Crystal Description Language (CDL)

CDL is a domain-specific language for describing crystal morphology using crystallographic notation. It combines crystal systems, point groups, and Miller indices to precisely define crystal forms.

Syntax Overview

A CDL expression follows this general format:

system[point_group]:hkl@distance + hkl@distance ...

Components

Crystal Systems

CDL supports all seven crystal systems:

Point Groups

Point groups define the symmetry operations applied to Miller indices. Each crystal system has specific valid point groups:

Miller Indices

Miller indices define crystal planes. Use curly braces with comma-separated values:

• Three indices: {h,k,l} for most systems
• Four indices: {h,k,i,l} for hexagonal/trigonal (Miller-Bravais)
• Negative values: Use minus sign, e.g., {10-10}

Common Forms

Combining Forms

Use + to combine multiple crystal forms:

# Truncated octahedron
cubic[m3m]:{111}@1.0 + {100}@1.3

# Quartz with prism and rhombohedra
trigonal[-3m]:{10-10}@1.0 + {10-11}@0.8 + {01-11}@0.9

The @distance value controls how "developed" each form is. Smaller distances result in larger face areas.

Examples

Diamond (Octahedron)

cubic[m3m]:{111}

Fluorite (Cube with Octahedron)

cubic[m3m]:{100}@1.0 + {111}@1.2

Beryl (Hexagonal Prism with Pinacoid)

hexagonal[6/mmm]:{10-10}@1.0 + {0001}@1.5

Quartz

trigonal[-3m]:{10-10}@1.0 + {10-11}@0.8 + {01-11}@0.9

Extensions

Twin Laws

Add twin laws with the twin: modifier:

cubic[m3m]:{111} twin:spinel_law

Modifications

Apply modifications like elongation or flattening:

tetragonal[4/mmm]:{110}@1.0 --elongate=1.5