The law of constancy of interface angles was first observed by the Danish physician Nicolas Steno (he was the personal physician of the Grand Duke of Florence) on quartz crystals (De solido intra solidum naturaliter contento, Florence, 1669) and also by Domenico Guglielmini (Riflessioni filosofiche dedotte dalle figure of Sali, Bologna, 1688), but it was observed by Jean-Baptiste Romé de l`Isle (Cristallographie, Paris, 1783), who accurately measured the interface angles of a large number of crystals with the goniometer designed by Arnould Carangeot (1783). The relationship was discovered in 1669 by Danish geologist Nicolaus Steno, who found that although quartz crystals differ from each other, the angles between the corresponding surfaces are always the same. In 1772, a French mineralogist, Jean-Baptiste L. Romé de l`Isle, confirmed Steno`s results and further stated that angles are characteristic of the substance. A French crystallographer, René-Just Haüy, usually considered the father of crystallography, showed in 1774 that known interface angles could be taken into account if the crystal consisted of tiny building blocks corresponding to today`s unit cells. The law of constancy of interface angles (or “first law of crystallography”) states that the angles between the crystalline faces of a given species are constant regardless of the lateral extent of these surfaces and the origin of the crystal and are characteristic of that species. He paved the way for Haüy`s law of rational indices. Steno`s Law, which states that the angles between two corresponding surfaces on the crystals of a solid chemical or mineral species are constant and characteristic of the species; This angle is measured between lines drawn perpendicular to each surface. The law, also known as the law of constancy of interface angles, applies to any two crystals, regardless of their size, where they occur, or whether they are natural or artificial. Crystallography is based on three fundamental laws. (ii) Law of rational indices: This law states that the ratio of the intersections of the different surfaces of a crystal with the three axes is constant and can be expressed by rational numbers that the intersections of any surface of a crystal along the crystallographic axes are either equal to the unit sections (i.e.
the sections formed by the unit cell). b, c, or some simple integer multiples, e.g. NA, N`B, N“C, where n, n` and n“ are simple integers. The integers n, n` and n“ are called blank indices. This law was promulgated by Hauy. (iii) Law of constancy of symmetry: According to this law, all crystals of a substance have the same elements of the plane of symmetry, the axis of symmetry and the center of symmetry. (i) Law of constancy of interface angles: This law states that the angle between the adjacent corresponding surfaces, the interface angles of the crystal of a given substance are always constant despite the different shapes and sizes and the type of growth of the crystal. The size and shape of the crystal depends on the crystallization conditions. This law is also known as the law of steno.