Zingg Classification¶

The Zingg classification is a scheme for categorizing crystal morphology based on two aspect ratios. It was introduced by T. Zingg (1935) and is widely used in crystallography, sedimentology, and pharmaceutical sciences.

Dimensions¶

For a crystal, the three principal dimensions are determined by Principal Component Analysis (PCA) of the point cloud:

Dimension	Symbol	Description
Long	L	Largest principal component extent
Middle	M	Intermediate principal component extent
Short	S	Smallest principal component extent

The dimensions satisfy S ≤ M ≤ L.

Aspect Ratios¶

Two ratios are computed:

Ratio	Formula	Range	Name in CGAspects
Primary	S / M	0 to 1	Primary Aspect Ratio
Secondary	M / L	0 to 1	Secondary Aspect Ratio

A ratio of 1 means the two dimensions are equal (equidimensional in that pair). A ratio near 0 means the crystal is very elongated or flat in that pair of dimensions.

Shape Classes¶

A threshold value of 2/3 divides each ratio into two ranges, giving four quadrants:

       M/L (Secondary Aspect Ratio)
   0        2/3        1
   ├─────────┼──────────┤
 1 │  Plate  │  Block   │
   │         │          │
2/3├─────────┼──────────┤
   │  Lath   │  Needle  │
 0 │         │          │
   └─────────┴──────────┘
        S/M (Primary Aspect Ratio)

Wait — the axes above should be read carefully. The standard Zingg plot convention places S/M on the Y-axis and M/L on the X-axis:

S/M (Y axis)   M/L (X axis)
  1  ┌───────────┬───────────┐
     │           │           │
     │   Plate   │   Block   │
 2/3 ├───────────┼───────────┤
     │           │           │
     │   Lath    │  Needle   │
  0  └───────────┴───────────┘
      0         2/3           1

Class	S/M	M/L	Shape Description
Plate	≥ 2/3	< 2/3	Disk-like; one short dimension, two similar longer dimensions
Block	≥ 2/3	≥ 2/3	Equant, roughly cubic; all three dimensions similar
Lath	< 2/3	< 2/3	Elongated and flat; one long, one medium, one short dimension
Needle	< 2/3	≥ 2/3	Rod-like; one very long dimension, two similar short dimensions

Examples¶

Crystal	S:M	M:L	Class
Cubic crystal	≈1	≈1	Block
Hexagonal plate	≈0.9	≈0.5	Plate
Acicular (needle-like)	≈0.9	≈0.2	Needle
Tabular lath	≈0.3	≈0.3	Lath

Use in CGAspects¶

The Crystal Info panel shows the shape class for the current frame. The Aspect Ratio Analysis produces a Zingg scatter plot where each point is one simulation run (or time step), coloured by a simulation variable (e.g., ΔG_cryst).

By plotting many simulations on the same Zingg diagram, you can see how simulation conditions map to crystal morphology — for example, how supersaturation affects whether a crystal grows as a plate or a needle.

Reference¶

Zingg, T. (1935). Beitrag zur Schotteranalyse. Schweizerische Mineralogische und Petrographische Mitteilungen, 15, 39–140.