\(\renewcommand\AA{\text{Å}}\)

2. GSASII Data object & variable organization

This chapter documents how data is organized within the data structures used in GSAS-II.

2.1. Summary/Contents

2.2. Parameter names in GSAS-II

Parameters in GSAS-II contain values that are used in diffraction computations. These include atom positions, but also factors that affect peak shapes or compensate for physical effects such as absoption. Many, but not all, can be optimized. The term variables is intended to refer to parameters that are being optimized in GSAS-II, but this usage is not always applied consistently within GSAS-II and in places the term variables may be applied to unvaried parameters.

Parameter in GSAS-II are uniquely named using the following pattern, p:h:<var>:n, where <var> is a variable name, as shown in the following table. Also, p is the phase number, h is the histogram number, and n is the atom parameter number If a parameter does not depend on a histogram, phase or atom, h, p and/or n will be omitted, so p::<var>:n, :h:<var> and p:h:<var> are all valid names.

Naming for GSAS-II parameter names, p:h:<var>:n

<var>

usage

\(\scriptstyle K\) (example: a)

Lattice parameter, \(\scriptstyle K\), from Ai and Djk; where \(\scriptstyle K\) is one of the characters a, b or c.

α

Lattice parameter, α, computed from both Ai and Djk.

β

Lattice parameter, β, computed from both Ai and Djk.

γ

Lattice parameter, γ, computed from both Ai and Djk.

Scale

Phase fraction (as p:h:Scale) or Histogram scale factor (as :h:Scale).

A\(\scriptstyle I\) (example: A0)

Reciprocal metric tensor component \(\scriptstyle I\); where \(\scriptstyle I\) is a digit between 0 and 5.

\(\scriptstyle L\)ol (example: vol)

Unit cell volume; where \(\scriptstyle L\) is one of the characters v or V.

dA\(\scriptstyle M\) (example: dAx)

Refined change to atomic coordinate, \(\scriptstyle M\); where \(\scriptstyle M\) is one of the characters x, y or z.

A\(\scriptstyle M\) (example: Ax)

Fractional atomic coordinate, \(\scriptstyle M\); where \(\scriptstyle M\) is one of the characters x, y or z.

AUiso

Atomic isotropic displacement parameter.

AU\(\scriptstyle N_0\)\(\scriptstyle N_1\) (example: AU11)

Atomic anisotropic displacement parameter U\(\scriptstyle N_0\)\(\scriptstyle N_1\); where \(\scriptstyle N_0\) is one of the characters 1, 2 or 3 and \(\scriptstyle N_1\) is one of the characters 1, 2 or 3.

Afrac

Atomic site fraction parameter.

Amul

Atomic site multiplicity value.

AM\(\scriptstyle M\) (example: AMx)

Atomic magnetic moment parameter, \(\scriptstyle M\); where \(\scriptstyle M\) is one of the characters x, y or z.

Akappa\(\scriptstyle O\) (example: Akappa0)

Atomic orbital softness for orbital, \(\scriptstyle O\); where \(\scriptstyle O\) is one of the characters 0, - or 6.

ANe\(\scriptstyle P\) (example: ANe0)

Atomic <j0> orbital population for orbital, \(\scriptstyle P\); where \(\scriptstyle P\) is one of the characters 0 or 1.

AD\(\scriptstyle O_0\),\(\scriptstyle O_1\)\(\scriptstyle O_0\) (example: AD0,00)

Atomic sp. harm. coeff for orbital, 1; where \(\scriptstyle O_0\) is one of the characters 0, - or 6 and \(\scriptstyle O_1\) is one of the characters 0, - or 6 and \(\scriptstyle O_0\) is one of the characters 0, - or 6.

AD\(\scriptstyle O_0\),-\(\scriptstyle O_1\)\(\scriptstyle O_0\) (example: AD0,-00)

Atomic sp. harm. coeff for orbital, 1; where \(\scriptstyle O_0\) is one of the characters 0, - or 6 and \(\scriptstyle O_1\) is one of the characters 0, - or 6 and \(\scriptstyle O_0\) is one of the characters 0, - or 6.

Back\(\scriptstyle J\) (example: Back11)

Background term #\(\scriptstyle J\); where \(\scriptstyle J\) is the background term number.

BkPkint;\(\scriptstyle J\) (example: BkPkint;11)

Background peak #\(\scriptstyle J\) intensity; where \(\scriptstyle J\) is the background peak number.

BkPkpos;\(\scriptstyle J\) (example: BkPkpos;11)

Background peak #\(\scriptstyle J\) position; where \(\scriptstyle J\) is the background peak number.

BkPksig;\(\scriptstyle J\) (example: BkPksig;11)

Background peak #\(\scriptstyle J\) Gaussian width; where \(\scriptstyle J\) is the background peak number.

BkPkgam;\(\scriptstyle J\) (example: BkPkgam;11)

Background peak #\(\scriptstyle J\) Cauchy width; where \(\scriptstyle J\) is the background peak number.

BF mult

Background file multiplier.

Bab\(\scriptstyle Q\) (example: BabA)

Babinet solvent scattering coef. \(\scriptstyle Q\); where \(\scriptstyle Q\) is one of the characters A or U.

D\(\scriptstyle N_0\)\(\scriptstyle N_1\) (example: D11)

Anisotropic strain coef. \(\scriptstyle N_0\)\(\scriptstyle N_1\); where \(\scriptstyle N_0\) is one of the characters 1, 2 or 3 and \(\scriptstyle N_1\) is one of the characters 1, 2 or 3.

Extinction

Extinction coef.

MD

March-Dollase coef.

Mustrain;\(\scriptstyle J\) (example: Mustrain;11)

Microstrain coefficient (delta Q/Q x 10**6); where \(\scriptstyle J\) can be i for isotropic or equatorial and a is axial (uniaxial broadening), a number for generalized (Stephens) broadening or mx for the Gaussian/Lorentzian mixing term (LGmix).

Size;\(\scriptstyle J\) (example: Size;11)

Crystallite size value (in microns); where \(\scriptstyle J\) can be i for isotropic or equatorial, and a is axial (uniaxial broadening), a number between 0 and 5 for ellipsoidal broadening or mx for the Gaussian/Lorentzian mixing term (LGmix).

eA

Cubic mustrain value.

Ep

Primary extinction.

Es

Secondary type II extinction.

Eg

Secondary type I extinction.

Flack

Flack parameter.

TwinFr

Twin fraction.

Layer Disp

Layer displacement along beam.

Absorption

Absorption coef.

LayerDisp

Bragg-Brentano Layer displacement.

Displace\(\scriptstyle R\) (example: DisplaceX)

Debye-Scherrer sample displacement \(\scriptstyle R\); where \(\scriptstyle R\) is one of the characters X or Y.

Lam

Wavelength.

I(L2)\/I(L1)

Ka2/Ka1 intensity ratio.

Polariz.

Polarization correction.

SH/L

FCJ peak asymmetry correction.

\(\scriptstyle S\) (example: U)

Gaussian instrument broadening \(\scriptstyle S\); where \(\scriptstyle S\) is one of the characters U, V or W.

\(\scriptstyle T\) (example: X)

Cauchy instrument broadening \(\scriptstyle T\); where \(\scriptstyle T\) is one of the characters X, Y or Z.

Zero

Debye-Scherrer zero correction.

Shift

Bragg-Brentano sample displ.

SurfRoughA

Bragg-Brenano surface roughness A.

SurfRoughB

Bragg-Brenano surface roughness B.

Transparency

Bragg-Brentano sample tranparency.

DebyeA

Debye model amplitude.

DebyeR

Debye model radius.

DebyeU

Debye model Uiso.

RBV\(\scriptstyle J\) (example: RBV11)

Vector rigid body parameter.

RBVO\(\scriptstyle U\) (example: RBVOa)

Vector rigid body orientation parameter \(\scriptstyle U\); where \(\scriptstyle U\) is one of the characters a, i, j or k.

RBVP\(\scriptstyle M\) (example: RBVPx)

Vector rigid body \(\scriptstyle M\) position parameter; where \(\scriptstyle M\) is one of the characters x, y or z.

RBVf

Vector rigid body site fraction.

RBV\(\scriptstyle V_0\)\(\scriptstyle W_0\)\(\scriptstyle W_1\) (example: RBVT11)

Residue rigid body group disp. param.; where \(\scriptstyle V_0\) is one of the characters T, L or S and \(\scriptstyle W_0\) is one of the characters 1, 2, 3, A or B and \(\scriptstyle W_1\) is one of the characters 1, 2, 3, A or B.

RBVU

Residue rigid body group Uiso param.

RBRO\(\scriptstyle U\) (example: RBROa)

Residue rigid body orientation parameter \(\scriptstyle U\); where \(\scriptstyle U\) is one of the characters a, i, j or k.

RBRP\(\scriptstyle M\) (example: RBRPx)

Residue rigid body \(\scriptstyle M\) position parameter; where \(\scriptstyle M\) is one of the characters x, y or z.

RBRTr;\(\scriptstyle J\) (example: RBRTr;11)

Residue rigid body torsion parameter.

RBRf

Residue rigid body site fraction.

RBR\(\scriptstyle V_0\)\(\scriptstyle W_0\)\(\scriptstyle W_1\) (example: RBRT11)

Residue rigid body group disp. param.; where \(\scriptstyle V_0\) is one of the characters T, L or S and \(\scriptstyle W_0\) is one of the characters 1, 2, 3, A or B and \(\scriptstyle W_1\) is one of the characters 1, 2, 3, A or B.

RBRU

Residue rigid body group Uiso param.

RBSAtNo

Atom number for spinning rigid body.

RBSO\(\scriptstyle U\) (example: RBSOa)

Spinning rigid body orientation parameter \(\scriptstyle U\); where \(\scriptstyle U\) is one of the characters a, i, j or k.

RBSP\(\scriptstyle M\) (example: RBSPx)

Spinning rigid body \(\scriptstyle M\) position parameter; where \(\scriptstyle M\) is one of the characters x, y or z.

RBSShRadius

Spinning rigid body shell radius.

RBSShC\(\scriptstyle X\) (example: RBSShC1)

Spinning rigid body sph. harmonics term; where \(\scriptstyle X\) is one of the characters 1, -, 2 or 0 ,, 1, -, 2 or 0.

constr\(\scriptstyle G\) (example: constr10)

Generated degree of freedom from constraint; where \(\scriptstyle G\) is one or more digits (0, 1,… 9).

nv-(.+)

New variable assignment with name 1.

mV\(\scriptstyle H\) (example: mV0)

Modulation vector component \(\scriptstyle H\); where \(\scriptstyle H\) is the digits 0, 1, or 2.

Fsin

Sin site fraction modulation.

Fcos

Cos site fraction modulation.

Fzero

Crenel function offset.

Fwid

Crenel function width.

Tmin

ZigZag/Block min location.

Tmax

ZigZag/Block max location.

\(\scriptstyle T\)max (example: Xmax)

ZigZag/Block max value for \(\scriptstyle T\); where \(\scriptstyle T\) is one of the characters X, Y or Z.

\(\scriptstyle T\)sin (example: Xsin)

Sin position wave for \(\scriptstyle T\); where \(\scriptstyle T\) is one of the characters X, Y or Z.

\(\scriptstyle T\)cos (example: Xcos)

Cos position wave for \(\scriptstyle T\); where \(\scriptstyle T\) is one of the characters X, Y or Z.

U\(\scriptstyle N_0\)\(\scriptstyle N_1\)sin (example: U11sin)

Sin thermal wave for U\(\scriptstyle N_0\)\(\scriptstyle N_1\); where \(\scriptstyle N_0\) is one of the characters 1, 2 or 3 and \(\scriptstyle N_1\) is one of the characters 1, 2 or 3.

U\(\scriptstyle N_0\)\(\scriptstyle N_1\)cos (example: U11cos)

Cos thermal wave for U\(\scriptstyle N_0\)\(\scriptstyle N_1\); where \(\scriptstyle N_0\) is one of the characters 1, 2 or 3 and \(\scriptstyle N_1\) is one of the characters 1, 2 or 3.

M\(\scriptstyle T\)sin (example: MXsin)

Sin mag. moment wave for \(\scriptstyle T\); where \(\scriptstyle T\) is one of the characters X, Y or Z.

M\(\scriptstyle T\)cos (example: MXcos)

Cos mag. moment wave for \(\scriptstyle T\); where \(\scriptstyle T\) is one of the characters X, Y or Z.

PDFpos

PDF peak position.

PDFmag

PDF peak magnitude.

PDFsig

PDF peak std. dev.

Aspect ratio

Particle aspect ratio.

Length

Cylinder length.

Diameter

Cylinder/disk diameter.

Thickness

Disk thickness.

Shell thickness

Multiplier to get inner(<1) or outer(>1) sphere radius.

Dist

Interparticle distance.

VolFr

Dense scatterer volume fraction.

epis

Sticky sphere epsilon.

Sticky

Stickyness.

Depth

Well depth.

Width

Well width.

Volume

Particle volume.

Radius

Sphere/cylinder/disk radius.

Mean

Particle mean radius.

StdDev

Standard deviation in Mean.

G

Guinier prefactor.

Rg

Guinier radius of gyration.

B

Porod prefactor.

P

Porod power.

Cutoff

Porod cutoff.

PkInt

Bragg peak intensity.

PkPos

Bragg peak position.

PkSig

Bragg peak sigma.

PkGam

Bragg peak gamma.

e\(\scriptstyle Y_0\)\(\scriptstyle Y_1\) (example: e11)

strain tensor e\(\scriptstyle Y_0\)\(\scriptstyle Y_1\); where \(\scriptstyle Y_0\) is one of the characters 1 or 2 and \(\scriptstyle Y_1\) is one of the characters 1 or 2.

Dcalc

Calc. d-spacing.

Back

background parameter.

pos

peak position.

int

peak intensity.

WgtFrac

phase weight fraction.

alpha

TOF profile term.

alpha-\(\scriptstyle P\) (example: alpha-0)

Pink profile term; where \(\scriptstyle P\) is one of the characters 0 or 1.

beta-\(\scriptstyle Z\) (example: beta-0)

TOF/Pink profile term; where \(\scriptstyle Z\) is one of the characters 0, 1 or q.

sig-\(\scriptstyle a\) (example: sig-0)

TOF profile term; where \(\scriptstyle a\) is one of the characters 0, 1, 2 or q.

dif\(\scriptstyle b\) (example: difA)

TOF to d-space calibration; where \(\scriptstyle b\) is one of the characters A, B or C.

C\(\scriptstyle G_0\),\(\scriptstyle G_1\) (example: C10,10)

spherical harmonics preferred orientation coef.; where \(\scriptstyle G_0\) is one or more digits (0, 1,… 9) and \(\scriptstyle G_1\) is one or more digits (0, 1,… 9).

Pressure

Pressure level for measurement in MPa.

Temperature

T value for measurement, K.

FreePrm\(\scriptstyle N\) (example: FreePrm1)

User defined measurement parameter \(\scriptstyle N\); where \(\scriptstyle N\) is one of the characters 1, 2 or 3.

Gonio. radius

Distance from sample to detector, mm.

2.3. GSAS-II Data Tree

A GSAS-II project is stored in a data file and is loaded into a wxPython data tree (wx.TreeCtrl) defined by GSASIIctrlGUI.G2TreeCtrl. Each entry in the tree has a text label and a data object associated with it. Note that all information used in a GSAS-II project is stored in the data tree, with the exception of images (which are too large). For images, a reference to the file location is saved and images are loaded from the file when needed.

To save a GSAS-II project, routine GSASIImiscGUI.ProjFileSave() is used to convert the tree contents to a “flat” format and write it to a file. The tree is transversed, and for each first-level tree item, a list is created, where the first item in that list is a two-element list containing the label of the tree item and the data object associated with the label. If there are second-level tree items that are children of that first-level tree item, additional items are added to the outermost list with pairs of text labels and data objects. Finally the outermost list is converted to a binary representation and written to disk with the Python pickle function. Note that GSAS-II does not use any data tree items other than first-level and second-level. Routine GSASIImiscGUI.ProjFileOpen() is used to read a GSAS-II project file and populate the data tree. GSAS-II project files are written with the .gpx extension.

Two pointers are kept for a selected tree entry in the GSAS-II data tree, saved as class variables in GSASIIdataGUI.GSASII (often referenced as G2frame). These are G2frame.PickId, which points to the selected data tree item, and G2frame.PatternId, which points to the parent of the data tree item, when G2frame.PickId points to a histogram. The two pointer may be the same when the first-level tree item for a histogram is selected.

2.3.1. Constraints Tree Item

Constraints are stored in a dict, separated into groups. Note that parameter are named in the following pattern, p:h:<var>:n, where p is the phase number, h is the histogram number <var> is a variable name and n is the parameter number. If a parameter does not depend on a histogram or phase or is unnumbered, that number is omitted. Note that the contents of each dict item is a List where each element in the list is a constraint definition objects. The constraints in this form are converted in GSASIImapvars.ProcessConstraints() to the form used in GSASIImapvars

The keys in the Constraints dict are:

key

explanation

Hist

This specifies a list of constraints on histogram-related parameters, which will be of form :h:<var>:n.

HAP

This specifies a list of constraints on parameters that are defined for every histogram in each phase and are of form p:h:<var>:n.

Phase

This specifies a list of constraints on phase parameters, which will be of form p::<var>:n.

Global

This specifies a list of constraints on parameters that are not tied to a histogram or phase and are of form ::<var>:n

Each constraint is defined as an item in a list. Each constraint is of form:

[[<mult1>, <var1>], [<mult2>, <var2>],..., <fixedval>, <varyflag>, <constype>]

Where the variable pair list item containing two values [<mult>, <var>], where:

  • <mult> is a multiplier for the constraint (float)

  • <var> a G2VarObj object. (Note that in very old .gpx files this might be a str with a variable name of form ‘p:h:name[:at]’)

Note that the last three items in the list play a special role:

  • <fixedval> is the fixed value for a constant equation (constype=c) constraint or is None. For a New variable (constype=f) constraint, a variable name can be specified as a str (used for externally generated constraints)

  • <varyflag> is True or False for New variable (constype=f) constraints or is None. This indicates if this variable should be refined.

  • <constype> is one of four letters, ‘e’, ‘c’, ‘h’, ‘f’ that determines the type of constraint:

    • ‘e’ defines a set of equivalent variables. Only the first variable is refined (if the appropriate refine flag is set) and and all other equivalent variables in the list are generated from that variable, using the appropriate multipliers.

    • ‘c’ defines a constraint equation of form, \(m_1 \times var_1 + m_2 \times var_2 + ... = c\)

    • ‘h’ defines a variable to hold (not vary). Any variable on this list is not varied, even if its refinement flag is set. Only one [mult,var] pair is allowed in a hold constraint and the mult value is ignored. This is of particular value when needing to hold one or more variables where a single flag controls a set of variables such as, coordinates, the reciprocal metric tensor or anisotropic displacement parameter.

    • ‘f’ defines a new variable (function) according to relationship \(newvar = m_1 \times var_1 + m_2 \times var_2 + ...\)

2.3.2. Covariance Tree Item

The Covariance tree item has results from the last least-squares run. They are stored in a dict with these keys:

key

sub-key

explanation

newCellDict

(dict) lattice parameters computed by GSASIIstrMath.GetNewCellParms()

title

(str) Name of gpx file

variables

(list) Values for refined variables (list of float values, length N, ordered to match varyList)

sig

(list) Standard uncertainty values for refined variables (list of float values, length N, ordered to match varyList)

varyList

(list of str values, length N) List of directly refined variables

varyListStart

(list) initial refined variables before dependent vars are removed

newAtomDict

(dict) atom position values computed in GSASIIstrMath.ApplyXYZshifts()

Lastshft

(list) The shifts applied to each variable in the last refinement run. (list of float values, length N, ordered to match varyList)

depSigDict

(dict) Values along with standard uncertainty values for dependent variables

covMatrix

(np.array) The (NxN) covVariance matrix

freshCOV

(bool) indicates if the covMatrix has been freshly computed

msg

Warning/error messages from the last refinement run

Rvals

(dict) R-factors, GOF, Marquardt value for last refinement cycle

Nobs

(int) Number of observed data points

Nvars

(int) Number of refined parameters

Rwp

(float) overall weighted profile R-factor (%)

chisq

(float) \(\sum w*(I_{obs}-I_{calc})^2\) for all data. Note: this is what GSAS-II calls \(\chi^2\), which is not the same thing as the reduced \(\chi^2\).

lamMax

(float) Marquardt value applied to Hessian diagonal

GOF

(float) The goodness-of-fit, aka square root of the reduced \(\chi^2\) squared, after refinement.

GOF0

(float) The goodness-of-fit, aka square root of the reduced \(\chi^2\) square, before refinement.

lastShifts

(dict) values of the shifts applied in the last refinement cycle (note: differs from Lastshft, which has values from the last run).

SVD0

(int) number of singular value decomposition (SVD) singularities

converged

(bool) True if last refinement run converged

DelChi2

(float) change in \(\chi^2\) in last refinement cycle

RestraintSum

(float) sum of restraints

RestraintTerms

(float) total number of restraints

Max shft/sig

(float) maximum shift/s.u. for shifts applied in last refinement run

2.3.3. Phase Tree Items

Phase information is stored in the GSAS-II data tree as children of the Phases item in a dict with keys:

key

sub-key

explanation

General

(dict) Overall information for the phase

3Dproj

(list of str) projections for 3D pole distribution plots

AngleRadii

(list of floats) Default radius for each atom used to compute interatomic angles

AtomMass

(list of floats) Masses for atoms

AtomPtrs

(list of int) four locations (cx,ct,cs & cu) to use to pull info from the atom records

AtomTypes

(llist of str) Atom types

BondRadii

(list of floats) Default radius for each atom used to compute interatomic distances

Cell

Unit cell parameters & ref. flag (list with 8 items. All but first item are float.)

0: cell refinement flag (True/False),

1-3: a, b, c, (\(\AA\))

4-6: alpha, beta & gamma, (degrees)

7: volume (\(\AA^3\))

Color

(list of (r,b,g) triplets) Colors for atoms

Compare

(dict) Polygon comparison parameters

Data plot type

(str) data plot type (‘Mustrain’, ‘Size’ or ‘Preferred orientation’) for powder data

DisAglCtls

(dDict) with distance/angle search controls, which has keys ‘Name’, ‘AtomTypes’, ‘BondRadii’, ‘AngleRadii’ which are as above except are possibly edited. Also contains ‘Factors’, which is a 2 element list with a multiplier for bond and angle search range [typically (0.85,0.85)].

F000X

(float) x-ray F(000) intensity

F000N

(float) neutron F(000) intensity

Flip

(dict) Charge flip controls

HydIds

(dict) geometrically generated hydrogen atoms

Isotope

(dict) Isotopes for each atom type

Isotopes

(dict) Scattering lengths for each isotope combination for each element in phase

MCSA controls

(dict) Monte Carlo-Simulated Annealing controls

Map

(dict) Map parameters

Mass

(float) Mass of unit cell contents in g/mol

Modulated

(bool) True if phase modulated

Mydir

(str) Directory of current .gpx file

Name

(str) Phase name

NoAtoms

(dict) Number of atoms per unit cell of each type

POhkl

(list) March-Dollase preferred orientation direction

Pawley dmin

(float) maximum Q (as d-space) to use for Pawley extraction

Pawley dmax

(float) minimum Q (as d-space) to use for Pawley extraction

Pawley neg wt

(float) Restraint value for negative Pawley intensities

SGData

(object) Space group details as a space group (SGData) object, as defined in GSASIIspc.SpcGroup().

SH Texture

(dict) Spherical harmonic preferred orientation parameters

Super

(int) dimension of super group (0,1 only)

Type

(str) phase type (e.g. ‘nuclear’)

Z

(dict) Atomic numbers for each atom type

doDysnomia

(bool) flag for max ent map modification via Dysnomia

doPawley

(bool) Flag for Pawley intensity extraction

vdWRadii

(dict) Van der Waals radii for each atom type

ranId

(int) unique random number Id for phase

pId

(int) Phase Id number for current project.

Atoms

(list of lists) Atoms in phase as a list of lists. The outer list is for each atom, the inner list contains varying items depending on the type of phase, see the Atom Records description.

Drawing

(dict) Display parameters

Atoms

(list of lists) with an entry for each atom that is drawn

Plane

(list) Controls for contour density plane display

Quaternion

(4 element np.array) Viewing quaternion

Zclip

(float) clipping distance in \(\AA\)

Zstep

(float) Step to de/increase Z-clip

atomPtrs

(list) positions of x, type, site sym, ADP flag in Draw Atoms

backColor

(list) background for plot as and R,G,B triplet (default = [0, 0, 0], black).

ballScale

(float) Radius of spheres in ball-and-stick display

bondList

(dict) Bonds

bondRadius

(float) Radius of binds in \(\AA\)

cameraPos

(float) Viewing position in \(\AA\) for plot

contourLevel

(float) map contour level in \(e/\AA^3\)

contourMax

(float) map contour maximum

depthFog

(bool) True if use depthFog on plot - set currently as False

ellipseProb

(float) Probability limit for display of thermal ellipsoids in % .

magMult

(float) multiplier for magnetic moment arrows

mapSize

(float) x & y dimensions of contourmap (fixed internally)

modelView

(4,4 array) from openGL drawing transofmation matrix

oldxy

(list with two floats) previous view point

radiusFactor

(float) Distance ratio for searching for bonds. Bonds are located that are within r(Ra+Rb) and (Ra+Rb)/r where Ra and Rb are the atomic radii.

selectedAtoms

(list of int values) List of selected atoms

showABC

(bool) Flag to show view point triplet. True=show.

showHydrogen

(bool) Flag to control plotting of H atoms.

showRigidBodies

(bool) Flag to highlight rigid body placement

showSlice

(bool) flag to show contour map

sizeH

(float) Size ratio for H atoms

unitCellBox

(bool) Flag to control display of the unit cell.

vdwScale

(float) Multiplier of van der Waals radius for display of vdW spheres.

viewDir

(np.array with three floats) cartesian viewing direction

viewPoint

(list of lists) First item in list is [x,y,z] in fractional coordinates for the center of the plot. Second item list of previous & current atom number viewed (may be [0,0])

ISODISTORT

(dict) contains controls for running ISODISTORT and results from it

ISOmethod

(int) ISODISTORT method (currently 1 or 4; 2 & 3 not implemented in GSAS-II)

ParentCIF

(str) parent cif file name for ISODISTORT method 4

ChildCIF

(str) child cif file name for ISODISTORT method 4

SGselect

(dict) selection list for lattice types in radio result from ISODISTORT method 1

selection

(int) chosen selection from radio

radio

(list) results from ISODISTORT method 1

ChildMatrix

(3x3 array) transformation matrix for method 3 (not currently used)

ChildSprGp

(str) child space group for method 3 (not currently used)

ChildCell

(str) cell ordering for nonstandard orthorhombic ChildSprGrp in method 3 (not currently used)

G2ModeList

(list) ISODISTORT mode names

modeDispl

(list) distortion mode values; refinable parameters

ISOmodeDispl

(list) distortion mode values as determined in method 4 by ISODISTORT

NormList

(list) ISODISTORT normalization values; to convert mode value to fractional coordinate dsplacement

G2parentCoords

(list) full set of parent structure coordinates transformed to child structure; starting basis for mode displacements

G2VarList

(list)

IsoVarList

(list)

G2coordOffset

(list) only adjustible set of parent structure coordinates

G2OccVarList

(list)

Var2ModeMatrix

(array) atom variable to distortion mode transformation

Mode2VarMatrix

(array) distortion mode to atom variable transformation

rundata

(dict) saved input information for use by ISODISTORT method 1

RBModels

Rigid body assignments (note Rigid body definitions are stored in their own main top-level tree entry.)

RMC

(dict) RMCProfile, PDFfit & fullrmc controls

Pawley ref

(list) Pawley reflections

Histograms

(dict of dicts) The key for the outer dict is the histograms tied to this phase. The inner dict contains the combined phase/histogram parameters for items such as scale factors, size and strain parameters. The following are the keys to the inner dict. (dict)

Babinet

(dict) For protein crystallography. Dictionary with two entries, ‘BabA’, ‘BabU’

Extinction

(list of float, bool) Extinction parameter

Flack

(list of [float, bool]) Flack parameter & refine flag

HStrain

(list of two lists) Hydrostatic strain. The first is a list of the HStrain parameters (1, 2, 3, 4, or 6 depending on unit cell), the second is a list of boolean refinement parameters (same length)

Histogram

(str) The name of the associated histogram

Layer Disp

(list of [float, bool]) Layer displacement in beam direction & refine flag

LeBail

(bool) Flag for LeBail extraction

Mustrain

(list) Microstrain parameters, in order:

  1. Type, one of u’isotropic’, u’uniaxial’, u’generalized’

  2. Isotropic/uniaxial parameters - list of 3 floats

  3. Refinement flags - list of 3 bools

  4. Microstrain axis - list of 3 ints, [h, k, l]

  5. Generalized mustrain parameters - list of 2-6 floats, depending on space group

  6. Generalized refinement flags - list of bools, corresponding to the parameters of (4)

Pref.Ori.

(list) Preferred Orientation. List of eight parameters. Items marked SH are only used for Spherical Harmonics.

  1. (str) Type, ‘MD’ for March-Dollase or ‘SH’ for Spherical Harmonics

  2. (float) Value

  3. (bool) Refinement flag

  4. (list) Preferred direction, list of ints, [h, k, l]

  5. (int) SH - number of terms

  6. (dict) SH -

  7. (list) SH

  8. (float) SH

Scale

(list of [float, bool]) Phase fraction & refine flag

Size

List of crystallite size parameters, in order:

  1. (str) Type, one of u’isotropic’, u’uniaxial’, u’ellipsoidal’

  2. (list) Isotropic/uniaxial parameters - list of 3 floats

  3. (list) Refinement flags - list of 3 bools

  4. (list) Size axis - list of 3 ints, [h, k, l]

  5. (list) Ellipsoidal size parameters - list of 6 floats

  6. (list) Ellipsoidal refinement flags - list of bools, corresponding to the parameters of (4)

Use

(bool) True if this histogram is to be used in refinement

MCSA

(dict) Monte-Carlo simulated annealing parameters

2.3.4. Rigid Body Objects

Rigid body descriptions are available for two types of rigid bodies: ‘Vector’ and ‘Residue’. Vector rigid bodies are developed by a sequence of translations each with a refinable magnitude and Residue rigid bodies are described as Cartesian coordinates with defined refinable torsion angles.

key

sub-key

explanation

Vector

RBId

(dict of dict) vector rigid bodies

AtInfo

(dict) Drad, Color: atom drawing radius & color for each atom type

RBname

(str) Name assigned by user to rigid body

VectMag

(list) vector magnitudes in \(\AA\)

rbXYZ

(list of 3 float Cartesian coordinates for Vector rigid body )

rbRef

(list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin definition, use center of atoms flag

VectRef

(list of bool refinement flags for VectMag values )

rbTypes

(list of str) Atom types for each atom in rigid body

rbVect

(list of lists) Cartesian vectors for each translation used to build rigid body

useCount

(int) Number of times rigid body is used in any structure

Residue

RBId

(dict of dict) residue rigid bodies

AtInfo

(dict) Drad, Color: atom drawing radius & color for each atom type

RBname

(str) Name assigned by user to rigid body

rbXYZ

(list of 3 float) Cartesian coordinates for Residue rigid body

rbTypes

(list of str) Atom types for each atom in rigid body

atNames

(list of str) Names of each atom in rigid body (e.g. C1,N2…)

rbRef

(list of 3 int & 1 bool) 3 assigned reference atom nos. in rigid body for origin definition, use center of atoms flag

rbSeq

(list) Orig,Piv,angle,Riding : definition of internal rigid body torsion; origin atom (int), pivot atom (int), torsion angle (float), riding atoms (list of int)

SelSeq

(int,int) used by SeqSizer to identify objects

useCount

(int)Number of times rigid body is used in any structure

RBIds

(dict) unique Ids generated upon creation of each rigid body

Vector

(list) Ids for each Vector rigid body

Residue

(list) Ids for each Residue rigid body

2.3.5. Space Group Objects

Space groups are interpreted by GSASIIspc.SpcGroup() and the information is placed in a SGdata object which is a dict with these keys. Magnetic ones are marked “mag”

key

explanation

BNSlattsym

mag - (str) BNS magnetic space group symbol and centering vector

GenFlg

mag - (list) symmetry generators indices

GenSym

mag - (list) names for each generator

MagMom

mag - (list) “time reversals” for each magnetic operator

MagPtGp

mag - (str) Magnetic point group symbol

MagSpGrp

mag - (str) Magnetic space group symbol

OprNames

mag - (list) names for each space group operation

SGCen

(np.array) Symmetry cell centering vectors. A (n,3) np.array of centers. Will always have at least one row: np.array([[0, 0, 0]])

SGFixed

(bool) Only True if phase mported from a magnetic cif file then the space group can not be changed by the user because operator set from cif may be nonstandard

SGGen

(list) generators

SGGray

(bool) True if space group is a gray group (incommensurate magnetic structures)

SGInv

(bool) True if centrosymmetric, False if not

SGLatt

(str)Lattice centering type. Will be one of P, A, B, C, I, F, R

SGLaue

(str) one of the following 14 Laue classes: -1, 2/m, mmm, 4/m, 4/mmm, 3R, 3mR, 3, 3m1, 31m, 6/m, 6/mmm, m3, m3m

SGOps

(list) symmetry operations as a list of form [[M1,T1], [M2,T2],...] where \(M_n\) is a 3x3 np.array and \(T_n\) is a length 3 np.array. Atom coordinates are transformed where the Asymmetric unit coordinates [X is (x,y,z)] are transformed using \(X^\prime = M_n*X+T_n\)

SGPolax

(str) Axes for space group polarity. Will be one of ‘’, ‘x’, ‘y’, ‘x y’, ‘z’, ‘x z’, ‘y z’, ‘xyz’. In the case where axes are arbitrary ‘111’ is used (P 1, and ?).

SGPtGrp

(str) Point group of the space group

SGUniq

unique axis if monoclinic. Will be a, b, or c for monoclinic space groups. Will be blank for non-monoclinic.

SGSpin

mag - (list) of spin flip operatiors (+1 or -1) for the space group operations

SGSys

(str) symmetry unit cell: type one of ‘triclinic’, ‘monoclinic’, ‘orthorhombic’, ‘tetragonal’, ‘rhombohedral’, ‘trigonal’, ‘hexagonal’, ‘cubic’

SSGK1

(list) Superspace multipliers

SpGrp

(str) space group symbol

SpnFlp

mag - (list) Magnetic spin flips for every magnetic space group operator

Superspace groups [3+1] are interpreted by GSASIIspc.SSpcGroup() and the information is placed in a SSGdata object which is a dict with these keys:

key

explanation

SSGCen

(list) 4D cell centering vectors [0,0,0,0] at least

SSGK1

(list) Superspace multipliers

SSGOps

(list) 4D symmetry operations as [M,T] so that M*x+T = x’

SSpGrp

(str) superspace group symbol extension to space group symbol, accidental spaces removed

modQ

(list) modulation/propagation vector

modSymb

(list of str) Modulation symbols

2.3.6. Phase Information

Phase information is placed in one of the following keys:

key

explanation

General

Overall information about a phase

Histograms

Information about each histogram linked to the current phase as well as parameters that are defined for each histogram and phase (such as sample peak widths and preferred orientation parameters.

Atoms

Contains a list of atoms, as described in the Atom Records description.

Drawing

Parameters that determine how the phase is displayed, including a list of atoms to be included, as described in the Drawing Atom Records description

MCSA

Monte-Carlo simulated annealing parameters

pId

The index of each phase in the project, numbered starting at 0

ranId

An int value with a unique value for each phase

RBModels

A list of dicts with parameters for each rigid body inserted into the current phase, as defined in the Rigid Body Insertions. Note that the rigid bodies are defined as Rigid Body Objects

RMC

PDF modeling parameters

Pawley ref

Pawley refinement parameters

2.3.6.1. Atom Records

If phasedict points to the phase information in the data tree, then atoms are contained in a list of atom records (list) in phasedict['Atoms']. Also needed to read atom information are four pointers, cx,ct,cs,cia = phasedict['General']['AtomPtrs'], which define locations in the atom record, as shown below. Items shown are always present; additional ones for macromolecular phases are marked ‘mm’, and those for magnetic structures are marked ‘mg’

location

explanation

ct-4

mm - (str) residue number

ct-3

mm - (str) residue name (e.g. ALA)

ct-2

mm - (str) chain label

ct-1

(str) atom label

ct

(str) atom type

ct+1

(str) refinement flags; combination of ‘F’, ‘X’, ‘U’, ‘M’

cx,cx+1,cx+2

(3 floats) the x,y and z coordinates

cx+3

(float) site occupancy

cx+4,cx+5,cx+6

mg - (list) atom magnetic moment along a,b,c in Bohr magnetons

cs

(str) site symmetry

cs+1

(int) site multiplicity

cia

(str) ADP flag: Isotropic (‘I’) or Anisotropic (‘A’)

cia+1

(float) Uiso

cia+2…cia+7

(6 floats) U11, U22, U33, U12, U13, U23

atom[cia+8]

(int) unique atom identifier

2.3.6.2. Drawing Atom Records

If phasedict points to the phase information in the data tree, then drawing atoms are contained in a list of drawing atom records (list) in phasedict['Drawing']['Atoms']. Also needed to read atom information are four pointers, cx,ct,cs,ci = phasedict['Drawing']['AtomPtrs'], which define locations in the atom record, as shown below. Items shown are always present; additional ones for macromolecular phases are marked ‘mm’, and those for magnetic structures are marked ‘mg’

location

explanation

ct-4

mm - (str) residue number

ct-3

mm - (str) residue name (e.g. ALA)

ct-2

mm - (str) chain label

ct-1

(str) atom label

ct

(str) atom type

cx,cx+1,cx+2

(3 floats) the x,y and z coordinates

cx+3,cx+4,cx+5

mg - (3 floats) atom magnetic moment along a,b,c in Bohr magnetons

cs-1

(str) Sym Op symbol; sym. op number + unit cell id (e.g. ‘1,0,-1’)

cs

(str) atom drawing style; e.g. ‘balls & sticks’

cs+1

(str) atom label style (e.g. ‘name’)

cs+2

(int) atom color (RBG triplet)

cs+3

(str) ADP flag: Isotropic (‘I’) or Anisotropic (‘A’)

cs+4

(float) Uiso

cs+5…cs+11

(6 floats) U11, U22, U33, U12, U13, U23

ci

(int) unique atom identifier; matches source atom Id in Atom Records

2.3.6.3. Rigid Body Insertions

If phasedict points to the phase information in the data tree, then rigid body information is contained in list(s) in phasedict['RBModels']['Residue'] and/or phasedict['RBModels']['Vector'] for each rigid body inserted into the current phase.

key

explanation

fixOrig

Should the origin be fixed (when editing, not the refinement flag)

Ids

Ids for assignment of atoms in the rigid body

numChain

Chain number for macromolecular fits

Orient

Orientation of the RB as a quaternion and a refinement flag (’ ‘, ‘A’ or ‘AV’)

OrientVec

Orientation of the RB expressed as a vector and azimuthal rotation angle

Orig

Origin of the RB in fractional coordinates and refinement flag (bool)

RBId

References the unique ID of a rigid body in the Rigid Body Objects

RBname

The name for the rigid body (str)

AtomFrac

The atom fractions for the rigid body

ThermalMotion

The thermal motion description for the rigid body, which includes a choice for the model and can include TLS parameters or an overall Uiso value.

Torsions

Defines the torsion angle and refinement flag for each torsion defined in the Rigid Body Object

2.3.7. Powder Diffraction Tree Items

Every powder diffraction histogram is stored in the GSAS-II data tree with a top-level entry named beginning with the string “PWDR “. The diffraction data for that information are directly associated with that tree item and there are a series of children to that item. The routines GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree() and GSASIIstrIO.GetUsedHistogramsAndPhases() will load this information into a dictionary where the child tree name is used as a key, and the information in the main entry is assigned a key of Data, as outlined below.

key

sub-key

explanation

Comments

(list of str) Text strings extracted from the original powder data header. These cannot be changed by the user; it may be empty.

Limits

(list) two two element lists, as [[Ld,Hd],[L,H]] where L and Ld are the current and default lowest two-theta value to be used and where H and Hd are the current and default highest two-theta value to be used.

Reflection Lists

(dict of dicts) with an entry for each phase in the histogram. The contents of each dict item is a dict containing reflections, as described in the Powder Reflections description.

Instrument Parameters

(dict) The instrument parameters uses different dicts for the constant wavelength (CW) and time-of-flight (TOF) cases. See below for the descriptions of each.

wtFactor

(float) A weighting factor to increase or decrease the leverage of data in the histogram . A value of 1.0 weights the data with their standard uncertainties and a larger value increases the weighting of the data (equivalent to decreasing the uncertainties).

Sample Parameters

(dict) Parameters that describe how the data were collected, as listed below. Refinable parameters are a list containing a float and a bool, where the second value specifies if the value is refined, otherwise the value is a float unless otherwise noted.

Scale

The histogram scale factor (refinable)

Absorption

The sample absorption coefficient as \(\mu r\) where r is the radius (refinable). Only valid for Debye-Scherrer geometry.

SurfaceRoughA

Surface roughness parameter A as defined by Surotti, J. Appl. Cryst, 5, 325-331, 1972. (refinable - only valid for Bragg-Brentano geometry)

SurfaceRoughB

Surface roughness parameter B (refinable - only valid for Bragg-Brentano geometry)

DisplaceX, DisplaceY

Sample displacement from goniometer center where Y is along the beam direction and X is perpendicular. Units are \(\mu m\) (refinable).

Phi, Chi, Omega

Goniometer sample setting angles, in degrees.

Gonio. radius

Radius of the diffractometer in mm

InstrName

(str) A name for the instrument, used in preparing a CIF .

Force, Temperature, Humidity, Pressure, Voltage

Variables that describe how the measurement was performed. Not used directly in any computations.

ranId

(int) The random-number Id for the histogram (same value as where top-level key is ranId)

Type

(str) Type of diffraction data, may be ‘Debye-Scherrer’ or ‘Bragg-Brentano’ .

hId

(int) The number assigned to the histogram when the project is loaded or edited (can change)

ranId

(int) A random number id for the histogram that does not change

Background

(list) The background is stored as a list with where the first item in the list is list and the second item is a dict. The list contains the background function and its coefficients; the dict contains Debye diffuse terms and background peaks. (TODO: this needs to be expanded.)

Data

(list) The data consist of a list of 6 np.arrays containing in order:

  1. the x-postions (two-theta in degrees),

  2. the intensity values (Yobs),

  3. the weights for each Yobs value

  4. the computed intensity values (Ycalc)

  5. the background values

  6. Yobs-Ycalc

2.3.7.1. CW Instrument Parameters

Instrument Parameters are placed in a list of two dicts, where the keys in the first dict are listed below. Note that the dict contents are different for constant wavelength (CW) vs. time-of-flight (TOF) histograms. The value for each item is a list containing three values: the initial value, the current value and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that cannot be refined. The first and second values are floats unless otherwise noted. Items not refined are noted as [*]

key

sub-key

explanation

Instrument Parameters[0]

Type [*]

(str) Histogram type: * ‘PXC’ for constant wavelength x-ray * ‘PNC’ for constant wavelength neutron

Bank [*]

(int) Data set number in a multidata file (usually 1)

Lam

(float) Specifies a wavelength in \(\AA\)

Lam1 [*]

(float) Specifies the primary wavelength in \(\AA\), used in place of Lam when an \(\alpha_1, \alpha_2\) source is used.

Lam2 [*]

(float) Specifies the secondary wavelength in \(\AA\), used with Lam1

I(L2)/I(L1)

(float) Ratio of Lam2 to Lam1, used with Lam1

Zero

(float) Two-theta zero correction in degrees

Azimuth [*]

(float) Azimuthal setting angle for data recorded with differing setting angles

U, V, W

(float) Cagliotti profile coefficients for Gaussian instrumental broadening, where the FWHM goes as \(U \tan^2\theta + V \tan\theta + W\)

X, Y, Z

(float) Cauchy (Lorentzian) instrumental broadening coefficients

SH/L

(float) Variant of the Finger-Cox-Jephcoat asymmetric peak broadening ratio. Note that this is the sum of S/L and H/L where S is sample height, H is the slit height and L is the goniometer diameter.

Polariz.

(float) Polarization coefficient.

Instrument Parameters[1]

(empty dict)

2.3.7.2. TOF Instrument Parameters

Instrument Parameters are also placed in a list of two dicts, where the keys in each dict listed below, but here for time-of-flight (TOF) histograms. The value for each item is a list containing three values: the initial value, the current value and a refinement flag which can have a value of True, False or 0 where 0 indicates a value that cannot be refined. The first and second values are floats unless otherwise noted. Items not refined are noted as [*]

key

sub-key

explanation

Instrument Parameters[0]

Type [*]

(str) Histogram type: * ‘PNT’ for time of flight neutron

Bank

(int) Data set number in a multidata file

2-theta [*]

(float) Nominal scattering angle for the detector

fltPath [*]

(float) Total flight path source-sample-detector

Azimuth [*]

(float) Azimuth angle for detector right hand rotation from horizontal away from source

difC,difA, difB

(float) Diffractometer constants for conversion of d-spacing to TOF in microseconds

Zero

(float) Zero point offset (microseconds)

alpha

(float) Exponential rise profile coefficients

beta-0 beta-1 beta-q

(float) Exponential decay profile coefficients

sig-0 sig-1 sig-2 sig-q

(float) Gaussian profile coefficients

X,Y,Z

(float) Lorentzian profile coefficients

Instrument Parameters[1]

Pdabc

(list of 4 float lists) Originally created for use in gsas as optional tables of d, alp, bet, d-true; for a reflection alpha & beta are obtained via interpolation from the d-spacing and these tables. The d-true column is apparently unused.

2.3.8. Powder Reflection Data Structure

The data tree entry for powder diffraction histograms contains an entry labeled Reflection Lists containing a dict keyed by phase name, for every phase linked to the histogram. Each entry is itself a dict with four entries, with keys:

key

explanation

RefList

This contains the reflection list, as described below.

FF

Contains a dict with two entries, El which contains a list of n element types and FF which contains a 55 x n np.array of of form factor values.

Type

Contains a string specifying the type of histogram, such as ‘PXC’

Super

Contains a bool value, which is True when the phase has a superspace spacegroup (3+1 dimension).

one element of which is ‘RefList’, which is a np.array containing reflections. The columns in that array are documented below.

index

explanation

0,1,2

h,k,l

3

multiplicity

4

d-space, \(\AA\)

5

pos, two-theta

6

sig, Gaussian width

7

gam, Lorenzian width

8

\(F_{obs}^2\)

9

\(F_{calc}^2\)

10

reflection phase, in degrees

11

intensity correction for reflection, this times \(F_{obs}^2\) or \(F_{calc}^2\) gives Iobs or Icalc

12

Preferred orientation correction

13

Transmission (absorption correction)

14

Extinction correction

Note that when the Super entry in the phase’s main dict is True, indicating that the phase is a 3+1 super-space group, the columns are:

index

explanation

0,1,2,3

h,k,l,m

4

multiplicity

5

d-space, \(\AA\)

6

pos, two-theta

7

sig, Gaussian width

8

gam, Lorenzian width

9

\(F_{obs}^2\)

10

\(F_{calc}^2\)

11

reflection phase, in degrees

12

intensity correction for reflection, this times \(F_{obs}^2\) or \(F_{calc}^2\) gives Iobs or Icalc

13

Preferred orientation correction

14

Transmission (absorption correction)

15

Extinction correction

2.3.9. Single Crystal Tree Items

Every single crystal diffraction histogram is stored in the GSAS-II data tree with a top-level entry named beginning with the string “HKLF “. The diffraction data for that information are directly associated with that tree item and there are a series of children to that item. The routines GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree() and GSASIIstrIO.GetUsedHistogramsAndPhases() will load this information into a dictionary where the child tree name is used as a key, and the information in the main entry is assigned a key of Data, as outlined below.

key

sub-key

explanation

Data

(dict) that contains the reflection table, as described in the Single Crystal Reflections description.

Instrument Parameters

(list) containing two dicts where the possible keys in each dict are listed below. The value for most items is a list containing two values: the initial value, the current value. The first and second values are floats unless otherwise noted.

Lam

(two floats) Specifies a wavelength in \(\AA\)

Type

(two str values) Histogram type : * ‘SXC’ for constant wavelength x-ray * ‘SNC’ for constant wavelength neutron * ‘SNT’ for time of flight neutron * ‘SEC’ for constant wavelength electrons (e.g. micro-ED)

InstrName

(str) A name for the instrument, used in preparing a CIF

wtFactor

(float) A weighting factor to increase or decrease the leverage of data in the histogram. A value of 1.0 weights the data with their standard uncertainties and a larger value increases the weighting of the data (equivalent to decreasing the uncertainties).

hId

(int) The number assigned to the histogram when the project is loaded or edited (can change)

ranId

(int) A random number id for the histogram that does not change

2.3.10. Single Crystal Reflection Data Structure

For every single crystal a histogram, the 'Data' item contains the structure factors as an np.array in item ‘RefList’. The columns in that array are documented below for non-superspace phases.

index

3+1 index

explanation

0,1,2

0,1,2

reflection indices, h,k,l

3

3+1 superspace index, m

3

4

flag (0 absent, 1 observed)

4

5

d-space, \(\AA\)

5

6

\(F_{obs}^2\)

6

7

\(\sigma(F_{obs}^2)\)

7

8

\(F_{calc}^2\)

8

9

\(F_{obs}^2(T)\)

9

10

\(F_{calc}^2(T)\)

10

11

reflection phase, in degrees

11

12

intensity correction for reflection, this times \(F_{obs}^2\) or \(F_{calc}^2\) gives Iobs or Icalc

Notes:

  • The annotation “(T)” in the second set of \(F^2(T)\) values stands for “true,” where the values are on an absolute scale through application of the scale factor.

  • The left-most column gives the entry index for three dimensional spacegroups, the column to the right of that has the index for 3+1 superspace phases, where there are four reflection indices h, k, l, m.

2.3.11. Image Data Structure

Every 2-dimensional image is stored in the GSAS-II data tree with a top-level entry named beginning with the string “IMG “. The image data are directly associated with that tree item and there are a series of children to that item. The routines GSASIIdataGUI.GSASII.GetUsedHistogramsAndPhasesfromTree() and GSASIIstrIO.GetUsedHistogramsAndPhases() will load this information into a dictionary where the child tree name is used as a key, and the information in the main entry is assigned a key of Data, as outlined below.

key

sub-key

explanation

Comments

(list of str) Text strings extracted from the original image data header or a metafile. These cannot be changed by the user; it may be empty.

Image Controls

azmthOff

(float) The offset to be applied to an azimuthal value. Accomodates detector orientations other than with the detector X-axis horizontal.

background image

(list:str,float) The name of a tree item (“IMG …”) that is to be subtracted during image integration multiplied by value. It must have the same size/shape as the integrated image. NB: value < 0 for subtraction.

calibrant

(str) The material used for determining the position/orientation of the image. The data is obtained from ImageCalibrants() and UserCalibrants.py (supplied by user).

calibdmin

(float) The minimum d-spacing used during the last calibration run.

calibskip

(int) The number of expected diffraction lines skipped during the last calibration run.

center

(list:floats) The [X,Y] point in detector coordinates (mm) where the direct beam strikes the detector plane as determined by calibration. This point does not have to be within the limits of the detector boundaries.

centerAzm

(bool) If True then the azimuth reported for the integrated slice of the image is at the center line otherwise it is at the leading edge.

color

(str) The name of the colormap used to display the image. Default = ‘Paired’.

cutoff

(float) The minimum value of I/Ib for a point selected in a diffraction ring for calibration calculations. See pixLimit for details as how point is found.

DetDepth

(float) Coefficient for penetration correction to distance; accounts for diffraction ring offset at higher angles. Optionally determined by calibration.

DetDepthRef

(bool) If True then refine DetDepth during calibration/recalibration calculation.

distance

(float) The distance (mm) from sample to detector plane.

ellipses

(list:lists) Each object in ellipses is a list [center,phi,radii,color] where center (list) is location (mm) of the ellipse center on the detector plane, phi is the rotation of the ellipse minor axis from the x-axis, and radii are the minor & major radii of the ellipse. If radii[0] is negative then parameters describe a hyperbola. Color is the selected drawing color (one of ‘b’, ‘g’ ,’r’) for the ellipse/hyperbola.

edgemin

(float) Not used; parameter in EdgeFinder code.

fullIntegrate

(bool) If True then integrate over full 360 deg azimuthal range.

GonioAngles

(list:floats) The ‘Omega’,’Chi’,’Phi’ goniometer angles used for this image. Required for texture calculations.

invert_x

(bool) If True display the image with the x-axis inverted.

invert_y

(bool) If True display the image with the y-axis inverted.

IOtth

(list:floats) The minimum and maximum 2-theta values to be used for integration.

LRazimuth

(list:floats) The minimum and maximum azimuth values to be used for integration.

Oblique

(list:float,bool) If True apply a detector absorption correction using the value to the intensities obtained during integration.

outAzimuths

(int) The number of azimuth pie slices.

outChannels

(int) The number of 2-theta steps.

pixelSize

(list:ints) The X,Y dimensions (microns) of each pixel.

pixLimit

(int) A box in the image with 2*pixLimit+1 edges is searched to find the maximum. This value (I) along with the minimum (Ib) in the box is reported by GSASIIimage.ImageLocalMax() and subject to cutoff in GSASIIimage.makeRing(). Locations are used to construct rings of points for calibration calcualtions.

PolaVal

(list:float,bool) If type=’SASD’ and if True, apply polarization correction to intensities from integration using value.

rings

(list:lists) Each entry is [X,Y,dsp] where X & Y are lists of x,y coordinates around a diffraction ring with the same d-spacing (dsp)

ring

(list) The x,y coordinates of the >5 points on an inner ring selected by the user,

Range

(list) The minimum & maximum values of the image

rotation

(float) The angle between the x-axis and the vector about which the detector is tilted. Constrained to -180 to 180 deg.

SampleShape

(str) Currently only ‘Cylinder’. Sample shape for Debye-Scherrer experiments; used for absorption calculations.

SampleAbs

(list: float,bool) Value of absorption coefficient for Debye-Scherrer experimnents, flag if True to cause correction to be applied.

setDefault

(bool) If True the use the image controls values for all new images to be read. (might be removed)

setRings

(bool) If True then display all the selected x,y ring positions (vida supra rings) used in the calibration.

showLines

(bool) If True then isplay the integration limits to be used.

size

(list:int) The number of pixels on the image x & y axes

type

(str) One of ‘PWDR’, ‘SASD’ or ‘REFL’ for powder, small angle or reflectometry data, respectively.

tilt

(float) The angle the detector normal makes with the incident beam; range -90 to 90.

wavelength

(float) The radiation wavelength (\(\AA\)) as entered by the user (or someday obtained from the image header).

Masks

Arcs

(list: lists) Each entry [2-theta,[azimuth[0],azimuth[1]],thickness] describes an arc mask to be excluded from integration

Frames

(list:lists) Each entry describes the x,y points (3 or more - mm) that describe a frame outside of which is excluded from recalibration and integration. Only one frame is allowed.

Points

(list:lists) Each entry [x,y,radius] (mm) describes an excluded spot on the image to be excluded from integration.

Polygons

(list:lists) Each entry is a list of 3+ [x,y] points (mm) that describe a polygon on the image to be excluded from integration.

Rings

(list: lists) Each entry [2-theta,thickness] describes a ring mask to be excluded from integration.

Thresholds

(list:[tuple,list]) [(Imin,Imax),[Imin,Imax]] This gives lower and upper limits for points on the image to be included in integrsation. The tuple is the image intensity limits and the list are those set by the user.

SpotMask

(dict: int & array) ‘esdMul’(int) number of standard deviations above mean ring intensity to mask ‘spotMask’ (bool array) the spot mask for every pixel in image

Stress/Strain

Sample phi

(float) Sample rotation about vertical axis.

Sample z

(float) Sample translation from the calibration sample position (for Sample phi = 0) These will be restricted by space group symmetry; result of strain fit refinement.

Type

(str) ‘True’ or ‘Conventional’: The strain model used for the calculation.

d-zero

(list:dict) Each item is for a diffraction ring on the image; all items are from the same phase and are used to determine the strain tensor. The dictionary items are: ‘Dset’: (float) True d-spacing for the diffraction ring; entered by the user. ‘Dcalc’: (float) Average calculated d-spacing determined from strain coeff. ‘Emat’: (list: float) The strain tensor elements e11, e12 & e22 (e21=e12, rest are 0) ‘Esig’: (list: float) Esds for Emat from fitting. ‘pixLimit’: (int) Search range to find highest point on ring for each data point ‘cutoff’: (float) I/Ib cutoff for searching. ‘ImxyObs’: (list: lists) [[X],[Y]] observed points to be used for strain calculations. ‘ImtaObs’: (list: lists) [[d],[azm]] transformed via detector calibration from ImxyObs. ‘ImtaCalc’: (list: lists [[d],[azm]] calculated d-spacing & azimuth from fit.

2.4. Parameter Dictionary

The parameter dictionary contains all of the variable parameters for the refinement. The dictionary keys are the name of the parameter (<phase>:<hist>:<name>:<atom>). It is prepared in two ways. When loaded from the tree (in GSASIIdataGUI.GSASII.MakeLSParmDict() and GSASIIfiles.ExportBaseclass.loadParmDict()), the values are lists with two elements: [value, refine flag]

When loaded from the GPX file (in GSASIIstrMain.Refine() and GSASIIstrMain.SeqRefine()), the value in the dict is the actual parameter value (usually a float, but sometimes a letter or string flag value (such as I or A for iso/anisotropic).

2.5. Texture implementation

There are two different places where texture can be treated in GSAS-II. One is for mitigating the effects of texture in a structural refinement. The other is for texture characterization.

For reducing the effect of texture in a structural refinement there are entries labeled preferred orientation in each phase’s data tab. Two different approaches can be used for this, the March-Dollase model and spherical harmonics.

For the March-Dollase model, one axis in reciprocal space is designated as unique (defaulting to the 001 axis) and reflections are corrected according to the angle they make with this axis depending on the March-Dollase ratio. (If unity, no correction is made). The ratio can be greater than one or less than one depending on if crystallites oriented along the designated axis are overrepresented or underrepresented. For most crystal systems there is an obvious choice for the direction of the unique axis and then only a single term needs to be refined. If the number is close to 1, then the correction is not needed.

The second method for reducing the effect of texture in a structural refinement is to create a crystallite orientation probability surface as an expansion in terms spherical harmonic functions. Only functions consistent with cylindrical diffraction suymmetry and having texture symmetry consistent with the Laue class of phase are used and are allowed, so the higher the symmetry the fewer terms that are available for a given spherical harmonics order. To use this correction, select the lowest order that provides refinable terms and perform a refinement. If the texture index remains close to one, then the correction is not needed. If a significant improvement is noted in the profile Rwp, one may wish to see if a higher order expansion gives an even larger improvement.

To characterize texture in a material, generally one needs data collected with the sample at multiple orientations or, for TOF, with detectors at multiple locations around the sample. In this case the detector orientation is given in each histogram’s Sample Parameters and the sample’s orientation is described with the Euler angles specifed on the phase’s Texture tab, which is also where the texture type (cylindrical, rolling,…) and the spherical harmonic order is selected. This should not be used with a single dataset and should not be used if the preferred orientations corrections are used.

The coordinate system used for texture characterization is defined where the sample coordinates (Psi, gamma) are defined with an instrument coordinate system (I, J, K) such that K is normal to the diffraction plane and J is coincident with the direction of the incident radiation beam toward the source. We further define a standard set of right-handed goniometer eulerian angles (Omega, Chi, Phi) so that Omega and Phi are rotations about K and Chi is a rotation about J when Omega = 0. Finally, as the sample may be mounted so that the sample coordinate system (Is, Js, Ks) does not coincide with the instrument coordinate system (I, J, K), we define three eulerian sample rotation angles (Omega-s, Chi-s, Phi-s) that describe the rotation from (Is, Js, Ks) to (I, J, K). The sample rotation angles are defined so that with the goniometer angles at zero Omega-s and Phi-s are rotations about K and Chi-s is a rotation about J.

Three typical examples:

  1. Bragg-Brentano laboratory diffractometer: Chi=0

  2. Debye-Scherrer counter detector; sample capillary axis perpendicular to diffraction plane: Chi=90

  3. Debye-Scherrer 2D area detector positioned directly behind sample; sample capillary axis horizontal; Chi=0

NB: The area detector azimuthal angle will equal 0 in horizontal plane to right as viewed from x-ray source and will equal 90 at vertical “up” direction.

2.6. ISODISTORT implementation

CIFs prepared with the ISODISTORT web site https://stokes.byu.edu/iso/isodistort_version5.6.1/isodistort.php [B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, “ISODISPLACE: An Internet Tool for Exploring Structural Distortions.” J. Appl. Cryst. 39, 607-614 (2006).] can be read into GSAS-II using import CIF. This will cause constraints to be established for structural distortion modes read from the CIF. At present, of the five types of modes only displacive(_iso_displacivemode…) and occupancy (_iso_occupancymode…) are processed. Not yet processed: _iso_magneticmode…, _iso_rotationalmode… & _iso_strainmode

The CIF importer G2phase_CIF implements class G2phase_CIF.CIFPhaseReader which offers two methods associated with ISODISTORT (ID) input. Method G2phase_CIF.CIFPhaseReader.ISODISTORT_test() checks to see if a CIF block contains the loops with _iso_displacivemode_label or _iso_occupancymode_label items. If so, method G2phase_CIF.CIFPhaseReader.ISODISTORT_proc() is called to read and interpret them. The results are placed into the reader object’s .Phase class variable as a dict item with key 'ISODISTORT'.

Note that each mode ID has a long label with a name such as Pm-3m[1/2,1/2,1/2]R5+(a,a,0)[La:b:dsp]T1u(a). Function G2phase_CIF.ISODISTORT_shortLbl() is used to create a short name for this, such as R5_T1u(a) which is made unique by addition of _n if the short name is duplicated. As each mode is processed, a constraint corresponding to that mode is created and is added to list in the reader object’s .Constraints class variable. Items placed into that list can either be a list, which corresponds to a function (new var) type constraint definition entry, or an item can be a dict, which provides help information for each constraint.

2.6.1. Displacive modes

The coordinate variables, as named by ISODISTORT, are placed in .Phase['ISODISTORT']['IsoVarList'] and the corresponding GSASIIobj.G2VarObj objects for each are placed in .Phase['ISODISTORT']['G2VarList']. The mode variables, as named by ISODISTORT, are placed in .Phase['ISODISTORT']['IsoModeList'] and the corresponding GSASIIobj.G2VarObj objects for each are placed in .Phase['ISODISTORT']['G2ModeList']. [Use str(G2VarObj) to get the variable name from the G2VarObj object, but note that the phase number, n, for the prefix “n::” cannot be determined as the phase number is not yet assigned.]

Displacive modes are a bit complex in that they relate to delta displacements, relative to an offset value for each coordinate, and because the modes are normalized. While GSAS-II also uses displacements, these are added to the coordinates after each refinement cycle and then the delta values are set to zero. ISODISTORT uses fixed offsets (subtracted from the actual position to obtain the delta values) that are taken from the parent structure coordinate and the initial offset value (in _iso_deltacoordinate_value) and these are placed in .Phase['ISODISTORT']['G2coordOffset'] in the same order as .Phase['ISODISTORT']['G2ModeList'], .Phase['ISODISTORT']['IsoVarList'] and ‘’.Phase[ISODISTORT’][‘G2parentCoords’]’’.’

The normalization factors (which the delta values are divided by) are taken from _iso_displacivemodenorm_value and are placed in .Phase['ISODISTORT']['NormList'] in the same order as as ...['IsoModeList'] and ...['G2ModeList'].

The CIF contains a sparse matrix, from the loop_ containing _iso_displacivemodematrix_value which provides the equations for determining the mode values from the coordinates, that matrix is placed in .Phase['ISODISTORT']['Mode2VarMatrix']. The matrix is inverted to produce .Phase['ISODISTORT']['Var2ModeMatrix'], which determines how to compute the mode values from the delta coordinate values. These values are used for the in GSASIIconstrGUI.ShowIsoDistortCalc(), which shows coordinate and mode values, the latter with s.u. values.

2.6.2. Occupancy modes

The delta occupancy variables, as named by ISODISTORT, are placed in .Phase['ISODISTORT']['OccVarList'] and the corresponding GSASIIobj.G2VarObj objects for each are placed in .Phase['ISODISTORT']['G2OccVarList']. The mode variables, as named by ISODISTORT, are placed in .Phase['ISODISTORT']['OccModeList'] and the corresponding GSASIIobj.G2VarObj objects for each are placed in .Phase['ISODISTORT']['G2OccModeList'].

Occupancy modes, like Displacive modes, are also refined as delta values. However, GSAS-II directly refines the fractional occupancies. Offset values for each atom, are taken from _iso_occupancy_formula and are placed in .Phase['ISODISTORT']['ParentOcc]. (Offset values are subtracted from the actual position to obtain the delta values.) Modes are normalized (where the mode values are divided by the normalization factor) are taken from _iso_occupancymodenorm_value and are placed in .Phase['ISODISTORT']['OccNormList'] in the same order as as ...['OccModeList'] and ...['G2OccModeList'].

The CIF contains a sparse matrix, from the loop_ containing _iso_occupancymodematrix_value, which provides the equations for determining the mode values from the coordinates. That matrix is placed in .Phase['ISODISTORT']['Occ2VarMatrix']. The matrix is inverted to produce .Phase['ISODISTORT']['Var2OccMatrix'], which determines how to compute the mode values from the delta coordinate values.

2.6.3. Mode Computations

Constraints are processed after the CIF has been read in GSASIIdataGUI.GSASII.OnImportPhase() or GSASIIscriptable.G2Project.add_phase() by moving them from the reader object’s .Constraints class variable to the Constraints tree entry’s [‘Phase’] list (for list items defining constraints) or the Constraints tree entry’s [‘_Explain’] dict (for dict items defining constraint help information)

The information in .Phase['ISODISTORT'] is used in GSASIIconstrGUI.ShowIsoDistortCalc() which shows coordinate and mode values, the latter with s.u. values. This can be called from the Constraints and Phase/Atoms tree items.

Before each refinement, constraints are processed as described elsewhere. After a refinement is complete, GSASIIstrIO.PrintIndependentVars() shows the shifts and s.u.’s on the refined modes, using GSAS-II values, but GSASIIstrIO.PrintISOmodes() prints the ISODISTORT modes as computed in the web site.

2.7. Parameter Limits

One of the most often requested “enhancements” for GSAS-II would be the inclusion of constraints to force parameters such as occupancies or Uiso values to stay within expected ranges. While it is possible for users to supply their own restraints that would perform this by supplying an appropriate expression with the “General” restraints, the GSAS-II authors do not feel that use of restraints or constraints are a good solution for this common problem where parameters refine to non-physical values. This is because when this occurs, most likely one of the following cases is occurring:

  1. there is a significant problem with the model, for example for an x-ray fit if an O atom is placed where a S is actually present, the Uiso will refine artificially small or the occupancy much larger than unity to try to compensate for the missing electrons; or

  2. the data are simply insensitive to the parameter or combination of parameters, for example unless very high-Q data are included, the effects of a occupancy and Uiso value can have compensating effects, so an assumption must be made; likewise, with neutron data natural-abundance V atoms are nearly invisible due to weak coherent scattering. No parameters can be fit for a V atom with neutrons.

  3. the parameter is non-physical (such as a negative Uiso value) but within two sigma (sigma = standard uncertainty, aka e.s.d.) of a reasonable value, in which case the value is not problematic as it is experimentally indistinguishable from an expected value.

  4. there is a systematic problem with the data (experimental error)

In all these cases, this situation needs to be reviewed by a crystallographer to decide how to best determine a structural model for these data. An implementation with a constraint or restraint is likely to simply hide the problem from the user, making it more probable that a poor model choice is obtained.

What GSAS-II does implement is to allow users to specify ranges for parameters that works by disabling refinement of parameters that refine beyond either a lower limit or an upper limit, where either or both may be optionally specified. Parameters limits are specified in the Controls tree entry in dicts named as Controls['parmMaxDict'] and Controls['parmMinDict'], where the keys are G2VarObj objects corresponding to standard GSAS-II variable (see getVarDescr() and CompileVarDesc()) names, where a wildcard (‘*’) may optionally be used for histogram number or atom number (phase number is intentionally not allowed as a wildcard as it makes little sense to group the same parameter together different phases). Note that prmLookup() is used to see if a name matches a wildcard. The upper or lower limit is placed into these dicts as a float value. These values can be edited using the window created by the Calculate/”View LS parms” menu command or in scripting with the GSASIIscriptable.G2Project.set_Controls() function. In the GUI, a checkbox labeled “match all histograms/atoms” is used to insert a wildcard into the appropriate part of the variable name.

When a refinement is conducted, routine GSASIIstrMain.dropOOBvars() is used to find parameters that have refined to values outside their limits. If this occurs, the parameter is set to the limiting value and the variable name is added to a list of frozen variables (as a G2VarObj objects) kept in a list in the Controls['parmFrozen'] dict. In a sequential refinement, this is kept separate for each histogram as a list in Controls['parmFrozen'][histogram] (where the key is the histogram name) or as a list in Controls['parmFrozen']['FrozenList'] for a non-sequential fit. This allows different variables to be frozen in each section of a sequential fit. Frozen parameters are not included in refinements through removal from the list of parameters to be refined (varyList) in GSASIIstrMain.Refine() or GSASIIstrMain.SeqRefine(). The data window for the Controls tree item shows the number of Frozen variables and the individual variables can be viewed with the Calculate/”View LS parms” menu window or obtained with GSASIIscriptable.G2Project.get_Frozen(). Once a variable is frozen, it will not be refined in any future refinements unless the the variable is removed (manually) from the list. This can also be done with the Calculate/”View LS parms” menu window or GSASIIscriptable.G2Project.set_Frozen().