magnetic moment, in the magCIF _atom_site_moment.crystalaxis_* convention. The basis is right-handed, with unit vectors along the cell axes. On hexagonal axes the moment (1, 1, 0) is therefore 1 μB and not √2 μB. rietx derives these three components. The moment enters the fit as phases.*.atoms.*.moment.dof*, a modulus and the angles that the site symmetry leaves free, and the components are written back from those at the end of a stage. They carry no esd. The esd of the magnitude is on the modulus entry.

Magnetic moment parameter

dof0 is the modulus of the moment in μB. A fit measures it, and it carries the esd. Any further entries are angles in radians inside the subspace that the magnetic symmetry of the site allows. There is one angle on a two-dimensional subspace and two on a three-dimensional one. A powder average determines |m| and, on a uniaxial structure, the angle to the unique axis. It determines no more. The directions it cannot determine are held and named in StageResult.held, and they are not returned as small numbers. Where the unique axis is not the pole of the frame (rhombohedral axes, about [111]), the fit first turns the moment about that axis. That changes the reported direction. The axis and the turn are recorded in StageResult.moment_flat_axes and StageResult.moment_turned. Seeding the modulus at exactly zero is refused, because the magnetic structure factor squared is proportional to m² and the derivative is zero there.

Rigid bodies

A rigid body moves a group of atoms as one unit. Its rotation and torsions refine as increments from the stored geometry.

Name	Parameter	Unit	Default	Typical
phases.*.rigid_bodies.*.origin.x phases.*.rigid_bodies.*.origin.y phases.*.rigid_bodies.*.origin.z	Rigid-body origin			0 to 1
phases.*.rigid_bodies.*.origin.dof.*	Rigid-body origin shift			a few hundredths, in the units of the coordinate it drives
phases.*.rigid_bodies.*.rotation.*	Rigid-body rotation step			under 0.5 rad from a sensible start
phases.*.rigid_bodies.*.torsions.*.twist	Rigid-body torsion step			a few degrees to a few tens of degrees from a sensible start

Rigid-body origin

The position of a rigid body’s origin, in fractional coordinates. Like an atom’s x, y and z, it follows the refined origin shifts and is written back after each stage. Free those shifts with phases.*.rigid_bodies.*.origin.dof.*.

Rigid-body origin shift

One direction in which a rigid body’s origin is free to move, as for an atom on its site. The body translates as one, and the coordinates of every member atom follow. Each value is a step from where the fit began, as for an atom’s position shift.

Rigid-body rotation step

One component of the rotation vector, in radians, that turns a rigid body about its origin from the orientation it had at the start of the fit. The three components together give the rotation Exp(δω), applied to the stored orientation. All three are zero at the start of every fit. When the fit is written back, the rotation is composed into the body’s stored quaternion. Each component is bounded to ±π.

Rigid-body torsion step

The turn, in degrees, of a body’s declared moving atoms about the line through its two axis atoms, measured from the stored angle of the torsion. A dihedral a–axis[0]–axis[1]–d whose d end is a moved atom changes by the same amount. One whose a end is moved changes by minus that amount. The value is zero at the start of every fit. At every stage’s commit it is added into the stored angle of the torsion, wrapped into (−180, 180].

Phase amount and intensity corrections

The phase scale carries how much of the phase the pattern shows. The others correct intensities for the specimen. Surface roughness is named under instrument.geometry. It changes intensities, so it is listed here.

Name	Parameter	Unit	Default	Typical
instrument.geometry.surface_roughness.a	Suortti roughness: surviving fraction		0.5	0.5-1. The default sits inside the range because at a = 1 the derivative with respect to b vanishes, and b could never move off its start
instrument.geometry.surface_roughness.b	Suortti roughness: layer depth		0.0	0.1-0.5; past about 3 the correction is dead and its gradient flat
instrument.geometry.surface_roughness.c	Pitschke roughness: strength		0.0	0-4; beyond 4 R can go negative inside the valid range
instrument.geometry.surface_roughness.tau	Pitschke roughness: τ		0.05	0.005-0.12, the span of the paper’s own four specimens
phases.*.scale	Phase scale		1.0	positive, spanning several orders of magnitude between phases
phases.*.extinction	Primary extinction	µm²	0.0	0 for a ground powder; 0.1 to 100 (blocks of 0.3 to 10 µm) where a strong reflection loses a visible share
phases.*.preferred_orientation.r	March-Dollase coefficient		1.0	0.6-1.4; a value outside 0.5-2 describes a texture few powder mounts produce
phases.*.texture.*	Texture coefficient		0.0	|C| under 1 at l = 2 for a lightly textured mount; several for a strongly platy one

Suortti roughness: surviving fraction

The a of the Suortti (1972) surface-roughness correction, R = [a + (1 − a)·exp(−b/sinθ)] / [a + (1 − a)·exp(−b)]. It is the fraction of intensity that survives even at grazing incidence, so 1 − a bounds how deep the low-angle depression can go. Refine it only together with b. At b = 0 the correction is the identity whatever a is.

Suortti roughness: layer depth

The dimensionless optical depth of the depleted surface layer in the Suortti (1972) correction. It sets the angle at which the depression falls. The depth of the depression comes from a. The correction is the identity at b = 0 and again at large b, so two values of b can reproduce the same depression. ROUGHNESS_UNCONSTRAINED therefore measures the modelled depression and not b itself. A stage that frees b starts it at 0.3, near where the data can see it, because b = 0 is the identity.

Pitschke roughness: strength

The strength of the Pitschke et al. (1993) surface-roughness correction, R = 1 − c·u·(1 − u), with u = τ/sinθ. At c = 0 there is no correction. The paper’s angle-independent porosity term is omitted here, because a constant prefactor is degenerate with the phase scale.

Pitschke roughness: τ

The dimensionless roughness parameter τ = t₀/β of the Pitschke et al. (1993) correction. You refine τ directly, because diffraction data cannot constrain the particle size behind it. The correction is monotone only while sinθ ≥ 2τ, and it would amplify intensity beyond sinθ = τ. ROUGHNESS_OUTSIDE_REGIME reports that case, because a bound on τ cannot express a limit that depends on the fitted range.

Phase scale

The multiplier on this phase’s calculated intensity. It is the only route by which the phase reaches the pattern. Quantitative phase analysis is computed from it through the Hill-Howard ZMV relation, so it carries the weight fractions. A scale that refines onto its lower bound means the data do not see the phase. The fit still reports convergence while the cell of the phase drifts unconstrained, and PHASE_UNCONSTRAINED names that case.

Primary extinction

The Sabine primary-extinction coefficient, a squared mosaic-block size. A powder has no secondary extinction. The coefficient attenuates the strong low-angle reflections of a well-crystallised specimen. At 0 there is no correction, so a phase that does not free it is unaffected. The calculated pattern still responds to it at 0, so the staged plans free it from 0 without a seed.

March-Dollase coefficient

The March-Dollase coefficient for preferred orientation along the declared hkl axis. At r = 1 there is no correction. Whether a value above or below 1 means platy or needle-like crystallites flips between reflection and transmission geometry, so read r against the mount and not from the number alone. The March factor divides by r, so r = 0 is a pole. The default lower bound of 1e-6 keeps r off it, and there is no default upper bound.

Texture coefficient

One coefficient C_l^n of the spherical-harmonics preferred-orientation correction, named c<l>_<n> after GSAS-II’s C(l,n). With every coefficient at 0 there is no correction. The Laue class decides which coefficients exist. The texture index J = 1 + Σ C²/(2l+1) summarises their size, and J = 1 is a random powder. A Bragg-Brentano coefficient is GSAS-II’s multiplied by P_l(0), because rietx measures the sample angle from the plate normal. In -3m1 the metric makes hkl and khl coincide although they are inequivalent. A term of opposite sign on that pair is then measured only through their |F|² difference, and its esd says so.

Microstructure

These widen a phase’s peaks beyond the instrument’s own width. Gaussian variances add to the instrument’s U, V and W. Lorentzian widths add to its X and Y. The Stephens coefficients make strain broadening depend on hkl.

Name	Parameter	Unit	Default	Typical
phases.*.lor_size	Lorentzian size broadening	deg 2θ	0.0	0-0.3 deg; 0.1 deg is roughly a 100 nm domain at Cu Kα
phases.*.lor_strain	Lorentzian strain broadening	deg 2θ	0.0	0-0.3 deg
phases.*.gauss_size	Gaussian size broadening	deg² 2θ	0.0	0-0.05 deg²
phases.*.gauss_strain	Gaussian strain broadening	deg² 2θ	0.0	0-0.05 deg²
phases.*.magnetic_lor_size	Magnetic Lorentzian size broadening	deg 2θ	0.0	0-0.3 deg; 0.1 deg is roughly a 100 nm magnetic domain at 2.4 Å
phases.*.magnetic_lor_strain	Magnetic Lorentzian strain broadening	deg 2θ	0.0	0-0.3 deg
phases.*.microstrain.s*	Stephens strain coefficient	10⁻¹² Å⁻⁴	0.0	0-500 for a sample with measurable anisotropic strain
phases.*.microstrain.dof.*	Stephens strain parameter			the isotropic seed is ε²·[M²] for a strain ε of 1e-4 to 1e-3

Lorentzian size broadening

The specimen’s 1/cosθ contribution to the Lorentzian FWHM. It is Scherrer broadening from finite crystallite size, and it adds to the instrumental X. Calibrate the instrument on a standard and hold U, V, W, X and Y. Then refine this parameter with its three companions, lor_strain, gauss_size and gauss_strain. The default upper bound is derived from the fitted 2θ range, since a line cannot be wider than the interval it was measured over. No default bound limits the crystallite size itself. BOUND_HIT reports the range bound if reached. Setting max to any finite value is your own claim and switches that default off. A refined size below 5 nm raises SIZE_UNUSUALLY_SMALL. That flag marks the value and does not bound it.

Lorentzian strain broadening

The specimen’s tanθ contribution to the Lorentzian FWHM. It is isotropic microstrain broadening, and it adds to the instrumental Y. Declaring a Stephens anisotropic strain block locks this parameter, because the isotropic direction of that block equals it. The default upper bound is derived from the fitted 2θ range, since a line cannot be wider than the interval it was measured over. It sits two orders of magnitude above any specimen, and BOUND_HIT reports it if reached. Setting max to any finite value, however large, is your own claim and switches that default off. A width past 1.5 deg raises STRAIN_UNUSUALLY_LARGE. That flag marks the value and does not bound it.

Gaussian size broadening

The specimen’s 1/cos²θ contribution to the Gaussian variance. Gaussian variances add, so it stacks on the instrumental U and W and does not replace them. Most specimens are better described by the Lorentzian pair. Free this parameter when the peak shape is measurably more Gaussian than the standard’s. It has the same default range bound as lor_size, squared. This parameter is a variance, so the limit on the width it contributes applies to its square root.

Gaussian strain broadening

The specimen’s tan²θ contribution to the Gaussian variance, stacking on the instrumental U. Freeing it while U is also free fits one quantity twice, and the guard reports the correlation. It has the same default upper bound as lor_strain, squared. This parameter is a variance, so the limit on the width it contributes applies to its square root.

Magnetic Lorentzian size broadening

Extra 1/cosθ Lorentzian FWHM applied to the magnetic part of this phase’s intensity and to nothing else. The magnetic peaks can therefore be broader than the nuclear ones. It is Scherrer broadening with the magnetic coherence length in place of the crystallite size. Antiphase and domain-wall boundaries, an incompletely grown order parameter near the Néel temperature and disorder that couples to the exchange all cut the magnetic coherence below the structural one. Zero is off. Refine it after the moment, and hold the moment while it settles. Both lower the calculated peak height, so freed together from a cold start they trade against each other, and STAGE_FREES_MAGNETIC_WIDTH_WITH_MOMENT says so. Read MAGNETIC_WIDTH_MOVED_MOMENT before dropping the term. A width whose esd exceeds its value can still be correlated with the moment. If releasing it moved the moment by more than the moment’s own error bar, holding it at zero biases the moment and does not simplify the model. The width is identifiable only where the magnetic-to-nuclear intensity ratio differs across reflections. A k ≠ 0 structure with magnetic-only satellites measures it. A k = 0 collinear structure usually cannot, and the width then comes back with an esd larger than its value. MAGNETIC_WIDTH_UNMEASURED names that case. The parameter exists only on a phase that declares magnetic_symmetry. It is held fixed wherever no magnetic component is drawn, which means an X-ray histogram and Le Bail or Pawley.

Magnetic Lorentzian strain broadening

Extra tanθ Lorentzian FWHM applied to the magnetic part of this phase’s intensity alone. It is the strain partner of magnetic_lor_size, and a magnetic order parameter that varies across the specimen produces it. Zero is off. The same turn-on order applies: refine the moment first, then this term, then both. The same identifiability limits apply too. It is measurable only where some reflection is more magnetic than another. On a real k ≠ 0 dataset this term can carry the effect in place of the size term. The magnetic_width plan therefore frees both and lets the report say which was measured. The parameter exists only on a phase that declares magnetic_symmetry. It is held fixed on an X-ray histogram and under Le Bail or Pawley.

Stephens strain coefficient

One S_HKL coefficient of the Stephens (1999) anisotropic strain model. It multiplies the monomial h^H k^K l^L, taken literally. The unit is 10⁻¹² Å⁻⁴. In Å⁻⁴ the physical values sit near 10⁻⁸, and a numerical derivative would step 100 times further than the value itself. Like the anisotropic displacement components, these coefficients are tied. The refined quantities are the microstrain.dof.k entries of the Laue-allowed subspace.

Stephens strain parameter

One allowed direction of the Laue-permitted S_HKL subspace, derived from the space-group operators. These are the quantities that refine, and the fifteen s coefficients are tied to them. Seed an all-zero block onto the isotropic limit with Stage.strain_seed, because at S = 0 the square root in the width has unbounded slope. Positivity of σ²(M) couples all fifteen coefficients as a cone, so it cannot be a bound on each coefficient. The default Levenberg-Marquardt solver holds it as a linear inequality. Under solver="trf" and in a joint fit, STEPHENS_STRAIN_NOT_POSITIVE reports it instead. Read that flag as ‘these coefficients are not quotable’. It is no evidence of anisotropy.

Instrument

These describe the diffractometer and where the specimen sits in it. Calibrate them on a standard with a certified cell, then hold them for a sample.

Peak positions

Each shifts every calculated 2θ by its own angular law. Which ones apply depends on the geometry, a flat plate or a capillary.

Name	Parameter	Unit	Default	Typical
instrument.zero_shift	Zero-point shift	deg 2θ	0.0	|Δ| < 0.05 deg on an aligned diffractometer
instrument.geometry.sample_displacement	Specimen displacement	mm	0.0	|s| < 0.05 mm on a carefully packed flat plate
instrument.geometry.sample_transparency	Specimen transparency		0.0	0-0.01 for a dense oxide; larger for a low-absorbing organic
instrument.geometry.capillary_offset_along_beam	Capillary offset along the beam	mm	0.0	|d| < 0.05 mm on an aligned spinner
instrument.geometry.capillary_offset_across_beam	Capillary offset across the beam	mm	0.0	|d| < 0.05 mm on an aligned spinner

Zero-point shift

A constant offset added to every calculated 2θ. It absorbs the zero-point misalignment of the goniometer. It is a property of the diffractometer. Calibrate it on a standard with a certified cell, then hold it. Freed together with the lattice parameters and the specimen displacement, it is close to degenerate with both. Calibrating on a held cell is the step that separates the three.

Specimen displacement

How far the specimen surface sits off the goniometer axis. It is positive toward the source and detector side of the focusing circle. On a Bragg-Brentano mount it shifts every line by −2s·cosθ/R (McCusker equation 3), where s is the displacement and R the goniometer radius. This is usually the largest systematic position error in a laboratory pattern. Its cosθ shape is close to the constant shape of zero_shift, so freeing both on one pattern usually reports a correlation. It has no default bound. Where the scan cannot separate it from the zero and the cell, the fit reports FLAT_DIRECTION and the cell’s esd grows to show it. Set a bound if you know your mount.

Specimen transparency

The coefficient of the sin 2θ position shift that a beam penetrating the specimen produces (McCusker equation 4). On a flat plate this is the transparency aberration. On a capillary the same sin 2θ shape is the along-beam offset instead. The parameter therefore belongs to a flat-plate geometry, and the report suggests it only there.

Capillary offset along the beam

How far the capillary axis sits from the rotation centre along the beam direction. It shifts positions as sin 2θ, the same shape that flat-plate transparency has. The report suggests this parameter for a Debye-Scherrer geometry.

Capillary offset across the beam

How far the capillary axis sits from the rotation centre perpendicular to the beam. It shifts positions as cos 2θ. Its shape therefore separates it from the along-beam offset, unlike the flat-plate pair.

Peak shape

The Caglioti U, V and W set the Gaussian width as a function of 2θ. X and Y set the Lorentzian width. The two axial terms set the low-angle asymmetry.

Name	Parameter	Unit	Default	Typical
instrument.geometry.axial_sl	Axial divergence: specimen length		0.0	0.01-0.05
instrument.geometry.axial_hl	Axial divergence: detector slit		0.0	0.01-0.05
instrument.profile.u	Caglioti U	deg² 2θ	0.0	0-0.05 on a laboratory diffractometer
instrument.profile.v	Caglioti V	deg² 2θ	0.0	−0.05 to 0
instrument.profile.w	Caglioti W	deg² 2θ	0.001	0.001-0.02 on a laboratory diffractometer
instrument.profile.x	Lorentzian X	deg 2θ	0.001	0.001-0.05 on a laboratory diffractometer
instrument.profile.y	Lorentzian Y	deg 2θ	0.0	0-0.05 on a laboratory diffractometer

Axial divergence: specimen length

The Finger-Cox-Jephcoat axial-divergence ratio S/L. It is the illuminated specimen length divided by the goniometer radius. It sets how strongly low-angle peaks lean toward low 2θ. Fit it on a standard together with axial_hl. The two are strongly correlated and are usually reported as a pair.

Axial divergence: detector slit

The Finger-Cox-Jephcoat axial-divergence ratio H/L. It is the receiving-slit height divided by the goniometer radius. It is the second half of the axial asymmetry. It is so strongly correlated with axial_sl that refining one and holding the other is a common protocol. One ratio alone still smears the peaks. Only both at zero switch the asymmetry off.

Caglioti U

The tan²θ term of the Gaussian variance, Γ_G² = U·tan²θ + V·tanθ + W. It carries the strain-like broadening of the instrument. A phase’s gauss_strain adds to it, because variances add under convolution. Instrument and specimen therefore stack here, and neither replaces the other. Refining U while the specimen’s gauss_strain is also free fits one quantity twice.

Caglioti V

The tanθ term of the Gaussian variance Γ_G² = U·tan²θ + V·tanθ + W, which model.profiles.caglioti.gaussian_fwhm computes. It is the Caglioti term that usually goes negative. U, V and Y have no floor of their own, because what must stay positive is the width, and the default solver holds both widths at every reflection. W and X are bounded below and cannot go negative. The width curve has its minimum at tanθ = −V/(2U). No specimen term adds to V, so V belongs to the instrument. A phase’s gauss_strain adds to U instead.

Caglioti W

The constant term of the Gaussian variance. It sets the width that the pattern would have at zero angle. Its lower bound is a small positive variance (1e-8 deg²) and is not 0. Below that clamp the width stops responding to U, V and W, and the fit stalls. Freeing W together with a free gauss_size fits the same constant twice at low angle.

Lorentzian X

The 1/cosθ term of the Lorentzian FWHM, Γ_L = X/cosθ + Y·tanθ. The 1/cosθ shape is Scherrer size broadening. A phase’s lor_size adds to X, because Lorentzian FWHMs add under convolution. GSAS and FullProf swap the X and Y labels. Identify the term by its shape: 1/cosθ is size broadening.

Lorentzian Y

The tanθ term of the Lorentzian FWHM. The tanθ shape is microstrain broadening, and a phase’s lor_strain adds to it. An anisotropic strain block replaces the specimen part of this term with an hkl-dependent width and locks lor_strain. The instrumental Y stays as it was. Y can go negative while X keeps the total width at or above zero.

Source

The first emission line’s weight is locked at 1. Every other line’s weight is relative to it.

Name	Parameter	Unit	Default	Typical
instrument.polarization	Polarisation factor		0.5	0.5 unmonochromated lab; 0.51-0.63 monochromated lab (graphite 002, Ag Kα to Cr Kα); 0.9-1.0 synchrotron
instrument.source.lines.*.wavelength	Emission wavelength	Å		1.540598 Å Cu Kα1, 0.7093 Å Mo Kα1, 0.3-1.0 Å synchrotron
instrument.source.lines.*.weight	Emission line weight		1.0	0.5 for Kα2 against Kα1

Polarisation factor

The K of the Lorentz-polarisation correction. Its polarisation numerator is K + (1 − K)·cos²2θ, computed by model.corrections.lorentz_polarization. K is the fraction of the beam polarised perpendicular to the diffraction plane. The beam optics fix it, so you declare it and no plan frees it. An unpolarised laboratory source gives 0.5. A diffracted-beam monochromator gives 1/(1 + cos²2θm), where 2θm is the monochromator angle. That is 0.556 for graphite (002) at Cu Kα and 0.630 for the same crystal at Cr Kα. The APS 11-BM instrument-parameter files carry 0.99. A constant-wavelength neutron source has K = 1. The numerator is then 1, the factor is the bare Lorentz factor, and rietx force-fixes the entry.

Emission wavelength

The wavelength of one emission line. Bragg’s law fixes only the product of the wavelength and the cell scale, so the two cannot be separated. A free wavelength with a free lattice parameter is a flat direction. The row reports needs_held_cell, and set_vary refuses to free the wavelength while any cell parameter is free. Refine it against a standard with a certified cell, or leave it at the tabulated value.

Emission line weight

The intensity of one emission line relative to line 0. Line 0 is locked at 1 because it is degenerate with the phase scales. Only a second or later line has a refinable weight. For a Kα doublet the starting value is the 2j+1 degeneracy ratio. Refine it only when a monochromator or a filter has changed that ratio.

Time of flight

These apply to a time-of-flight source in place of the angular terms.

Calibration

Name	Parameter	Unit	Default	Typical
instrument.source.difc	TOF calibration DIFC	µs/Å		740 µs/Å on an 8.7° bank, 5000-13000 µs/Å at 90-150°
instrument.source.difa	TOF calibration DIFA	µs/Ų	0.0	−20 to +2 µs/Ų; 0 on a bank that never needed one
instrument.source.tzero	TOF calibration TZERO	µs	0.0	|TZERO| < 100 µs on a calibrated bank
instrument.source.difb	TOF calibration DIFB	µs·Å	0.0	0 on almost every bank

TOF calibration DIFC

The linear term of the flight-time relation, TOF = DIFC·d + DIFA·d² + TZERO + DIFB/d. It equals (m_N/h)(L1 + L2)·2 sin θ_bank, so it holds the whole flight path and the bank angle. To leading order d = TOF/DIFC. It is fixed by default because it is a calibration, refined against a standard. Freeing it beside a free lattice parameter is the time-of-flight form of the wavelength-cell degeneracy. Free one of the two and hold the other.

TOF calibration DIFA

The quadratic term of the flight-time relation. It is small and often negative, and zero is a legitimate value on a well-behaved bank. Over a limited d range it imitates a cell scale better than any other term does. Refining it beside a free lattice parameter opens a flat direction that a single bank cannot close. Calibrate it on a standard with the certified cell held.

TOF calibration TZERO

The constant offset of the flight-time relation, in microseconds. It is the emission-time origin of the moderator. It differs from instrument.zero_shift, an offset in degrees 2θ that a bank’s table does not carry. GSAS ZERO, GSAS-II Zero and Mantid TZERO all name this quantity. The field uses Mantid’s name because no one can mistake it for the angular offset.

TOF calibration DIFB

The 1/d term of the flight-time relation, GSAS-II’s difB. Neither the GSAS manual nor Mantid’s documented relation carries it, and it is zero in most projects. It exists so that a reader built to the three-term relation cannot drop a non-zero value without notice. Dropping one would move every peak with nothing said.

Peak shape

Name	Parameter	Unit	Default	Typical
instrument.source.profile_tof.alpha0	TOF rise rate α₀	µs⁻¹	0.0	0-1 µs⁻¹; often left at 0 with all of α in α₁
instrument.source.profile_tof.alpha1	TOF rise rate α₁	Å/µs	0.0	0.1-2 Å/µs
instrument.source.profile_tof.beta0	TOF decay rate β₀	µs⁻¹	0.0	0.01-0.2 µs⁻¹
instrument.source.profile_tof.beta1	TOF decay rate β₁	Å⁴/µs	0.0	0-0.05 Å⁴/µs
instrument.source.profile_tof.sig0	TOF Gaussian variance σ₀²	µs²	0.0	0-500 µs²
instrument.source.profile_tof.sig1	TOF Gaussian variance σ₁²	µs²/Ų	0.0	100-400 µs²/Ų (√σ₁² ≈ 10-20 µs/Å)
instrument.source.profile_tof.sig2	TOF Gaussian variance σ₂²	µs²/Å⁴	0.0	0-50 µs²/Å⁴
instrument.source.profile_tof.gam0	TOF Lorentzian FWHM γ₀	µs	0.0	0-20 µs; 0 on a type-1 bank
instrument.source.profile_tof.gam1	TOF Lorentzian FWHM γ₁	µs/Å	0.0	0-30 µs/Å
instrument.source.profile_tof.gam2	TOF Lorentzian FWHM γ₂	µs/Ų	0.0	0-5 µs/Ų

TOF rise rate α₀

The d-independent part of the rate of the leading exponential, α(d) = α₀ + α₁/d. It describes the rise of the back-to-back pair, which is the short-flight-time side of the peak. A larger α gives a sharper leading edge. The shape has amplitude αβ/(α+β), and its width becomes infinite as either rate goes to zero. An all-zero block is therefore a profile that nobody calibrated.

TOF rise rate α₁

The 1/d term of the rise rate, and usually the whole of it. GSAS-II spells this one alpha. It enters as α₁/d, so the leading edge sharpens toward short d. That trend is the moderator pulse seen through the flight-time map. No specimen effect is involved.

TOF decay rate β₀

The d-independent part of the rate of the trailing exponential, β(d) = β₀ + β₁/d⁴. Normally β < α, and that makes a time-of-flight peak lean toward long flight times. The asymmetry comes from the moderator, so it has no angular analogue in an axial-divergence correction.

TOF decay rate β₁

The 1/d⁴ term of the decay rate. The fourth power confines it to the short-d end of a bank. On a range that does not reach there, the data cannot see it.

TOF Gaussian variance σ₀²

The constant term of the Gaussian variance, σ²(d) = σ₀² + σ₁²·d² + σ₂²·d⁴. It is a variance and is used as written, so do not square a value read from a .iparm file again. It is the flight-time counterpart of Caglioti W. Like W, it is the width that the bank would show as its own abscissa goes to zero.

TOF Gaussian variance σ₁²

The d² term of the Gaussian variance, and normally the dominant one. Its square root, √σ₁², reads directly as µs per Å and is a constant Δd/d. The resolution of a time-of-flight bank improves (√σ₁² falls) as the bank angle goes back toward 180°.

TOF Gaussian variance σ₂²

The d⁴ term of the Gaussian variance, σ²(d) = σ₀² + σ₁²·d² + σ₂²·d⁴. It is the instrument’s share of a variance that grows as d⁴.

TOF Lorentzian FWHM γ₀

The constant term of the Lorentzian FWHM, γ(d) = γ₀ + γ₁·d + γ₂·d². It is a FWHM, unlike the σ terms beside it, which are variances. With all three γ terms at zero the profile is pure Gaussian (GSAS type 1).

TOF Lorentzian FWHM γ₁

The d term of the Lorentzian FWHM. It is GSAS-II’s X for a TOF bank. GSAS-II’s letters differ from GSAS’s. A FWHM linear in d is a constant Δd/d. Lorentzian strain-like broadening takes that shape on a bank.

TOF Lorentzian FWHM γ₂

The d² term of the Lorentzian FWHM. It is GSAS-II’s Y for a TOF bank. It carries the extra curvature of the Lorentzian width across d that γ₀ and γ₁ together do not follow.

Incident spectrum

Name	Parameter	Unit	Default	Typical
instrument.source.incident_spectrum.p*	Incident-spectrum coefficient			Whatever the instrument-parameter file states. A bank whose reduction already divided by vanadium declares ITYP 0 and has no coefficients at all

Incident-spectrum coefficient

One coefficient of the moderator spectrum that a time-of-flight bank’s data still carries. The coefficients are numbered P1, P2, … as in the GSAS manual (p. 128-129). The source’s incident_spectrum.itype, read from the ITYP record of the file, says which function they belong to. Type 1 is a sum of exponentials of the flight time in milliseconds. Type 2 replaces its second term with a Maxwellian. Types 3-5 are Chebyshev polynomials. The units differ from coefficient to coefficient. P1 is an intensity, and the odd ones inside the exponentials are reciprocal powers of milliseconds, so the family declares no unit. The coefficients are held by default. GSAS refined the file’s values against a vanadium run, and a smooth envelope in wavelength is degenerate with an isotropic displacement parameter.

Background

The background is a smooth curve plus any extra components declared beside it. A hump is drawn as part of the background curve. A declared peak gets tick marks of its own, labelled (extra).

Curve

Name	Parameter	Unit	Default	Typical
instrument.background.c*	Background coefficient		0.0	4-8 terms for a flat laboratory background; c0 is of the order of the observed background counts
instrument.background.scale	Measured-background scale		1.0	1 for an estimated baseline; within 20-40 % of 1 for a measured blank
instrument.background.air	Air-scatter term		null	absent unless the pattern diagnostics report a low-angle rise; 1e-3 as a seed where they do

Background coefficient

One coefficient of the shifted-Chebyshev background, y_bkg = Σ c_n T_n(x), with x the fitted 2θ range normalised to [−1, 1]. The model is linear in these coefficients, so their derivatives are the basis functions themselves, and you can free them from the first stage. Adding terms until Rwp stops falling is a poor test. A background flexible enough to imitate the peaks biases displacement parameters up and scales down while Rwp improves. Read FitReport.background instead.

Measured-background scale

Multiplies the fixed curve that the fixed_plus_chebyshev background holds, y_bkg = Σ c_n T_n(x) + s·f(2θ). In TOPAS terms, bkg_file("f.xy", @, s) refines s and bkg_file("f.xy") holds it at 1. The number is comparable to TOPAS’s digit for digit because it scales the curve as stored. Hold it at 1 for an estimated baseline, which has no scale to get wrong. Free it for a measured blank. A blank is never on the specimen’s scale, because the two scans differ in monitor normalisation and counting time, and the specimen attenuates the container’s own scattering. The polynomial on top cannot correct this, because it is additive and the error is multiplicative. Free the scale only against a low-order polynomial. Expect HIGH_CORRELATION against c0 and read it as an expected report.

Air-scatter term

Scales an additive 1/(2θ) term for the low-angle air-scatter rise. The P-spline background carries it beside its spline coefficients. It is absent unless declared, and auto_background declares it only when rietx.background.diagnose reports the rise. The shape is broad, so freeing it without cause gives the background one more way to imitate a peak. An absent term has no path, so no plan can free it. A fit whose residual says the term would have cut χ² reports AIR_SCATTER_UNDECLARED.

Extra components

These are named apart from the background curve, so a stage that frees the background does not free them too.

Name	Parameter	Unit	Default	Typical
instrument.extra_components.*.position	Background-peak position	deg 2θ	0.0	wherever the diffuse feature sits, for example 14.4 on NIST BT-1
instrument.extra_components.*.height	Background-peak height	counts	0.0	of the order of the hump’s rise above the smooth background
instrument.extra_components.*.fwhm	Extra-component width	deg 2θ	5.0 for a hump, 0.1 for a peak	a hump: several times the instrumental FWHM at that angle, ~6 on the BT-1 case it was measured on. A peak: the instrumental FWHM itself, since it is a reflection
instrument.extra_components.*.center	Extra-peak centre	deg 2θ		where you can see the intruding line, bounded a few tenths either side
instrument.extra_components.*.area	Extra-peak area	counts·deg 2θ	0.0	the intruding line’s integrated counts above the background
instrument.extra_components.*.eta	Extra-peak mixing		0.5	0.3-0.9 for a lab peak; leave it fixed unless the peak is strong enough to carry a fourth parameter

Background-peak position

The centre, in °2θ, of an explicit Gaussian background term, such as a diffuse or amorphous hump or a cryostat or sample-container contribution. It has no default bounds. It is not a Bragg position, so only the data constrain it. Set min and max if you know the fitted range. A declared term is inert (vary=False, height 0) until a stage frees it, and nothing in the package adds one on its own. Freeing position, height and width together amounts to a reflection with no cell behind it. HUMP_TOO_NARROW flags a fitted width near the instrumental resolution.

Background-peak height

The peak intensity of an explicit Gaussian background term, in the pattern’s count units. Its lower bound is 0, the off state. At height 0 the term is zero everywhere, so a declared peak that no stage frees gives the same result, bit for bit, as no peak.

Extra-component width

The full width at half maximum, in °2θ, of a declared extra component. The two kinds treat it differently. A hump comes from disorder, so its width is many times the instrumental resolution, and that breadth makes it a background term. A fitted width that approaches the resolution is a reflection being absorbed, and HUMP_TOO_NARROW reports it. A peak stands for a real reflection from something that is not one of your phases, so a sharp width is the point. No width guard fires for a peak. Its floor exists only because the profile divides by Γ. Each kind has a small positive floor, 0.1 for a hump and 0.005 for a peak. The floors come from the coarsest and the finest scan step that anything can be refined from.

Extra-peak centre

The apparent centre, in °2θ, of a declared sharp peak that your phases cannot explain, such as a sample holder diffracting at its own specimen distance, a mount or an unidentified impurity line. It is the position of the primary emission line. The zero-point shift, the displacement and transparency shifts and the axial asymmetry are not applied to it. A holder sits at its own distance and has its own aberrations, and this parameter absorbs all of them. For the same reason you cannot read a d-spacing from it. Unlike a hump’s position, it needs finite min and max. The evaluation window is frozen when the stage starts and is sized from those bounds. That freezing lets the centre refine without leaving its window. A declared peak is inert (vary=False, area 0) until a stage frees it. Of the presets only mccusker_structural frees it, in its extra_components stage. Nothing adds a peak that you did not declare.

Extra-peak area

The integrated intensity of a declared sharp peak, in the pattern’s count units times °2θ. It is an area because that is what a reflection intensity is. The parameter is not called scale on purpose. Every *.scale path is force-fixed under Le Bail and Pawley, and a declared peak still has to refine there. Its lower bound is 0, the off state. At area 0 the term is zero everywhere, so a declared peak that no stage frees gives the same result, bit for bit, as no peak. An area that refines to its zero bound means the data do not see the peak. The centre then reports no esd. That absence is the evidence that the peak was not needed.

Extra-peak mixing

The Lorentzian fraction of the pseudo-Voigt of a declared sharp peak. 0 is a pure Gaussian and 1 is a pure Lorentzian. Both ends are legitimate values, so the bound is [0, 1] with no floor inside it. The upper bound also sizes the frozen evaluation window. The half-width at which the discarded area of the profile stays within tolerance depends steeply on η: about 1 FWHM at η = 0 and about 16 FWHM at η = 1. If you know the peak is near-Gaussian, set the maximum of eta low and the window shrinks a great deal.

Named variables

A named variable is a parameter you declare yourself, outside the model. Model parameters follow it through ties.

Name	Parameter	Unit	Default	Typical
vars.*	Named variable			the range of the parameters it drives

Named variable

A parameter of your own, declared with Refinement.add_variable and addressed as vars.<name>. It corresponds to the prm of TOPAS. Model parameters follow it through ties, so a constraint can name a shared quantity and need not pick one parameter as the master. The diffraction model reads no variable directly. A variable reaches the pattern only through the parameters tied to it. Its unit and bounds are the ones it was declared with. Declared with the bounds of the parameter it replaces, it gives the same answer. Declared without them, it can go where that parameter could not.