The most commonly used type of histogram for GSAS-II is the powder diffraction (PWDR) entry. These entries have a fairly large number of child entries, as shown in Table 15.5. The contents for some of these entries are described further below.
| Child item name | Description and discussion |
| Comments | Metadata and annotations read from the data file are placed here. Nothing here can be edited. |
| Limits | Shows the range of the data and allows for the portion of data to be restricted. Regions of the pattern that should be ignored (excluded regions) can also be designated. It is also possible to designate regions of the histogram that should be plotted with a different intensity scale (magnification regions) here. |
| Background | Provides controls and results for fitting background for individual peak fits (see Chapter 18) or Rietveld fits (see Chapter 11). |
| Instrument Parameters | The parameters here will depend on the data type and affect the peak shape, peak positions and the peak intensities. See below and Tables 15.6, 15.7, and Table 15.8. |
| Sample Parameters | The sample parameters include a histogram scale factor and intensity/peak-position correction factors. There are also terms that describe the diffraction geometry and sample orientation as well as document any other measurement conditions. See §15.3.2 for more details. |
| Peak List | This contains a list of diffraction peaks when individual peak fitting is used. |
| Index Peak List | This contains a copied list of diffraction peaks from the Peak List that is used for assigning a unit cell to a pattern (autoindexing). The reflection indices (hkl values) generated from the cell are shown here. |
| Unit Cells List | This serves three purposes: the controls for autoindexing are found here; there are controls that allow the reflection positions from a specified unit cell to be visualized by superimposing them on the histogram; there are several types of cell searches that can be performed and the results are displayed here. |
| Reflection Lists | When a Rietveld refinement is performed, lists of reflections are generated for each phase included in the current histogram. The reflection lists are shown here, with a notebook tab used to select the phase. |
The instrumental parameters for a PWDR entry will be different depending on the type of included data. The data type is determined by a code assigned to the data that indicates the radiation source. Further monochromatic and dual-radiation (lab source, typically CuK\(\alpha _1\)-CuK\(\alpha _2\)) instruments also will have different parameters. For monochromatic instruments the parameters shown in Table 15.6 are used, but for dual wavelength instruments the parameters shown in Table 15.7 are appropriate. For time of flight (TOF) diffraction there is yet another table, Table 15.8. Note that most of the values in the Instrument Parameters child data tree item determine the instrumental contribution to the peak profile while other parameters determine peak positions. The polarization term affects peak intensities.
| Parameter Name | Description and discussion |
| Azimuth | The location of the detector or the central angle from integration of an area detector wedge (caking) |
| Lam | The wavelength for the radiation. This can be refined, but this is quite unusual. This can be done only if a set of lattice parameters is fixed or there is a simultaneous fit where another histogram has a fixed wavelength. |
| Zero | An offset added to all \(2\theta \) values. The value has units of degrees x 100. Originally in Rietveld work this term was refined to account for sample displacement, but now there are much better correction terms available in the Sample Parameters data tree item. You are strongly encouraged to leave this value as 0.0, unless you have determined this directly. Refining it is strongly discouraged. |
| Polariz. | The polarization of the beam in the diffraction plane vs. the perpendicular plane. This will be 0.5 for neutrons; something on the order of 0.95 for a synchrotron bending magnet source and on the order of 0.99 for a synchrotron insertion device source. This can only be refined in the unusual circumstance when the \(\rm U_{iso}\) or \(\rm U_{ij}\) terms in the structure are known and are fixed. |
| U, V & W | The Gaussian width parameters, as described in §14.5.1, where \(\sigma ^2\ =\ U\ \tan ^2{\theta }\ +V\ \tan {\theta }+W\) and \(\sigma =FWHM\ /\ \sqrt {8\ln {2}}\). The preferred way that GSAS-II is used will have these terms be fit to a standard and are not be refined for samples. |
| X, Y & Z | The Lorentzian width terms, where \(FWHM = \Gamma = X / \cos \theta + Y \tan \theta + Z\). Note that CW instruments usually do not have any significant instrumental Lorentzian broadening, so these values are often all 0. If values have been determined from a standard, use them, but Z is still expected to be 0. If they are not known, set them to 0 and refine sample broadening terms (see §14.7.) |
| SH/L | The Finger-Cox-Jephcoat axial divergence correction, as discussed in 14.5.3, expressed as \((S+H)/L\). While the S and H terms are typically difficult to refine, this term tends to refine with good stability, but ideally the value is determined when the instrument |
| Parameter Name | Description and discussion |
| Azimuth | The location of the detector or the central angle from integration of an area detector wedge (caking) |
| Ka1 & Ka2 | The wavelengths for the radiation. These can be set to known values using the ”Source type” pull-down menu. |
| I(L2)/I(L1) | The relative intensity ratio for the two wavelengths, expressed as the intensity of the second, longer and weaker Ka2 wavelength relative to the primary Ka1 wavelength. |
| Zero | An offset added to all \(2\theta \) values. The value has units of degrees x 100. Originally in Rietveld work this term was refined to account for sample displacement, but now there are much better correction terms available in the Sample Parameters data tree item. The alignment process for lab instruments ensures that this offset should be negligible. You are strongly encouraged to leave this value as 0. Refining it is strongly discouraged. |
| Polariz. | The polarization of the beam in the diffraction plane vs. the perpendicular plane. This will be 0.5 for instruments without a monochromator and will be \(1 / [1 + \cos ^2(2\theta _m)]\) where \(2\theta _m\) is the Bragg angle for the monochromator. This can only be refined in the unusual circumstance when the \(\rm U_{iso}\) or \(\rm U_{ij}\) terms in the structure are known and are fixed. |
| U, V & W | Gaussian width parameters, as described in §14.5.1, where \(\sigma ^2\ =\ U\ \tan ^2{\theta }\ +V\ \tan {\theta }+W\) and \(\sigma =FWHM\ /\ \sqrt {8\ln {2}}\). The preferred way that GSAS-II is used will have these terms be fit to a standard and are not be refined for samples. |
| X, Y & Z | Lorentzian width terms where \(FWHM = \Gamma = X / \cos \theta + Y \tan \theta + Z\). Note that CW instruments usually do not have any significant instrumental Lorentzian broadening, so these values are often all 0. If values have been determined from a standard, use them, but Z is still expected to be 0. If they are not known, set them to 0 and refine sample broadening terms (see §14.7.) |
| SH/L | The Finger-Cox-Jephcoat axial divergence correction, as discussed in 14.5.3, expressed as \((S+H)/L\). While the S and H terms are typically difficult to refine, this term tends to refine with good stability, but ideally the value is determined when the instrument |
| Parameter Name | Description and discussion |
| Flight path | The distance between the neutron moderator and the detector in m. It is best when this is the same for any detectors that are summed. |
| 2-theta | The average \(2\theta \) angle for the summed detectors. It is best when this is the same for any detectors that are summed. |
| difA, difB & difC | Conversion equation between TOF in microsec and d-space/Q, \(t = {\rm Zero} + {\rm difC}\ d + {\rm difA}\ d^2 + {\rm difB}/d\). The difB term is usually 0. difC is occasionally refined to account for sample displacement. |
| alpha | The rise-side double exponential peak shape parameter. Determined from instrument calibration. |
| beta0, beta1 & betaQ | The fall-side double exponential peak shape parameters, \(\beta = \beta _0 + \beta _1 d^{4} + \beta _q d^{2}\). Determined from instrument calibration. |
| sig-0, sig-1, sig-2 & sig-q | Gaussian width parameters, \(\sigma =FWHM / \sqrt {8\ln {2}}\) and \(\sigma = \sigma _0 + {\sigma _1}{d^{2}} + {\sigma _2}{d^{4}} + {\sigma _q}{d}\). Determined from instrument calibration. |
| X, Y & Z | Lorentzian width terms, \(\Gamma = FWHM ={X}{d}+{Y}{d^{2}}+Z\). TOF instruments may have some inherent Lorentzian broadening, with X & Y non-zero, but Z is not needed. Determined from instrument calibration. |
The Sample Parameters data tree item contains a number of parameters related to the sample and experimental conditions, a few of which can be refined. These are tabulated in Tables 15.9, 15.10, 15.11 and 15.12. Most significant is the histogram scale factor. This is used to scale the computed diffraction data to match the intensity scale for the observed pattern, since the magnitude of the observed intensities will depend on experimental settings such as the sample size, instrumental configuration and data collection time. While it is possible to perform diffraction measurements on an absolute scale, so that this scale factor value is known, this is not easy and is rarely done. For almost all work, the scale factor is fitted before fitting of any other diffraction parameters is attempted, other than perhaps background. The scale factor can be thought of as an arbitrary positive value that will almost always need to be fitted. Note, however, that the phase fraction parameters can be used to replace the histogram scale factor. This is discussed further in §25.4 and §13.1.1.
There are different terms here that correct for deviations in peak positions or changes to the diffraction intensities. The terms that will be available depend on the type of diffraction measurement, see Tables 15.10, 15.11 and 15.12.
The sample parameters also include several goniometer or detector setting angles. These normally will not be needed, but become vital for characterization of texture when several measurements must be combined from different settings. The GSAS-II goniometer angles are defined with a coordinate system where the origin is located at the diffractometer center. This should also be the sample position. The Y-axis points from the sample towards the radiation source (the opposite direction of the x-ray/neutron beam). The X-axis is perpendicular to the incident beam and in the diffraction plane towards \(2\theta =0\). The Z-axis is perpendicular to X and Y and is chosen in the direction to complete the right-handed coordinate system. This will be upwards and vertical when the X-axis is to the right. The goniometer angles are defined with \(\omega \) as the rotation of the sample stage relative to the incident beam. \(\chi \) as the tilt angle of the goniometer head, \(\phi \) as the azimuthal rotation of the sample spindle and the azimuth angle as the orientation angle of the detector bank section of a 2D image where \(0^\circ \) is in the diffraction plane.
Finally, there are six constants that can be specified to document experimental conditions. The first three of these (time, temperature and pressure) have fixed labels, but the other three labels can be changed for a project. When changed for one histogram, the same labels are used for all histograms in the project. Note that the values provided for the measurement conditions do not change the results from any GSAS-II computations, but will be noted in tabulations when sequential fits are performed.
| Parameter Name | Description and discussion |
| Instrument Name | This name is used in the generation of CIF exports that place the diffraction data into a pdCIF file. |
| Diffractometer type | This can be either Bragg-Brentano or Debye-Scherrer. For neutrons use Debye-Scherrer. |
| Histogram scale factor | As described in the text, this is an arbitrary term that scales the computed powder diffraction pattern to match the experimental histogram. |
| Goniometer omega, chi, phi and azimuth | These angles describe how the sample is oriented. Typically only needed for texture characterization where multiple sample or detector settings are used. |
| Clock time | An optional value that ideally will be imported with the measurement. It specifies a time stamp in seconds for when each measurement is made in a multi-histogram dataset. |
| Sample temperature | This value ideally will be imported with the measurement. It specifies the sample temperature (in K). It will be provided in a project-based CIF export of the results, so it is best if this number is correct when not set from the input file. |
| Sample pressure | An optional value that ideally will be imported with the measurement. It specifies the applied hydrostatic pressure (in MPa). |
| Sample humidity, Sample voltage & Applied load | Optional experimental setting values. As noted in §15.3.2, these fields can be relabeled for any parametric setting that is changed in a multibank fit. |
| Parameter Name | Description and discussion |
| Goniometer radius | This is the distance from the sample to the detector in mm. |
| Sample X displ. perp to beam | This measures the deviation of the sample position from the center of the diffraction circle towards the beam source. The value is in \(\mu m\) if the Goniometer radius is correct. This is typically refined in most Rietveld fits, but only in the late refinement stages. |
| Sample Y displ. \(||\) to beam | This measures the deviation of the sample position from the center of the diffraction circle perpendicular to the beam. The value is in \(\mu m\) if the Goniometer radius is correct. The effect of this offset is only discernible with very high angle (\(\gg 90^\circ \)). This should be fixed at 0. except when diffraction data are collected to \(>140^\circ \ 2\theta \) (typically with neutrons) and even then refined with care and only in the late refinement stages. |
| Sample absorption (\(\mu R\)) | This specifies the loss of x-rays/neutrons due to absorption and other types of scattering. It should be adjusted for the sample packing density. It can be varied, but this usually requires that the \(\rm U_{iso}\) values be fixed. |
| Parameter Name | Description and discussion |
| Goniometer radius | This is the distance from the sample to the detector in mm. |
| Sample displacement | This corrects for the sample not being placed exactly at the center of the diffraction circle. This term will almost always need to be refined in a Bragg-Brentano fit. The units are \(\mu m\), if the Goniometer radius is correct. |
| Sample transparency | This corrects for the change in depth that the x-ray beam penetrates as a function of the angle of incidence. It only makes sense for samples with absorption (low density). It can usually be refined. |
| Sample roughness A & B | When an absorbing x-ray sample has a rough surface, the intensities of very low angle peaks can be diminished. These terms can be refined to account for that. This is usually not needed. Refine only with care. |
| Parameter Name | Description and discussion |
| Sample absorption (\(\mu R/ \lambda \)) | This specifies the loss of neutrons due to absorption and incoherent scattering. It should be adjusted for the sample packing density. This is a wavelength-dependent quantity, so provide this evaluated at 1 Å, or divide by the wavelength where this is computed. It can be varied, but will usually interact highly with \(\rm U_{iso}\) values. |