CrystalDiffract User's Guide

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® CrystalDiract Crystal Diract Interactive Powder Diraction Software

Works with CrystalMaker®: Inter Interactive active Crystal Cr ystal Structures Visualization

User’s Guide

 Version  V ersion 5.2 for Mac • Version 1.4 for Windows

 Table  T able of Contents Chapter 1: Getting Started .................................. ................ .................................... ................................... ................. 1 Using this Guide..................................................................... .................................. ......................................... ...... 1 Interface Reference Convention ................................................... ................................. .................. 2 System Requirements ................................................................... ............................... .................................... 2 Installation .................................................................. ............................... ..................................................... .................. 2  What is CrystalDiract? Cr ystalDiract? ............................................................... ................................. .............................. 3 CrystalMaker Integration Integration ............................................................. ................................ ............................. 6 Chapter 2: CrystalDiract Crys talDiract Interface ................................... ................. .................................... ....................7 ..7  Window Design ........................................................................... ....................................... .................................... 7 Displaying a Diraction Pattern ................................................... ................................. .................. 7 Scrolling and Zooming ................................................................. ................................... .............................. 9 Measuring a Pattern.......................................................... Pattern.................................................................... .......... 10 Output .................................................................. ............................... ......................................................... ...................... 10 Help and Updates ................................................................... ................................ ....................................... .... 10 Chapter 3: Simulating Diraction ................................... ................. .................................... ..................... ... 11 Calculating the Pattern ............................................................... ................................... ............................ 11 Radiation Type.................................................................. ype............................... ............................................. .......... 12 Diraction Modes .................................................................. ............................... ....................................... .... 12 Peak-Shape Functions ................................................................ .............................. .................................. 14 Peak Widths ..................................................................... .................................. ............................................. .......... 15 Editing Structural Data .............................................................. .................................. ............................ 16 Interactive Parameter Control .................................................... .............................. ...................... 17 Mixtures...................................................................... ................................... ................................................... ................ 19 Viewing Diraction Data ........................................................... ............................... ............................ 20 Chapter 4: Working with Patterns.................................... .................. .................................... ..................... ... 21  Working  Working with Observed Data..................................................... Data............................... ...................... 21 Managing Multiple Patterns Patterns....................................................... ................................. ...................... 23 General Plot Settings................................. Settings.................................................................. ................................. 25 Individual Pattern Pattern Settings Settings ......................................................... ................................... ...................... 26 Customizing your Workspace Workspace ..................................................... ............................... ...................... 28 Chapter 5: Printing & Saving .................................... .................. .................................... ........................... ......... 29 Saving Your Your Work Work ................................................................... ................................ ....................................... .... 29 Saving Preferences .................................................................. ............................... ....................................... .... 29 Exporting Data ....................................................................... .................................... ....................................... .... 29 Printing ....................................................................... .................................... ................................................... ................ 30 Chapter 6: Toolbar Reference .................................... .................. .................................... ........................... ......... 31 Chapter 7: e CrystalMaker  Crystal Maker ® Oce ....................................................33 Introduction to CrystalMaker.................... CrystalMaker..................................................... ................................. 33 Single-Crystal Diraction .......................................................... .............................. ............................ 34 Index

...........................................................................................35

 Table  T able of Contents Chapter 1: Getting Started .................................. ................ .................................... ................................... ................. 1 Using this Guide..................................................................... .................................. ......................................... ...... 1 Interface Reference Convention ................................................... ................................. .................. 2 System Requirements ................................................................... ............................... .................................... 2 Installation .................................................................. ............................... ..................................................... .................. 2  What is CrystalDiract? Cr ystalDiract? ............................................................... ................................. .............................. 3 CrystalMaker Integration Integration ............................................................. ................................ ............................. 6 Chapter 2: CrystalDiract Crys talDiract Interface ................................... ................. .................................... ....................7 ..7  Window Design ........................................................................... ....................................... .................................... 7 Displaying a Diraction Pattern ................................................... ................................. .................. 7 Scrolling and Zooming ................................................................. ................................... .............................. 9 Measuring a Pattern.......................................................... Pattern.................................................................... .......... 10 Output .................................................................. ............................... ......................................................... ...................... 10 Help and Updates ................................................................... ................................ ....................................... .... 10 Chapter 3: Simulating Diraction ................................... ................. .................................... ..................... ... 11 Calculating the Pattern ............................................................... ................................... ............................ 11 Radiation Type.................................................................. ype............................... ............................................. .......... 12 Diraction Modes .................................................................. ............................... ....................................... .... 12 Peak-Shape Functions ................................................................ .............................. .................................. 14 Peak Widths ..................................................................... .................................. ............................................. .......... 15 Editing Structural Data .............................................................. .................................. ............................ 16 Interactive Parameter Control .................................................... .............................. ...................... 17 Mixtures...................................................................... ................................... ................................................... ................ 19 Viewing Diraction Data ........................................................... ............................... ............................ 20 Chapter 4: Working with Patterns.................................... .................. .................................... ..................... ... 21  Working  Working with Observed Data..................................................... Data............................... ...................... 21 Managing Multiple Patterns Patterns....................................................... ................................. ...................... 23 General Plot Settings................................. Settings.................................................................. ................................. 25 Individual Pattern Pattern Settings Settings ......................................................... ................................... ...................... 26 Customizing your Workspace Workspace ..................................................... ............................... ...................... 28 Chapter 5: Printing & Saving .................................... .................. .................................... ........................... ......... 29 Saving Your Your Work Work ................................................................... ................................ ....................................... .... 29 Saving Preferences .................................................................. ............................... ....................................... .... 29 Exporting Data ....................................................................... .................................... ....................................... .... 29 Printing ....................................................................... .................................... ................................................... ................ 30 Chapter 6: Toolbar Reference .................................... .................. .................................... ........................... ......... 31 Chapter 7: e CrystalMaker  Crystal Maker ® Oce ....................................................33 Introduction to CrystalMaker.................... CrystalMaker..................................................... ................................. 33 Single-Crystal Diraction .......................................................... .............................. ............................ 34 Index

...........................................................................................35

Chapter 1: Getting Started  Welcome to CrystalDiract: a program designed  Welcome designed to make powder powder diraction intuitive, intuitive, interactive, and perhaps even fun! We hope you nd this program useful and entertaining.  is part of the User’s User’s Guide is designed to give a quick overview of what the program is, its scope, plus information on how to install the program, followed by tips on using the rest of this User’s Guide. Using this Guide

Searching for Topics

 is User’s Guide should provide provide a very  comprehensive comprehensive outline of the major program features. We don’t expect you to read it from coverto-cover, but would recommend the following key  sections:

 We  We have tried to provide a comprehensive comprehensive yet yet logically-structured guide. If you need to nd specic information, here are some suggestions: s uggestions:

 A  should browse Chapter 2: •  A CrystalDiract Interface .

2. If you are viewing the guide electronically, electronica lly, you can click on the Contents or Contents or Index   Index page page entries to go directly to the corresponding pages.

Tis is designed to give you a quick orientation to the program; the interface changes from version to version, and will certainly be dierent to other   programs you may have have used, so it’s it’s important to to  get your bearings earlier, earlier, rather than than later!  •

I     , we strongly  recommend that you complete the Tutorial,  which is available from CrystalDiract’s Help menu. Te series of short, structural exercises is designed  to illustrate some of the most important program  features and should address most of the the queries that   you might have when using the software.

 e User’s Guide describes describes the program interface, followed by sections on simulating diraction, how  to put data into the program—then describing display and manipulation, before nishing with out of the program: printing and how to get data out of exporting data.

1. is guide includes a able of Contents (at Contents  (at the beginning) and an Index  an  Index (at (at the end).

3. If you need to search for a keyword or phrase,  you should be able to use the Search command in a PDF viewer such as Adobe (Acrobat) Reader or Apple Preview. A Note about a bout the Demonstration Version This User’s Guide is designed for the Full-Feature version of CrystalDiffract. If you are using the free, Demonstration Version, Version, some some features may not be available: • The Demonstration Version is designed to give give you a favour of favour of the full program, using a range of examples structures. However, you cannot save les, record program settings, or specify preferences. • The Demonstration version does not let you import observed data les (although you can read such data if  they have been saved in a diffraction experiment). If you are using the Demonstrat ion Version, we we strongly recommend that you explore the saved diffraction experiments provided: these demonstrate a range of  features that are possible with the full version of the program.

Chapter 1: Getting Started

1

Interface Refer Reference ence Convention

Installation

In the following chapters we refer to elements of  the program’s interface (such as button names, menu commands and keys on your keyboard) using a typewriter font .

Mac and Windows versions have dierent installation procedures: •

 You  You will also encounter many references references to menu commands written in an abbreviated manner, such as “Edit > Copy ”, which means “from the Edit menu choose the Copy command”.

As a modern Mac application, CrystalDiract  includes all its essential resources (including online  help and this User’s User’s Guide), neatly packaged within the application “bundle”.

Mac & PC Shortcut Keys

Mac and Windows operating systems use dierent key combinations for menu shortcuts (“accelerator keys”). In this guide we make repeated reference to command and option keys, which are included on the standard Mac keyboard Windows users should use the following translation:  Mac

Windows 

command

control

option

alt

System Requir Requirements ements  To  To run CrystalDiract on a Mac, you will require Mac OS X 10.4 “Tiger” , 10.5 “Leopard”, 10.6 “Snow Leopard”, or 10.7 “Lion”.  To  To run CrystalDiract on a PC, you you will require Microsoft Windows XP (Service (Ser vice Pack 2), Vista or  Windows 7. e program will not run on earlier  versions of Windows, such as NT or 2000.

installation is a simple matter of draggingand-dropping the CrystalDiract application from the CD-ROM, to your hard disc (e.g., to  your Applications   your Applications folder). folder). Mac

We would also recommend that you copy the  Examples Files to Files to your hard disc—possibly to  your own Documents folder. Documents folder. •

Windows users

will need to run the installer program. is gives the option of installing the essential program les (application, online help, user’s guide), plus supporting resources (examples les).

Licensing your Installation

 e rst time you launch CrystalDiract you are prompted to personalize your copy of the program.  is process also creates a preferences preferences le. Registering Your Licence

It is very important that your licence is registered  with us, as we can only provide technical technical support (and upgrades) to registered users.  You  You can register when you install the software, by clicking the Register button in the reminder dialog that appears following your installation. install ation.  Alternatively,  Alternatively, you can register later, later, by choosing the Help > Register CrystalDiffract command. Multi-User Licence Registration We only require one registration per licence. So, if you have a multi-user licence, such as a Research Group, Classroom or Site L icence, only the ofcial “keeper” of the licence needs to register with us. Once Once we have received that registration, the other users are entitled to receive technical support, within the terms of the specic licence.

2

Chapter 1: Getting Started

What is CrystalDiffract?

Crystalline Materials

CrystalDiract is a program for  e starting point for simulating a diraction understanding diraction properties pattern is a crystal structure: the unique of crystals: specically, where a arrangement of atoms inside a basic building brick, powdered crystal sample (comprising or “unit cell” of material. Crystals typically contain millions of tiny crystallites ) is exposed billions of unit cells, neatly stacked in a threeto a radiation beam, resulting in patterns of  dimensional lattice. scattered intensity, which can be recorded as lines on a lm, or as intensity peaks by a detector. CrystalDiract diers from its sister program, SingleCrystal, which is designed to simulate diraction patterns from a one, single crystal, when exposed to x-rays, neutrons or electrons. CrystalDiract can simulate the key powder diraction techniques used today, including traditional single (or dual-) wavelength X-ray and neutron scattering, plus newer white radiation (energy-dispersive) and time-of-ight techniques. CrystalDiract lets you manipulate diraction patterns in real time, changing sample and instrumental parameters such as peak widths,  wavelength, particle size and strain. You can measure intensities and distances on screen, compare patterns from dierent materials in the same window, and simulate multi-phase mixtures. For the experimental scientist, CrystalDiract lets you load observed data, for easy comparison  with simulated data: an ideal way to characterize materials or interpret the results of synthesis experiments.

 A crystal structure is derived f rom a basic unit that is tiled  in three dimensions to form an extended crystal lattice.

It is the very regularity of such structures that allows diraction in the rst place. e preciselyoriented planes of atoms, repeated almost ad  innitum, provide miniature diraction gratings for  X-ray or neutron radiation.

Finally, CrystalDiract lets you print your diraction patterns, or export them in a range of  data formats.

 A tiny section through the crystal lattice of sodium chloride  (“halite”, or “rock salt”). Here we see a regular arrangement  of chlorine ions (green) and sodium ions (yellow). Chapter 1: Getting Started

3

Why use Powder Diffraction?

Monochromatic Radiation

Powder diraction has a number of advantages over single-crystal techniques. Sometimes it is dicult to nd (or grow) good quality single crystals, whereas powders are much easier to manage. Single-crystal diraction (using X-rays or neutrons) is quite an arduous process, requiring precise orientation of the sample (or, in the case of  electron microscopy, specially-prepared, thin crystal akes). Data collection tends to be very slow, as individual scattered beams are measured (although new, area detectors, are making this faster).

In most laboratory sources, X-rays are generated by  ring a beam of electrons at a metal target—usually  copper (Cu) or molybdenum (Mo). A characteristic  X-ray spectrum is emitted, which is ltered, so that only the strongest, Cu K a peak emerges (this is actually a doublet, comprising K a1 and K a2 peaks, although sometimes the weaker, K a2 peak is also ltered out). is monochromatic radiation is then directed at the specimen. One typically moves the beam, relative to the sample, scanning through a range of angles, q.  ere is a reciprocal relationship between q, and inter-planar distances in the crystal (“d-spacings”),  which give rise to diraction peaks. is is summarized in the famous Bragg Equation:

 With powder diraction, one has the advantage of speed and convenience. A powdered sample has multiple “crystallites” and, assuming these are randomly distributed, at least one crystal will be oriented correctly to cause diraction. Data collection times tend to be faster, since only a “onedimensional” pattern is being collected.

l = 2d sin q

 which provides the condition for coherent scattering of the radiation (wavelength l), directed at an angle q (the Bragg Angle) with respect to the d-spacing of a set of planes in the crystal.

 e most-important powder diraction techniques—which can be simulated by  CrystalDiract—are described below.

Derivation of the Bragg Equation

N(hkl) 1

1

2

2 θ

θ

(hkl) θ

θ

t  

   t

θ

d

Consider a crystal with a set of planes, (hkl), shown here in blue. The interplanar spacing is denoted by d, and the plane normal is N(hkl). If a beam of monochromatic radiation (wavelength l), shown here in red, strikes these planes at a glancing angle, q, then constructive interference between adjacent wavelets ➀ and ➁ occurs when their path difference (t + t) is equal to an integral number of wavelengths.

4

Thus,

nl=2t

where: t = d sin q

hence,

n l = 2 d sin q

(the Bragg Equation).

Chapter 1: Getting Started

By measuring scattered intensity as a function of  scattering angle, one is in eect measuring the scattering strengths of dierent sets of planes (with dierent d-spacings) inside the crystal. Ultimately, this scattering strength is controlled by the arrangements of atoms in dierent directions in the crystals—and hence one can learn something about the crystal structure from its diraction properties. White Radiation

Many diraction experiments are carried out at synchrotron sources. Here, charged particles are accelerated to relativistic speeds, and emit x-rays as they travel around a curved beam path. So-called “White Radiation”, comprising a broad spread of wavelengths, can be generated; this is useful in diraction experiments because it allows rapid measurements, without the need to mechanically  scan a detector over a range of angles. An energydispersive detector records the scattered intensities as a function of energy (and hence wavelength).

Time-of-Flight Diffraction

Some diraction experiments use pulses of  neutrons with a range of energies. ese travel at dierent speeds, depending on the energy of the neutrons, and are directed down a long “beam line” towards a powder sample. Diraction is recorded by neutron detectors arranged around the sample, at a xed two-theta angle (2q). e number of pulses is recorded as a function of the time-of-ight of the neutrons (which is typically in the range of a few  milliseconds to several hundred milliseconds).  As for energy-dispersive diraction, an extended diraction pattern can be recorded at a xed Bragg angle because the sample is subjected to neutrons of dierent energies, and hence wavelengths.

Chapter 1: Getting Started

5

CrystalDiract works with CrystalMaker (left) letting you visualize crystal structures and simulate their diraction  properties—in various experimental modes—in comparison with other patterns and observed data.

CrystalMaker Integration If you would like to be able to build  your own crystals which you can load into CrystalDiract, you will require CrystalMaker®: an award-winning program for building, displaying, manipulating and animating all kinds of crystal and molecular structures. CrystalMaker provides seamless display of data les from major databases and supports a wide  variety of le formats. Just drag-and-drop a text le into CrystalMaker for automatic format detection and structure display. CrystalMaker lets you display a structure then,  with a single menu command, see its diraction pattern appear in CrystalDiract.

6

Chapter 1: Getting Started

Further information about CrystalMaker is given at the end of this guide, or you can  visit crystalmaker.com and download a free Demonstration Version. Although CrystalDiffract allows you to edit some a spects of a cr ystal’s structure (e.g., lattice parameters and site occupancies), it does not allow you to edit atomic coordinates or to build new structures. We believe that the best way to edit these structures is via a CrystalMaker: this allows you to actually see the structure, so you can check that the coordinates and/or symmetry settings are reasonable, before you proceed to generate diffraction patterns.

Chapter 2: CrystalDiffract Interface  is chapter provides a basic introduction to CrystalDiract’s user interface, including how  to load a diraction pattern and manipulate it. Window Design

Displaying a Diffraction Pattern

CrystalDiract has a single-window program interface with a toolbar, and a Graphics pane for plotting your diraction patterns. Additional panes are available for displaying lists of Patterns or Parameters.

CrystalDiract can read from three kinds of  les: text les, crystal structure les, and saved diraction session les.

 At the top of each window is a toolbar  with buttons/icons for measuring and manipulating diraction patterns (see Chapter 7: oolbar Reference  for a description of the individual controls).

Do one of the following: •

Drag-and-drop a le onto the CrystalDiract application icon;

Mac users can toggle the toolbar on or o by  clicking the lozenge-shaped button, on the right-hand side of the window’s titlebar.



Launch CrystalDiract, then drag-and-drop a le into the window that appears.



In CrystalDiract, choose File > Open then use the le dialog to specify the le(s) to be opened.



Drag-and-drop a le into the Patterns List, then click the new entry’s checkbox;

Toolbar

 At the centre of the window  is the Graphics pane, where diraction patterns are plotted. Below this is a scrollbar for moving through the x -axis range, and an Info Bar which displays cursor- or status information.

To load a le in a new window:

Graphics Pane

 is is a list of experimentaland sample parameters, grouped into folder-like categories. You can edit parameters interactively, using a slider control, and observe how the diraction pattern changes. Parameters List

Each window can display a list of diraction patterns. You can drag text les, CrystalMaker binary les and folders into this list.  e corresponding patterns can be displayed in the Graphics pane by clicking checkboxes. Patterns List

Displayed patterns can be selected by clicking on their Patterns List entries. Selection allows you to edit individual patterns, and move them relative to the rest of the display.  You can resize the Patterns List by clicking-anddragging the drawer edge (Mac) or the pane divider (Windows).

To open a le in an existing window:

Do one of the following: •

Choose: File

> Open in Same Window .



Drag-and-drop your le(s) into the window. Data will be added in the form of one or more new diraction patterns.

Crystal Files

 You can simulate a diraction pattern for a crystalline material, by supplying a CrystalMaker “crystal” le (le type CMDF , extension .cmdf or .crystal ). CrystalDiract will use structural data from the le to generate a diraction pattern. Please note that Demonstration Mode restricts you to reading only the latest CrystalMaker binary le format. However, the full-feature version can read from older les.

Chapter 2: CrystalDiffract Interface

7

Graphics Pane

Toolbar

Parameters List

Info Bar

Patterns Drawer

Te CrystalDiract-for-Mac program interface, showing calculated and observed diraction patterns 

Patterns List

Te CrystalDiract-for-Windows interface, showing diraction patterns in “Film” mode  8

Chapter 2: CrystalDiffract Interface

Parameters Palette

Text Files

Scrolling and Zooming

 You can load an observed diraction pattern, as a plain text le (le type TEXT , extension .txt or .dat) . e le should contain an xy listing of   your diraction points (where the y   value is the intensity), with one point per line.

 You can use the horizontal scroll bar to quickly  scroll through a diraction pattern. For ner control, choose the Hand tool from the toolbar then click and drag the pattern.

Session Files

 e third type of le that CrystalDiract can read is its own “session le” format (letype CRDF, extension .crdf or .crystaldiffract ).  A session le is a saved diraction experiment,  which represents a complete record of your work in a particular window, with one or more diraction patterns, including structural data (for simulated patterns) and intensities. Sharing Data With CrystalMaker 

 You can also provide crystal structure data directly from within CrystalMaker, via that program’s Transform > Powder Diffraction submenu. Simply view and edit your structure in CrystalMaker; choose the relevant menu command, and then observe the diraction pattern in CrystalDiract.

 You can adjust the range of x-axis values by using the Zoom tool to zoom in or out around a clicked point. To enter an explicit range, use the Plot > Plot Limits command.

Arrow

Hand

Zoom

Distance

CrystalDiract’s tool buttons 

Scaling Commands

 e Toolbar includes a number of scaling tools that can be used to adjust the x - and y -axis ranges. You can adjust the x - and y -axis scales, and auto-scale the y (intensity) axis, or both the x - and y -axes (the latter option attempts to t the entire diraction pattern range inside the Graphics pane). auto-scale y

x-scale

y-scale

auto-scale x & y

CrystalDiract’s axis scaling tools 

Use CrystalMaker to visualize (and verify!) the structure  before you proceed to simulate its diraction properties.

Chapter 2: CrystalDiffract Interface

9

Measuring a Pattern

Printing 

 e Arrow tool allows you to measure points on the simulated diraction pattern. Choose this tool from the Toolbar, then click in the Graphics pane so that a vertical cursor appears. Information about the current point is displayed in the Info Bar at the bottom of the window.

 e full version of CrystalDiract lets you print high-resolution diraction patterns, which are scaled to t your chosen page size.

Using the Arrow tool to measure a diraction peak

 You can move the vertical cursor by clicking and dragging it with the Arrow tool (note that when the Arrow tool is placed over the vertical cursor, the mouse pointer changes to a double arrow ( ) to indicate that dragging is possible).

Saving Preferences

CrystalDiract uses default settings for the window  size, diraction mode, plot styles, etc. Although  you can edit these for individual windows, the default settings are used whenever a new window is created, or when you start up the program.  You can view and edit the current program settings using a tabbed preferences dialog. To display this, choose the Preferences menu command. When  you have nished making your changes, click the dialog’s Save button; your settings will then be available for any new windows, and are saved in a preferences le, ready for your next session. •

To restore the program’s “Factory” settings, click the dialog’s Restore Factory Settings button.



To apply any saved preferences to the current  window, use the Apply Preferences menu command.

Indexing a Pattern

 You can display peak labels for a selected diraction pattern using the Pattern menu. Labels can contain any combination of Miller Indices, d-spacings, x-values, and so on. e Peak Threshold setting denes a minimum intensity   value, below which no labels will be displayed is is useful for complex diraction patterns which may have many low-intensity peaks.

Output CrystalDiract provides a range of data output options, via the File > Export submenu. ese include exporting a complete diraction pattern, at user-dened resolution; a diraction data report (Miller indices, d-spacings, intensities, multiplicities, etc.), or a table of Structure Factors.

Help and Updates Most controls have tool tips associated with them. For detailed help, choose the Help > CrystalDiffract Help command. Help les are displayed in a Help Viewer application (Mac) or  window (Windows). We also include a number of  support topics on our website, and links to these are included on the program’s Help menu. Checking for Updates

 We regularly provide free, incremental program updates. ese include new features, interface enhancements and occasional bug xes. You can check whether an update is available using the Help > Check for Update command.

 ere is also an option to let the program check   You can also save a diraction experiment as a self- for updates automatically (Help > Check for contained “Session File”, you can print, and you can Updates Automatically ); the program will check  at weekly intervals, and alert you if a newer version record your favourite settings in a Preferences le. of the software is available. You can then download this from our website. 10 Chapter 2: CrystalDiffract Interface

Chapter 3: Simulating Diffraction  e Diract menu lets you alter aspects of a “virtual” diraction experiment, such as the radiation type, the experiment type (angle- or energy-dispersive), and various instrumental parameters. Calculating the Pattern CrystalDiract calculates diraction patterns using the types, and positions, of atoms in a unit cell of  a crystal. e program assumes an ideal structure (although you can specify an isotropic strain). Site occupancy data and atomic displacement parameters are used to determine the amount of  scattering from each site. CrystalDiract uses atomic scattering factors (x-ray diraction) or neutron scattering lengths for the atoms in your structure. Editing Scattering Factor Data

CrystalDiract uses a table of atomic scattering factors and neutron scattering lengths, saved as a text le called  ASF.dat “ ”. CrystalDiract-for-Mac saves the ASF.dat le inside the application bundle. To view the contents of the application package, control-click on the CrystalDiract program icon and choose the Show Package Contents command from the popup menu that appears.

 You can edit the ASF.dat data le if you wish to modify or add new data. e format is very simple. Each data line should contain: •

a two-character element symbol (which CrystalDiract will match with element symbols in your structure);



nine numbers correspond to the atomic scattering factor coecients a 1 b1 a 2 b2 a 3 b3 a 4 b4 c listed in the International Tables for Crystallography;



one number, corresponding to the coherent nuclear scattering length for that element.

 e data le can also contain comments: these should be prefaced by an exclamation mark “!”. Note: the ASF.dat le must be a text-only le with le type TEXT . If you edit the le in a word processor, you should ensure that it is saved in a text-only format.

Locating the package contents 

CrystalDiract-for-Windows has the ASF.dat le saved in the Application Data folder.

Chapter 3: Simulating Diffraction 11

Simulation Preferences

Radiation Type

 You can use the Diffract menu to switch between  To speed up the simulation of diraction data  x-ray or neutron diraction. e diraction pattern (e.g., for massive structures such as proteins), is recalculated, using x-ray scattering factors or  you can suppress all reexions below a minimum d-spacing. You can also limit the maximum number neutron scattering lengths that are stored with the program. of reexions (so that only those with the highest d-spacings are used). To set your simulation preferences:

Diffraction Modes

Choose: CrystalDiffract > Preferences (Mac), or Edit > Preferences (Windows).

CrystalDiract can simulate a number of  experimental types, which cover the main techniques for powder diraction:

1

2

Navigate to the Prole tab.

group, set the Minimum d-spacing eld, enable the Limit number to option and enter a maximum number of reexions. 2

In the Generate

Reexions

 Angle-Dispersive Diffraction

 Traditional laboratory diractometers operate using constant radiation wavelength, with diraction measured as a function of Bragg Angle (theta, q). is is called angle-dispersive diraction. 3 Click the Save button to store your new settings. CrystalDiract allows you to simulate angle ese will apply to any new windows. dispersive diraction, plotting diracted intensity  as a function of: 2q, d-spacing, or reciprocal d-spacing.  You can specify the wavelength using the Diffract > Wavelength command.

Te Prole pane of the Preferences dialog  Tip: If you have edited your Preferences and wish to apply the changes to an existing window, choose the  Apply Preferences command, available from the CrystalDiffract menu (Mac) or the Edit menu (Windows).

12 Chapter 3: Simulating Diffraction

Te Wavelength sheet showing CuK a1 and K a 2 radiation

 e Wavelength sheet lets you specify  monochromatic (single-wavelength), or dual wavelength radiation. Traditional laboratory x-ray  tubes typically maximise intensity by emitting dual  wavelengths, e.g., Cu K a1 and K a2 lines.

Energy-Dispersive (EDS) Diffraction

Time-of-Flight Diffraction

 A relatively-new type of diraction involves using ‘white’ radiation that has a spread of wavelengths.  e Bragg equation relates wavelength (l) to the d-spacing of a set of lattice planes, and the Bragg  Angle (q):-

Some neutron diraction experiments use yet another kind of diraction: a neutron spallation source creates pulses of neutrons with a range of  energies. ese travel at dierent speeds, depending on the energy of the neutrons, and are directed down a long “beam line” towards a powder sample.

l = 2d sin q

If l can be varied, then diraction from a range of  d-spacings can be recorded at the same q angle. It is therefore not necessary to mechanically scan a detector through a range of q/2q angles. However, in order to resolve diraction from dierent d-spacings, the stationary detector must be able to discriminate between scattered radiation of  dierent wavelengths. Since the wavelength of radiation is related to its energy, an energy-dispersive detector can be used to record an extended diraction pattern as a function of energy. You can specify a 2q value for this experiment, using the Diffract > Energy command.

Diraction is recorded by neutron detectors arranged around the sample, at a xed two-theta angle (2q). e number of pulses is recorded as a function of the time-of-ight, t , of the neutrons (which is typically in the range of a few  milliseconds to several hundred milliseconds).  As for energy-dispersive diraction, an extended diraction pattern can be recorded at a xed Bragg angle because the sample is subjected to neutrons of dierent energies, and hence wavelengths.  We can analyse the time-of-ight process by  combining De Broglie’s hypothesis, l = h / mn vn

Te ISIS neutron spallation source at the Rutherford-Appleton Laboratory, near Oxford, England. Neutrons are directed  along beam lines, arranged radially, around the target (the cur ved light-blue chamber in the centre of the photo). ime-of ight diraction is used at one such beam line, the High-Resolution Powder Diractometer (HRPD). Chapter 3: Simulating Diffraction 13

(where h is Planck’s constant, mn is the neutron mass and vn is its velocity)  with Bragg’s Law, thus: l = h / mn vn = 2 d sin q

Now, given a primary ightpath (the distance from the moderator to the sample) of L1 and a secondary ight path (sample to detector) of L2, and corresponding times of ight t 1 and t 2, we have: vn = (L1 + L2) / (t 1 + t 2) = L / t   where L is the total ight path and t is the total time-of-ight. thus, h t / mn L = 2 d sin q hence: t = 2 d L (mn/h) sin q  us, we have a linear relationship between the total time-of-ight, t , and the overall ight path, L. is is why the highest-resolution neutron diractometers have the longest ight paths (e.g., ~100m at the HRPD instrument in the Rutherford-Appleton Laboratory). CrystalDiract lets you specify the overall ight path, L, as well as the two theta value for the diraction experiment, using the Diffract > Time-of-Flight command.

Peak-Shape Functions In an ideal diraction experiment, the shape of a diraction peak would be determined solely by the sample, reecting its mean particle size, particle shape and structural state (including strain). In practise, for most samples the shape of  diraction peaks is mainly determined by the diraction technique and geometry. For example, neutron diraction experiments tend to result in peaks with a Gaussian shape, whilst synchrotron diraction may result in a Pseudo-Voigt peak  shape. CrystalDiract’s Diract menu lets you choose between dierent shape functions: •

Delta Function



Lorentzian



Gaussian

• Pseudo-Voigt  e Delta Function is simply a “spike” of zero  width. is provides a very quick way of showing the positions of many peaks in a complex pattern.  e Lz function has a distinctive splayed appearance: peaks having very wide tails, like the mouth of a trumpet.  e G function is shaped like the prole of a church bell, with a more rounded appearance

Gaussian (top) and Lorentzian (bottom) proles for the  same diraction peak. Notice the lower peak maximum fo r  the Lorentzian prole, with its intensity distribution spread  over a wide range of x values.

14 Chapter 3: Simulating Diffraction

than the Lorentzian function, and with less extensive “tails”. Finally, the P-V function is a mix between the Gaussian and Lorentzian functions. It is characterized by a mixing parameter, E , which determines the Lorentzian character of the nal function:Result = E × Lorentzian + (1 – E ) × Gaussian  You can edit the E parameter using the Diffract > Eta command, and entering a new value in the sheet or dialog that appears.

Peak Widths  e limited resolution of a diraction experiment may result in diraction peaks that are substantially  broadened. For most practical experiments, this “instrumental broadening” is the major contribution to the widths of observed diraction peaks. CrystalDiract lets you specify the amount of  instrument broadening, in terms of the full width at half-maximum for a diraction peak. (e units depend on the current choice of x -axis: two-theta, d-spacing, reciprocal-d, energy in keV, or time-ofight in milliseconds.) Particle Size Broadening 

 e width of a diraction peak also depends on crystal size. is is a reciprocal relationship, so for large crystals there is very little peak broadening, but for very small crystals (fractions of a micron in diameter), diraction peaks can become noticeably  broadened. In a powder sample, we normally refer to a mean particle size, and this can be simulated using the Diffract > Particle Size command. Strain Broadening 

 A strained crystal can be thought of as containing regions with slightly dierent unit cell dimensions. In fact, there is likely to be a continuous spread of unit cell dimensions throughout the sample, resulting in a diraction pattern with a slightly  “blurred” appearance.  e amount of strain in the sample can be summarized by a “percent strain”. is is the standard deviation for the variation of cell parameters in the sample (in an ideal crystal there  would be one unique cell parameter, whereas in a strained crystal there might be a normal distribution of cell parameter values, characterized by a standard deviation, ranging from zero for the ideal crystal to a few percent for a very-highly  strained crystal). Use the Diffract > Percent Strain command to specify a value for the strain.

Chapter 3: Simulating Diffraction 15

Editing Structural Data CrystalDiract lets you edit aspects of a selected  pattern’s underlying crystal’s structure, so you can determine how this aects diraction. You can edit lattice parameters and site occupancies—and also omit sites from the diraction calculation. Edit Crystal Sheet

Choose the Edit > Crystal command to display  the Edit Crystal window. Lattice parameters are shown at the top, with a scrolling list beneath, showing all sites in the crystal’s asymmetric unit. Each site row has a checkbox, which denes  whether or not that site will be included in the intensity calculation. You could, for instance, decide to “turn o ” certain sites, so as to determine their inuence on the nal diraction pattern.  You can edit site occupancies by typing a formula into the Site Occupancy eld. You can enter up to three element symbols and their corresponding occupancies. e total occupancy must not exceed 1.0. For example, you might enter something like:

 e remaining elds cannot be edited. ey show  the atom’s fractional coordinates (xyz) and, if  available, the atomic displacement parameter data (anisotropic values and isotropic values).  To view the atomic displacement parameters,  you may need to resize the sheet, by clicking and dragging its size box. Alternatively, use the horizontal scrollbar to show the atomic displacement parameter elds, as the example opposite shows.  You can sort your data by clicking on a column header. Click again to reverse the sort order. You can also move columns, by clicking-and-dragging their column headers.  When you have nished your editing session, click  the OK button to replot the diraction pattern. Tip: You can visualize atomic displacement parameters a s “thermal ellipsoids”, using recent versions of CrystalMaker.

Si 0.7 Al 0.3

or:

Ca 0.56 Mg 0.41 Al 0.03

Te Edit Crystal sheet can be resized horizontally and vertically, in order to show a range of sites and their atomic  displacement parameter data (Uij and Uiso)

16 Chapter 3: Simulating Diffraction

Interactive Parameter Control

Energy Dispersive

 e Edit Crystal window lets you change multiple site occupancies and/or cell parameters, with the diraction pattern subsequently recalculated. A more interactive way of editing the structure is to use the Parameters List to gradually change one structural variable (e.g., unit cell angle) whilst the diraction pattern is replotted in real time.

If you have chosen an energy-dispersive simulation mode, then you can interactively change the two-theta angle for your sample/detector geometry.

 To show the Parameters List, click the Toolbar’s Parameters button:

Time-of-Flight

For neutron diraction, in the time-of-ight simulation mode, you can interactively change the two-theta angle (for the sample/detector geometry) and the overall neutron ight path length. Instrument

 Alternatively, choose: Window > Show Parameters List ; or (with the Graphics pane focussed) press the p key on your keyboard. Parameter Groups

 e Parameters List contains a series of  hierarchical entries, each with its own disclosure triangle, and representing dierent aspect of the diraction experiment:  Angle Dispersive

 is lets you interactively change the wavelength for a traditional, angle-dispersive (monochromatic radiation) experiments.

 is group lets you change aspects related to  your simulated diraction apparatus: the peak   width (instrumental peak broadening), the “Eta” parameter—which controls the peak shape, if a “pseudo-Voigt” prole has been chosen—and the zero correction. If you are working with observed data, then you can also adjust the relative scaling (Scale Factor) between observed and calculated datasets. For example, if you have an observed dataset whose intensity range is from zero to 1000, and your calculated pattern has intensities from zero to 1, then you would want to scale your observed pattern by a factor of 0.001.

Using the Parameters List  to simulate an orthorhombic  distortion (red pattern) in a   previously-tetragonal crystal  (blue pattern). Te distortion (a ≠ b) has  caused peak splitting (e.g., 400 and 040). Clicking and dragging the  slider thumb continually  changes the highlighted  variable (the b cell edge  length) and replots the  diraction pattern in real  time.

Chapter 3: Simulating Diffraction 17

Background

Using the Parameters List

CrystalDiract lets you apply a basic background function to your calculated patterns. is function has the form: A + Bx + C/x. e individual parameters, A, B and C, can be adjusted interactively.

 You can open (expand) a hierarchical entry by  clicking it, or its disclosure triangle. Individual Parameter entries can then be selected with the mouse, which causes a slider bar and a text edit eld to appear below the list, allowing you to edit that item’s value. (When editing the text, press the Enter or Return keys to replot the structure.)

Sample

 e full-feature version of CrystalDiract lets you simulate the eect of Particle Size and (isotropic) strain. Mixture

If you have a multi-phase mixture (of calculated patterns), you can adjust their relative proportions using the Mixture group (this is discussed more in the next section). Unit Cell

 You can interactively edit the unit cell parameters (edge lengths, a, b, c; angles a, b, g) for a selected  calculated pattern, using this group. Please note that CrystalDiract does not perform an energy minimizations of the structure; one is simply  “deforming” the unit cell, whilst keeping atoms in their  existing sites, as dened by their fractional coordinates.  Nevertheless, this is a useful range of settings when assessing the eect of a phase transition on the  diraction properties.

Local and Global Parameters

Some Parameter entries are shown on a pink  background. ese are local parameters, which relate to the currently-selected pattern, or patterns. Examples include unit cell parameters and site occupancies. Parameter entries shown on a grey background are global parameters, which aect all patterns, regardless of selection status. Examples include  wavelength and peak width. Possible Applications

 e Parameters List is designed to be educational as well as functional. Here are some possible uses: •

Simulating    (e.g., cubic →tetragonal → orthorhombic) by  changing cell parameters and watching how  diraction peaks split.



Simulating the eect of    by changing the unit cell volume (isotropic expansion/compression is assumed).



Visualizing the inuence of one   on the nal diraction pattern, by  dragging its site occupancy slider from 1 to 0.



Changing the    x by   varying the proportions of individual phases, perhaps to match an observed diraction pattern—and hence to determine its approximate composition.

Site Occupancies

If a calculated pattern is selected, then you can interactively adjust the occupancies of its individual sites, using this group. If a particular site is disordered (e.g., has a mixed occupancy such as  Al0.5Si0.5) then the individual occupants are listed on separate lines.

Please note that, as with the Unit Cell adjustments, CrystalDiract does not optimize the structure   following any of these adjustments. However, it does let  •  you assess the chemical contribution to peak intensities. •

18 Chapter 3: Simulating Diffraction

Understanding how mean  z and/or   aects the diraction pattern. Fine-tuning a calculated diraction pattern to   v , e.g., by changing Peak Width, Eta value, Zero Error, etc.

Mixtures CrystalDiract allows you to simulate mixtures  with unlimited numbers of components, simply  using the existing patterns in your diraction  window. You can “create” the mixture by turning on mixture mode. To do this, use the Plot > Mixture command, or click the Toolbar’s Mix button.

 To remove phases from a mixture, turn o the corresponding checkboxes in the Structures list. Tip: The Structures list’s Actions menu has an Equalize Phase Proportions command, which allows you to reset all volume fractions to equal values, with their sum total equal to 1.

 When in Mixture mode, you can continue to edit structural data for individually-selected diraction patterns, just as you might do in “Separates” mode. Mixture Plot Settings oolbar Mix (left) and Unmix (right) buttons 

In Mixture mode, all calculated diraction patterns are combined into a single, calculated mixture. Similarly, any observed diraction patterns are combined into a single, “observed mixture”. Editing Mixtures

 You can edit the relative phase proportions for calculated mixtures, using the Mixture settings in the Parameters List. All calculated patterns are listed, and you can adjust the volume fractions for each component; as you do this, the volume fractions for the remaining components are automatically updated, to ensure that the overall sum of components is xed, at 1.

In Mixture mode, you can edit the plot settings, including line style, width, colour and so on— provided that at least one pattern in your mixture is selected . If both a calculated and observed mixture are displayed in the same window, you should carefully  check that the appropriate pattern is selected (e.g., a calculated pattern, for the calculated mixture) to ensure that the plot settings are applied to the correct mixture.  You can choose to apply labels to diraction peaks in the mixture, in the same way that labels are applied for individual patterns. Select the patterns that you wish to label (e.g., by clicking on their entries in the Strucures list), then choose the Pattern > Show Labels command. All peak  labels are colour-coded by component. Undoing a Mixture

 You can “unmix” a mixture, and restore the display  to separate diraction patterns, using the Plot > Separate command, or by clicking the Toolbar’s Unmix button.

 Editing the volume fraction of Silicon in a simulated  three-phase mixture 

Chapter 3: Simulating Diffraction 19

Viewing Diffraction Data  You can quickly view a tabulated listing of  diraction data, using the Edit > Diffraction Data command:

Te Edit Diraction Data window

 e resulting window lets you sort data, according to your chosen parameter (e.g., d-spacing or intensity). You can opt to save the sorted listing as a text le, by clicking the Save button.

20 Chapter 3: Simulating Diffraction

Chapter 4: Working with Patterns CrystalDiract allows you to mix multiple simulated diraction patterns in the same  window. You can combine these with real, experimentally-observed data: useful for characterizing samples, synthesis results, checking for impurities, and even basic phase identication. You can control how individual patterns are plotted using the Plot and Pattern menus, with choice of plot type, styles, colours, line widths, markers, labels, etc. Working with Observed Data

 Applying Plot Styles

 e full-feature version of CrystalDiract lets you load one or more text les in any window. ese could contain real, observed data, and you can display these will simulated (calculated) diraction patterns for easy characterization.

 You adjust the plot styles for observed diraction patterns, in exactly the same way as for calculated patterns: rst select the patterns you wish to change, then choose the relevant commands from the Pattern menu.

Loading Observed Data

Observed & Calculated Data Compared

Observed datasets should be saved in plain-text les. e rst line of the le should contain a title (this is ignored by CrystalDiract). Subsequent lines should contain pairs of xy values—with one datapoint per line, for example:

 When you append an observed data le to a  window that already contains calculated data, CrystalDiract changes the relative scale setting for the observed data in order to best match the two patterns.

Title line plus xy data… 10.00 23.45 10.10 23.44 10.20 22.95 10.30 24.56 10.40 27.87

 You can manually control the relative scaling for a selected observed pattern, using the two y-scaling buttons on the toolbar:

Note: If you are using the Mac version, it is important to check that the data le is a Mac le, with letype “TEXT”.

It is possible to reposition a selected pattern (calculated or observed), by introducing x and/ or y osets. You can use the Shift arrows on the toolbar to do this. Any osets can be reset to zero by clicking the small round button at the centre of  the arrows:

To open a le in a new window:



Choose the File

> Open

Te oolbar’s Relative Scale buttons 

command

To add les to an existing window:

Do one of the following: •

Choose: File

> Open in Same Window ,

or:



Drag the les into the Graphics pane, or



Drag the les into the Patterns List, then turn on their checkboxes.

Te oolbar’s Shift controls 

 You can also use the Arrow tool to click and drag a diraction pattern, when plotted in Graph mode.

Chapter 4: Working with Patterns 21

Observed and calculated time-of-ight neutron diraction patterns (top graph). Te observed data are plotted as crosses, with calculated data plotted using a smooth line. Te lower graph shows the residual func tion (observed minus calculated)

Displaying the Residual Function

Identifying an Unknown Substance

 When working with observed and calculated data  you have the option of displaying a separate graph or lm showing the dierence (observed minus calculated) between the two datasets: the “residual” function. is is controlled via the Plot > Show Residual or Plot > Hide Residual commands.

Being able to compare an observed diraction pattern with one or more calculated patterns for known substances can be very useful when trying to identify an unknown substance. You can load the observed diraction pattern, then add a sequence of  CrystalMaker binary les (File > Open in Same Window ), until a good match is found.

 e legend for the residual graph/lm also displays the sum-of-squares dierence between the calculated and simulated data: error =

Σ (obs - calc)2

 is value corresponds only to the currentlydisplayed plot range. It can be a useful reference  when attempting to ne-tune the calculated data in order to match the observed data.  e Plot > Data Style submenu allows you to choose how the observed data are plotted (e.g., crosses, squares, lines between points, etc.).

22 Chapter 4: Working with Patterns

 A more convenient way of comparing phases is to use the Patterns List, which is described next.

Managing Multiple Patterns

To rename a pattern:

 e Patterns List lets you keep track of your observed and calculated diraction patterns. New  patterns are automatically added to this list when  you load them from crystal les, observed data les—or when you open a previously-saved session.

1

 You can use the Patterns List to select individual patterns, show or hide them (in the Graphics pane), rename them, duplicate them, or simply to browse individual patterns from a large list.

Select the pattern in the list.

Press the Return or Enter keys on your keyboard (or click on the selected name). 2

 When you have nished editing, press Return or Enter to nish, or click outside the selected row. (To cancel an edit, press the Escape key.) 3

To delete one or more patterns: 1

Select the relevant entries in the list.

Do one of the following:

2

Press the Delete key on your keyboard.



Click the Patterns icon in the Toolbar, or

To change the colour of a plotted pattern:



Press the s key on your keyboard, or





Choose the menu command: Window Patterns List .

To Display the Patterns List:

> Show

 e Patterns list may be displayed as either a slide-out drawer (Mac), or as a window pane (Windows).

Click on the pattern’s colour swatch (on the right-hand side of the Pattern List) and choose a new colour from the popup menu. For more colour choices, choose the Other... command from the bottom of the menu.

Comparing Diffraction Patterns

 e Patterns List can hold as many patterns as you like: you can drag les and folders—perhaps your entire CrystalMaker Structures Library—into the list. Individual patterns can be selected, and the list supports standard editing conventions, such as multiple selections (shift- and command -clicking).

 e Patterns list really comes into its own when comparing an observed diraction pattern with a number of calculated patterns. Having decided on a number of possible candidates to match the observed data, drag and drop their CrystalMaker binary les into the Patterns list. You can then quickly compare each diraction pattern with the observed data by turning its checkbox on or o.

To plot one or more patterns:

To display only one pattern at a time:

Do one of the following:



Using the Patterns List



Check or uncheck the pattern’s checkbox.



Select one or more pattern(s) to be plotted or hidden, then choose the Plot or Hide commands from the Patterns List Actions menu.

Hold down the option/alt key and click a pattern’s checkbox. Any plotted patterns will be hidden, and only   your clicked pattern plotted. Plot Settings

Chapter 4: Working with Patterns 23

Working with multiple patterns in the same window, using the Patterns List. Here, one item’s name is being edited.

24 Chapter 4: Working with Patterns

General Plot Settings

Stacked Graphs

 e Plot menu lets you change the general way in In Graph mode you can use the Plot > Stack  which all diraction patterns are displayed. You can command to stack multiple diraction patterns also customize aspects of the Graphics pane display,  without danger of overlap. You can undo the including the plot range, gridlines and colours, stacking by choosing: Plot > Collapse . and so on. For specic adjustments to individual diaction patterns, use the Pattern menu. Film or Graph

 You can choose to plot your diraction pattern as a graph of intensity versus x -value, or you can opt to display a greyscale representation which resembles a traditional photographic x-ray lm. Film mode is particularly useful when comparing multiple diraction patterns: these are then stacked, making it easy to compare positions and intensities of diraction lines.

Stacked graphs showing how the diraction pattern of a  crystal changes with temperature, and the progress of a  displacive phase transition.

Comparing calculated and observed data in Film mode. Te central diraction pattern corresponds to observed data   for a mixture of analcime and silicon; the “ideal ” calculated   patterns for Silicon and Analcime are displayed above and  below.

Chapter 4: Working with Patterns 25

Overlaying Peak Positions

Individual Pattern Settings

For a complex diraction pattern there may be many overlapping peaks. e Plot > Overlay Peak Positions submenu allows you to identify  the positions of individual diraction peaks.

 e Pattern menu provides a series of commands  which act upon any currently selected diraction patterns. You can change plot colours, graph attributes, such as line styles and widths, marker sizes—and control the labelling of diraction patterns.

 You can superimpose a series of peak markers showing the peak centres, and their relative intensities. Alternatively, you can overlay the actual proles of individual peaks, in a choice of  plot styles: solid lines, dashed lines or a “solid ll” prole.

Labelling Peaks

 e Pattern menu gives you various options for labelling the peaks of selected diraction patterns. Labels can contain any combination of: •

Phase name



Miller Indices (hkl)



D-spacings



x-axis values

 Alternatively, you can opt for “blank” labels, where only arrows are plotted.

 Analysing a simulated mixture, by overlaying the peak  positions for individual phases 

Overlaying peak positions using a solid prole is particularly useful for indicating dierent phases in a multi-component mixture, as illustrated above. Tweaks

 You can display gridlines in the diraction window: thin lines marking the major x- and y-axis values; the colour of the gridlines is set using the Plot > Grid Colour command. You can also show or hide a legend, which acts as a key for the observed and Strong peaks labelled with Miller Indices. Individual peak calculated data, and for mixtures, the legend lists all  proles are shown by the dotted lines. Notice that only the  phases and their proportions. strongest peaks are labelled in this example.

26 Chapter 4: Working with Patterns

Graph Settings

To turn labels on: 1

Select the pattern(s) you wish to label.

2

Choose: Pattern

> Show Labels .

To specify the label type:

In Graph mode, you have extensive control over the appearance of all diraction patterns. You can edit individual patterns by selecting them (individually, or collectively), and then applying settings from the Pattern menu.

Select the pattern(s) whose labels you wish to modify. 1

2 >

Choose one or more settings from the Pattern Label Style submenu.

(Note: e label text, and peak arrow, are drawn in the same colour as the host diraction pattern.) Controlling the Extent of Labelling 

In order to prevent the diraction pattern from becoming too cluttered, you can suppress annotation for weak peaks. e Pattern > Label Threshold submenu lets you specify the minimum relative intensity for which annotation should be used.

 Examples of dierent plot and marker styles. From bottom: solid; translucent; thick solid line; thin dashed line; lines  with dots; crosses.

Data can be plotted using lines between points (with a choice of smooth or dashed lines), or as individual markers (with a choice of  marker styles, such as dots, squares and crosses)— or you can choose a combination of lines and markers. Plot Style

 You can specify an explicit marker size, in pixels, or opt for an Auto setting, in which CrystalDiract scales the marker size depending on the plot size and resolution. Marker Size

 You can specify an explicit line  width (in pixels), or opt for an Auto setting. Line Width

 You can apply dierent colours to dierent diraction patterns. Plot Colour

Tip: You can also edit plot colours using the Patterns List. Popup menus adjacent to e ach (plotted) entry let you quickly choose one of a number of preset colours.

Chapter 4: Working with Patterns 27

Customizing your Workspace

Cloning Windows (Mac)

CrystalDiract lets you open as many windows as memory permits.

 You can “clone” a window, in order to preserve the original data, and give you free rein to experiment  with new settings—maybe editing the structure and then wishing to compare the new diraction pattern with the old diraction pattern. Ensure that the window to be cloned is the frontmost diraction window, then choose the Window > Clone Window command.

On the Mac version, you can arrange multiple  windows neatly on screen: either stacked on on top of each other, with small osets between adjacent windows, or tiled down the screen—using the Window menu’s Stack and Tile commands, respectively. Synchronizing Windows (Mac)

 When comparing dierent structures in dierent  windows you can use the Window> Synchronize command to adjust every window’s settings to match those of the current (uppermost) window. For example, the radiation type, x -axis range,  y -scale, peak widths and so on, are all reset to your current settings.

28 Chapter 4: Working with Patterns

Chapter 5: Printing & Saing CrystalDiract uses high-quality graphics for its on-screen drawing, and this also provides high-resolution printed output. When you have nished, you can save your “diraction experiment” in a single le, ready for immediate display next time you use the program.  A tabbed dialog shows the currently-active settings; any changes you make are saved in your preferences le, and used for any new windows (existing  windows retain their own settings). You can also opt to restore the original, “factory” settings.

Saving Your Work CrystalDiract allows you to save a window’s diraction experiment in a self-contained “session” le. is retains the window size and layout, your plot settings and all data required to plot the displayed diraction patterns.

If you wish to apply your changed preferences to any existing windows, use the Apply Preferences command, which is available from the CrystalDiffract menu (Mac) or the Edit menu (Windows). is command will replot your current patterns, using the new, default settings. Your plot range, wavelength, diraction mode, etc., will all be reset to match your default settings.

Saving Preferences CrystalDiract uses default settings which you can inspect, edit, and save, with the Preferences command.

Exporting Data  e File > Export submenu items allow you to generate text les in various dierent formats:  is le contains a detailed listing of all reexions in the powder pattern(s),  with their intensities, hkl values, d-spacings and multiplicities. Diffraction Data

Tip: You can quickly view and sort these diffraction data on screen, by choosing: Edit > Diffraction Data .

Te Preferences dialog.

Part of a  Diraction Data le for  spinel.

ref no.

(N)

h

k

l

d(hkl)

2-Theta

Intensity

[ [ [ [ [ [ [ [ [ [ [ [

3 8 11 12 16 19 24 27 32 35 36 40

1 0 1 2 0 1 2 1 0 1 2 0

1 2 1 2 0 3 2 1 4 3 4 2

1 2 3 2 4 3 4 5 4 5 4 6

4.66499 2.85671 2.43621 2.33250 2.02000 1.85368 1.64932 1.55500 1.42836 1.36577 1.34667 1.27756

19.0076 31.2843 36.8626 38.5650 44.8299 49.1048 55.6807 59.3842 65.2661 68.6613 69.7751 74.1568

1.14849e-02 1.15645e-02 3.58979e-02 4.44064e-04 2.11695e-02 2.96662e-05 3.44335e-03 1.75771e-02 2.82416e-02 1.29683e-03 5.47933e-05 1.12600e-03

1] 2] 3] 4] 5] 6] 7] 8] 9] 10] 11] 12]

I/Imax

m(hkl)

32.0 32.2 100.0 1.2 59.0 0.1 9.6 49.0 78.7 3.6 0.2 3.1

8 12 24 8 6 24 24 32 12 48 24 24

Chapter 5: Printing & Saving 29

 is le contains a complete If multiple diraction patterns are displayed in list of reexions in three-dimensional space (this the same window, then the exported le contains is a wider range than is displayed on the screen, as multiple columns, corresponding to the y -data for the reexions have not been combined into a oneall selected diraction patterns. So, for example, if  dimensional powder pattern). e intensities and three patterns, A, B and C were selected, then each the real- and imaginary parts of the structure factor row of the exported prole would contain four are included. Data are sorted in order of decreasing  values: x  y  A y B y C. d-spacing.  is simple le format can easily be imported into many graph plotting programs or spreadsheets, Profile  is le is a tab-delimited listing of xy  data points, corresponding to the x -range currently  making it a great way of exporting high-resolution displayed. You can specify the step between diraction proles. adjacent x -axis values, allowing high-resolution output. Structure Factors

Printing x “Spinel - MgAl2O4” 18.50000 0.00000e+00 18.55000 0.00000e+00 18.60000 0.00000e+00 18.65000 2.94836e-14 18.70000 9.62476e-11 18.75000 7.98450e-08 18.80000 1.74030e-05 18.85000 1.01539e-03 18.90000 1.62704e-02 18.95000 7.37977e-02 19.00000 1.07549e-01 19.05000 3.72673e-02 19.10000 4.09937e-03 19.15000 1.25509e-04 19.20000 1.03963e-06 19.25000 2.27941e-09 19.30000 1.30270e-12 19.35000 0.00000e+00 19.40000 0.00000e+00 19.45000 0.00000e+00

 e full-feature version of CrystalDiract will print the contents of the current window at the highest-possible resolution, as determined by your printer’s resolution and the available memory. If   you nd that line widths and/or marker sizes are too small, choose larger sizes from the Pattern > Line Width and Marker Size submenus. Saving a PDF File (Mac)

CrystalDiract for Mac takes advantage of a built-in system feature: the ability to “print” to a PDF le. When you choose the Print command, the resulting Print sheet has a PDF button which,  when gives the option of exporting a PDF graphics le containing your diraction pattern, scaled to t the current page size.

Part of a Prole output le for spinel.

Part of a  Structure Factor  output le for  spinel.

ref no. [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [ 10] [ 11] [ 12] [ 13]

30 Chapter 5: Printing & Saving

h -1 -1 1 1 1 -1 -1 1 -2 0 0 0 2

k -1 1 -1 -1 1 1 -1 1 0 0 0 -2 0

l 1 1 1 -1 -1 -1 -1 1 0 2 -2 0 0

d(hkl) 4.6650 4.6650 4.6650 4.6650 4.6650 4.6650 4.6650 4.6650 4.0400 4.0400 4.0400 4.0400 4.0400

2-Theta 19.008 19.008 19.008 19.008 19.008 19.008 19.008 19.008 21.982 21.982 21.982 21.982 21.982

Lp 35.22 35.22 35.22 35.22 35.22 35.22 35.22 35.22 26.06 26.06 26.06 26.06 26.06

F(Re) -55.70 -55.70 -55.70 -55.70 -55.70 -55.70 55.70 55.70 -0.00 -0.00 -0.00 -0.00 -0.00

F(Im) 0.00 -0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00 -0.00 -0.00 0.00

Intensity 3.99490e+02 3.99490e+02 3.99490e+02 3.99490e+02 3.99490e+02 3.99490e+02 3.99490e+02 3.99490e+02 3.61257e-11 3.67034e-11 3.67034e-11 3.53770e-11 3.61257e-11

Chapter 6: Toolbar Reference Each CrystalDiract window has a horizontal toolbar at the top, which allows you to choose specic tools for manipulating or measuring a diraction pattern, and adjust the scaling settings. is chapter summarizes the various toolbar buttons or icons.

Te CrystalDiract oolbar (Mac version) Show/Hide Parameters List (p)

Tool Buttons

Show/Hide Patterns List (s)

Axis-Scaling Tools

Relative Scale

Shift Controls

Mix/Unmix Film/Graph mode

Showing the Toolbar 

can then drag the cursor with the mouse.

 You can show or hide a window’s Toolbar by  clicking the lozenge-shaped button on the top right-hand side of the title bar. You can also save  your toolbar preference, with the Preferences dialog.

 As you move the cursor over a diraction pattern, information about that pattern is displayed in the Info bar.

Tools

 ere are four tool buttons, located on the left-hand side of the toolbar. Only one tool can be selected at any time, and the mouse cursor changes according to the currently-active tool.  You can select a tool either by clicking its tool button, or if the Graphics pane is focussed (e.g.,  you recently clicked in it with the mouse), you can choose a tool by by pressing the appropriate letter on your keyboard (shown in parentheses, below).

 e Arrow tool also lets you click-and-drag a diraction prole (graph), thereby changing its xand y-axis osets.  is tool lets you scroll the diraction pattern: you can click-and-drag the graphics pane, moving the diraction display to the left- or the right. is is a more precise way of repositioning the prole than using the horizontal scroll bar. Hand (h)

 is “magnify” tool allows you to zoom in on a clicked point in the diraction pattern. To zoom out, hold down the option or shift keys on  your keyboard as you click with this tool. Zoom (z)

 e distance (“measurement”) tool has two functions: a measurement tool, and a zoom tool. To measure the distance between two points on a diraction pattern, click in the Graphics  window where you want to begin measuring, then click where you want to stop. e region between the two points is shown highlighted, and the horizontal distance is printed in the Info bar. A “Zoom” button also appears: clicking this expands the scale so that the highlighted region lls the  window. Distance (d)

Arrow (a)

Hand (h)

Zoom (z)

Distance (d)

CrystalDiract’s tool buttons 

 e Arrow tool lets you measure data in the diraction window, using a vertical cursor. Click once in the Graphics pane to display the cursor or to move the cursor to a new location; you Arrow (a)

Chapter 6: Toolbar Reference 31

 Axis Scaling Tools

Other Controls auto-scale y

x-scale

y-scale

auto-scale x & y

Clicking this icon  will show or hide the Parameters list, inside the current window. Showing the Parameters list causes the Graphics pane to shrink, so if you have a small screen you may wish to keep the list hidden until  you need to use it. Show/Hide Parameters (p)

CrystalDiract’s axis scaling tools 

 is icon (which may be hidden if the window size is small) lets  you quickly show or hide the Patterns List.  is is located in either a drawer (Mac) or pane (Windows). e Patterns List lets you browse multiple diraction patterns, edit plot colours, and change the selection status of individual patterns. Show/Hide Patterns (s)

CrystalDiract provides tools for expanding or contracting the x and y axes, and for auto-scaling the display to t within the current plot range.  e auto-scaling takes two forms: you can auto-scale the y-axis, so that the existing plot range ts snuggly within the vertical bounds. You can also auto-scale both x and y axes, so that all diraction patterns t entirely within the Graphics pane. Relative Scale

 You can quickly toggle between “lm” and “graph”mode, by clicking this button. e icon changes, depending on which mode is currently active. Film/Graph Mode

 You can adjust the y -scale for observed datasets, relative to the graph’s y -axis and any calculated data. is can be useful when trying to match calculated and observed diraction patterns. Note: when observed data are appended to a graph of  calculated data (or vice versa) the relative scale for the observed data is adjusted to give the best match with the  y -axis range for the calculated data.

 e y -scale values can also be adjusted using the Parameters list: select the (observed) datasets you  wish to edit, then adjust the Scale Factor setting,  which is part of the Instrument parameter group.

Te “Film” and “Graph” toolbar icons 

 is is perhaps one of the most useful tools, allowing you to instantly toggle between display of individual diraction patterns, and a simulated multi-phase mixture. e toolbar icon changes, depending on whether or not a mixture is currently plotted: Mix/Unmix

Shift Controls

It is possible to shift selected diraction patterns horizontally, left or right, or vertically up or down.  ese adjustments allow correction for zero errors in the diraction experiment, and for constant background levels.  To reset any shifts to zero, click the round icon at the centre of the group of arrows.

Te oolbar’s shift controls 

32 Chapter 6: Toolbar Reference

Te toolbar Mix (left) and Unmix (right) buttons 

Chapter 7: The CrystalMaker® Office Dierent tasks require dierent interfaces. You wouldn’t control a train from inside a car, and you wouldn’t expect to y a plane using a steering wheel. e same applies to scientic software: our “CrystalMaker Oce” is modular, with components designed to give you the best user experience and performance, whilst ensuring a quick and easy workow.

Te crystal structure of Epidote, viewed in CrystalMaker (left). Te corresponding EM diraction pattern and  stereographic projection are shown in SingleCrystal (bottom right), with a simulated x-ray powder diraction pattern in CrystalDiract (top right).

Introduction to CrystalMaker

Easy Data Processing 

 To really make the most of CrystalDiract, you’ll require CrystalMaker®: our agship program for building, displaying, manipulating and animating all kinds of crystal/molecular structures and their behaviour.

CrystalMaker provides drag-and-drop import of text data les in a wide range of le formats, including CIF, FDAT, GSAS, ICSD, MOL, PDB, SHELX, VASP, XYZ and many more.

CrystalMaker features an elegant and intuitive user interface, available in optimized versions for Mac and Windows (including Windows 7).

CrystalMaker can export data to a wide range of formats. You can also import/export tables of  element colours & radii. is makes it easy to switch between dierent bonding topologies: from semiconductors to silicates, and from proteins to perovskite.

Chapter 7: The CrystalMaker Ofce 33

Spectacular Graphics

CrystalMaker provides superb, photo-realistic graphics, including stunning 3D stereo graphics in colour (red/blue glasses included with the program)—with exible annotation capabilities including lines, arrows, textboxes and scalebars, and high-resolution output.  Animations and Video

CrystalMaker is unique in providing automatic, cross-platform QuickTime and VR output. You can easily build multi-structure/frame animations and output them as movies, or record your work  using the Video Recorder palette. Structures Library 

CrystalMaker comes with a comprehensive library of over 600 fully-annotated les, ready for immediate display (and includes all the major rockforming minerals). Ideal for teaching and research! Diffraction Link 

CrystalMaker lets you share your structural data  with CrystalDiract, without the need to save les, switch applications, and load data: •

Simply choose a command from one of  CrystalMaker’s Diffraction sub-menus, and CrystalDiract will generate a diraction pattern.

Single-Crystal Diffraction CrystalMaker can be extended to provide singlecrystal diraction simulation and analysis, thanks to our SingleCrystal program. is reads from CrystalMaker binary les and from graphics les (e.g., JPEG images), letting you compare images of  real diraction patterns with simulated patterns. SingleCrystal has advanced stereographic projection capabilities: display poles and traces for lattice planes or vectors, with the option of  showing symmetry-related planes, with extensive customization.  All graphics can be copied to the clipboard or exported to disc, with a choice of vector or pixel formats. 34 Chapter 7: The CrystalMaker Ofce

 About Us CrystalMaker Software Ltd is an award winning company, founded by two former university lecturers. Our mission is to improve the understanding of science, through the use of  innovative computer software. Our company’s research and development is supported by extensive international contacts and academic collaborations. Our company address is: CrystalMaker Software Ltd Centre for Innovation & Enterprise Oxford University Begbroke Science Park Woodstock Road Begbroke Oxfordshire, OX5 1PF UK Voice: Fax: E-mail: Web site:

+44 1865–854804 +44 1865–854805 [email protected] http://www.crystalmaker.com

Sales and Ordering Information  We produce and sell our own software throughout the world. Direct selling means higher-quality  software at a fair price!  We accept orders in U.S. dollars, Euros or British Pounds Sterling. Please refer to our web site for the latest pricing information.  We accept purchase orders from universities, institutes or corporations (please fax or e-mail for fastest service), as well as credit cards. You can fax  your details to us, or order online, using our new, multi-currency online ordering system: http://www.crystalmaker.com/sales

Inde A

E

 Angle-Dispersive Diraction denition 12 parameter control 17  Arrow tool description 10 reference 31  Atomic Displacement Parameter 16  Atomic Scattering Factors 11  Axis Scaling Tools 32

Editing Structural Data 16 Energy-Dispersive Diraction denition 13 parameter control 17 Eta in Pseudo-Voigt function 15 Export Options 29

B

Film Mode 25

Background parameter control 18 Bragg Angle derivation of  4 for energy-dispersive diraction 12

G

C Calculating Diraction 11 Cloning Windows 28 Colour of graph 27 Crystalline Materials denition of  3

D Data displaying diraction data 20 exporting 29 Delta Function 14 Diraction angle-dispersive 12 energy-dispersive 13 time-of-ight 13 Distance Tool reference 31 D-Spacing Limit 12

F

Gaussian Function 14 Graphics Pane description 7 Graph Mode 25 Gridlines 26

H Hand tool reference 31

I Identifying an Unknown Substance 22 Indexing a Pattern displaying peak labels 10 Instrument parameter control 17 Instrumental Broadening 15

L Licensing during installation 2 Line Width 27 Lorentzian Function 14

Index 35

M

P

Marker Size in Graph mode 27 Mixtures description 19 parameter control 18 Monochromatic Radiation 12

Parameters List description 7 examples of use 18 Particle Size Broadening 15 Patterns List 7, 23 deleting an entry  23 renaming a pattern 23 Peak Positions indicating with markers 26 overlaying 26 Peak-Shape Functions 14 Peak Widths instrumental broadening 15 particle size broadening 15 strain broadening 15 Personalize dialog 2 Phase Transitions simulating 18 Plot Range setting explicitly  9 Plot Settings 23 Plot Style in Graph mode 27 Portable Data Format (PDF) 30 Preferences 10, 29 Preferences le 2 Pressure simulating eects 18 Printing 30 Prole File 30 Pseudo-Voigt Function 15

N Neutron Diraction angle-dispersive 13 scattering length data 11 time-of-ight 13 Neutron Scattering Length 11

O Observed Data 21 Opening a Crystal 7

R Radiation Type 11 Registration of licence 2 Relative Scaling of observed and calculated patterns Residual Function 22

36 Index

21, 32

S

U

Sales and Ordering 34 Sample parameter control 18 Saving Your Work  in a session le 29 Scaling Commands 9 Scattering Factors editing 11 Scrolling a Diraction Pattern 9 Session File 29 Shift Control 21, 32 Simulation of a powder pattern 11 Single-Crystal Diraction 34 Site Occupancies editing 16 parameter control 18 Size Eects. See Particle Size Broadening Sorting diraction data 20 Stacked Graphs 25 Strain Broadening 15 Structure Factors File 30 Superimpose peak markers 26 Synchronizing Windows 28 System Requirements for running CrystalMaker 1

Unit Cell parameter control 18 Unmix Button 19 Updates automatic update checking 10

W  Wavelength specifying 12  Windows cloning 28 synchronizing 28

X  X-ray Diraction angle dispersive 12 atomic scattering factors for 11  wavelength options 12

Z Zooming a Diraction Pattern 9 Zoom Tool reference 31

T  Temperature simulating eects 18  ermal Ellipsoids. See Atomic Displacement Parameter  Time-of-Flight Diraction denition 13 parameter control 17  Toolbar description 7 reference 31 showing or hiding 31  Two eta 12

Index 37

38

CrystalDiract®: An interactive diraction program for Mac and Windows. Special thanks to Charles Prewitt, Gordon Nord, Yoshitaka Matsushita, Christian Baerlocher and Helge Stanjek First edition: Second edition: ird edition:

12 March 2000 7 November 2001 23 February 2002 updated for Mac version 4.1.0 

Fourth edition:

20 January 2004

Fifth edition:

17 January 2005

Sixth edition:

2 January 2006 updated for Mac version 5.1

Seventh edition: Eighth edition: Ninth edition:

25 March 2006 updated for Windows version 1.0  22 January 2007 5 November 2010 (last revised: 20 April 2012) updated for Mac version 5.2 & Windows version 1.4 

Copyright © 1995–2012 CrystalMaker Software Ltd. All Rights Reserved. No part of this manual may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means, without the prior written permission of the copyright owner. CrystalMaker Software Ltd make no representations, express or implied, with respect to this documentation or the software it describes, including without limitations, any implied warranties of merchantability or tness for a particular purpose, all of which are expressly disclaimed.  is User’s Guide was prepared on a Mac, using Adobe InDesign and Photoshop, in combination with CrystalMaker software. e main fonts used were Adobe Caslon Pro and Gill Sans.

 Mac is a trademark of Apple, Inc., registered in the U.S.A. and other countries.  Microsoft, Windows and the Windows logo are trademarks, or registered trademarks of Microsoft Corporation. CrystalMaker, CrystalDiract and SingleCrystal are trademarks or registered trademarks of CrystalMaker Software Ltd.

CrystalMaker®  S O F T W A R E CrystalMaker Software Limited Centre for Innovation & Enterprise Oxford University Begbroke Science Park   Woodstock Road, Begbroke, Oxfordshire, OX5 1PF, UK  Tel: +44 1865–854804 • Fax: +44 1865–854805 [email protected] • http://www.crystalmaker.com

39

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