Home >> Encyclopedia Americana, Volume 8 >> Cromer to Curves Of Double Curvature >> Crystallography


crystals, angles, substance, chemical and simple

CRYSTALLOGRAPHY. Crystallography is broadly divided into ((geometrical or morpho-. logical ((physical crystallog raphyo and ((chemical crystallography.) In a narrower sense and as a natural result of the fact that the geometrical relations were first studied the term crystallography is restricted to a study of the relations between the bounding faces of crystals and in that sense it is used here, separate articles being devoted to the other divisions.

The tasks in consideration of crystal form in elementary work are determinations of recognition of type symbols, approxi mate angle measurements and interpretation of crystal descriptions, and in more advanced work are exact measurements of angles, projection and delineation, determination of indices and elements and- calculation of theoretical angles from elements and indices.

As developed in the article on CRYSTALS (q.v.) the individual solids which result from the solidification of a chemical element or com pound possess a regular internal structure but may be completely bounded by plane surfaces or partially bounded by plane surfaces or lack all plane boundaries.

These planes are not at haphazard positions with respect to each other, but at positions de pendent upon the regular internal structure and are found to obey certain laws.

t.aw of Constancy of Interfacial Angles.

— all crystals of the same substance the angles between corresponding faces are constant. A corollary to this law is that aside from the crystals of the isometric system the crystals of each chemical substance have a separate and definite set of angles.

The Law of Symmetry.— Different crystals of the same substance often show unequal num bers of faces, different angles and notably differ ent shapes, but there is in practically every crystal some repetition or recurrence of equal angles or similarly grouped faces, although such faces often are unequally distant from the cen tre, unequal in size and different in shape, and are comparatively rarely equal. Crystals may be regarded as possessing grades of symmetry in the sense of symmetry of direction with repetition of equal angles and crystals obey the law that all crystals of any one substance are of the same grade of symmetry.

The Law of Simple Mathematical Ratio.— If the bounding planes or faces of crystals are defined in position by referring them to co ordinate axes after the manner of analytical geometry, the axes being chosen by rules later stated, a simple and very important relation is found to exist •between all true crystal faces of crystals of any one substance which may be expressed as follows: If the relative intercepts of all the faces are reduced so that the same term in each is unity then in all crystals of the same chemical sub-. stance, if the intercepts of any face are divided, term by term, by the corresponding intercepts of any other face, the quotients will be simple numbers or simple fractions or infinity.