Steno's Law

Steno’s Law, also called the Law of Constancy of Interfacial Angles, states that the angles between equivalent faces on crystals of the same mineral are always the same - regardless of sample size, the relative sizes of the crystal faces, or where the crystals were collected. ^[1] This holds for quartz crystals and for all other minerals: the face angles of a given mineral are invariant across specimens, localities, and sizes. ^[1]

Why It Holds

Steno’s Law is not an empirical coincidence - it follows directly from the crystalline nature of minerals. Because a mineral’s atoms are arranged in a regular and repeating lattice, the orientations of crystal faces relative to that lattice are fixed. A crystal face forms parallel to a specific set of lattice planes, and those planes always have the same orientation relative to the crystal axes regardless of how large or small the crystal grew. Two faces on a large quartz crystal and the same two faces on a tiny quartz crystal from the other side of the world both developed parallel to the same atomic planes, so the angle between them is identical. ^[1]

Practical Application

Steno’s Law makes it possible to identify a mineral’s point group and crystal system from well-formed crystals by measuring face angles, even without chemical analysis or X-ray diffraction. ^[1] The angles between faces are measured with a contact goniometer - a simple protractor with a movable arm placed on adjacent crystal faces. ^[1] The internal angle between two faces - the angle between lines perpendicular to those faces - is the value reported and compared against known standards. ^[1] Because crystals are rarely perfect and equivalent faces may have different sizes, some care is needed in making these measurements - but the consistency that Steno’s Law predicts holds up reliably in practice. ^[1]

References

1. Nesse, W. D. (2017). Introduction to Mineralogy, 3rd ed. Oxford University Press.

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