Tabular processor for X-ray diffractometry
Help and documentation for version 4.8
Tabular processor for X-ray diffractometry helps with common calculations in the practice of X-ray structure analysis: calculate the lattice parameters (edges, angles), estimate the quality of results, search the indices of reflections from unknown structures, calculate the reflection grid for known lattice, check the goniometer and specimen alignment.
Most available operations are accessible via main menu (use a mouse or F10 key). The context help is available any time by F1 key or Help button in the program dialogs (exceptions: Open and Save file dialogs may show the Windows help by F1 key, use Help button; Print dialog does not have Help button, use F1). To find a specific term or expression in this documentation, use the combination Ctrl+F in this help window.
The toolbar and key commands allow to perform many operations without opening the main menu. Many useful commands are shown on the bottom line, also the context information and helpful tips can be seen here. Some menus can be called locally by left-click on the corresponding text line, like emission, lattice type, cell centring and change indices.
Note: the colours used here in the illustrations mostly follow the classic colour scheme. For other schemes, the tones may slightly differ; if you use high contrast themes or visual accessibility settings in Windows, the colours may differ significantly.
Calculated lattice types: from cubic to triclinic. Calculated data: lattice edges, angles, cell volume; c/a relation for hexagonal, tetragonal and orthorhombic lattices; orthorhombic splitting.
Limits by indices h k l : from 0 to 99 Limits by interplanar distances: 0.02...99 Å Limits by lattice edges a, b, c: 2...99 Å Limits by lattice angles : 1...179o Precision of edge calculation : 0.00001 Å Maximum table size : 440 lines Number of labelled phases : 5
All calculations can be performed in ångströms (Å) or in nanometres (nm) as a length unit.
F1 - context help F3 - open a file (also Ctrl+O) F4 - select the emission (wavelength) F5 - set the lattice type (syngony) F6 - calculate the lattice parameters F7 - set the Bravais cell centring F8 - clear selected data in the table F9 - print the table (also Ctrl+P) F10 - enter the main menu F11 - mark the lines as a phase Esc - cancel; stop of auto recalculation Ctrl+N - new table (clear all current data) Ctrl+S - write table to current *htm or *.par file Ctrl+E - write to *htm, *.par, *.txt, *.csv file Ctrl+R - read one of the recent files Alt+N - see or input information about specimen Alt+E - input 2θ correction and precision Alt+F - choose the font for main screen and print Alt+O - see or change the program options Alt+M - calculate density and attenuation length Alt+P - calculate specimen displacement Alt+A - calculate angles and d for known h k l Alt+G - generate h k l, calculate reflections Alt+I - indexing the reflections in the table Alt+D - details of calculation, recommendations Alt+R - show the results of indexing Alt+K - change the indices in the table Alt+X - exit the program (also F12)
Enter - edit data in the current line (also F2)
Ctrl+X - cut current line and copy data to buffer
Ctrl+C - copy current line to buffer
Ctrl+V - insert data from buffer to new line
Ctrl+I - insert an empty line in current place
Ctrl+Z - undo the last line operation
Space - select or unselect current line
Ctrl+L - select all lines with calculated 2θ
Ctrl+A - select all lines with valid data
Ctrl+T - invert selection of all valid lines
A - arrange the lines in specified direction
Shift+A - set the column and direction for arrange
Ins - select a phase or class for a line
Shift+Up,
Shift+Dn - select or unselect a sequence of lines
Shift+Home,
Shift+End - select or unselect the lines from
current line to top or end of the table
N - assign an ordinal number to a line 1...4 - assign a specified phase, (1)...(4) S - mark a line as standard substance X - exclude a line from calculations B - set a line as basic for indexing
Enter - input value, go to next field or line Esc - restore value in the field, exit edit mode Tab - go to next field Shift+Tab - go to previous field Ctrl+Z - undo the last field edit operation
Home - move marker to begin of the table End - move marker to end of the table PgUp, PgDn - move marker up or down by one page Wheel - scroll the marker first, then table Shift+wheel - scroll the table Ctrl+(Num+) - increase font: zoom in Ctrl+(Num-) - decrease font: zoom out Ctrl+wheel - zoom in / zoom out
(rms - root mean square, dev - abs. deviation,
prec - precision of 2θ, i.e. ±2th)
excellent: dev < prec for all lines
very well: rms dev < rms prec × 1
well: rms dev < rms prec × 2
satisfactory: rms dev < rms prec × 3
poor: rms dev > rms prec × 3
quality decreases:
by 1, if lines number < parameters number × 2
(for lattices with 3 and more parameters)
by 1, if lines number = parameters number + 1
(for all lattices)
not defined, if lines number = parameters number
This menu includes the operations with the table.
Open - read a data file in available format Clear - clear entire table or particular data Save - write table to current *htm or *.par file Save as - write to *htm, *.par, *.txt, *.csv file Print - output table and results to printer Recent list - read one of the recent files (up to 9) Exit - exit the program, also use F12
This menu includes the operations with lines; convenient keyboard shortcuts are also available.
Undo - undo the last line or edit operation
Edit - input data or edit the fields in the
current line
Cut - delete current line, store its data
in the buffer
Copy - copy current line to the buffer
Paste - restore line from the buffer
Insert - insert an empty line in current place
Select - select/unselect line for calculation
Select calc - select all lines with calculated 2θ
Select all - select all lines with valid data
Invert all - invert selection of all valid lines
Arrange - set the column and direction for arrange
Set class - select a phase or class for a line
This menu allows to set the different specimen-related data and conditions of diffractometry.
Specimen - input the information about specimen
Emission - select the emission from the list
or input the wavelength manually
Lattice type - set the syngony (Bravais type)
for specimen or current phase
Cell centring - set the Bravais cell centring
Correction - set angles of standard substance
for 2θ correction; set precision
Font - select the font for main screen
Options - see or change the configuration
of the program
This menu allows to perform different calculations available in the program, like lattice parameters, theoretical angles or indexing.
Parameters - calculate lattice parameters
by selected lines of current phase
Details - show chart and report of calculation,
recommendations for improvement
Density and 1/μ - calculate theoretical density
and attenuation length
Displacement - calculate specimen displacement
by minimal deviation of results
Angles by h k l - calculate reflections by given
parameters for known h k l
Generate lines - generate reflections by given
parameters, syngony and cell
Indexing - find the possible indices of lines
by given lattice type and cell
Results - show the results of indexing,
found by two criteria
Change indices - exchange indices of current phase
or invert indices with negative k
Mark lines as - mark lines as belonging to a phase
This menu allows to get the help and information about the program.
Context - help on current program mode or status General - table of content of this help system Check for update - check if the new version is available Manual update - update by a file of program archive About - current program version and developers
Win32 version: Windows XP or later, mouse
(Windows 7 or later is highly recommended).
Monospaced font: Lucida Console 12...16 pt.
Internet connection (only for version update).
Two archives can be downloaded on the RTP home page. The main archive contains three files with the main program components. You can also download the archive with test examples, which contain the diffraction tables of various samples or PDF data; some examples may be useful to understand the indexing process. All archives use a Windows cabinet (CAB) format and can be opened and unpacked in Explorer or in other programs working with archives. Before downloading, browser may show a warning about download of unknown file; you need to allow it. Such warning is a common precaution which should never be ignored.
rtp32.exe - executable file (required) rtp.chm - help file (required) rtpwl.ini - wavelength list (optional) rtpam.ini - atomic masses (optional)
The main components of the program, rtp32.exe and rtp.chm, can be placed in any directory on an internal or external drive. The files with wavelength list rtpwl.ini and atomic masses rtpam.ini are optional; if exist, they should be placed in the same directory. File rtpwl.ini is added only if it does not exist and skipped otherwise, when it may have the user-defined wavelenghts. Changelog history.txt is shown after the update, only for information.
The shortcut to executable rtp32.exe can be created manually and placed wherever you want, e.g. on the desktop. To specify a directory with data files, input it in the "Start in:" field of the shortcut. The configuration file rtp.ini also will be saved here. If need, you can create several shortcuts to different directories and configurations. Launching the program directly in Explorer is also possible but not recommended if the data files are stored elsewhere, or when the program's directory may be write-protected because of read-only drive or no write permission for user account, so rtp.ini will not be saved.
Note: it is not recommended to place the program components in a directory with extended Unicode symbols, e.g. with Cyrillic letters; use the path with Latin characters and digits. Otherwise some problems may occur with the help system (you may not be able to open the help file independently).
Program does not keep specific information in Registry; all configuration is stored in rtp.ini. To uninstall the program, simply delete its components including the files used for update, rtp32.cab and rtp32upd.cmd, and created shortcuts. If you want to move the program to another machine, make a copy of all components and diffraction data to external drive (it would be better to copy the files with directory structure), then transfer these files to a new PC. Finally, create new shortcut(s) on the desktop.
Check for update is accessible in the "Help" menu. It checks the build date and time on the program's home page; if the more recent version is available, you can Update it directly from the program. Make sure that all lattice calculations are performed and results are saved, if need. If the update was successful, the text file with the list of changes history.txt will be shown in the Notepad editor. You can close it and open the updated program as usual. Updates may include new operations, improvements and corrections of found errors.
Check for updated version can also be performed automatically on regular basis, daily or weekly. This setting is available in Options; the date of the last check is stored in configuration file (dates of update use the calendar of your PC, they are not related to build dates).
If PC has a problem with Internet connection, you will see an error message. Try to check the connection using a web browser, then try to open Home page in the "About" dialog. In some configurations, Windows Firewall may block the Internet access for any program not included in the permission list, so you can check and download a new version only in a web browser. Another possible error may happen if the new files cannot be saved. Check if the directory with the program components is not write-protected and has the write permission for current user account.
If Internet is not available or a machine is not connected to network, you can perform manual update by a local copy of main program archive. This file, usually rtp32.cab, can be downloaded on any machine with Internet connection and transferred, for example, by a portable drive.
Update can be started from the "Manual update" menu. You need to select the downloaded *.cab archive in the file window. Please note that archive of currently used version is stored in the program's directory, so choose the new archive instead. If you prefer to unpack the archive and update each file separately, note that at least the files rtp32.exe and rtp.chm should be replaced with new versions. Do not replace rtpwl.ini if you have changed it by including your own wavelength list; the same is true for the list of atomic masses rtpam.ini.
Configuration file stores the program settings and list of recent files; it uses UTF-8 text format. It is created in a working directory and updated upon exit, if you worked with files or changed any setting.
Almost all configuration settings can be viewed and changed in the options dialog, with exception of the last used wavelength, 2θ precision, font and delta. It is recommended not to change the file rtp.ini directly; use the program dialogs instead. Open this file in a text editor like Notepad only if need to check whether the current configuration might be a cause of a problem.
clock - clock on the screen: none=0, show=1
(can be changed by left-click the clock)
scheme - colour scheme: classic=1, light=2, dark=3,
system=4 (for contrast desktop themes)
mark - mark of current field in the table:
none=0, dotted=1, solid=2, colour=3
update - check for update interval: never=0, daily=1,
weekly=2, date of the last check (dd.mm.yyyy)
font - name of font for main window, font size, style
(please change the font only in Font dialog)
lines - number of table lines visible on the screen
wave - last used wavelength, length unit (A or nm)
precise - last used 2θ precision
pdfprec - default 2θ precision for PDF-2 cards
precmode - precision mode: constant=1, cosine=2
delta - multiplier of 2θ precision for indexing
radius - distance from specimen to detector slit, mm
standard - up to 5 interplanar distances of a standard, Å
[recent] - list of the recently opened or saved files
Thank you for using this program, and good luck in the researches using the X-ray diffractometry! Any opinions about the program, information about possible problems, issues as well as other useful recommendations will be received with gratitude.
Basic ideas and some code used in the program were developed in late 1980's by staff of X-ray research laboratory of the Institute of Inorganic Materials in Moscow: Andrey V. Golubev, Michael A. Poddyakov, Konstantin I. Avertsev, Iaroslav N. Chebotarev.
K. Avertsev — ideas and algorithm of the shuffle method used for indexing.
A. Golubev — ideas and algorithm of generation of indices for different lattices and cells centrings.
M. Poddyakov — first version of the program, basic code of solving the matrix using the Gauss method, calculation of lattice parameters up to monoclinic.
Ia. Chebotarev — calculation of triclinic lattice, 2θ correction, user interface, help system, Win32 version of the program.
Contact in Telegram: @Slavic (please ask questions without icons and stickers which can be counted as spam)
Select a data file from list (change the directory or drive if necessary). By default here are shown the files *.par and *.htm created by this program and *.aid files exported from the PDF-2 database [1] (an option in PCPDFWIN software).
Files *.par contain all common data available in the program interface: the table of reflections, calculated parameters, specimen structure, description and notes; this is a default format. Hypertext *.htm files contain the same information with added HTML code, which allows to see the data in a web browser. In addition, they show the non-reliable data in colour similar to the table on the program screen. Both file types use UTF-8 text format.
Import of the PDF cards *.aid depends on the information in a particular card. For most modern cards, the program inputs the table of reflections (d, I and h k l) and calculates 2θ using the wavelength stored in the card. The substance name and chemical formula are input as well and become available in the specimen dialog. However, some old cards (before 1970) may have lack of specific data: no indices, wavelength, undefined structure. You will see a warning in such case. Some cards may have too low precision of d; if so, the program will reconstruct the 2θ precision and use it instead of default value. Otherwise the precision is taken from the options, field "Default PDF precision".
By selecting the *.txt files in the drop-down list below the file window you can import the list of 2θ or d and some additional data, prepared in ASCII *.txt format. This list may include the header with the specimen name and wavelength beginning from ";" or "#" (optional).
Any data line must have 2θ or d value. Intensities and indices h k l are optional. Such files can be created manually or by the programs processing the raw data from XRD devices, header can be added later.
; Nickel FCC ; 1.54051 A 44.51 100 1 1 1 51.85 40 2 0 0 76.37 20 2 2 0
The data files may have different extensions, depending on the program where the diffraction data were exported from. For example, the program Match! may export the list of d and I values (File, Export, Peak data) to a file with extensions *.dif or *.csv. You may rename such file to *.txt or select the option *.* in the drop-down list. Here is an example of exported data file of Zr powder (hexagonal lattice, wavelength 1.39217 Å, original format without header):
2.806608 281.7 2.579302 315.4 2.465013 1000.0 1.897778 205.0
If the file has a header with wavelength, it will be used to calculate 2θ or d (see below). To avoid possible problems with uncommon wavelength, you can optionally add the length unit "A" or "nm" after the value (see the first example). If other information presents in the header, it will be counted as a specimen name and additional notes and stored in the specimen information, up to 4 lines of notes. If no header exists (as in the second example), the file name will be used as a specimen name. After the input, you can change the information lines manually.
There are also two specific text formats: AMS files and Winfit! data; they are described below.
Select the data type
Import logic attempts to determine whether the first column may be 2θ or d by the values in 3 data lines (do they follow in increment or decrement, are they more or less than 10.0 etc). This logic is heuristic and sometimes may make incorrect conclusions, especially if the file has less than 3 lines or if the wavelength of data is different from current. Import dialog shows the first lines, which can help you to choose the correct type. You need to confirm data type: 2th values or d values.
For d values type, also check whether the length unit (Å or nm) is correct. If the wavelength is not known, import logic attempts to determine the unit and shows a warning to prevent possible problem. If current unit in the program is different than in the file, you need to Cancel the import and switch the length unit in the emission menu, then open this file again. Wavelength in a file header allows to avoid this problem.
Check the wavelength
After the import, if the wavelength was included to the file header but does not have a length unit, the program uses the heuristic approach to determine the length unit (see details in the select the emission section). Otherwise, if the wavelength was not included, like in the second example, you need to select it manually.
Add required data
To perform the lattice calculation, you need to select the proper lattice type and set the precision by 2θ. Initial precision for these files is the last used precision in the dialog correction and precision, stored in program configuration (0.01 degree by default); you can set 2θ precision before or after the import. Then input the indices h k l. Alternatively, you can try to obtain the indices using the indexing process.
These are the files with diffraction data of minerals in special *.txt format of American Mineralogist Crystal Structure Database [2] (use the link "Download diffraction data" after the search in database). The program imports the reflection table, which includes both d and 2θ (the program counts d values as original), as well as name of mineral and space group, which are stored in the specimen information. Precision by 2θ is used the same as for PDF files: options, "Default PDF precision". Because the lattice type is not mentioned directly, instead of analysing the space group, the program makes conclusion from the lattice parameters. However, some oddities may occur, like the "cubic" parameters for the group P1 (triclinic) are recognised as cubic lattice. You can select different lattice manually, calculate it and compare the results.
The program can recognise the data from *.txt files, saved in a text editor like Notepad after pasting the data from the clipboard of the Winfit! program [3], where the list of peaks was obtained after fitting the raw XRD data (Winfit does not have the direct option of writing these results to a file). The name of the file with raw data is shown in the first line, the program uses it as a specimen name; the integral intensities (Area) are imported to the "I" column.
The lines imported from a common *.txt or Winfit! files can be added to existing table with keeping all current data. This allows to combine several files with reflections from particular areas of diffractogram into integrated table. For example, some areas of diffractogram may be obtained in different time; some raw processing programs may have a limitation by points per single fit etc.
When you open a new *.txt file, if the table is not empty, the program asks whether to Clear current table and then load new data (this is a default action), or keep the table and Add new data after the end. In the last case, the specimen name and other information will not be replaced, only new file name added to recent list. New file may have a wavelength in the header, and if it is different from current or has different length unit (Å or nm), data in imported lines will be recalculated to current wavelength.
Without wavelength in the header, if the supposed length unit in a file is different than in the table, you will see the warning in the dialog. If the units are different, you need to Cancel the import, switch the unit in the emission menu and open the file again.
Newly imported lines always get the ordinal numbers in the table. If you want to differentiate them from previous lines, you can mark current lines as a phase with certain number before adding.
After the import, it would be a good idea to check the specimen information and add some notes about the diffraction table, if you use this option.
This menu allows to clear the entire table and calculated results (Clear all, the default option) with keeping only the wavelength and structure, or clear the particular parts of data. If you suppose to use current data later, save the table to a file.
Other options allow to clear:
— table data
Clear the entire table and keep the lattice parameters (if you generate the reflections by current parameters, the existing lines will be cleared anyway);
— non-selected
Clear the table of non-selected lines. This can help to clear the table of the lines which are non-reliable or belong to other additional substances;
— phase labels
Clear all phase labels and numerate the lines in ascending. The information about structure of different phases will be lost. The lattice type and cell centring of last calculated phase will be assigned to all lines. If no phase was calculated, the structure of the phase with lower number will be taken;
— basic marks
Clear all marks of the lines as basic for indexing, if you want to select other basic lines;
— indices h k l
Clear the indices, if you want to input different indices or use indexing by shuffle (first successful indexing cycle will update the indices anyway);
— 2th, d, I
Clear these data, if you want to apply the existing indices to a new substance. In particular, you may use a previously calculated specimen, PDF or AMS card as a structure prototype to calculate angles and d for known h k l (this calculation updates 2θ and d, deletes the precisions but keeps the intensities);
— results
Clear the calculated 2θ, deviation and lattice parameters, if you want to perform different calculations (any new calculation overwrites the previous results anyway). Note: if you clear both the table data and results, only the specimen information will remain.
You do not need to clear all data to calculate another specimen or phase with the same structure. Instead, you may input new 2θ or d values in the existing lines, change the specimen name and delete extra lines if need, then select the lines for calculation.
You attempt to clear the table while the data have never been saved to a file. As a result, all the table and calculated results will be lost. If you suppose to use current data later, save the data to a file first.
To save the table and calculated results, input a file name and select the format *.htm or *.par in the drop-down list below file window; the extension, if not specified, will be added automatically. Change the directory or drive if necessary. You can also select any existing file and use its name as a pattern or overwrite it.
If the table has not been saved and filename does not yet exist, the specimen name will be set as a suggested filename in the "Save" dialog. You can use it as is or edit if need.
The files *.par have a conventional UTF-8 text format, format of *.htm files is HTML. They contain all information about specimen, wavelength, full table of reflections and results of calculation if it was performed. They do not include some specific details visible in the program interface; the same limitations are applied to the printed tables.
You can save (export) the table data in different formats: *.par, *.htm, *.txt and *.csv. Choose the appropriate format in the drop-down list below the file window.
Formats *.par and *.htm are preferred for saving the data; besides the table, they keep the information about specimen, wavelength and the results of calculations. Text-like format *.par is more old, while hypertext *.htm is more modern. It contains the same data with added HTML code, which allows to view a table in a web browser. Like on the main screen, it shows in colour the indices, which should not present in current lattice, and significant 2θ deviations (more than 3 × precision).
ASCII *.txt format is useful for phase analysis. This format contains the header with specimen name and wavelength, followed by the data lines with 2θ and I values (if no any intensities are known, 100 will be set instead). Use an option "Import ASCII" in the phase analysis program to import this table.
; Nickel FCC ; 1.54051 44.510 100.0 51.850 40.0 76.370 20.0
CSV (comma-separated values) file format is compatible with spreadsheets, for example, MS Excel. The table is exported completely, and calculated data are placed after the end of the table. This option allows to perform additional calculations, comparisons and visual presentations. Usually the files with *.csv extension can be opened in the installed spreadsheet by default.
Confirm the output of the table and calculated results to printer. You can select a printer and change the printing preferences using the standard Windows interface.
Printing is implemented on basic level, it can help in common work, but cannot produce presentation-quality materials (you can save the table to a file *.par and import it into a convenient text or presentation editor). The table is printed in black-and-white mode: the colour marks of large deviations and non-permitted indices, if they present, are not reproduced. Printing uses the same monospaced font as on the main screen (Lucida Console by default), font size 14 points, standard font style. Page layout is designed for A4 paper, margins 15-20 mm; US letter size is also suitable.
Another option to have more control on printing is to save the table and results in HTML format and open it in a web browser. Most browsers, like Google Chrome, have an option to show a preview of the pages before printing, change the layout, margins and scale (zoom level) and also are able to print in colour if the table has such marks.
Check whether the table and calculated results have been written to a file, if necessary. This warning is shown only if you have some unsaved data.
# ‹h k l› 2th ±2th d ±d I 2th calc dev. 1 1 1 1 44.510 0.020 2.0338 0.0009 100.0 2 200 3
To calculate the lattice parameters, fill in the fields: h k l, 2th and ±2th or d and ±d. Intensities are optional, they do not affect the results. To input or edit the data in a field, move the horizontal marker to chosen line using a mouse wheel or arrow keys on the keyboard, then left-click the field or press Enter key. You can also use the arrow keys to select the field: the header of current column is marked with the pair of angle brackets. In addition, mark of current field can be selected in options.
The lines, which have enough data for calculation, become selected by default and are marked by bluish background , which means that these lines will be used to get the results. For indexing, the indices may be skipped (and such lines cannot be selected for lattice calculation), but the intensity values, if known, may be very helpful.
If the indices h k l are marked by yellow, they do not correlate with current lattice type or cell centring (see more details in these sections).
Adjacent lines of the same phase with the same 2θ and d values (they may have different indices h k l) are automatically marked with the bracket-like group labels to the right from the ordinal number or phase label. This makes easier to see the coincident lines, especially in the results of indexing.
Enter - input a value, go to the next field/line Esc - restore value in the field, exit editing Tab - go to next field Shift+Tab - go to previous field Shift+Right, Shift+Left - select characters in the edit field Backspace - delete selection Ctrl+X - cut selection and copy it to buffer Ctrl+C - copy selection to buffer Ctrl+V - paste selection in current place Ctrl+Z - undo the last field edit operation
Left click - edit a field in current line;
- input if clicked outside of field
but within current line;
- cancel if clicked outside of field
on another line or out of the table
Right click - cancel if clicked outside of field
If you press Enter key to input the values in the fields, the program logic will attempt to assist your input. For example, h k l values less than 10 may be input without spaces. If the number of digits in the next index is the same or less than in current, the digits can be input "naturally", like 122 (1 2 2), 1014 (10 1 4) etc. However, if the number of digits in the next index is more than in current, need to add 0 before current index, like 08122 (8 12 2). For zero index, one zero is enough (see more details in the table below). If you are not sure whether the conversion will be correct, use spaces to separate the indices.
In the first line, after the input of 2th and ±2th, the d and ±d fields will be filled in automatically according to current wavelength, and the field I will be skipped. (If you want to input I anyway, use the Tab key or left-click that field.) In the next lines only 2th value is required, the precision ±2th will be copied from the previous line or calculated depending on your precision mode (see correction and precision). You can change the suggested value and input a value of your choice instead.
Undo operation (Ctrl+Z or "Undo" toolbar button) works separately for field editing and line operations. In a field, any change can be undone once to previous value or string; second undo restores the last value. Operation with a line (Edit, Cut, Paste, Insert) can be undone in normal (non-edit) mode. In particular, after editing a line you can exit the edit mode (Esc) and restore all previously changed values; it may help if you occasionally deleted or modified a field. However, changing any field in another line will make undo of previous line non possible.
Input Converted Digits Notes hkl h k l 3 any every h k l has 1 digit hhkl hh k l 4 non-zero hh, k, l 0kkl 0 kk l 4 from 0 0 for h, kk, l 00ll 0 0 ll 4 from 00 0 for h, 0 for k, ll hhkkl hh kk l 5 non-zero hh, kk, l 0hkkl h kk l 5 from 0 0h for h, kk, l 00kll 0 k ll 5 from 00 0 for h, 0k for k, ll hh0ll hh 0 ll 5, 0 inside hh, 0 for k, ll 0h0ll h 0 ll 5, two 0 0h for h, 0 for k, ll hhkkll hh kk ll 6 any every h k l has 2 digits
# h k l 2th ±2th d ±d I 2th calc dev. 1 1 1 1 44.510 0.020 2.0338 0.0009 100.0 2 2 0 0 51.850 0.020 1.7618 0.0006 40.0 3 2 2 0 76.370 0.020 1.24596 0.00028 20.0 4
Selected lines of each phase are marked by a colour: they have a bluish background or green background with the marker at least until the "I" column. You cannot select the lines with errors or incomplete data; they will have a white background until correction.
On the illustration the lines 1 and 2 are selected, while the line 3 is not. Marker is placed on the line 1, its right part is yellow because the results are not yet obtained. Note that the line 3 has a bluish line number: it shows that this line is ready to be selected, unlike the empty line 4.
If the table has the lines belonging to more than one phase, you need to move the marker to any line of the phase which you want to calculate. Only one phase can be chosen for calculation, the lines of other phases are inactive (pale).
Space - select or unselect current line
Shift+Up,
Shift+Dn - select/unselect a sequence of lines
Shift+Home,
Shift+End - select/unselect the lines from current
line to top or to end of the table
Enter - input or edit data in the current line
Ctrl+X - cut current line and copy data to buffer
Ctrl+C - copy current line to buffer
Ctrl+V - paste data from buffer to new line
Ctrl+I - insert an empty line in current place
Ctrl+Z - undo the last line operation
Ctrl+L - select all lines with calculated 2θ
Ctrl+A - select all lines with valid data
Ctrl+T - invert selection of all valid lines
Ins - set a phase or class for a line
See above the keys for editing data in a field.
Left click - set the marker at cursor position;
- call the class menu in "#" column;
- edit a field in the columns from
"h k l" to "I" in the current line
Right click - select or unselect a line
Wheel - scroll the marker first, then table
Shift+wheel - scroll the table
Initially all lines in a new table or in a table imported from PDF or AMS database do not have any special labels besides a line number. This is a common case when the table includes only a single substance. Otherwise you may use the labels to differentiate the lines, in particular, the lines of the standard substance or separate two or more phases. Note that every phase has an independent lattice type and cell centring (primitive cubic type is assigned by default).
# h k l 2th ±2th d ±d I 2th calc dev. 2 2 0 0 51.850 0.020 1.7618 0.0006 40.0
✓ Numbers
Phase 1
Phase 2
Phase 3
Phase 4
Standard
Excluded
Basic |
To assign a class to a particular line, you can left-click the line in the column "#" or press the Ins or "Context" key (or Shift+F10 combination) to show the context menu of class selection. Choose a class label for this line:
Numbers - a line with ordinal number
Phase 1...4 - one of specified phases, (1)...(4)
Standard - a line of the standard substance, (s)
Excluded - a line excluded from calculations, x
Basic - a basic line for indexing
The selected class is shown instead of ordinal number; a basic line has an asterisk mark "*" right from a line number or phase label (the excluded lines cannot be marked as basic). Please note: using the context menu is not necessary, all labels can be set or changed directly by the corresponding keys, like key "1" to assign the phase 1 etc. Some advices related to selection of the basic lines can be found in the indexing section.
Note that program has a limit of the lines labelled as a standard (s) for angle correction, depending on number of possible reflections of standard substance at current wavelength, maximum of 5. You can see this number in the correction and precision dialog. Extra lines cannot improve the correction, but can be used to calculate the standard as a separate phase.
Excluded lines do not participate in any calculation. Using this label has a sense if you want to mark them later as belonging to some phase, otherwise it would be reasonable to delete ("Cut" in the "Line" menu) such lines. You can also delete all non-selected lines in the clear menu.
# h k l 2th ▲ ±2th d ±d I 2th calc dev. 1 1 1 1 44.510 0.020 2.0338 0.0009 100.0 44.502 0.008 2 2 0 0 51.850 0.020 1.7618 0.0006 40.0 51.857 -0.007 3 2 2 0 76.370 0.020 1.24596 0.00028 20.0 76.393 -0.023 4
You can arrange (sort) the lines in the table by class numbers #, experimental angles 2th, interplanar distances d, intensities I and absolute values of deviations. To do this, left-click the table header with bright blue background. Alternatively, use the keys Alt + column number. The direction of arrangment is shown by the triangle in the chosen header, like by ascending of 2θ on the illustration above. By the second left-click the direction switches to opposite etc.
Selection of the column and direction is also available from the menu "Line" or by the right part of toolbar button "Arrange". Alternatively, use the Shift+A combination. Key A allows to perform arrangement immediately in specified direction or cancel it. Toolbar button also shows the arrangment, it looks pressed when the lines are in order.
Arranging is not repeated automatically: it is shown only when changing of the data in selected column does not break the specified order. This prevents the undesired change of line positions if the lines are edited or selected / unselected when the recalculation is active. To arrange the lines again, left-click the header of chosen column or press the A key.
Remark: left-click the h k l table header calls the change indices menu.
A - arrange the lines in specified direction Shift+A - set the column and direction for arrange Alt+1 - arrange by class # and 2th Alt+3 - arrange by 2th Alt+5 - arrange by d Alt+7 - arrange by I Alt+9 - arrange by abs. deviation
In particular, arranging by deviations is useful after calculation of lattice parameters: it allows to see the lines with most significant deviation and unselect them or correct the mistakes in their data.
Arranging by classes is possible only if some of them were defined. The lines with ordinal numbers are arranged first, then the phases (1), (2) etc., then standard substance (s) and excluded lines " x ". Within any class, the lines will be arranged by ascending of 2θ.
In this dialog you can input a specimen name and short description of specimen or its phases, if they are specified. These fields are optional: filling them in or using only a unique filename is a matter of personal style. Any line may have up to 68 characters or be empty (on the main screen, specimen name is limited by 26 characters). Non-empty lines will be written at the end of the file *.htm or *.par. When you read a PDF card or AMS file, a substance name is taken from the data; a chemical formula in PDF card is taken as well. If you have input the formula in the theoretical density dialog, it will be stored here too.
Below the editable fields, some additional lines may be shown. One is a line with information about applied goniometer and specimen corrections: constant correction and specimen displacement. These data present only after correction by standard substance or calculation of specimen displacement. If you have calculated the molar mass of the formula unit and the theoretical density, they will be shown in another line. These lines are non-editable and will be saved to a file or printed as is; you can select some text with mouse and copy to clipboard, if need.
Emission: 1.540600
Choose the emission type or wavelength from the list of emissions, which are commonly used in the X-ray diffractometry, in the "Emission" menu or by left-click on current value. You can also input the wavelength manually. The last used value is stored in the configuration file. This menu also allows to select the length unit: ångströms (Å) or nanometres (nm). If the length unit was changed when the table has some data, you need to calculate the lattice parameters again.
The internal table of wavelengths (which are more traditional than physically true) can be replaced with data from the file rtpwl.ini, which should be placed in the program's directory. This file can include up to 20 data lines, each includes the name, wavelength and short description. The example below is based on the work of G. Hölzer and others [4].
; Wavelenght list for RTP32 ; replaces the internal table (max. 20 lines) ; G. Holzer et al., Phys. Rev. A, 56 (6), 4561 (1997) ; Name Lambda Description &Cu-Ka1 1.540593 Emission of copper, line K-alpha1 Cu-K&b 1.392235 Emission of copper, line K-beta A&g-Ka1 0.559363 Emission of silver, line K-alpha1 C&o-Ka1 1.788996 Emission of cobalt, line K-alpha1 Co-Kb 1.620826 Emission of cobalt, line K-beta C&r-Ka1 2.289726 Emission of chromium, line K-alpha1 Cr-Kb 2.084881 Emission of chromium, line K-beta &Fe-Ka1 1.936041 Emission of iron, line K-alpha1 Fe-Kb 1.756604 Emission of iron, line K-beta &Mo-Ka1 0.709300 Emission of molybdenum, line K-alpha1 Mo-Kb 0.632253 Emission of molybdenum, line K-beta &Ni-Ka1 1.657930 Emission of nickel, line K-alpha1 Ni-Kb 1.500152 Emission of nickel, line K-beta &W-La1 1.476345 Emission of tungsten, line L-alpha1
You may create your own rtpwl.ini using this one as an example. All wavelenghts should be input in ångströms (they will be shown in nanometres if you choose this option in the menu). If you use the non-Latin characters, like Greek letters, save the file in the UTF-8 format.
The program uses the heuristic approach to determine whether the manually input value is in Å or nm. Every value is checked against the values in the table within relative difference 0.00067 (the relative differences in the wavelengths listed in scientific media and databases usually are less than 0.0002). If the value is found, the emission type and its unit are determined as well. However, wavelength with difference more than 0.0002 is counted as non-standard. Otherwise the values less than 0.49 are counted as nm (for reference, less common Ag Kβ is about 0.49701 Å). If you use a rare short-wave emission like W Kα1 (0.20901 Å) or Au Kα1 (0.18020 Å), add it to rtpwl.ini to prevent a mistake in length unit.
Cu Kα1, Å |
Tooltip for the wavelength field shows the name of current emission and the energy in kiloelectronvolts (keV); the energies for the emissions listed in the menu are also shown in the context tip on the screen bottom. This value may be helpful to estimate the thickness of diffraction area by chemical composition of the specimen (more details are in the calculate attenuation length section).
Energy of X-ray photon is calculated by the formula:
E = hc/λ
where h — Planck constant, c — speed of light, λ — wavelength. Coefficient hc is 1.23984198 eV⋅μm (which is equal to keV⋅nm).
Input the specific wavelength for current experimental data, if it does not present in the common list. The last used value will be stored in the configuration file. Please read the details and recommendation in the previous section.
Lattice: A orthorhombic
Select the Bravais lattice type (syngony) for investigated crystal substance or phase in the "Lattice type" menu or by left-click on the syngony name. If the table has more than one phase, the current phase is defined by current position of the marker. When you add a new phase to the table or assign new class label to existing line, it gets the default "P cubic" type. Check this and correct for every new table or new phase, if needs.
For the rhombohedral, monoclinic and triclinic syngonies, where the negative indices are possible, the program checks if a particular negative h, k or l may be valid; if not, these indices will be marked in the table by yellow h k l. Check and correct the yellow indices accordingly.
For indexing, if a syngony is unknown, it is recommended to begin the process from the most symmetric types.
Select the Bravais cell centring for current lattice type in the "Cell centring" menu or by left-click on the centring letter. If some indices in the table should not present in the chosen centring because of extinction, they will be marked by yellow. The option "find highest" allows to find the most symmetric centring for all indices of current phase.
The program allows to select only those centrings, which are possible from the crystallographic point for current lattice type [5]. All other centrings are inactive and cannot be selected. In the practice of X-ray analysis, however, the less restrictive approach may exist, like, for example, a face-centred triclinic cell. They are not minimal or do not have the full set of symmetry translations, but sometimes these models may be useful to describe a distortion or phase transformation of more symmetric cells; they also may exist in some PDF cards. When the program opens such card, non-standard centring will be marked by yellow centring letter. This lattice still can be calculated, but if you change the centring, it cannot be restored back in the program interface.
Point at one of the lines belonging to a known phase which you would like to calculate or define its lattice type or cell centring. Empty and excluded lines cannot be used for calculations. Please move the marker accordingly.
In this dialog you can input and calculate the data required for 2θ correction, change 2θ precision for all lines in the table, change the precision mode. To correct the angles 2θ, which may be shifted from ideal positions because of detector or specimen misalignment, you can use the experimental angles of standard substance. You can also correct the angles by calculated attenuation length in the material.
The required theoretical angles of standard substance are calculated from interplanar distances, which are stored in the configuration file, at current wavelength. Use options to see or change these data. Note that 3 decimal signs for calculated angles is only a visual limitation here, the program internally uses all available signs.
Standard #:
To use the standard substance correction, input here from 1 to 5 experimental angles (see the technical details below). Single angle gives the constant correction; two or more allow to calculate the specimen displacement and correct the experimental angles more precisely.
Please note that usage of two or more standard lines is highly recommended; the constant correction by single line may give reliable results only in narrow area around this angle.
Adding the lines of standard substance to the table is not required, but can be helpful. In this case, you can input their line numbers with "#" symbol, e.g. #4. You may input "#" without a number, then the line nearest to the theoretical angle will be taken. You can use this if the class label (s) is assigned to standard lines instead of ordinal numbers (caution: the class label is not checked here; if the nearest angle belongs to investigated phase, it will be taken instead of standard, so check the angle when it will be shown in this field after calculation).
Press Calculate if you want to see the correction (constant and displacement values) without changing the table. Press Apply to correct the angles of all lines in the table. Calculated constant correction and specimen displacement / detector radius will be shown in the specimen dialog and saved as a remark in *.par or *.htm file.
2th rms deviation:
This root mean square deviation is calculated for 3 or more angles of the standard substance. After calculation of constant correction and specimen displacement, the angles of standard are compared with their ideal calculated positions. This value is not used in other calculations, but can help to estimate the consistency of standard. It should be quite small, typically about 0.01 degree or less, close to goniometer precision. Higher deviation may be a result of incorrect separation of the standard and adjacent specimen lines or an input error. If so, consider to re-check these angles, but if the calculated correction and displacement are high too, need to check the goniometer adjustment.
Constant correction:
This field shows the constant (zero-point) correction calculated by the lines of standard substance. You can also input here the constant correction for your detector manually and calculate the shifted angles.
In the contemporary XRD devices, the zero-point correction is applied automatically after goniometer adjustment or, if need, it can be input manually in the control software, so the experimental angles are already fixed and additional correction before calculation of parameters is not required. However, for old-style optical goniometers such correction still should be added manually.
Specimen displacement, mm:
This field shows the specimen displacement calculated by two or more lines of standard substance, in millimetres. A positive value means the shift of specimen plane toward the diffraction angle, negative — backward.
If you input the constant correction and/or specimen displacement manually, then Calculate will give the expected angles of standard substance for such misalignment. This may be useful to reproduce the alignment of specimen and/or adjustment of goniometer.
Specimen displacement can also be calculated independently by the minimal divergence of results of investigated material, in this case the lines of standard substance (two or more) are used only for constant correction. See calculate specimen displacement section for details.
Attenuation length, mm:
This field allows to input the attenuation length 1/μ in the investigated material at current wavelength. By default it is empty and should not be used if the calculation of attenuation length has not been performed. After calculation of length, field shows it in millimetres. This value is applied only once, then the field becomes empty until the next calculation of length.
Effect of the shift of diffraction angle from attenuation is quite small for 1/μ about 0.01 mm (10 mcm) and can be ignored for materials with lesser attenuation length or for layers with thickness much less than 1/μ. It should be taken into account in the materials with 1/μ about 10 mcm or more, when the specimen thickness is significant.
Important: unlike the correction by the standard substance, which is applied to all lines in the table, this correction is phase-specific. If the table has several phases, be sure that attenuation length and lattice parameters belong to chosen phase.
You can change the calculated 1/μ here, but generally this is not recommended (see the remark below). However, if you have calculated the theoretical angles from parameters, you can invert the attenuation effect by adding the minus sign to this value to make the angles 2θ close to real diffractometry.
Remark: in a porous specimen like pressed from powder, the density of material may be noticeably less than theoretical density. If this value is below about 85...90%, additional correction should be made to count the increasing of the diffraction depth. The effective attenuation length can be get by multiplying of 1/μ in solid material by ρ/ρexp where ρ is the theoretical density, ρexp is the experimental density.
If you know the porosity φ, the multiplier is 1/(1-φ).
Set 2th precision:
Here you can change the precision for all lines in the table; this affects the results estimation and indexing. For a pattern, use "#" and line number, e.g. #2. Without a number, the first line will be taken as a pattern. Please note that in the cosine mode the precision of any line will depend on 2θ. If you set only the precision, the buttons Apply and Calculate are equal. This value is stored in the configuration file as "precise" and can be set without data in the table.
Precision mode:
This mode, constant or cosine, defines the suggested precision of 2θ when filling in the table as well as the precision which is set for all lines in this dialog. It also affects the calculation of root mean square deviation.
In the constant mode, the program suggests the same ±2th for all lines. This may be useful when the precision is mainly determined by detector step, whilst the diffraction lines are relatively narrow and 2θ range is limited.
In the cosine mode, the suggested precision depends on 1/cosθ. This is suitable for wide 2θ range and broadening diffraction lines. It decreases the relative weight and contribution to the results of the lines at large angles 2θ, which often are weak and less reliable.
Cosine mode should be used only for manual input of data in the table. When the data are input from a file, precision mode is returned to constant.
While this dialog allows to calculate both the correction data (constant and displacement) by experimental 2θ of standard substance or the expected 2θ of the standard by direct correction data, the priority of calculation depends on existing data and active field. If only experimental 2θ or only direct correction exist, the button Calculate performs the calculation of missed data — either the correction or expected angles of the standard, while the button Apply calculates the correction or takes existing direct values and applies them to lines in the table.
However, if some experimental angles and direct correction present at the same time, the priority depends on active field (an edit field with text cursor or selection). If the correction or displacement field is active, the dialog calculates all expected angles of the standard; if any other field is active, new correction data are calculated from existing angles.
Formula used:
correction = constant−2×cosθ×displacement/radius
Constant (zero-point) correction should be added to all experimental angles to compensate the shift of detector from ideal position. Specimen displacement gives the correction depending on cosθ. Both these parameters are obtained using the least squares method from cosine — deviation data set. Calculation of displacement also uses the detector radius (typical value is 200 mm, see options).
Remark: this formula is slightly simplified, it does not take into account that the displacement changes the goniometer geometry and effective radius. However, the difference from strict calculation is far beyond of typical 2θ precision (about 0.0001 degree per 1 mm of displacement or even less).
Two parameters, which define the angle correction: constant (zero-point) shift and specimen displacement, were calculated or input directly. To correct the position of all reflections, they should be applied to angles in the table. After that, they will be shown in the specimen dialog. You can cancel this operation and input the correction-related data again.
This dialog allows to choose the font for main program screen. List of fonts shows the scalable monospaced fonts (with fixed symbols width) installed in your system. The default font is Lucida Console, 14 points. The chosen font name, size and style are stored in the configuration file.
The number of available fonts depends on version of your operating system, language and additionally installed fonts. For Western languages, usually only a few fonts are available; for Asian and Eastern languages there may be more. However, not every font may have the characters needed for program interface and description of phases. It is recommended to choose the font which has at least the Western and Greek symbols and your national alphabet, if need. List of alphabets supported by each font is shown in the drop-down list "Script".
Selected font affects the size of the main screen. Font size can be changed immediately without opening this dialog: use the keyboard or mouse commands shown below. You can also resize the table vertically by dragging the top or bottom borders of the window, it changes the table size visible on the screen (from 8 to 41 lines, 16 by default).
Note: the font selected here is also used for printing, but the size and style are not (the fixed font size and standard style are used instead).
Ctrl+(Num+) - increase font: zoom in Ctrl+(Num-) - decrease font: zoom out Ctrl+wheel - zoom in / zoom out
Here you can see and change the settings which are stored in the configuration file rtp.ini.
Colour scheme:
You can choose a scheme for main program screen: classic, light, dark, system. System scheme automatically switches between light and dark, following current desktop theme. It is recommended with high contrast themes (can be set in Windows accessibility settings).
Mark of current field:
This option allows to change the look of current field in the table, which can be directly edited by Enter or F2 key. The choice none does not mark this field, dotted or solid show the border around it, colour shows the field with the distinctive coloured background. Find a combination of scheme and mark which is better suited your visual perception.
Auto update check:
Program can check for update automatically on regular basis: never, daily, weekly. This check performs one time when the program is started without opening a file. If a new version is available, you will see the information about this and can decide whether to update now or later. Set automatic check only if your PC has a stable Internet connection, otherwise use manual check in the "Help" menu. Note that new program versions are being released not very often, so weekly check may be more reasonable.
Default PDF precision: 0.010
The cards exported from PDF-2 database may not contain any specific information about precision, so this value is used as default 2θ precision; it is also used for AMS data. More exactly, PDF cards may have different presumed precison, depending on the number of meaning digits after the decimal sign in the d values. Modern PDF cards, including the theoretically calculated, have at least 5 meaning digits, so this default precision, typical for modern XRD equipment, is applied to these data. However, some old cards may have only 3 or 4 meaning digits (the extra digits required by format are zeroes). The program checks this and can restore the approximate 2θ precision basing on meaning digits of d and wavelength; in such case the default precision is not used. When importing AMS data, this defaut value is used to calculate precision by d.
Radius of detector circle, mm: 200
This is a distance between specimen and first slit of detector, in millimetres. It allows to calculate the exact value of specimen displacement by two or more experimental angles of standard substance in the correction and precision dialog. It is also used for calculation of 2θ correction by attenuation length. It does not affect other results.
Standard #:
You may input from 1 to 5 interplanar distances of external standard, used for calculation of correction. Diffraction angles of the standard are calculated at current wavelength and shown in the correction and precision dialog. All distances here should be input in the current length unit (Å or nm), which is set in the emission menu.
Default built-in data: natural diamond at 25oC [6]. Replace this if you use a different standard like alpha quartz, magnesium oxide etc. To restore the default data, clear or input 0 in all 5 fields.
; Natural diamond at 25C, a=3.566986 A ; T. Hom et al., J. Appl. Cryst. (1975) 8, 457-458 ; d h k l 2.0594003 1 1 1 1.2611200 2 2 0 1.0754867 3 1 1 0.8183227 3 3 1
To calculate the lattice, the lines must have non-empty h k l and valid 2th. Use the "Calculate" toolbar button or F6 key to calculate lattice parameters by selected lines of current phase. If the table has more than one phase, the current phase is defined by current position of the marker. To calculate other phase, move the marker to any line of that phase first.
Before the first calculation, please make sure that you have set the correct emission and lattice type of current phase.
Name: Nickel FCC Emission: 1.540510 Lattice: F cubic Parameter precision diverg. Parameter precision diverg. a= 3.5232 0.0010 0.0005 V= 43.734 0.036 0.018 [ 2/3 ] 2th rms dev= 0.007: very well # h k l 2th ±2th d ±d I 2th calc dev. 1 1 1 1 44.510 0.020 2.0338 0.0009 100.0 44.502 0.008 2 2 0 0 51.850 0.020 1.7618 0.0006 40.0 51.857 -0.007 3 2 2 0 76.370 0.020 1.24596 0.00028 20.0 76.393 -0.023 4
After successful calculation, the lattice parameters, their precision and divergence are shown in the top window; the calculated 2th angles and deviations are added to the lines in the table. The common results of lattice calculation are the parameters and cell volume. For some lattices the relation c/a is also calculated, and for orthorhombic lattice — the split rate (b-a)/(b+a).
Errors (uncertainties) of any calculated parameter are described by precision and divergence. Precision is an error caused by the limited precision of the original data: ±2th or ±d, while divergence is a result of difference between the ideal calculated lattice and real experimental data. Because of different nature, precision and divergence can be counted statistically independent.
Precision, in most cases, is limited by instrumental errors and quality of determination of peak position, which is limited by profile width. It can be improved by more precise measurement of diffraction angles, which includes the instrumental errors of diffractometry (goniometer precision, instrumental broadening due to horizontal and vertical divergence of X-rays and collimation, specimen shape and thickness), improving the statistical reliability (reasonable angle step and exposition time, signal/noise and peak/background ratio), increasing the number of lines used for calculation and careful separation of overlapping lines.
Divergence can be improved by excluding the outliers (see details of calculations) and more precise alignment of specimen, but for better improvement, if possible, need to understand the physical factors of the difference from ideal lattice model.
In the lines used in calculation, the columns 2th calc and deviation show the theoretical position of 2θ for indices h k l and difference between calculated and experimental angles. For unselected lines of the same phase, 2th calc and deviation, if they can be calculated from h k l, are shown as inactive (pale).
The deviation values more than 3 × precision are marked in the table by yellow. If a single line or small part of all lines show the significant deviation, it may be a result of accidental error or mistake. Consider to unselect such lines from calculation. However, if the total number of lines with high deviation is significant, it may be a result of the systematically poor data (experimental precision is much worse than ±2th input in the table), bad specimen alignment, presence of the lines of another phase, or incorrect lattice model. In the last case try to choose different syngony.
[12/14] 2th rms dev= 0.015: very well
The line below the parameters shows the quality of the results. Quality is estimated by comparison of the root mean square deviation of 2θ (2th rms dev) with the root mean square experimental precision (see the estimation section in the quick reference). If the lattice model is correct, for the most of lines the deviation should not be much more than the precision.
Two numbers separated by slash to the left from the estimation show the number of lines used in calculation and total number of lines of current phase. Their background shows the recalculation mode: bluish if this mode is active (on the illustration above), common background if the recalculation is not active. Recalculation is also shown as pressed "Calculate" button on the toolbar and in the main menu. When the recalculation is active, any selection or unselection of the lines of current phase will update the results. To cancel the automatic recalculation, press "Esc", or press "Calculate" again, or left-click these numbers with mouse.
Space - select/unselect line for calculation
Shift+Up,
Shift+Dn - select/unselect a sequence of lines
Ins - set or change class of current line
Left click - set the marker at cursor position;
- call the class menu in "#" column
Right click - select/unselect current line
The main algorithm is based on the method of least squares. The system of linear equations is obtained from original data using the classic Bragg law. The resulting matrix with dimension equal to parameters number of current lattice is solving using the Gauss method. The errors, which are due to 2θ precision, are obtained from the solution of this matrix. The errors due to the divergence between the calculated model and original data are obtained by solving another matrix which is composed by deviations between calculated and original 2θ.
The angles 2θ are calculated from lattice parameters using the standard equation for interplanar distances (1/d2) for current lattice type.
This dialog can be called by the "Details" toolbar button or in the main menu after successful calculation of lattice parameters (otherwise it suggests to perform the calculation first). It has the chart, some statistical information and recommendations.
Chart shows the distribution of deviations among all lines used for calculation. It allows to quickly see the lines with significant deviation (outliers). Areas of the chart have the different colours corresponding to the intervals of root mean square experimental precision by 2θ with multipliers:
green - area within 1 × precision green yellow - areas within 2 × precision yellow - areas within 3 × precision orange - areas beyond 3 × precision
Chart has two modes: stripe and scatter. Stripe chart is shown by default; to switch to the scatter chart, select the check box "Show the scatter of deviations".
On this chart, labels on axis X show the deviation in degree among the calculated lines. Labels on axis Y are not displayed, if the intensities of the lines are not known. If they present, axis Y shows the intensities in logarithmic scale, by default from 1 to 100, or more, if there are lines with higher intensities (for example, from 1 to 999 in the PDF cards with theoretically calculated data). Labels at the top border show the multipliers of experimental precision of the coloured areas, it may help people with non-perfect colour vision.
Vertical dashed line shows the mean deviation (it counts the +/- signs, unlike the root mean square deviation). This line shoud be near 0 on the axis X, usually within goniometer precision. Significant shift (about a half of experimental 2θ precision or more) shows that the distribution of deviations is asymmetric (skewed). If the shift is more than either a half of precision or 0.05 degree, you will see a warning message. It may be a result of specimen displacement or zero-point shift of detector, but the real cause should be found out. Attempt to fix the displacement when the data are wrong is unlikely to succeed.
In this mode, axis X shows the angles 2θ, while axis Y shows the deviation, both are in degree. Like on the stripe chart, the areas are marked by the colours, but because of different axes X and Y, colour areas are horizontal. Mean deviation is not shown here, line at zero level is a divider for convenience. Scatter pattern of the dots allows to estimate the results in different way than on the stripe chart.
In particular, specimen in correct position gives the horizontal distribution of the dots, its misalignment results in a slope: rising trend is caused by a negative specimen displacement (or negative shift of detector from zero point), while falling trend means that the displacement (or zero-point shift) is positive. Curved distribution, usually with local minimum, may be an indication that current phase has a significant attenuation length.
Remark: if the scatter of deviations is mostly a result of statistical errors rather than specimen or XRD state, the pattern may be less informative than the mean deviation or the graph of specimen displacement.
Statistical information below the chart shows the number of lines with different absolute deviations as shown on the chart — less than 1 × precision, less than 2 × precision, less than 3 × precision and the total number of "good" and "bad" lines.
Dialog informs whether the results are good. If not, you can attempt to improve them by unselecting some lines with too high deviation (lines with deviation more than 3 × precision are marked in the table by yellow in the "deviation" column).
Important: before unselecting the lines, be sure that specimen is in right position, otherwise attempts to improve calculation may give wrong parameters. Check the specimen displacement and look at the result: significant displacement means that it may be reasonable to check the goniometer adjustment and re-align the specimen.
To find all outliers, arrange the lines by deviation. Alternatively, follow the program's suggestion by pressing Unselect button.
Important: you do not need to unselect all suggested lines. Always look at the estimation of results; sometimes unselecting only a few outliers may significantly improve the results. At least you should unselect the lines until no lines left in the "orange" areas.
If the number of outliers is big and the results are not good and cannot be improved this way, you should verify the experimental data: indices h k l, angles 2θ and lattice type. You can also revise the experimental precision ±2th and assign more appropriate value to the lines.
Dialog also shows the information if the table has some not yet selected or unselected lines of current phase with the deviation within 2 × precision, and suggests to Select these lines, which may statistically improve the results. Use such suggestion with caution: the program does not know anything about the physical state of the investigated substance, it estimates the result basing only on formal principles. For example, you might intentionally unselect some lines which supposedly belong to another phase (like a distorted or transformed lattice). If you mark these lines as a different phase, the program will no longer suggest to select them.
This operation allows to calculate the theoretical (X-ray) density of the material by the chemical formula and calculated cell volume. Dialog of calculation of the density is also used to calculate the attenuation length of an element or compound.
Theoretical density is a density of the material with ideal defectless crystal structure; it is often used to evaluate the changes in the crystal structure after the phase transformation or doping by different elements and is also used as a value which the density of real material in monocrystalline form with minimal possible amount of defects and impurities should approach to.
Calculation of theoretical density uses the chemical formula of the compound, which gives the atomic composition, the number of formula units in the crystall cell, which is a structure unit, and atomic mass of the elements, which gives the molar mass:
ρ = z×M/(V×NA)
where ρ is the density, z is the number of formula units in the cell, M is the atomic mass of the formula unit (molar mass), V is the cell volume,
NA is the Avogadro number, 6.02214076⋅1023 1/mol.
Remark: traditional symbol of the number of formula units is capital Z, which is the same as the symbol of atomic number. To avoid ambiguity, this documentation uses the small z letter for the formula units.
Atomic masses of the elements used in the program are mostly taken from the PubChem open chemistry database [7]. File rtpam.ini, if exists in the program's directory, replaces the internal table of atomic masses partially or entirely. It has two lists: common list with all elements in the current (2023) periodic table and list of isotopes. Common list in the file included in RTP archive is the same as internal, and if these data are suitable for your work, you may not add it. If you prefer some more traditional or more precise masses, add rtpam.ini and replace that data in a text editor or include only those elements to your file.
List of isotopes presents only in rtpam.ini. It has the masses of some commonly used isotopes and serves mostly as an example; it may be extended and include up to 30 different isotopes. Here are the data lines from both lists for comparison:
;Number Mass Symbol ;common elements 26 55.845 Fe ;isotopes 26.55 54.9382934 55Fe
Number in the common list is the atomic number Z, while in the isotope list it also includes the mass number A separated by dot. Mass is the atomic mass in g/mol, average of naturally existing or most stable isotope in the common list and exactly known in the isotope list. Symbol in the common list is the chemical symbol of element, while in the isotope list it is the combination of mass number and chemical symbol. Symbols are used for reference, the list of chemical symbols is built in the program.
To use an isotope in a formula, need to enclose its symbol in round brackets, like (55Fe). Brackets are important, otherwise the number will be counted as a multiplier instead of mass number. If an isotope does not present in the list, the mass number will be used as atomic mass (with loss of precision).
Remark: using the square brackets for an isotope is not recommended, because this type of marking is used for selectively labelled compounds (not supported in the program), where the isotopes, written directly before the formula, are not the part of composition.
To calculate the density, you need to input the number of formula units per one cell in the theoretical density dialog, field "Units". It can be known from the description of partucular structure or taken from the structure prototype. Here are some examples:
simple cubic 1 (8×1/8) BCC, HCP 2 (8×1/8+1) FCC 4 (8×1/8+6×1/2) C (diamond) 8 (8×1/8+6×1/2+4) CsCl 1 SiO2 (α-quartz) 3 NaCl, CaF2 4
This number does not affect the calculation of molar mass of the formula unit M, but is required for correct calculation of the density.
Numbers are stored in the line of specimen information after the formula, separated by two slashes as a comment. If the calculation of density is performed again, the formula is shown in the dialog without comment and the number is copied to the units field.
Remark: sometimes the information about the number of units or atomic positions in the cell may be not easy to find. If so, the number may be determined empirically. Assume that the cell has one unit: input number 1 and calculate what the density would be in such case. Then take the experimental density or measure it using a laboratory equipment and divide by the calculated value. The nearest integer (usually slightly greater than the result) is the number of units.
You need to input the formula of chemical composition (formula unit, molecular formula) or the list of atoms and their amount in the unit. Program is able to decrypt the typical formulae and count the atomic composition. Sometimes the formula may be found in the information about specimen. For example, program reads the formula from PDF cards and stores it in the line with number 1. Select such line in the drop-down list, which shows the lines of specimen information starting from "Notes". On the other side, AMS files include the formula quite rarely, somewhere before the database code. In such case, or when the table is created from diffraction data, select an empty line and input the formula in the field, or copy it from another electronic source and edit if need.
Formula should be input in one line without subscript or superscript characters; additional spaces may present for clarity. It may have up to 8 chemical elements; specific isotopes are counted as separate elements. Be careful about letter case and similarly looking symbols. Always check the atomic composition after decryption of the formula to avoid mistakes.
Brackets are limited to 4 levels of nesting and should be paired; only the round ( ) and square [ ] brackets are supported; braces are not. State of aggregation should be removed: all substances are expected to be solid (s) or crystal (cr). Valence, oxidation state and charge numbers are not supported and should be removed from the formula too.
For example, SO42− ion should be written as SO4.
Signs * (asterisk) or ⋅ (middle dot) between different components of the formula like hydration groups may present and are required if need to separate a multiplier of specific component. Such parts of formula may be included in brackets for clarity, for example, *5H2O or *5(H2O). Numbers of elements or groups in the brackets may be non-integer, like for non-stoichiometric compounds, mixtures or substitutional solid solutions. For numbers less than 1, zero must present before the decimal dot. Formulae with the variable composition like olivine (Mg,Fe)2SiO4 cannot be properly decrypted; the parts of components should be clearly specified.
Examples of formulae:
Al2(SO4)3 aluminium sulfate (55Fe)3O4 iron-55(II,III) oxide Ca6[B5O9]3Cl3*3H2O hilgardite (mineral[2])
After input of all required information in the dialog, press Calculate button. You will see the line with atomic composition and the line with result: molar mass M in g/mol and density ρ in g/cm3. Attenuation length 1/μ, calculated for current wavelength, is shown in suitable length unit (μm or mm). If the formula cannot be properly decrypted because of error or complexity, you will see an error message and need to correct it until the error disappears. If the cell volume is not known, only molar mass will be shown.
Remark: you can calculate the density without diffractometry data. Select the lattice type and input the lattice parameters in the calculate lines for known h k l dialog, which gives the cell volume even if the table is empty.
After successful calculation, press Store to keep the formula and number of units in the selected line of specimen information. Result of calculation will be added to the information list in a separate line.
Example: calculation of the density of zircon (tetragonal structure with a = 0.6607 nm, c = 0.5982 nm). Attenuation length is calculated for Cu Kα emission.
Units: 4
Formula: ZrSiO4
Atoms: Zr 1; Si 1; O 4
Result: M = 183.305 g/mol, rho = 4.6626 g/cm^3,
1/mu = 26.2 mcm
This operation uses the same dialog which calculates the theoretical density. Attenuation length 1/μ is the thickness of a material where the intensity of X-ray emission on the surface decreases in e times (to about 37%), where e is a base of natural logarithm (2.71828...) and μ is the linear attenuation coefficient. Knowing this length is important to estimate the thickness of the area analysed by X-ray diffractometry. In particular, it can be used for more precise 2θ correction.
Two types of calculation of the attenuation length 1/μ are implemented in the program:
Decreasing of the intensity of rays in the depth of a material from initial intensity on the surface at normal incidence is described by the Beer-Lambert law:
I = I0×exp(-μx)
where I is attenuated intensity, I0 is initial intensity, x is the length.
Linear attenuation coefficient μ depends on the photon energy E (it is shown in the tooltip to wavelength) and atomic number Z. The dependence is non-linear and includes the atomic photoeffect, coherent (Rayleigh) and incoherent (Compton) scattering.
For multi-component specimen, μ is additive and can be calculated by the formula:
μ/ρ = ∑ wi×(μ/ρ)i
where μ/ρ is the mass attenuation coefficient of mixture or compound,
wi is the proportion of the component i in the specimen,
(μ/ρ)i is the mass attenuation coefficient of the component i.
Remark: calculation of attenuation length implemented in this program is based on the code and data available on the Mucal periodic table web page [8]. Original data, where some elements are missing, have been updated with more recent data [9]. Currently the elements 1...94 and X-ray emissions with energies from 5 to 100 keV are supported (including all wavelengths in the RTP emission list).
Besides the parameter 1/μ, which is defined for normal X-ray incidence, the parameter of attenuation of diffracted ray depending on angle θ can also be useful — the depth of the half of diffracted intensity, where the integral intensities of the diffracted rays from the layers above and below are equal:
d1/2 = sinθ×ln(2)/2×1/μ ≈ 0.35×sinθ×1/μ
For example, for Cu Kα emission (E = 8.048 keV), the 1/μ in aluminium (Z = 13) is about 70 μm, in uranium (Z = 92) — 1.7 μm, so the half diffraction depth for θ = 30° is about 12 μm and 0.3 μm, respectively. For the more short-wave Mo Kα emission (E = 17.480 keV), the half diffraction depths are about 130 μm and 1 μm.
Effect of the shift of diffraction angle from attenuation is somehow similar to the specimen displacement, but the shift depends on θ with maximum around 45 degree due to multiplier sinθ × cosθ: at the small angles the diffraction depth is low, at the large angles the angle shift of depth is low. The shift is quite small for 1/μ about 10 mcm (like titanium at Cu Kα emission, see below) and can be ignored for materials with lesser attenuation length or for layers with thickness much less than 1/μ.
This calculation is performed when you input a symbol of single element in the "Formula" field and when the calculation of lattice parameters was not performed (parameters are empty). "Units" field is not used in this calculation. Chosen element is assumed at standard temperature and pressure in the most stable phase state. Note that some elements at standard conditions are gases or liquids.
Calculation shows the molar mass M of chosen element in g/mol and attenuation length 1/μ in suitable length unit (μm or mm). Note that in the correction and precision dialog this value is always shown in mm.
Example: calculation of the attenuation length in titanium at Cu Kα emission (titanium has the HCP structure with 2 atoms per cell, this value is not used here).
Units: 2 Formula: Ti Atoms: Ti 1 Result: M = 47.867 g/mol, 1/mu = 11.0 mcm
Remark: if the main table has some diffraction lines and the lattice parameters were calculated, you may clear only the parameters and keep the table using the "Clear", "results" menu or toolbar button. This also clears the calculated 1/μ in the "Correction and precision" dialog.
This calculation is performed with the calculation of theoretical density. You need to calculate the cell volume, input the number of formula units in the cell and chemical formula. All elements in this calculation are counted in the crystal state; the atomic density of particular element is calculated by division of the mass of atoms in the cell by cell volume.
In practical X-ray diffractometry, the diffraction planes of investigated material are usually differ from the goniometer plane by the value called specimen displacement. In a typical case of specimen alignment to a holder using a glass plate, the displacement may be only a few micrometres (μm), but if the specimen surface is not well polished and has some roughness or for powder specimens, the real displacement may be much more. Methods of internal and, more often, external standard substance placed on the specimen surface (like a diamond powder) are used to compensate such misalignment; this correction is supported by the program. However, such correction may be not ideal if the reflecting areas of specimen phase and standard substance are different.
Another way to find the displacement and compensate it uses the displacement model which is applied to set of diffraction lines to find the position when the divergence of calculated results from ideal structure is minimal. If used properly, it allows to find the displacement with precision up to 1 μm. However, this operation should be used with care because improper calculation may result in additional uncorrectable errors instead. In general, it should be used only when the shift of the diffraction angles is a result of specimen misalignment and is not due to another reason like internal stress, phase non-uniformity, phase transformation etc.
Important: before performing this calculation, be sure that the constant (zero-point) correction is close to 0, i.e. is no more than goniometer precision. Otherwise the calculated displacement may be far from real and lead to incorrect lattice parameters. If the constant correction is not zero but is known for current goniometer adjustment, correct it manually in the correction and precision dialog. You can also calculate and apply this correction by two or more lines of standard substance (the displacement calculated by standard lines will be used only as a first approximation). Warning: correction by only a single standard line is highly undesirable and may result in additional errors.
Please note that calculations use the radius of detector circle as a base length. Check this parameter in options and correct if need.
First, you need to calculate lattice parameters: it gives an initial value of 2θ root mean square deviation (2th rms dev) which is used as a starting point for next comparisons.
Initial dialog allows to set the interval of displacement, in millimetres. Default value is 0.2, possible limits are from 0.005 to 2.0. Search of minimal deviation will be performed in the interval from negative to positive given value. A positive value means the shift of specimen plane toward the diffraction angle, negative — backward.
Greater value of the limit allows to find bigger displacement, but the time of search increases and the graph becomes more rough; lesser limit makes the graph more fine. However, if the found displacement is within the limit, the results will be the same.
Dialog with the results shows the graph of dependence of the root mean square deviation by 2θ on the simulated specimen displacement. Axis X shows the displacement in mm, where current position is at zero point, axis Y — 2th rms deviation in degree. Line of dependence should have a local minimum, if the displacement is within the interval which is set in the initial dialog.
Check box "Show the line of mean precision" allows to show the horizontal dashed line at the mean experimental precision by 2θ. Position of the line can help to estimate the effect of correction: more significant if current deviation is above this line and less in other case. When the line is shown, the scale of Y axis may change, so unselect the check box if you want to decrease the limit of displacement or look at the dependence more closely.
Below the graph you will see the information about minimal found deviation and corresponding displacement. If the difference between current and minimal deviation is very small and beyond of typical precision, this difference is also shown in round brackets.
Press Apply to correct the specimen misalignment, if it is significant (more than a few micrometres, depending on material). This will recalculate the angles of all lines in the table, not only the lines of calculated phase. Lattice parameters of current phase will be updated automatically; other phases, if they present, should be recalculated manually. The applied displacement will be shown on the bottom in the information about specimen dialog along with constant correction, if it was used.
Please note that applied displacement cannot be undone immediately. If it was performed by mistake, reload the initial table if it has been saved to a file before this operation. Alternatively, you can reverse the correction: look at the current displacement in the dialog information about specimen and input the inverse value in the correction and precision dialog, "Specimen displacement" field.
Sometimes you may see additional messages at the bottom of this dialog:
Specimen is in right position, no correction required
You will see this information if the found displacement is less than 0.001 mm or 0.2×1/μ. This is normal for all theoretically calculated lines or if the correction has already been applied.
Improvement of deviation is much less than precision
This message is shown if the effect of correction would not be significant, because the experimental precision is the main factor of uncertainty. It happens when current deviation is already less than precision and correction will decrease it by less than 10% of precision. Correction still can be applied to improve the calculation of lattice parameters.
Minimal deviation is found at current limit of displacement
This happens if the found displacement is equal to current limit: minimum is reached at the border, which you can also see on the graph. Press Change and increase the limit in the first dialog. If the found displacement is large, about 1 mm or more, it is recommended to check the specimen alignment and repeat the diffractometry.
Minimum of deviation is somewhere outside of possible limit
This message means that supposed displacement is too large, more than the limit of 2 mm. You can apply current value and calculate displacement again, approaching the minimum step-by-step, but checking the specimen alignment is highly recommended. If it will have no effect, check the goniometer adjustment using the test samples and fix the problem, then repeat the diffractometry.
For calculation of new 2θ and d values by given indices and parameters, the indices in the column h k l should be filled in. You may either input them manually or use a previously calculated specimen or PDF card as a structure prototype. Then fill in the lattice parameters.
Limits for edges a, b, c — 2...99 Å or 0.2...9.9 nm, for angles alpha, beta and gamma — 1...179 degrees (this is a formal limitation, real angles usually are within the limits about 45...135 degree).
This operation may be performed without any h k l in the table: the cell volume and additional lattice parameters like c/a relation or orthorhombic splitting will be calculated anyway.
The fields in this dialog, as well as parameters fields in the generate reflections by parameters dialog, allow to input one of the arithmetic operators + - * / with two arguments. This may be useful to calculate the edges for a cell with multiplicities, based on multiple cells with simple structure, and vice versa. The original values may be a result of previous lattice calculation, which you need to multiply or divide. Examples: 2*5.348 or 30.609/3
Remark: the parameters from this and the next dialogs are not recalculated automatically after changing the length unit. You need to calculate the parameters from calculated lines or input the parameters in other unit again.
To calculate the reflections with generated indices h k l, first select the lattice type and set the cell centring, if it is known, or leave the type "P" (primitive). Then fill in the lattice constants and set the minimum and maximum values of 2θ "2th range". The number of possible h k l combinations is limited by the table size (440 lines), so if this limit exceeds, the program will show warning and decrease the upper 2θ value. If you want to get more results, look at the last calculated angle and use it as a reference point for new 2th range.
Limits for edges a, b, c — 2...99 Å or 0.2...9.9 nm, for angles alpha, beta and gamma — 1...179 degrees, for 2th range — 0...179 degrees.
About the arithmetic operations in the fields see the remark in the previous section.
These operations allow to exchange two of the indices h, k, l, or perform the circular shift of the indices to the right or left, or invert the indices h k l where the value k is negative. All actions are performed with the lines of current phase, which is defined by the marker position. When the recalculation is active, you can immediately see the result.
Exchange of two indices can help to change the presentation of lattice, where assigning the parameters to the cell edges sometimes may vary in different sources (the conventional rule is that assigning is determined by the space group). Most often these differences may occur in the orthorhombic and hexagonal lattices. It can also be helpful after indexing.
Circular shift (or rotation) of the indices in the right (h k l → l h k) or left (h k l → k l h) direction may be useful for low-symmetry lattices starting from orthorhombic. It can also be done by two sequential exchange operations, like exchange h and k, exchange h and l for shift to the right.
The purpose of inversion of h k l is to make the indices of triclinic lattice, where negative k is allowed, compatible with monoclinic indices, where k can be only non-negative. This change of presentation may be useful for triclinic structures imported from PDF or AMS databases.
Control with keys/mouse: Alt+K or left-click the h k l table header.
You can mark a group of lines as a specific phase by certain number from 1 to 4, define them as the lines of standard or excluded lines. These lines will have a label instead of their ordinal number: (1) to (4), (s) or " x ". If all lines in the table have the ordinal numbers, they all will be labelled as a chosen phase. But if the table already has some phases, only the lines of current phase with the marker will be changed. To assign a label individually to a specific line, use the context class menu or keyboard command.
This operation can be applied separately to selected and non-selected lines, if they present in the table. In such case, you will see a question, whether to mark all lines or only the selected or unselected ones, depending on current position of marker. Such approach is useful to mark only the calculated or non-calculated lines as another phase.
The common purpose of phase labels is to differentiate the lines belonging to different substances. In particular, you can label the existing lines before adding new lines of other phase to the table using import of *.txt file (all imported lines get the ordinal numbers). Then the difference between them will remain visible after arranging the lines or lattice calculation.
It would be a good idea to write a short note about specified phase in the specimen information.
To remove the specific phase labels and restore the ordinal numeration, set the marker to one of these lines and choose an option "Numbers" (N). To remove all the phase labels in the table, use an option "clear phase labels" in the clear menu.
Here are some advices which may help to improve the calculation of lattice parameters. They are mostly related to widely used flat specimens, either polished or pressed from powder, with a thin layer of external standard placed on the surface. For other types of specimens, these suggestions may also be helpful because they show the sequence of operations when current step is based on previously calculated data. Anyway, use these advices wisely!
First of all, you should perform the correction of 2θ by the standard substance. When correction is calculated, you get two parameters of alignment: constant (zero-point) correction and specimen displacement. Constant correction is the most important, while specimen displacement is often approximate because the diffraction area of the specimen is shifted to the depth from the standard substance on the surface. On a properly adjusted goniometer, constant correction should be very small. If it is significant, much more than goniometer precision, consider to check the goniometer adjustment, re-align the specimen and repeat the diffractometry.
Relating to the specimen displacement, a small value about a few tenth fractions of millimetre or less can be also found and compensated independently on the last step. Compensation of greater displacement, about 1 mm or more is possible but less reliable, so a better solution is to re-align the specimen and get the diffraction data again.
Calculation of the lattice parameters from initial data allows to evaluate the consistency of data, avoid serious errors and mistakes and also get the cell volume which is required for next step. Check the details of calculation, look at the root mean square deviation of 2θ (2th rms dev.) and check the outliers (with deviation much more than 3 × precision of 2θ).
At this point, you should try to understand the origin of high deviation of every outlier. It may be a result of simple mistype of a value in the table, wrong line attribution (incorrect indices h k l or a line belongs to another phase), inaccurate separation of the overlapped lines. In the last case it is recommended to repeat the separation using the calculated 2θ (2th calc) of this line as initial position. If there are no such problems or they are solved and calculation results are good, you can go to the next step.
This calculation allows to obtain the molar mass M, density ρ and attenuation length 1/μ; the last is required for 2θ correction depending on the diffraction depth. To perform the calculation of theoretical density, you need to know the number of formula units in the cell, chemical formula of the compound or its atomic composition; the cell volume is already known. After calculation, store the initial data and results in a line of specimen information, otherwise you will need to input the formula in this dialog again for new calculation.
Look at the parameter 1/μ: if it is less than about 10 mcm or if you investigate a layer with thickness much less than 1/μ, the next step may be skipped. Otherwise you should use this value for more precise angle correction.
With calculated 1/μ, you can return to correction and precision dialog, where all other fields besides this one should be empty (remember, it will show the length in millimetres). If the density of specimen is significantly less than theoretical because of porosity, calculate the effective attenuation length, see the formula in the remark to "Attenuation length" field. After applying the length, the angles of current phase in the table will be corrected like if all diffraction planes are shifted to the specimen surface, and 2θ become the "true" Bragg angles. Angles of other phases, if they also present, will remain unchanged. After that, it is recommended to perform the calculation of specimen displacement which can decrease the effect of possible specimen misalignment.
Please remember that this correction, like any other corrections, should be applied only once. Then the field "attenuation length" becomes empty until this value is calculated again.
Calculation of the specimen displacement is the last possible step of improvement of the calculation of lattice parameters. To perform it successfully, you need to check the conditions:
If all conditions are good, perform this calculation and look at the results: the minimal 2θ root mean square deviation, its improvement from current value and the specimen displacement when this minimum is found. For very good alignment, displacement should be very small. For real diffraction data, it may be hundredth or tenth fractions of mm. If the value is much less than attenuation length, this correction may be ignored, otherwise apply it and calculate the parameters last time.
If the displacement is large, like several tenths of mm or more, consider to re-align the specimen and perform the diffractometry again.
Two methods of searching the indices are implemented in the program:
Shuffle (permutation) method uses the generated array of h k l, which are sequentially assigned to selected basic lines to get the lattice parameters; a grid of possible reflections is calculated and checked for coincidences until the minimal percent of described lines is reached, then the results are shown in the table. You can set the basic mark "*" on the suitable lines manually (see the recommendations below), otherwise they will be taken from the top of the table. Limitation: this method does not work for triclinic lattice because it would be inefficient and very time-consuming. Please use the specialised software or try indexing by known h k l, if such indices exist.
Method by known h k l assumes that the total number of selected lines with known indices is sufficient to calculate the lattice parameters with quality "satisfactory" or even better. Grid of reflections is built from these parameters, then the lines without indices are checked for coincidence. Basic lines are not used in this method, only the limits by h k l and sometimes 2th range should be set (other limits are ignored).
This method may be useful when some indices, usually belonging to a few first or strongest lines, should be the same as in a structure prototype, but the differences in lattice parameters make hard to directly attribute the remained lines.
Two described methods can work in sequence: if you have a lot of lines of the substance with low-symmetric lattice, which the shuffle method is not able to process for reasonable time or because of internal overflow, you can perform the indexing of less number of first lines with lower limits by h k l, select the best result and then identify the rest of lines using the method by known h k l.
For the shuffle method, good choice of basic lines may greatly affect the success of indexing. Their number should be equal to the number of lattice parameters, e.g. one for cubic, two for hexagonal, tetragonal and rhombohedral lattice etc. Lines are counted from the top of the table, so if the number of lines marked as basic is not enough for current lattice, additional lines will be taken from the top; if too many lines are marked, the extra lines will be ignored.
Selecting the best basic lines may require several attempts of trial and error. First of all, note that the default selection of basic lines from the top of the table is usually not the best: the exact lattice parameters calculated from the lines with smaller 2θ may have significant errors, preventing the attribution of the lines with larger 2θ. It would be more reasonable to select the lines in the middle or even near to the end of 2θ range. On the other side, take into account the intensities: the more intensive non-overlapped lines usually are more reliable. Try to mark different lines (most intensive and with large 2θ) until you get the suitable results.
Sometimes a wrong selection may be hard to predict, for example, if you occasionally chose the lines which are linearly dependent or do not include one axis (like h k 0 in tetragonal lattice). In this case you may get poor results or no results at all. Changing one basic line to another one may resolve such issue.
In a shuffle cycle, the basic lines get the current combination of indices from generated h k l array, indices in the array are arranged by increasing of sum of squares; the repetitions in cubic, rhombohedral, hexagonal and tetragonal lattices are skipped. Then the lattice parameters are calculated from basic lines and checked against given limits by a b c and V. A grid of possible reflection angles is built from the h k l array and is used to search for the reflections adjacent to experimental angles within the delta × precision interval. Indices of reflections may be checked for cell centring with higher symmetry (which is limited by higher possible centring of basic lines). If the percent of adjacent lines is high enough, their indices are used to calculate the lattice parameters more precisely, and the results are shown in the table and in the dialog with the result of current cycle (in the interactive mode).
Every successful cycle is checked for cell volume and number of described lines; if one of both of them are better than obtained in previous cycles, they are memorised to be shown in the dialog with the results of indexing when all cycles are completed.
This dialog allows to input the parameters which define the indexing process. Before using this dialog, you need to set the supposed lattice type.
For the shuffle method, it is highly recommended to choose the basic lines (use the context menu or "B" key, also see advices in the previous section).
For the method by known h k l, it is suggested to calculate the lattice parameters by known lines and, if the number of selected lines is more than number of lattice parameters, check that quality is "satisfactory" or better. This method uses only the limits by h k l, delta and 2th range when need.
Limits by h k l: 5 5 5
The higher limits increase the chance of success, even with non-minimal cell, but increase the total number of cycles and calculation time. A size of h k l array in Win32 version of the program is 4096. For a primitive cell and for cubic lattice h k l must not exceed (46 46 46) with multiplicities, for orthorhombic lattice — (15 15 15) and for monoclinic one — (12 12 12). If a cell is non-primitive, limits can be increased.
For indexing by shuffle of monoclinic lattice, the limits more than (4 4 4) may be very time consuming and inefficient. Try to set the limits when the array size (shown in the information line) would be around 100...200. You can decrease 2th range and then use less limits by h k l to try to identify some (like 10...15) first lines. Indexing by known h k l, on the other side, is performed without multiple cycles and is quite fast, hence use the limitations from previous paragraph.
If you input less than 3 values in this one and next fields (for any lattice), missed values will be copied from the last input value. For indexing by known h k l, if some values are less than the maximal indices in the table, program shows the warning and asks whether you want to Increase the limits which are less than in the table or Continue without changes.
Limits by a b c: 10 10 10 (length in Å) or 1 1 1 (length in nm)
Set a maximum size of cell in 3 dimensions. Higher values increase a chance to find the non-minimal cells, while too low values will make the correct indexing completely impossible. Always check that these values are not less than in a prototype cell. Possible limits 2...99 Å or 0.2...9.9 nm.
If you do not have a prototype, use this approach: they should be no less than the maximal sum of d and ±d × delta. For hexagonal lattice type, need to multiply d by 2/√3. If supposed cell symmetry is high, need to take into account the possible extinctions. For example, third index in HCP lattice starts from two: (0 0 2), so the limit should be no less than max of 2 × (d + 4 × ±d), if the delta multiplier is 4.0.
Limit by beta: 125
This setting is available only for monoclinic lattice. Beta angles beyond 110...120 degree may exist, but are quite rare; proper limitation reduces the time of calculation. Like for cell edges, too low value will prevent from getting the correct results. Possible limits 90...150.
Limit by V: . . . (cell volume in Å3 or nm3)
Volume limitation can decrease the number of non-minimal found cells, especially when the limits by a b c are high. This field is empty by default and is not used. If you decide to set this limit, it would be reasonable to use the volumes obtained in previous calculations as a reference point.
If the limits by a b c were increased in this dialog but the limit by V was not, the program shows a request if old volume becomes a limitation. You can continue indexing or cancel it and either change the limit manually or clear this field.
Threshold, in %: 80
Minimal percent of indexed lines. Recommended value 70...90, possible limits 25...100.
Delta multiplier: 4.0
This value is a multiplier of 2θ precision, which defines an interval of 2θ for search for adjacent reflections. In some cases a value from 3 to 5 may be reasonable: 3.0 is a strict limit when all lines should be within the interval of satisfactory quality, may be useful for indexing by known h k l; 5.0 is a less restrictive limit to find the lines in more wide area, may be useful for shuffle. Possible limits 1.0...10.0.
Generally, if you have the problems with indexing, try to set the more appropriate 2θ precision before changing this parameter.
2th range: 0 180
Normally the angle limits for indexing are taken automatically from the unidentified lines with lowest and highest 2θ with adding delta × precision on both sides. The setting here creates the additional limitations which may help in the case of error too many h k l combinations. Selecting a more narrow range of angles may greatly reduce the number of possible combinations, especially for low-symmetric lattices.
For the shuffle method, this setting allows to select only a part of existing lines, if their number is too big. Decreasing the upper limit may be enough: the lines with lower 2θ may be identified with lower limits by h k l. After that, the remained lines can be described using the method by known h k l without 2θ restriction.
Besides these cases, it is recommended to keep the default non-restrictive values; to restore them, clear this field.
Interactive search mode
Selecting this check box allows to perform the indexing by shuffle in interactive mode, when the dialogs with intermediate results are shown after every successful cycle. This can be useful if you want to see some possibly interesting results which were not shown after performing the non-interactive search because they did not meet the best search criteria (minimal cell volume or maximum of described lines). When the check box is clear, all intermediate dialogs are skipped and the results of indexing are shown when all cycles are completed.
When initial settings are ready, press Start to begin the indexing process by shuffle (for a lattice from cubic to monoclinic), or press By known hkl if the lattice parameters can be calculated by selected lines.
On the bottom line of the screen you can see current information about indexing cycle: size of h k l array, number of successful cycles and current indices assigned to first basic lines (for orthorhombic or monoclinic lattice). The cycles by h k l are going on in ascending of the sums of their squares. If the parameters calculated for basic lines are within the limitations defined in the indexing settings and the percent of lines which are located near theoretical positions calculated from these parameters is high enough, the cycle is counted successful. The described lines are marked by bluish background in the table and calculated lattice parameters are shown on the screen.
If the indexing is being performed in non-interactive mode, you can interrupt it (use Esc key) and either change the indices of the first basic line to next combination (to skip the rest of shuffle with current indices) or exit the cycle and see the obtained results.
You can interrupt the indexing process by pressing the Esc key; also indexing will be interrupted if you attempt to close the program window or exit the program. Attempt to perform any other operation shows the warning that chosen operation will stop the indexing. If you confirm this by OK, indexing will be stopped and current data in the table used for operation. If you Cancel, indexing will continue.
Interrupt is possible only for low-symmetric lattices, indexing of lattices with high symmetry is usually fast enough. Interrupting the cycles may take some time.
After the interrupt by Esc, the dialog shows the number of successful cycles and possible options. You can Continue the indexing in normal way, or change the indices of the first basic line to the Next h k l combination, or Stop the cycles and show the dialog with the results of indexing.
Next combination may be useful to quickly skip current h k l if some of the indices are high and unlikely may give more results, so better to begin the next cycle with initial low indices. Before choosing of stop, take into account that the intermediate results may be greatly incomplete. Use stop if you want to change some settings or correct other mistakes, or if the indexing process with current settings takes too long time.
When the interrupt is a result of attempt to close the program, the options in this dialog change. Instead of the next combination, you can Close the program immediately. Warning: all progress of the indexing will be lost.
This dialog shows the result of current indexing cycle: the number of described lines and cell volume; you can see current lattice parameters in the table (move the dialog if need). You can Continue the indexing in normal way or change the indices of the first basic line to the Next h k l combination.
You can also Stop the indexing, if you want to change the initial settings or check the current results more carefully. In the last case, press Cancel in the next dialog, then you can save or print the table.
After the finish, the operation "Results" shows the dialog with the results of indexing until the original data in the table are the same (lines are unchanged, no operations like arrange or calculation of displacement were performed). You can select or unselect the lines, calculate the lattice parameters and look at the details of calculation. To perform other operations, save the table and work with the copy.
Indexing is finished, when the indices of first basic line reach the maximum h k l values, then the program shows the dialog with found results. Two criteria of selection are used: by minimal cell volume and by maximum of described (identified) lines. If several results with the same volume are found, the first is taken because the indices h k l are minimal at the begin of shuffle; if several results with the same number of lines are obtained, the result with minimal volume is used. If both the number of lines and volume are the same, the result with higher cell centring will be taken.
You can choose which result, Min volume or Max lines you would like to see in the table, or cancel to keep the last successful result. Besides these choices, pay attention to the results where the cell is more symmetric (if a structure prototype may have a non-primitive cell) and where the indices of basic lines are relatively small. If need, you can repeat the indexing with different basic lines, different cell centring and compare the minimal volume and percent of described lines.
To choose other result, use "Results" in the menu "Calculate" or the corresponding toolbar button; it will show this dialog until the table is not changed and calculation of parameters or any correction is not performed. If you find both results valuable, save each of them to separate file before doing any calculation or changing the lines.
If the initial settings were unsuitable (incorrect basic lines were selected, threshold is too high, limits by h k l or lattice constants are too small, incorrect lattice type or cell were chosen), the results will be probably unreliable. You may also see the message like "Failed in finding any indices". Try to change some initial indexing settings and repeat the process.
The results of indexing are shown immediately because all operations are performed in a single cycle. If successful, the unidentified lines get the possible indices but remain not selected (white or yellow with the marker), so they can be easily distinguished from the selected lines which were used to calculate the lattice parameters. If you want to improve the parameters by adding the described lines, select them manually or by combination Ctrl+A and perform the calculation.
If more than one possible h k l combination was found for a line within delta × precision interval, the program creates the copies of this line with all found combinations and shows them as a group with the same 2θ angle. You can choose the lines in the group by a criteria such as minimal 2θ deviation, or by indices h k l which belong to a most symmetric cell, or the specific h k l combination does or does not exist in a structure prototype. To improve the lattice parameters by newly identified lines, select only one most likely existing line in each group; you may either not select or delete other lines.
The most common cause of unsuccessful indexing is too large deviation of unidentified lines from the calculated position — more than delta × precision. You can either change the delta multiplier or, better, set the more appropriate 2θ precision in the correction and precision dialog.
Also try to change one or more basic lines to avoid a problems with too large deviation of chosen lines or unlucky choice of dependent indices; slightly decrease the threshold. Besides that, try to increase the limits by h k l and edges, set the primitive cell and change the lattice type to another possible.
File or directory is not found, cannot be opened or is write-protected. More likely you made a mistake typing the name. Another possible reason: you deleted of moved to another place a file which was stored in the recent list; this file will be removed from the list and you need to find it using open the table dialog. Less often you may see this error when you do not have an access to external drive or lack of required permissions. If the file is write-protected and cannot be saved with the same name or in the same place, try to change its name or use another directory or drive in save as dialog.
You have chosen the name of the file which already exists. If you want to rewrite it, confirm it in the dialog, otherwise cancel and try to choose another name. Alternatively, you can change a directory or drive and save the file there.
Data in this file cannot be properly input because the file is either damaged or its format is not supported by current version of the program. Please check whether the file has the format *.htm, *.par, *.aid, or one of supported *.txt formats, which is suitable for data input.
Note that although the files *.par have the UTF-8 text format, changing any data in them is highly recommended only inside the program RTP and not in the editors like Notepad etc. If you open a file in external editor to take data for reports, presentations etc., try to select the read-only mode, or at least do not save it.
This file does not contain the information about the wavelength. Most often this may happen when the wavelength is missed in the header of the imported text file, however, some PDF files may also omit this information. Normally such PDF cards are counted incomplete and eventually become marked as deleted.
Your current wavelength has not been changed and was used to calculate 2θ or d, depending on primary data in the file. You can keep it or choose another wavelength which corresponds to original data. The most common emission Cu Kα1 (1.54056 in PDF) may be a reasonable choice. If you imported the interplanar distances or PDF data, then selecting the appropriate emission type from the list is enough, because in such case the exact wavelength value is not so important for parameters calculation.
This message means that a file does not contain an information about lattice type of the substance. This may happen, for example, if you opened a very old PDF card. Primitive cubic type is assigned by default to this lattice. As a result, an attempt to calculate the lattice parameters may give wrong results.
You need to select the real lattice type if it is known. Otherwise, try to assign the probable types which can be concluded from existing h k l combinations, then perform the calculation and see how many errors (very large deviations) are in the results. Alternatively, you can try to use the indexing procedure.
The minimal number of the lines with linearly-independent indices, which are selected for calculation, must not be less than number of lattice parameters in given syngony; for statistical reliability this number should be more than minimal. Try to select more lines or add them to the table.
Indexing requires at least one extra line over the number of lattice parameters. Besides that, for indexing by known h k l the number of known and selected lines should be enough to calculate the parameters.
Most of PDF-2 cards, including the theoretically calculated data, have at least 5 digits after the decimal sign in the d values, so the default precision defined in the options is applied to these data. However, some old cards (circa 1950-1980) may have only 3 or 4 meaning digits (the last digits required by the card format are zeroes). If this occurs, the program restores the approximate 2θ precision basing on the number of meaning digits of d and current wavelength; in such case the default precision is not used. The calculated value is normalised to the nearest value in the standard precision row. If need, you can set 2θ precision manually in the correction and precision dialog.
There may be a number of reasons to change current wavelength when the table contains some data. You might read (import) a file without information about wavelength, or you want to see 2θ at different emission than in imported card or your previous calculation. You might also skip to set the correct wavelength before input data in the table manually.
In this dialog you need to choose how to recalculate the existing data. If the angles 2θ are original, like the data from XRD device, need to calculate new d from 2th; otherwise, if the d values should be counted original, like in PDF cards, need to calculate new 2th from d. You may also Cancel the change and return to previous wavelength.
Changing the wavelength may require to calculate new 2θ precisions. If the angles are original, precisions remain unchanged. They also remain the same if the d values are original, but all lines have the same 2θ precision equal to default PDF precision in options or the last set 2θ precision in the correction and precision dialog. Otherwise the precisions are calculated separately for each line from d and its current precision. As a result, even in the constant mode they may be different.
In any case, if the new precisions calculated this way are not representative, you can change them in the correction and precision dialog.
The number of lines with linearly-independent indices is less than minimal number required for calculation, which is equal to the number of lattice parameters. More often this may happen at calculation of low-symmetric lattices, especially when the total number of lines is low or when you attempt to unselect too many lines with high deviation.
Try to select more lines for calculation or choose some other lines instead.
This error may happen if you attempt to generate reflections by parameters, but you have selected very narrow 2θ range or the upper 2θ limit is too low. You might also set unusually large wavelength. Try to increase 2θ range until the error disappears.
This error means that the number of h k l combinations generated for the limit by indices in the Settings for indexing dialog is not enough to continue the indexing process. This number should not be less than the number of lattice parameters plus one. Return to the indexing dialog and increase some of h k l limits.
This error message usually happens at the begin of indexing, but may also happen if you try to generate the reflections of the large cell in large 2θ range. It informs about the overflow of the array of possible h k l combinations, which is limited by 4096 in current Win32 version of the program.
In the indexing mode, if a cell centring is primitive, use these estimations: h k l must not exceed (46 46 46) (with multiplicities) for cubic lattice, (15 15 15) for orthorhombic, (12 12 12) for monoclinic, (9 9 9) for triclinic. If a cell is non-primitive, limits can be increased. For shuffle method, decrease one or more maximum values by h, k or l, until the overflow disappears. In the indexing by known h k l method, you can keep recommended indices but instead decrease the 2θ range, selecting the narrow area around the unidentified lines.
In the generation mode this may happen if the edges are large and the 2θ range is very large as well. For example, for cubic lattice, Cu Kα emission and 2θ range 0...179 degrees the maximum edge a is 53 Å. However, the table becomes full at much lesser 2θ range 0...40 degrees. For tetragonal lattice the edge limits are approximately 20 Å, for orthorhombic — 15 Å, for monoclinic — 12 Å, for triclinic — 9.5 Å. To prevent this kind of overflow, use a reasonable upper 2θ limit or decrease it until this error disappears. You may still see the warning about the table size overflow, but the program will automatically decrease the upper 2θ to acceptable value.
When you perform the generation reflections by parameters, the number of possible h k l combinations for given 2θ range exceeds the table size (440 lines), and the program has decreased the upper 2θ limit. As a result, all possible reflections beyond this limit are missed. See the last calculated angle at the end of the table and use it as a reference point for another 2θ range.
This error may also happen after indexing by known h k l, when added lines with the same 2θ but different indices reach the table size. As a result, indices of the next lines after the last properly identified remain partially or completely unknown. It is recommended to save current results, then delete the identified lines (except the last one: keep a single line with 2θ and clear its indices). Then you can perform the indexing of remained lines again.
Indexing by known h k l begins from calculation of lattice parameters from selected lines with known indices. The quality of calculation directly affects the success of indexing; because of this, the quality should be at least "satisfactory" or better. "Poor" quality means that root mean square deviation is more than 3 × precision, so indexing cannot continue.
First of all, check if the lattice type is correct and the precision is real. Then perform the calculation of lattice parameters and look at the recommendation in details. Try to unselect the lines with too high deviation and select other lines until you get the "satisfactory" quality or better if possible. As a last resort, you can select the minimal set of lines equal to the number of lattice parameters, when estimation of quality is not performed.
To perform indexing by known h k l, the lines which indices you want to identify should have the empty h k l field and belong to the same phase as known lines, if the phase is specified. Unselected lines with non-zero indices and 2θ angles are counted as known. Please make sure that unidentified lines present in the table; also if the table has more than one phase, move the marker to any line of specified phase.
The lattice parameters have been calculated by the lines with known indices h k l, but an attempt to find the indices of any unidentified line was failed. A probable reason is, the real precision of 2θ angles is significantly poorer than the precision which is currently set for these lines. Try to change the 2θ precision to more correct value. Otherwise these lines may belong to another phase with different crystal structure or less symmetric cell.
This message means that calculated results do not have a physical sense, e.g. negative values were obtained. More probably this may happen because of some mistakes like wrong indices or angles, for example, when the same indices are assigned to significantly distant lines.
Thoroughly check all data in the table. Also try to select more lines, if possible, then unselect one or several lines until this error disappears. These unselected lines may have significant deviation, often far beyond the average.
Another possible cause of this error: the number of linearly-independent indices is less than number of lattice parameters. Add more lines for calculation.
Chemical formulae, which are input in the theoretical density dialog, may contain some errors preventing the proper decryption of the formula and, as a result, the calculation of molar mass and density cannot be performed. In such case, you will see one of error messages in the line for atomic composition. Sometimes the decryption algorithm may show errors for valid but too complex formula: please send an example of such formula with explanation to author for test. Note that algorithm was not designed for complex organic compounds and polymers.
This error means that you made a mistake in a symbol of one of chemical elements. Program can recognise only the standard short names of 1 or 2 letters; other non-standard, temporary, obsolete variants or abbreviations like Tu, Yt, Ln, Me etc. are not accepted. Some such names may be mistakenly interpreted as two existing elements. This error may also happen when the letter case is incorrect (decryption algorithm can correct some mistakes, but not all). Check the formula and look at the official symbols of elements in the up-to-date periodic table, for example, in the PubChem database [7].
Such error may happen if the number of closing brackets is not equal to opening brackets, if the closing bracket presents before opening or if the different types of brackets are used as opening and closing on the same level. In any such situation, the coefficient after closing bracket cannot be properly applied. Check that all brackets are correct and paired.
Number of formula units in the cell should be integer, currenty supported values are within the limits 1...128. Check this value.
Formula may have up to 8 different types of atoms (common chemical elements and specific isotopes), otherwise it cannot be decrypted because of complexity. If you work with such compounds, contact the author or try to combine some less important or similar (by atomic mass) elements.
Most likely the wrong coefficient or multiplier is equal to zero, is too large or contains non-translatable characters. Check the value and avoid to use the extended Unicode characters. Note that arithmetic operations like 2-0.15 are not allowed here. Values should be calculated before using in a formula.
Most likely the algorithm has recognised a part of the formula as two consequent coefficients, which is not allowed. Remove the second value or add the missed element or brackets. If this is a multiplier written before the group, like a coefficient of hydration, do not forget to use the separator like * (asterisk) or ⋅ (middle dot).
If you specified the atomic mass of an isotope in the brackets after the element name, check that the value is within the limits 1...330 (g/mol), according to possible masses in current periodic table.
Formula line is empty or cannot be interpreted as a chemical formula: no elements are found. Please note that this dialog cannot be used to input or edit any specimen information besides the formula; if you need this, use the information about specimen dialog instead.
Such error occurs if there is a comma inside the brackets, which means that some elements are mixed or exchanged in unspecified proportion, like olivine (Mg,Fe)2SiO4. Without definite information of element quantity, the molar mass and density cannot be calculated. This can be solved in two different ways. First, you can specify the amount of each element in the compound, like (Mg0.6Fe0.4)2SiO4. Second, you can calculate the density for each variable element separately. Then, depending on the purpose of research, you can describe the possible interval of the density or calculate the mean value and uncertainty.
There is an internal limitation of formula complexity: it may have no more than 4 levels of nested brackets, including round and square brackets and also brackets of isotopes; nesting of the square brackets is not supported. Try to rewrite and simplify the formula if possible. Alternatively, instead of the formula you can write the list of atoms and their amount in the unit, like it is shown in the decrypted atomic composition.