Diamond Version 5 User Manual: Distances and angles

Extended geometric infos: Angles between planes etc.

This article in brief:
- Distances of atoms from planes or lines as well as angles between planes and/or lines can be measured interactively.
- Calculating angles between plane and/or line objects.
- Calculating distances of atoms from a plane or line object.
- Table of extended geometric infos.
- Extended geometric infos in the data sheet.

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Measuring angles between or distances from planes/lines

Diamond offers a comprehensive function to measure angles between planes and/or lines as well as to measure distances of atoms from planes or lines. The command to start this measuring mode is Measure Planes etc. in the Tools menu. An icon is also available in the Measure toolbar:

In detail this command can measure:
- the angle between two planes,
- the angle between a plane and a line,
- the angle between two lines,
- the distances of one or more atoms from a plane,
- the distances of one or more atoms from a line,
- the planarity of at least three atoms,
- the linearity of at least two atoms.

The following screenshot (from Diamond version 3 when this function was introduced) shows measuring an angle between two planes defined by six atoms each. The result is shown in the structure picture pane as a yellowish info tip window. The data pane uses the table of created atoms (where the current atom selection is reflected) and in the bottom right the Properties view showing the results of the "extended geometric information":

The results of geometric measurements and calculations are recorded in the Diamond document and are formatted in the data sheet, together with the other structure parameters. On the left you see a cut-off of the data sheet of data set "ta1215" with a planarity check, a measurement of atoms' distances from a plane and the above depicted measured angles between two planes. For details, see below at "Extended geometric infos in the data sheet".

In principle, this extended measurement mode works like this:

1. Define the first object, which can be a plane or a line.

2. Then define the second object, which can be another plane or line (in this case Diamond calculates an angle) or one or more atoms (then it calculates distances of these atoms from the plane #1 or line #1, rsp.

After running the Measure Planes etc. command, Diamond turns to a measurement mode, similar to the measuring of distances interatomic distances, angles, and torsion angles, and the mouse cursor changes its shape. You now have to select or define the first object for which you would like to measure a distance or angle:

If you would like to define a plane as first object, please click on two or more different atoms, and double-click on the last atom afterwards; Diamond will calculate a least-squares plane based on the selected atoms internally.

Note: Do not mismatch this internally used plane with the plane objects described in the article "Plane and line objects".

If you would like to define a line as first object, simply click on one atom, and double-click on the second atom afterwards; Diamond will calculate a line through the two atoms. In case you would like Diamond to calculate a least-squares line through more than two atoms/points, you have to keep the Shift button pressed when finishing the line definition by double-clicking on the last atom you would like to contribute to the line, in order to distinguish your selection from the selection of atoms contributing to a least-squares plane.

If you would like to select an atom, simply double-click on the atom in the structure picture. In case you would like to select more than one atom for which you would e.g. like to calculate their distances to a certain plane or line, you have to press the Ctrl button while double-clicking the last atom, in order to distinguish your selection from the selection of atoms contributing to a least-squares plane or line.

Once you have defined/selected the first object, you have to do the same with the second one, following the guidelines given above.

When you have defined/selected the second object, a small tool tip window close to the mouse cursor will display the result (angle/distance between objects), along with some additional information about the objects (planes/lines/atoms) involved in the measurement. The information window will vanish if you move the mouse cursor, however, the corresponding result of the measurement will be listed in the "Extended geometric infos" table which can be displayed in the Tables pane to the right of the structure picture.

Note:

• We strongly recommend to use the hints given in the status bar at the bottom while selecting objects!
• The lines or planes defined in the measurement mode are created only temporary for the measurement and not added to the list of planes or lines objects!
• The measurement mode can be finished intermediately by pressing the Escape key.

You can check the planarity of a plane or the linearity of a line without defining a second plane or line or atom (this would calculate an angle or distance). Simply define plane #1 or line #1, rsp., by double-clicking on the last atom of plane #1/line #1, then double-click into blank space, which means the second object is empty (no atoms). This leads to an extended geometric information about planarity or linearity, rsp. This planarity/linearity check (and other extended geometric informations) appear in the data sheet - but only in comprehensive configuration.

Calculating angles between plane and/or line objects

There are three commands available from the Calculate sub-menu of the Tools menu to calculate angles between two plane objects, between two line objects, or between a plane and a line object. Unlike the above described measuring, this requires plane and/or line objects to be defined before. The creation of plane and line objects is described in the article "Plane and line objects".

The Angle Between Two Planes command opens the Angle Between Planes dialog, where you can calculate the angle between two planes. This command is only available, if at least two plane objects have been created.

The Angle Between Planes dialog enables you to calculate the angle between two selected planes (as well as the angle between two selected lines or the angle between one plane and one line, depending on the command you selected in the Tools/Calculate menu). If you have selected planes/lines in the "Table of planes" or "Table of lines" before calling this dialog, they will be preselected for Select first/second plane/line.

Once a plane/line has been selected for both Select first plane/line and Select second plane/line, the angle and the corresponding standard uncertainty will be displayed at the bottom of the dialog.

Note: If you have selected two planes for the calculation of the angle, and these planes are parallel, the distance between them is given, too.

The Angle Between Two Lines command works similar but requires at least two line objects to be created.

The Angle Between Plane and Line command calculates the angle between a plane and a line. This command is only available if at least one plane object (either least squares plane or lattice plane) as well as one line object have been created.

Calculating distances of atoms from a plane or line object

The Tools -> Calculate sub-menu also offers two commands to calculate distances of one or more atoms from a plane object or from a line object. These commands are only available, if at least one plane object has been created before and at least one atom is currently selected in the structure picture.

The Distance(s) from Plane command opens the Distances of Atoms from Plane dialog, where you can calculate the distances of one or more selected atoms from a plane:

Select plane/line: Here you can select the plane or line to which you would like to calculate the distance(s) of the selected atom(s). The list contains the titles of the lines/planes that are currently present. For the currently selected line/plane, the origin (i.e. the method used for its creation) is given below.

Distances: This list contains the actual distances (d [Å]) to the plane/line for all currently selected atoms, along with the corresponding standard deviations (s(d) [Å]) and (d/s)². For the distance values, a positive sign indicates that the corresponding atom is further away from the origin than the plane/line, while a negative sign indicates that it is closer to the origin than the plane/line.

Show constituent atoms: If you enable this checkbox, the atoms which have been used to create the current plane/line will also be displayed in the Distances table, along with their distance values to it. These atoms are marked by an '*' in the first column.

The Distance(s) from Line command opens the "Distances of Atoms from Line" dialog, where you can calculate the distance between one or more selected atoms and a line. The command/dialog is only available if at least one line object has been created as well as at least one atom is currently selected in the structure picture.

Table of extended geometric infos

The table of extended geometric infos is available through the command View -> Table -> Extended Geometric Infos.

The following types of extended geometric informations are listed in the table of extended geometric infos:
- Angle between two planes
- Angle between a plane and a line
- Angle between two lines
- Distance(s) of atom(s) from a plane
- Distance(s) of atom(s) from a line
- Planarity check
- Linearity check.

The columns in the table show:
- The ID (number) of the extended geometric info
- A short description of object #1: h, k, l, and n*d (lattice plane), or "P" (plane) or "LSP" (least-square plane) followed by the N atom labels, or "L" (line) or "LSL" ( least-square line).
- A short description of object #2 or the number of atoms ("P", followed by atom labels) or none.
- The angle, if given, in degrees.

The properties view shows more details of the extended geometric info currently selected in the table above the properties view, using the following rows:
- The ID (number) of the extended geometric info
- The type of information, e.g. "Angle between plane and line"
- The angle value in degrees, if an angle was measured, or an asterisk otherwise
- The type of object #1, e.g. "Plane through 6 atoms"
- m1, m2, m3 of the plane or line equation
- The distance from origin, in Angstroem, if it is a plane, or X0, Y0, Z0 of the line equation, if it is a line

This is followed by N rows for the N atoms the plane or line consists of or the N atoms whose distances from the plane or line have been measured:
- label of the atom,
- distance value d in Angstroem,
- the deviation d/s².

Extended geometric infos in the data sheet

The results of measuring angles between planes and lines or distances of atoms from planes or lines or the calculations of angles or distances are collected as extended geometric informations and appear in the data sheet - but only in comprehensive configuration or optionally in a user-defined configuration. They do not appear in the brief configuration of the data sheet. To switch data sheet configurations, see the article "Data sheet contents".

The contents of an extended geometric information in the data sheet are nearly the same as in the properties view (see above) but formatted in HTML format.

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