GeoRealm

Draw your own lattice planes

This simulation generates images of lattice planes. To see a plane, enter a set of Miller indices (each index between -6 and 6), the numbers separated by a semi-colon, then click "View" or press Enter.

Enter Miller indices (index max 6), e.g. ()

X Y Z

The gold dot (•) on the diagram indicates this plotting origin.

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How to Use the Lattice Plane Visualizer

This tool helps you visualize crystallographic planes within a unit cell using Miller Indices (hkl).

1. Entering Miller Indices:

  • Enter three integer values for h, k, and l, separated by semicolons (e.g., 1;1;1 or -1;0;2).
  • Each index can range from -6 to 6.
  • After entering the indices, click the "View" button or press Enter.

2. Understanding the Visualization:

  • The Unit Cell: The cube represents a standard unit cell.
  • Axes: The lines (default green) show the X, Y, and Z crystallographic axes.
  • The Lattice Plane: The colored polygon (now whitish-gray) shows the (hkl) plane.
  • Plotting Origin (Gold Dot •): The gold dot (•) on the diagram indicates the conceptual origin from which the plane's intercepts are plotted onto the displayed unit cell. Its coordinates (e.g., (0,0,0) or (1,0,0)) are shown below the input field. This origin shifts based on negative Miller indices:
    • If 'h' is negative, the plotting origin shifts to (1,0,0) of the displayed cell.
    • If 'k' is negative, the plotting origin shifts to (0,1,0) of the displayed cell.
    • If 'l' is negative, the plotting origin shifts to (0,0,1) of the displayed cell.
    • (These shifts are cumulative if multiple indices are negative).

3. Special Cases:

  • Zero Index: If an index is 0 (e.g., 1;0;1), the plane is parallel to the axis corresponding to that zero index.
  • (000) Plane: This plane is undefined and cannot be drawn.

Experiment with different Miller indices to understand their relationship with the orientation of lattice planes!