International
Tables for
Crystallography
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

International Tables for Crystallography (2006). Vol. G, ch. 3.3, pp. 121-123

Section 3.3.5. Analysis

B. H. Tobya*

aNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8562, USA
Correspondence e-mail: brian.toby@nist.gov

3.3.5. Analysis

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The categories relating to the information derived from the measurements are as follows:

Processed intensities, positions and data processing (§3.3.5.1[link])
PD_DATA group
 PD_DATA (items beginning with _pd_proc_*)
PD_PROC group
 PD_PROC_INFO
 PD_PROC_LS
Simulated intensities and their positions (§3.3.5.2[link])
PD_DATA group
 PD_DATA (items beginning with _pd_calc_*)
PD_CALC group
 PD_CALC
Diffraction peak table (§3.3.5.3[link])
PD_PEAK group
 PD_PEAK
 PD_PEAK_METHOD
Reflection assignments and intensities (§3.3.5.4[link])
 REFLN

In Rietveld and other studies, processed or simulated intensities are presented alongside measured values. This leads to the presence of both derived and measured values in the same category (PD_DATA). However, the purposes of the data items that refer to processed and simulated data points are made clear by the way they are named. Overall descriptions of processed and simulated intensity data are covered by the categories PD_PROC_INFO, PD_PROC_LS and PD_CALC. The two categories PD_PEAK and PD_PEAK_METHOD are used to describe lists of peak positions, which would typically be used to search and match powder profiles. Some additional data items relevant to the table of Bragg reflections are defined as additions to the existing REFLN category in the core CIF dictionary.

3.3.5.1. Processed intensities, their positions and processing information

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The data items in these categories are as follows:

(a) Part of PD_DATA [Scheme scheme13]

(b) PD_PROC_INFO [Scheme scheme14]

(c) PD_PROC_LS [Scheme scheme15]

The pdCIF dictionary distinguishes between values that are measured directly and values that are derived from these observations. For example, in a constant-wavelength instrument, diffraction intensities are recorded as a function of [2\theta]. One may derive d-space values from the [2\theta] values using the value of the wavelength and corrections for the [2\theta] zero-point error and the sample displacement. One may also derive a new set of data points from the observations, for example by summing adjacent data points when the increment between the data points is much smaller than is warranted by the peak widths. For peak searching and other non-quantitative purposes, the diffraction intensities may be smoothed or otherwise modified. Note that the unprocessed measurement values are retained using the data items _pd_meas_*. Since the original measurements are still available, modifications like these do not result in the loss of the original data. In fact, by placing processed values in multiple blocks, a single CIF may contain measurements that have been processed in more than one way.

It is good practice to use the _pd_proc_info_author_* and _pd_proc_info_datetime data items. It is also a good idea to describe how the measurements were processed using _pd_proc_info_data_reduction.

The _pd_proc_* data items in this list may be used to calibrate the [2\theta] or energy values of the data. These are defined in the items _pd_proc_2theta_corrected, _pd_proc_2theta_range_*, _pd_proc_d_spacing, _pd_proc_energy_*, _pd_proc_recip_len_Q and _pd_proc_wavelength.

When corrections, scaling or other processing, such as averaging or smoothing, are applied to the intensities, the results are stored using the _pd_proc_intensity_* data items. Note that if the number of data points does not change, it might be most convenient to include the processed intensities in the same loop as the observed values. This is not always possible, so these items can be placed in a separate loop if there is no longer a one-to-one correspondence between the [2\theta] or energy positions for the _pd_proc_intensity_* values and the _pd_meas_counts_* or _pd_meas_intensity_* values.

For energy-dispersive measurements, the incident spectrum must be determined for normalization. This can be recorded using _pd_proc_intensity_incident. For other types of normalization, _pd_proc_intensity_norm should be used.

For full-pattern fitting, there is a series of _pd_proc_ls_* data items for recording settings and results. For example, agreement factors can be recorded using the _pd_proc_ls_prof_*_factor data items. Some data items may be included in the loop(s) containing the measured or the processed data: _pd_proc_ls_weight specifies the weight assigned to each point and _pd_proc_intensity_bkg_calc specifies the fitted background. Note that background values are usually generated by extrapolation from fixed values set during the refinement or are determined from a function that is fitted to the observations, and occasionally both are used together. The function that has been fitted can be described using _pd_proc_ls_background_function, while fixed points are listed using _pd_proc_intensity_bkg_fix. If sections of the pattern are not fitted, this is indicated using _pd_proc_info_excluded_regions.

3.3.5.2. Simulated data

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The data items in these categories are as follows:

(a) Part of PD_DATA [Scheme scheme16]

(b) PD_CALC [Scheme scheme17]

It is common to calculate powder-diffraction intensities from a crystallographic model. This is necessary for Rietveld refinements, where the model is fitted to the experimentally observed intensities. It is also used to simulate the diffraction pattern of a material for which the structure is known, perhaps for comparison with a measured diffraction pattern.

A crystallographic model can be described in CIF using data items from the core CIF dictionary, as described in Chapter 3.2[link] . To record the results of the simulation, the data items _pd_calc_intensity_net or _pd_calc_intensity_total are used. The difference between these two data items depends on the treatment of background. If the pattern is simulated with a fitted background added to it, _pd_calc_intensity_total is used; otherwise _pd_calc_intensity_net is used. The values will typically be placed in a loop with the processed (_pd_proc_*) data items or the observed (_pd_meas_*) data items. If neither observed nor processed data are present (e.g. for a simulation), or if, for some reason, the simulation has been performed with a different [2\theta] range or step size, the appropriate _pd_proc_* data items are used to define the [2\theta] values etc. used for the simulation.

3.3.5.3. Diffraction peak table

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The data items in these categories are as follows:

(a) PD_PEAK [Scheme scheme18]

(b) PD_PEAK_METHOD [Scheme scheme19]

The bullet ([\bullet]) indicates a category key. The arrow ([\rightarrow]) is a reference to a parent data item. Items in italics are defined in the core CIF dictionary.

When diffraction intensities are first measured, particularly when attempting to identify unknown phases in a material, the first step in the analysis is often to compile a list of peak positions. These peak positions are commonly used to search the Powder Diffraction File, which contains lists of peak heights and positions for approximately 100 000 materials (International Centre for Diffraction Data, 2004[link]).

Information on diffraction peaks is recorded in the PD_PEAK section of the pdCIF. Peak positions are recorded using _pd_peak_2theta_maximum or _pd_peak_2theta_centroid, for positions determined from the intensity maxima or from the peak centroids, respectively. It is also possible to record peak positions using _pd_peak_d_spacing. Peak intensities are recorded using _pd_peak_intensity and _pd_peak_pk_height, for the integrated peak area or the intensity value at the peak maximum, respectively. Peak widths are recorded using _pd_peak_width_2theta and _pd_peak_width_d_spacing.

A separate loop is used to list reflections, as will be discussed in Section 3.3.5.4[link]. To link reflections to peaks (one peak may consist of many reflections), each peak is assigned a unique code using _pd_peak_id, which is then referenced in the reflection table using _pd_refln_peak_id.

When intensities are measured using radiation with more than one wavelength, for example when both Cu Kα1 and Kα2 radiation are used or when a monochromator passes both [\lambda] and [\lambda/2] radiation, peaks may be assigned a wavelength symbol using _pd_peak_wavelength_id, where the wavelength symbol is defined in a separate _diffrn_radiation_wavelength_id loop. However, for many experiments, the assignment of wavelengths to peaks will be impractical owing to reflection overlap. It is usually better practice to specify wavelength labels in the reflection table using _pd_refln_wavelength_id.

3.3.5.4. Reflection assignments and intensities

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In addition to the REFLN data items defined in the core CIF dictionary, the following items are defined:

REFLN [Scheme scheme20]

The arrow ([\rightarrow]) is a reference to a parent data item. The dagger ([\dagger]) indicates a deprecated item, which should not be used in the creation of new CIFs. Items in italics are defined in the core CIF dictionary.

In a single-crystal experiment, a reflection table contains the initial experimental observations for structural analysis. In contrast, the reflection table for a powder-diffraction experiment is a derived result that depends on the model used to apportion intensity between overlapping reflections. Another difference is that in a single-crystal experiment, the reflection list will refer to only one phase (one hopes), while it is common to have reflections from more than one phase in a powder-diffraction reflection list.

A list of reflections in a powder-diffraction pattern is commonly generated by Rietveld analysis, where Hugo Rietveld's algorithm (Rietveld, 1967[link], 1969[link]) is used to estimate the intensity of each reflection. Alternatively, when the structure of one or more phases is not known, it is possible to use full-pattern intensity-extraction methods such as the algorithms developed by Pawley (1981[link]) or Le Bail et al. (1988[link]). In fact, intensity information obtained by full-pattern intensity extraction is often used for ab initio structure determination.

Most of the information in the reflection table will be defined using data items from the core CIF dictionary (see Section 3.2.2.2[link] and Chapter 4.1[link] ). For example, _refln_index_h, _refln_index_k and _refln_index_l will be used for the indices. The structure factors and reflection intensities are specified using _refln_intensity_calc, _refln_intensity_meas, _refln_F_squared_calc and _refln_F_squared_meas; reflection positions are defined using _refln_d_spacing. To link a reflection with a powder-diffraction peak, the pdCIF data item _pd_refln_peak_id is used. The value for _pd_refln_peak_id serves as a pointer to an entry in the peak table which has been labelled, using the data name _pd_peak_id, with the same symbol. Likewise, to link a reflection to a phase, the pdCIF data item _pd_refln_phase_id points to a phase defined using _pd_phase_id in the phase table. Since a single reflection may be observed with more than one wavelength, for example, with [\lambda/2] or Kα2 wavelengths, the pdCIF dictionary defines a wavelength link, _pd_refln_wavelength_id, that defines a wavelength label. However, since version 2.1, the core CIF dictionary defines _refln_wavelength_id and this should be used in preference to _pd_refln_wavelength_id. The data items _refln_wavelength_id and _pd_refln_wavelength_id both point to a wavelength label defined using _diffrn_radiation_wavelength_id.

The International Centre for Diffraction Data abstracts peak positions and heights for inclusion in the Powder Diffraction File. This information would be found in the _pd_peak section of a pdCIF. However, in many studies, particularly in Rietveld refinements, peak tables are never generated. In principle, it should be possible to calculate peak positions and peak heights (or better still, peak areas) from the information in a reflection table. An algorithm for this would be very useful.

References

International Centre for Diffraction Data (2004). Powder Diffraction File. International Centre for Diffraction Data, 12 Campus Boulevard, Newtown Square, Pennsylvania, USA. http://www.icdd.com .
Le Bail, A., Duroy, H. & Fourquet, J. L. (1988). Ab initio structure determination of LiSbWO6 by X-ray powder diffraction. Mater. Res. Bull. 23, 447–452.
Pawley, G. S. (1981). Unit-cell refinement from powder diffraction scans. J. Appl. Cryst. 14, 357–361.
Rietveld, H. M. (1967). Line profiles of neutron powder-diffraction peaks for structure refinement. Acta Cryst. 22, 151–152.
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71.








































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