The Rietveld analysis of X-ray powder diffraction patterns is used widely for obtaining the structural information of clay minerals. However, the complex hydration behavior and the variability of interlayer contents are often considered difficult to be described correctly by a simple structure model. In the present work, the use of Cu-triethylenetetramine Cu-trien -exchanged nontronites has been proposed to simplify the interlayer structure.
What's this all about?
This method provides a potential to obtain the structural information of nontronites, for example, the layer charge density, occupancies of cis -octahedral sites, and the iron content by the Rietveld analysis from the X-ray powder diffraction patterns.
The approach was demonstrated on three Cu-trien-exchanged nontronite samples. The Rietveld refinements were carried out first on the purified samples and the results showed a good peak fitting between measured and calculated patterns. The refined iron content and the occupancies of cis -octahedral sites are in general agreement with the reference data, which have been obtained from chemical and thermal analyses. The refinement of layer charge density showed lower values compared with the reference.
It may be due to the assumption of temperature factor of Cu-trien in the interlayer. A raw sample with natural impurities was chosen to test the applicability of this method. The refinement pattern of the raw sample led to good agreement with the observed data. The results of the iron content and the occupancies of cis -octahedral sites showed the same tendency as purified samples.
This study showed that this approach allows for obtaining some structural details of nontronites directly from X-ray powder diffraction patterns of Cu-trien-exchanged samples.
Nontronite is the iron-rich dioctahedral smectite. Only two-thirds of the octahedral positions are occupied by cations in dioctahedral smectites.
In general, octahedral sheet shows two different configurations, that is, cis - and trans -octahedron that relate to the disposition of hydroxyl groups. In the cis -octahedron, the OH groups are on the same side, whereas in the trans -octahedron, the OH groups are on the opposite side.
Tsipursky and Drits found that natural dioctahedral smectites may cover a wide range of cis -vacant cv and trans -vacant tv proportions. Based on the oblique-texture electron diffraction and X-ray diffraction analyses, Besson et al. In general, nontronites show turbostratic stacking disorder Biscoe and Warren, due to the weak bonds between the layers Moore and Reynolds, This kind of structural defect leads to non-Bragg diffraction effects and restricts the applicability of the conventional Rietveld method Bish, to smectite.
Several attempts of the Rietveld refinement have been done on turbostratically disordered structure Taylor and Matulis, ; Viani et al. However, these authors assumed more or less the ordered structure models, but not a real turbostratically disordered structure.
The BGMN software can describe turbostratic disorder features of the diffraction patterns successfully by using the structure model containing a single-layer approach Ufer et al. This method allowed an acceptable quantification of the smectite content in bentonites Ufer et al. Later, it was applied for the Rietveld refinement of illite-smectite mixed-layer minerals Ufer et al.
However, this approach cannot handle the complex hydration behavior in the interlayer Sato et al. Sposito et al. Ferrage et al. It seems that the correct description of the interlayer configuration is another difficulty for the Rietveld analysis of nontronites, except for the turbostratically disordered structure. Therefore, a defined and stable occupancy of the interlayer space, which is independent of humidity, may provide a potential for the modeling of such modified interlayer structures.
In general, the intercalation of ethylene glycol EG in smectites is used for the characterization of smectites and vermiculites MacEwan and Wilson, However, EG is not sufficiently stable for long-time measurements. The Cu-triethylenetetramine Cu-trien is a kind of stable complex and used routinely in the determination of the cation exchange capacity CEC Meier and Kahr, Federal government websites often end in.
The site is secure. This section is taken largely from Cranswick and Swainson . Additional information is given there, with many figures showing the interface window and many specific examples. The program offers many options, but the instructions here are limited to those you are expected to use in these tasks.
Open a new or existing.
If you wish to create a new file, type in the desired name and click the read usa-button. Enter crystal structure data for phases in the. Note that qualitative analysis must be done JADE is one of a number of graphical display programs for XRD data before undertaking the refinement. Note that the GSAS program refines rhombohedral structures in the hexagonal setting.
To enter structure data, select the phase tab and then the add phase usa-button. This will bring up an add new phase dialog where you input the phase title, the Space Group R —3 c make sure to include the spacesand the unit cell values.
Then select the add usa-button. GSAS will then give a symmetry analysis output for you to check to make sure you have entered the space group correctly use the International Tables or similar database to validate the output.
Select continue once you are satisfied with the structure data. Select the add atoms usa-button to go back to the main EXPGUI screen where all the crystallographic information is now visible. The structure database contains vibrational parameters, which are generally best retained and not refined. An alternate way to add phase data is to import it directly from the database.
This approach can be used after you gain experience entering the structure data manually. When you select the add phase usa-button and a new box appears, use the option in the lower right to import the phase data. Four options for import file format are provided--select the GSAS. After selecting a specific. If the. Select Continue and a list of symmetry operators appears; upon acceptance of the defaults, a list of atoms, coordinates, occupancies and vibrational parameters is displayed.
Select add atoms to complete the import of the remaining structure data as a new phase. You may wish to replace the default phase title in EXPGUI to the actual phase name, otherwise it reflects the path and filename of the. Create or open an instrument parameter file.
For the tasks in these instructions, open the file provided, which contains the parameters from Stutzman for the powder data used here. But if you wish to create a new file, select from the top menu Powder, Instedit. The instrument parameter file format is discussed in the GSAS manual page Perform refinements. For each refinement, run genles using the usa-buttons, preceeded by powpref when you have changed specific variables such as peak profile cutoff, or peak profile, sample displacement, or an instrument parameter.
GSAS generally will warn you if you are attempting to run genles after changing a key parameter.They're a collection of various tutorials from recent schools and user meetings. Please note that these tutorials have been created over several years in Topas v4 and up.Peter W. Stephens: Rietveld Refinement
In several cases there may now be better ways of tackling the problem or setting up the input file. Some topics will need topas v5 or v6. Please tell me if you find problems. They will definitely all work if you go back to jEdit 4. You can try these procedures on any of the other data sets provided. Tutorial 6 - Peak Fitting: How to perform individual peak fitting in topas, often the first step before indexing.
Tutorial 7 - Indexing: How to index a powder pattern in topas. The aim of the tutorial session is not to necessarily fully understand what your doing, but to make sure you're happy with the "mechanics" of the overall process of Rietveld refinement. The examples there have far more detail and contain screen shots of approximately what you should see at each stage. Tutorial 8 - How to run a prewritten input file. Tutorial 10 - TiO 2 Rietveld starting from a template file.
Tutorial 11 - Pawley Fitting: Pawley fitting is a structure-independent whole-pattern fitting method. It's a good way of finding if a unit cell is correct and also finding the "best possible" fit you'd get by Rietveld.
Tutorial 12 - ZrW 2 O 8 Rietveld: Simple Rietveld refinements of lab data, constant wavelength neutron and time of flight neutron data - make sure you have john's local. Tutorial 13 - Multiphase Rietveld refinement Tutorial Tutorial 14 - Y 2 O 3 data recorded on id31 at the esrf Tutorial 15 - ZrW 2 O 8 Rietveld: Simple Rietveld refinements of lab data, constant wavelength neutron and time of flight neutron data - make sure you have john's local.
Note this is the same as tutorial 12 above. Tutorial 16 - PbSO 4 neutron data Jeremy discussed are here. Tutorial 17 - Combined Refinement: Builds from earlier tutorial on ZrW 2 O 8 and shows how to simultaneously fit X-ray and neutron data. Also discusses structure solution from X-ray and neutron data. See also gsas 3 and gsas 4.
Peak Shapes Peak shapes are another fundamental aspect of a diffraction pattern. Tutorial 18 - This tutorial explores convolutions to fit a single peak in a pattern using the convolution approach discussed in lectures. Tutorial 19 - In this tutorial you'll investigate the various peak shape functions that are used in Rietveld refinement packages.
You'll use experimental fwhm vs 2-theta data in excel to come up with functions that might describe a real data set. You'll then try these functions in topas. Tutorial 20 - Fundamental Parameters peak shape fitting.
Several of the tutorials e. Tutorials in this section provide more examples. Tutorial 23 - Rietveld refinement of an organic molecule using restraints and rigid bodies. See also gsas 7. Tutorial 24 - A complex use of rigid bodies to refine 3 molecules in asymmetric unit with z-matrix description of local bodies to constrain internal symmetry.
Data recorded on id Neutron and X-ray Combined Refinement How to perform a combined refinement using neutron and X-ray data.A set of general guidelines for structure refinement using the Rietveld whole-profile method has been formulated by the International Union of Crystallography Commission on Powder Diffraction.
The practical rather than the theoretical aspects of each step in a typical Rietveld refinement are discussed with a view to guiding newcomers in the field.
The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features specific to data from neutron both constant-wavelength and time-of-flight and synchrotron radiation sources are also addressed. The topics covered include i data collection, ii background contribution, iii peak-shape function, iv refinement of profile parameters, v Fourier analysis with powder diffraction data, vi refinement of structural parameters, vii use of geometric restraints, viii calculation of e.
These studies were designed to evaluate a cross section of the currently used Rietveld software, to examine the effect of different refinement strategies, to assess the accuracy and precision of the parameters obtained in a Rietveld refinement, and to compare different instruments and methods of data collection. The results highlighted some of the problem areas and led to a series of recommendations regarding both data-collection and refinement strategies.
These guidelines cover the practical aspects of the Rietveld method and focus on data collected on a laboratory instrument. With the advent of graded multilayer optics and linear position-sensitive detectors, capillary measurements in the laboratory are being used with increasing frequency, so both reflection Bragg—Brentano and transmission Debye—Scherrer, Guinier geometries are considered.
While the use of Rietveld refinement for quantitative analysis is not dealt with specifically, the guidelines are also valid for this application. However, for additional information on this topic, the reader is referred to the paper by Hill In the following sections, the practical aspects of each step of a typical Rietveld refinement including some of the critical factors in the data collection itself are discussed, in the hope that the rapidly growing powder diffraction community can benefit from a relatively concise presentation of the pitfalls awaiting them and of some of the possible solutions.
Each topic is handled separately to enable easy reference. For more detailed information, the reader is referred to The Rietveld Method edited by R.
Guidelines for the publication of the results of Rietveld analyses can be found in the paper by Young et al. It has been assumed that the Rietveld refinement software used is reliable.
For a Rietveld refinement, it is essential that the powder diffraction data be collected appropriately. Factors to consider prior to data collection are the geometry of the diffractometer, the quality of the instrument alignment and calibration, the most suitable radiation e. It is not the purpose of this paper to delve into the intricacies of data collection, but it is perhaps appropriate to indicate briefly where common errors occur. For Bragg—Brentano geometries, it is important that the incident beam be kept on the sample at all angles to ensure a constant-volume condition.
Quite often, the divergence slits used are too wide and the beam hits the sample holder at low angles, so the intensities measured at these angles are too low. Some programs can correct for this, but most do not. If a correction is used, the shape of the sample holder i.
It should not be assumed that using a rotating circular sample will eliminate the problem.Rietveld refinement is a technique described by Hugo Rietveld for use in the characterisation of crystalline materials. The neutron and X-ray diffraction of powder samples results in a pattern characterised by reflections peaks in intensity at certain positions. The height, width and position of these reflections can be used to determine many aspects of the material's structure.
The Rietveld method uses a least squares approach to refine a theoretical line profile until it matches the measured profile. The introduction of this technique was a significant step forward in the diffraction analysis of powder samples as, unlike other techniques at that time, it was able to deal reliably with strongly overlapping reflections.
This terminology will be used here although the technique is equally applicable to alternative scales such as x-ray energy or neutron time-of-flight. The only wavelength and technique independent scale is in reciprocal space units or momentum transfer Qwhich is historically rarely used in powder diffraction but very common in all other diffraction and optics techniques. The relation is. The most common powder XRD refinement technique used today is based on the method proposed in the s by Hugo Rietveld.
It employs the non-linear least squares method, and requires the reasonable initial approximation of many free parameters, including peak shape, unit cell dimensions and coordinates of all atoms in the crystal structure. Other parameters can be guessed while still being reasonably refined. In this way one can refine the crystal structure of a powder material from PXRD data. The successful outcome of the refinement is directly related to the quality of the data, the quality of the model including initial approximationsand the experience of the user.
The Rietveld method is an incredibly powerful technique which began a remarkable era for powder XRD and materials science in general. Powder XRD is at heart a very basic experimental technique with diverse applications and experimental options.
It is possible to determine the accuracy of a crystal structure model by fitting a profile to a 1D plot of observed intensity vs angle. It is important to remember that Rietveld refinement requires a crystal structure model and offers no way to come up with such a model on its own.
Before exploring Rietveld refinement, it is necessary to establish a greater understanding of powder diffraction data and what information is encoded therein in order to establish a notion of how to create a model of a diffraction pattern, which is of course necessary in Rietveld refinement. A typical diffraction pattern can be described by the positions, shapes, and intensities of multiple Bragg reflections. Each of the three mentioned properties encodes some information relating to the crystal structure, the properties of the sample, and the properties of the instrumentation.
Some of these contributions are shown in Table 1, below. The structure of a powder pattern is essentially defined by instrumental parameters and two crystallographic parameters: unit cell dimensions, and atomic content and coordination.Rietveld refinement is a tool that tries to model a full powder diffraction profile based on crystal structure data, specimen and instrument effects.
This is achieved by introducing certain functions that describe typical phenomena in powder diffraction experiments, like 2theta errors or peak broadening, and by fitting the corresponding parameters afterwards. The parameters are varied using a least-squares procedure, in order to minimize the difference between the calculated and the experimental powder diffraction pattern. The Rietveld method was first introduced by Hugo Rietveld in and Details of the method are available in the literature: H.
Rietveld, Acta Cryst.
Rietveld, J. Young ed.
Parametric Rietveld refinement
One of the key issues of Rietveld refinement is that the method is rather sensitive to problems and errors in the model, resulting in non-convergence and other issues.
Hence, it has become a common agreement for many scientists that a successful phase analysis should be proven by a successful Rietveld refinement converging at low R- and chi 2 -factors. In addition, running Rietveld refinements on your diffraction pattern will give you an opportunity to think and learn more about your sample, your experiment and your model.
Here we give you some advice which important facts you should always keep in mind when running Rietveld refinement calculations, as well as some tips what you can do in case of problems. Today a variety of excellent programs for Rietveld refinement are available, so there is little need to invent the wheel again and again.
Rodriguez-Carvajal, Physica B55 to actually perform the calculations. You do not have to interact with FullProf directly though; instead, you can use the Match!
When you run Match! If this is not possible, you will be asked if you would like to manually select this path. Finally, if this is not successful e. If there is no valid path to FullProf available at its end e.
Setting up and running Rietveld refinement calculations Once you have defined the path to FullProf, you are ready to setup and run Rietveld refinement calculations from within Match!.In this paper the method of parametric Rietveld refinement is described, in which an ensemble of diffraction data collected as a function of time, temperature, pressure or any other variable are fitted to a single evolving structural model.
Parametric refinement offers a number of potential benefits over independent or sequential analysis. Keywords: powder diffraction ; non-ambient ; Rietveld refinement. It is well established that by performing diffraction studies as a function of an external variable frequently temperature, time, pressure or chemical environment one can learn more about a system than from a single diffraction experiment. Examples include extracting information about vibrational frequencies David et al. Such applications are becoming increasingly widespread, especially in the field of powder diffraction, where the advent of high-intensity sources and area detectors at both central facilities and home laboratories means that extremely rapid high-quality measurements can now be performed in minutes in a home laboratory or at a neutron source, and in a matter of seconds or less at a synchrotron.
The traditional way to treat data from such studies has been to use Rietveld refinement to analyse individual data sets independently. If, for example, one recorded powder diffraction patterns at different temperatures, each requiring refinement of 20 parameters, one would perform independent refinements using parameters in total.
It is clear, however, that these parameters are not completely independent. In such a study, one often does not want to determine n parameters at m temperatures, but how the n key parameters evolve with temperature.
Rietveld Structure Refinement of Cu-Trien Exchanged Nontronites
There are also often parameters which ought to remain unchanged throughout the diffraction experiment. In this paper we describe a general methodology for addressing this issue in which any parameter can be described by a single overall value or by a function describing its evolution throughout the data collection, and can be simultaneously refined from a large body of diffraction data.
The philosophy behind the method is, of course, similar to the use of multiple data sets across an X-ray absorption edge, multiple banks of a time-of-flight neutron data set or combined neutron and X-ray data sets to improve structural precision.
The method we describe is, however, entirely general, extremely flexible and can be used in a wide variety of situations. We note that the mind-set to adopt when applying this approach is similar to that when using restraints or constraints in other areas of crystallography. The software is also fast, robust and can handle an essentially unlimited number of parameters. The general form of an input file used for parametric fitting is shown schematically in Fig.
A typical control file for a case such as example 2 below has been deposited as supplementary information. Individual variables within these blocks can be assigned convenient names. Simple instructions also allow the values of selected parameters to be output to a text file after refinement. Other variables might be expected to show a simple dependence on temperature. For example, it is frequently found that the sample height in a high-temperature laboratory Bragg—Brentano experiment varies linearly with temperature due to thermal expansion of the furnace.
One would then describe the sample height at each set temperature e. In some situations see below one might wish to impose known physical behaviour during a refinement. In example 2we apply the known thermal expansion of calibration materials during multi-phase Rietveld refinement. This is done in the overall fixed variables section.
In TOPAS this can be expressed by defining a 0c n and as fixed values in the overall section of the input file and passing this information into each individual data set. The relevant format would be:. If the cell parameter forced on the refinement by the prescribed equation here! The relevant section of the input file would become:. The constraint equations described above are entirely general: they can be applied to any refinable quantity coordinates, occupancies, ADPs, etc.
Refinements can also be performed from a variety of random starting positions. A local Fortran routine then automatically replaces this label with one specific for each temperature, allowing input files for parametric refinement to be generated rapidly. Temperatures are extracted automatically, either from data file headers or from experiment log files. Input files also included instructions to produce text files of all refined parameters and their standard uncertainties.
All powder diffraction data reported here were recorded using a Bruker d8 advance diffractometer equipped with a Cu tube, Ge incident-beam monochromator and Vantec or Braun linear PSD position-sensitive detector. Low-temperature measurements were recorded using an Oxford Cryosystems pHeniX cryostat.
For furnace measurements, the sample was ramped to temperature and held at constant temperature throughout the diffraction experiment; in the cryostat the temperature was ramped continuously and a single average temperature determined for each diffraction pattern from experimental log files. Two examples of parametric refinement in this paper relate to the determination of accurate and precise cell parameters of materials as a function of temperature.