Cerius<sup>2</sup> Builders

Cerius² Builders

2 Crystal Builder

The C²·Crystal Builder module provides a robust and versatile crystal builder and editor. It also includes plane and facet tools to aid in visualization of crystal structures.

Crystal structures are of fundamental importance in materials science. Many other Cerius² modules perform calculations and simulations on crystalline structures, including:

Crystal Packer
Diffraction-Crystal
Diffraction-Faulted
DLS
HRTEM
LEED/RHEED
Morphology
Rietveld
Sorption

This chapter contains information on:

Building and unbuilding crystals

Displaying crystals

Calculating cell formula, density, and volume

Finding symmetry in a crystal

For information about See
Loading and saving crystal structure files. The discussion of loading and saving structure files in Cerius² Modeling Environment.
Crystal file formats. Files appendix, Cerius² Modeling Environment.
Building crystal surfaces. Surface Builder.
Building crystal interfaces. Interface Builder.
Energy minimization of crystals. Crystal Packer module, Cerius² Computational Instruments Property Prediction; Minimizer module, Cerius² Simulation Tools.
Calculations and simulations involving crystals. Cerius² Computational Instruments Property Prediction and Cerius² Analytical Instruments.

For information about	See
Loading and saving crystal structure files.	The discussion of loading and saving structure files in Cerius² Modeling Environment.
Crystal file formats.	Files appendix, Cerius² Modeling Environment.
Building crystal surfaces.	Surface Builder.
Building crystal interfaces.	Interface Builder.
Energy minimization of crystals.	Crystal Packer module, Cerius² Computational Instruments Property Prediction; Minimizer module, Cerius² Simulation Tools.
Calculations and simulations involving crystals.	Cerius² Computational Instruments Property Prediction and Cerius² Analytical Instruments.

Building and unbuilding crystals

Following some introductory material (below), this section contains information on:

: Building a molecular crystal using general symmetry positions
: Building a crystal from a 2D periodic model
: Building an ionic crystal using space groups
: Changing lattice vectors
: Creating superstructures from crystals
: Unbuilding a crystal

The C²·Crystal Builder module enables you to build many types of crystals, from small ionic models to large polymer models. Fragment types can be mixed so that solvent fragments are incorporated into polymer crystals or small-molecule fragments into zeolite structures. (See Cerius² Modeling Environment for definitions of fragments, models, molecules, etc.)

Usually the crystallographic asymmetric unit consists of only a portion of the unit cell. In such cases, it is more convenient to work with a crystal chemical unit, which consists of a complete molecule, rather than only a part. In C²·Crystal Builder, the term asymmetric unit refers to any unit, whether a complete fragment or part of a polymer chain or a group of ions, that can be replicated throughout the unit cell of the crystal.

General procedure

The following are the three necessary steps in building a crystal. Although they need not be, these steps are often performed in the following order:

Specify the asymmetric unit. This can be done by loading or sketching a model or by placing individual atoms by entering their coordinates.
Specify the crystal lattice type for the unit cell, that is, the crystallographic parameters a, b, c (cell lengths) and , , (cell angles).
Select a space group (either by mnemonic or number) or build it from the various symmetry operators.

Accessing the tools

Controls belonging to the C²·Crystal Builder module are contained on the CRYSTAL BUILDER card, which is located by default on the BUILDERS 1 deck of cards. To access the CRYSTAL BUILDER card, click its name so that this card moves in front of the others (if it is not already there:

The important commands for building a crystal are grouped in the Crystal Building control panel, which is accessed by selecting the Crystal Building menu item on the CRYSTAL BUILDER card. Tools on this control panel are used to build the crystal and to open other control panels needed to input various crystal parameters.

How it works

The building process is started by clicking the BUILD CRYSTAL pushbutton in the Crystal Building control panel. The crystal is always built in the current model space, and exactly what happens depends on the contents of the current model space:

If a nonperiodic or 2D-periodic model is current, it is used as the asymmetric unit for building the crystal.
If the model space is empty, a unit cell box is displayed and atoms can be placed in it afterwards.
If a crystal is already present in the current model space, it is rebuilt using the current crystal-building settings.

You can return to the asymmetric unit at any time by clicking the UNBUILD CRYSTAL pushbutton in the Crystal Building control panel.

In addition to building regular crystals, you can create superlattices and superstructures with the C²·Crystal Builder module. Generating a superlattice resets the crystal symmetry to P₁ and converts all atoms displayed in the model window (including those that are symmetry copies) into real atoms. In generating a superstructure, the unit cell is removed and all atoms in the model become part of the nonperiodic structure.

Building a molecular crystal using general symmetry positions

Constructing the starting model

To construct the asymmetric unit, load and/or build a model (in a new model space) using the Sketcher control panel or other Visualizer tools (see the discussion of building models in Cerius² Modeling Environment).

Accessing the tools

Select the Crystal Building menu item on the CRYSTAL BUILDER card to open the Crystal Building control panel.

Open the Crystal Build Preferences control panel by clicking the Preferences... pushbutton on the Crystal Building control panel.

Open the Cell Parameters control panel by clicking the Cell Parameters... pushbutton on the Crystal Building control panel. Alternatively, select the Unit Cell/Cell Parameters menu item on the CRYSTAL BUILDER card.

Open the General Positions control panel by clicking the Edit... pushbutton to the right of the POSITIONS control on the Crystal Building control panel. Alternatively, select the Symmetry/General Positions menu item from the CRYSTAL BUILDER card.

Starting the process

For most crystal structures, the default display style is best. If this has been changed, you need to choose DEFAULT from the Visualization style popup in the Crystal Build Preferences control panel.

If you want bonds across unit cell boundaries and between symmetry copies of atoms to be calculated automatically, assure that the Automatically calculate bonds check box in the Crystal Build Preferences control panel is checked (see the discussion of bond calculation criteria in Cerius² Modeling Environment).

Important

If the Automatically calculate bonds check box is checked, bonding is automatically recalculated for any crystal loaded from a file. This may result in chemically unreasonable bonds being formed between atoms that are close together. As a result, you may want to turn this option off or adjust the bonding calculation parameters appropriately before loading a crystal later in your Cerius² session.

If the Automatically calculate bonds check box is checked, bonding is automatically recalculated for any crystal loaded from a file. This may result in chemically unreasonable bonds being formed between atoms that are close together. As a result, you may want to turn this option off or adjust the bonding calculation parameters appropriately before loading a crystal later in your Cerius² session.

Specifying unit-cell shape

To specify the cell size and shape, enter its dimensions and angles in the appropriate entry boxes in the Cell Parameters control panel. If some of these parameters are restrained by symmetry considerations or if some angle values are mutually incompatible, you cannot change their values, or related values are changed to match, whichever is appropriate.

Building the crystal

To construct the basic unit cell around the model, click the BUILD CRYSTAL pushbutton in the Crystal Building control panel.

Specifying crystal symmetry

To specify the crystal symmetry, set the Choose Symmetry Description control in the Crystal Building control panel to POSITIONS.

The crystal symmetries used for building are listed in the General Positions control panel. Primitive is the default lattice, so:

If you want a lattice other than primitive, choose the centering type from the Centering popup in the General Positions control panel.

If you want to constrain the cell parameters to a particular lattice type, set the Lattice Type popup in the General Positions control panel. By setting the lattice type and the centering, you can specify any of the conventional Bravais lattices.

You can enter the general symmetry positions in the Add Symmetry Operator entry box in the General Positions control panel.

Technical notes

The format is:

: rot₁, trans₁, rot₂, trans₂, rot₃, trans₃

Where rot₁, rot_2, and rot₃ are expressions from the set {x, y, z, -x, -y, -z, x-y, y-z, z-x, -x+y, -y+z, -z+x}, which are used to generate the rotational part of the symmetry operation, and where trans1, trans₂, trans₃ are positive and rational fractions, from the set {+1/6, +1/4, +1/3, +1/2, +2/3, +3/4, +5/6} or the decimal equivalents.

Examples of symmetry operators are:


-x   -y  -z
-x    y  -z +0.5
-y  +1/2  -x +1/2   z +1/2
 y  -x+y   z +1/6
 z    y   x

Symmetry positions are tested for consistency with the current unit cell parameters, and bad positions are rejected. For example, you cannot enter the symmetry position corresponding to a sixfold rotation axis if the current unit cell is cubic. Conversely, if the cell parameters are altered after the symmetry position is entered, you are warned that some of the symmetries in use are not consistent with the symmetry of the lattice.

Whenever any change is made to the cell parameter values, the crystal is updated and redisplayed, although it is not rebuilt (that is, connectivity is unchanged).

Editing the symmetry

If you make a mistake, remove a symmetry entry by entering the number of the symmetry entry (from the General Position Operators list box in the General Positions control panel) in the Remove Symmetry Operator entry box. To remove all symmetry entries, use the Clear List of General Positions action button and confirm the action.

Additional information

Please see the on-screen help for additional information about the controls in all the panels mentioned here.

Building a crystal from a 2D periodic model

Constructing the starting model

Load a 2D periodic model (i.e., a surface model) into the current (empty) model space. This can be done by loading such a model from file or by using the C²·Surface Builder (see Surface Builder) to create one.

Accessing the tools

Select the Crystal Building menu item on the CRYSTAL BUILDER card to open the Crystal Building control panel.

Open the Crystal Build Preferences control panel by clicking the Preferences... pushbutton on the Crystal Building control panel.

Open the Find Space Group control panel by selecting the Symmetry/Find Symmetry menu item from the CRYSTAL BUILDER card.

Specifying the crystal

Enter the Vacuum Thickness that you want (in the Crystal Build Preferences control panel). This is the thickness of the empty layer that is created when you make the surface into a crystal. The crystal cell vector perpendicular to the surface is taken to be the thickness of the surface atoms plus the vacuum thickness.

Choose the Orientation for the vacuum slab in the Crystal Build Preferences control panel. The vacuum layer is oriented normal to the specified Cartesian axis.

The thickness of the surface, together with the vacuum thickness, determines the cell dimension normal to the vacuum slab.

Building the crystal

Click the BUILD CRYSTAL pushbutton in the Crystal Building control panel. The 2D surface structure is converted into a 3D crystal. The crystal cell parameters are obtained from the surface mesh parameters.

Finding the symmetry

The crystal is created without any symmetry defined. If you want to find the symmetry of the crystal you need to use the Find Space Group control panel.

If you want the crystal model to be redisplayed according to any symmetry that is found, check the Update Model check box in the Find Space Group control panel. Atoms that are found to be symmetry copies of one another (within the Tolerance) are moved so that they are exact symmetry copies.

To start a program that searches for any symmetry that may exist in the current crystal, click the Find Space Group Symmetry action button in Find Space Group control panel. (Periodicity is included if the crystal can be represented with a smaller unit cell.) The symmetry that is found is reported to the text window.

Additional information

Please see the on-screen help for additional information about the controls in all the panels mentioned here.

Building an ionic crystal using space groups

Begin with an empty model space.

Accessing the tools

Select the Crystal Building menu item on the CRYSTAL BUILDER card to open the Crystal Building control panel.

Open the Crystal Build Preferences control panel by clicking the Preferences... pushbutton on the Crystal Building control panel.

Open the Space Groups control panel by clicking the Edit... pushbutton to the right of SPACE GROUP on the Crystal Building control panel. Alternatively, select the Symmetry/Space Groups menu item from the CRYSTAL BUILDER card.

Open the Add Atom control panel by clicking the Add Atoms... pushbutton on the Crystal Building control panel. Alternatively, select the Build/Add Atom... menu item from the menu bar in the Visualizer's main control panel.

Starting the process

For most crystal structures built by this method, the default display or "original" style is best, so choose DEFAULT or ORIGINAL from the Visualization style popup in the Crystal Build Preferences control panel.

In the ORIGINAL style, atoms appear exactly as specified by their coordinates. In the DEFAULT style, atoms with coordinates outside the unit cell are drawn translated to within the cell or to the most appropriate location in relation to the connectivity. Fragments whose centers of geometry are on cell faces, edges, and corners are repeated on the opposite face, edges, or corners.

Building the crystal

To construct the basic unit cell within which to build the model, click the BUILD CRYSTAL pushbutton in the Crystal Building control panel.

Specifying crystal symmetry

To specify the crystal symmetry, set the Choose Symmetry Description control in the Crystal Building control panel to SPACE GROUP.

Enter the space group number or name in the Space Group entry box (of the Space Groups control panel), by typing it or by choosing it from the associated pulldown. Alternatively, enter the name or number of a space group in the same class as the one you want, then use the Step through groups arrows to find the desired space group. The space groups that are stepped through are restricted to the crystal class to protect against accidentally changing the crystal cell parameters.

If the space group has more than one Option, choose the Option that you want to apply.

Review the Space Group Information and Symmetry Positions list boxes in the Space Groups control panel for details on the chosen space group.

Technical notes

The space groups used by Cerius² are those that appear in the International Tables of Crystallography, Volume A (1989). Only the brief symbol is required the Space Group entry box. Cerius² also recognizes all nonstandard space group settings.

The space group symbol consists of a maximum of four fields of letters and numbers, separated by spaces, and is entered in the Space Group entry box. Input is not case sensitive. Bars above numbers are represented by minus signs in front, and subscripts are entered immediately following the number to which they belong.

Here are some examples of space group specifications:


Space group number 1:   P 1
Space group number 2:   P -1
Space group number 17:  P 2 2 21
Space group number 88:  I 41/a
Space group number 193: P 63/m c m
Space group number 226:   F m -3 c

Choosing certain space groups forces changes to some cell parameters. For example, selecting a cubic space group sets the cell angles to 90° and sets a = b = c.

Some space groups have several options in the International Tables of Crystallography. For the current space group, these are given in the Option pulldown. For example, all monoclinic space groups have a choice of b or c as the unique cell axis. Some also have three alternatives for the cell, giving a total of nine different settings for one space group. Each setting has a different full space group symbol, but they share the same brief symbol. Some orthorhombic, tetragonal, and cubic space groups have more than one choice for the origin of the unit cell, and these are also listed. Some trigonal space groups offer a choice of rhombohedral axes (a = b = c, = = ) or hexagonal axes (a = b ¦ c, = = 90°, = 120°). Use the pulldown to select the appropriate option.

Specifying unit-cell shape

Choosing the coordinate system

To specify what coordinate system you want to use in constructing the model of the asymmetric unit, use the coordinate system popup (located next to the coordinates entry box in the Add Atom control panel). Set the popup to XYZ for the Cartesian system or ABC for the fractional system.

Constructing the asymmetric unit

For each individual real atom (i.e., those that are not symmetry copies), you use controls in the Add Atom control panel to enter an element type and the x, y, z or a, b, c coordinates.

You may also want to specify other options: Hybridization, a nonzero Charge, Occupancy, Name, and isotropic and/or anisotropic temperature factors. Click the ADD ATOM pushbutton after each atom is specified. The new atom and any symmetry copies appear in the model window.

Editing the asymmetric unit

If you make a mistake and want to remove an atom, use the UNDO pushbutton. You can also select the atom in the model window and choose the Edit/Delete menu item from the menu bar on the main Visualizer control panel. The symmetry copies of the atom are also deleted.

Additional information

Please see the on-screen help for additional information about the controls in all the panels mentioned here. For additional information about the Add Atom control panel, see the discussion of build operations in Cerius² Modeling Environment.

Changing lattice vectors

The facility for altering lattice vectors allows you to redefine the lattice vectors of a crystal without changing the crystal structure.

You might simply want to reorient the lattice so that the a, b, and c axes point in new directions. An example might be preparing a crystal for the C²·HRTEM module, where the beam direction is specified relative to the crystal lattice.

You may need to alter lattice vectors when you want to reduce a conventional unit cell to a smaller primitive unit cell. Changing the lattice popup in the Lattice Redefinition control panel to PRIMITIVE before clicking the Change action button redefines lattice vectors for the primitive unit cell.

Accessing the tools

Open the Lattice Redefinition control panel by selecting the Unit Cell/Redefine Lattice menu item from the CRYSTAL BUILDER card.

Changing the lattice vectors

To preview the new vectors before actually applying them to the crystal, check the Show new lattice vectors check box.

To specify new lattice vectors, assure that the lattice popup is set to USER-SPECIFIED and enter the three desired values in the New entry boxes, specifying them in terms of the three current lattice vectors. The new vectors should be true lattice vectors and should form a right-handed set. They form the three new cell sides.

The new vectors appear as light blue lines on the model if the Show new lattice vectors check box is checked.

Changing to a primitive lattice

Alternatively, if you want to change from a conventional lattice to a primitive lattice, change the lattice popup to PRIMITIVE.

The New entry boxes are set as appropriate to change the current model to a primitive lattice. As long as the popup is set to PRIMITIVE, you cannot edit the new lattice vectors.

Applying the changes to the current crystal

Click the Change to action button to change the lattice from the old to the new vectors.

Caution

The redefined crystal overwrites the current model, so you should first save the current model or copy it to another model space if you want to preserve it.

The redefined crystal overwrites the current model, so you should first save the current model or copy it to another model space if you want to preserve it.

Technical notes

If the lattice popup is set to USER-SPECIFIED, the old lattice is lost, as are symmetry descriptions.

If the lattice popup is set to PRIMITIVE, Cerius² keeps the symmetry descriptions in the model, transforming them as appropriate, and also remembers the old lattice parameters (they are stored with the model) so that you can change them later to a conventional lattice description.

Additional information

Please see the on-screen help for additional information about the controls in all the panels mentioned here.

Creating superstructures from crystals

Converting a crystal into a superstructure removes the applied symmetry and changes the symmetry-copies of atoms into real atoms. Two types of superstructure can be created from a crystal model:

A periodic superlattice--The superlattice is a crystal of P₁ symmetry. Building a primitive superlattice is a way of reducing symmetry without altering the crystal structure. Moving atoms and other edits are often easier with a P₁ model, because there are no symmetry constraints to interfere, as in the higher symmetries.

: The superlattice may be quite large, made up of several unit cells. Building a large superlattice and then editing it is a good way of introducing disorder into a crystal structure. For information about disorder, see the relevant chapter in Cerius² Modeling Environment.

A nonperiodic superstructure--A nonperiodic superstructure has the same structure as a crystal, but Cerius² treats it like a nonperiodic structure. Thus, you can perform manipulations and calculations on the nonperiodic structure (such as a charge equilibration calculation) that cannot be done on a crystalline model.

This section contains information on:

: Generating a primitive superlattice
: Generating a noncrystalline superstructure
: Generating a superstructure from a facetted crystal

Caution

The current surface is lost when the superlattice or superstructure is built. If you want to save the current surface, copy it into a new model space and/or save it to a file before creating the superstructure.

The current surface is lost when the superlattice or superstructure is built. If you want to save the current surface, copy it into a new model space and/or save it to a file before creating the superstructure.