GAMGI Interfaces: Plane Measure

# Plane Measure

- Length
- Area
- Angle

Measure Area properties involving planes.

### Quantity

The supported Area properties are listed below. Planes and other objects selected may belong to different structural systems (cells, molecules, etc.), bonded or not. Only objects in the current layer can be chosen.

An easy technique to select the objects is to click the mouse sucessively over their visual representations, in the sequence shown in the dialog. After the last needed object is selected, GAMGI automatically starts the calculation.

Plane Node Area

The area per node in a crystallographic plane. The plane parent must be a cell object.

The area per node is calculated for the selected plane object, dividing the volume per node by the distance between planes: A = V / d. To ensure correct results, the real distance between adjacent planes must be used. GAMGI uses the following algorithm: 1) determine the smaller possible indices from the plane indices. For primitive lattices or primitive vectors these are always the true Miller indices.

2) for C, I, F, R centered lattices, with conventional vectors, the structure factor might be zero for these indices. In this case, there are equivalent planes at 1/2 (base-centered, body-centered and face-centered lattices) or 1/3 (rombohedral) of the distance to the origin. In this case, use the following rules to obtain the true Miller indices:

    C: unless h+k == 2n, (h k l) becomes (2h 2k 2l)
    I: unless h+k+l = 2n, (h k l) becomes (2h 2k 2l)
    F: unless h,k,l have same parity, (h k l) becomes (2h 2k 2l)
    R: unless -h+k+l = 3n, (h k l) becomes (3h 3k 3l)

For example, conventional planes (100) in cI and hR lattices are in fact (200) and (300) planes respectively, so the true distance between adjacent planes is actually d/2 and d/3, where d is the uncorrected distance. This correction is not taken into account when determining the Plane Separation, only when calculating the Plane Node Area and the Plane Node Density.

3) if the plane indices are smaller or equal to the Miller indices, the correct distance between planes is the distance for planes with Miller indices, as planes with smaller indices must be multiples of Miller planes, with the same area/node. If the plane indices are higher than the Miller indices, then the planes are either Laue planes or multiples of Laue planes, and in both cases an error message is issued, because the area/node is not uniquely defined for these planes.

For example, conventional planes (100) and (200) in cI have an area/node equal to a**2, but planes (300) and (400) have no unique area/node, varying between 0 and a**2. The Miller indices are (200).

Plane Node Density

The number of nodes per unit area in a crystallographic plane (the inverse of the previous quantity). The plane parent must be a cell object.

### Value

After selecting a quantity, enter the name of the objects and press Ok. If all objects are recognized, GAMGI does the calculation and shows the result in the Value entry.

When a calculation ends, GAMGI keeps the objects identification. To start a new calculation, just click the mouse over a new object: GAMGI automatically cleans the previous data and inserts the new object identification. When a new quantity or page is chosen, previous data is automatically removed.
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