Weiss indices are a set of three numbers that are used to describe a specific plane or direction in a crystal lattice. They were developed by the German mineralogist Theodor Weiss in the early 20th century. Weiss indices are denoted by the letters h, k, and l and are always integers.


Miller indices are another system used to describe crystal planes and directions. They were developed by the British mineralogist William Hallowes Miller in the 19th century. Miller indices are denoted by three numbers enclosed in square brackets [hkl], where h, k, and l can be any integers or fractions.


The conversion between Weiss indices and Miller indices can be done using the following steps:

1. Weiss indices to Miller indices:
To convert Weiss indices (h, k, l) to Miller indices [hkl], follow these steps:
- Take the reciprocals of the Weiss indices: (1/h, 1/k, 1/l).
- Multiply each reciprocal by a common factor to obtain integers.
- Remove any common factors between the three reciprocals.
- Finally, enclose the resulting numbers in square brackets [hkl].

2. Miller indices to Weiss indices:
To convert Miller indices [hkl] to Weiss indices (h, k, l), follow these steps:
- Take the reciprocals of the Miller indices: (1/h, 1/k, 1/l).
- Find the least common multiple (LCM) of the reciprocals.
- Multiply each reciprocal by the LCM to obtain integers.
- Finally, round off the resulting numbers to the nearest integers to get the Weiss indices (h, k, l).


Let's consider an example to demonstrate the conversion between Weiss indices and Miller indices.

Weiss indices to Miller indices:
Given Weiss indices: (2, 3, 4)
- Reciprocals: (1/2, 1/3, 1/4)
- Multiply by a common factor: (6, 4, 3)
- Remove common factors: (3, 2, 3)
- Enclose in square brackets: [323]

Miller indices to Weiss indices:
Given Miller indices: [323]
- Reciprocals: (1/3, 1/2, 1/3)
- LCM of reciprocals: 6
- Multiply by LCM: (2, 3, 2)
- Round off to nearest integers: (2, 3, 2)

Therefore, the conversion between Weiss indices and Miller indices is (2, 3, 2) ↔ [323].