TEE ITOMOGENEOUS INTERTTAL STRUCTURE OF TALS.
That there exist in crystals some homoge neous internal structure has been sufficiently illustrated. The further consideration subdi vides into (a) the kinds of homogeneous crystal structure possible, (b) the nature of the struc tural unit.
The Possible Varieties of Homogeneous Crystal The discussion is simpli fied by the method of Seeber (l824) who sub stituted for the molecules their centres of gravity. It is then only necessary to consider from a geometric standpoint those types of homogeneous repetition of points in space which conform to the law of rational parameters, and their agreement with the 32 varieties of crystal symmetry already theorized from a considera tion of external form.
Such an arrangements of points is called a space lattice in which each point is in a similar position with respect to those surrounding it. Frankenheim in 1842 and Bravais more exactly in 1848 showed that there were 14 different types of space lattice, in each of which the units were parallel and similarly orientated. Each conforms to the symmetry of one of the 32 classes and in each planes through any three points conform to the law of rational para meters.
The broader principle of homogeneity of Wiener (1869), that regular arrangement of atoms consists in every atom having the re maining atoms arranged about it in the same manner, and the method of movements used by Jordan in discussing the possible types of regular repetition in space were applied by Sohncke to the consideration of crystal struc ture.
Sixty-five regular point systems were ob tained, each consisting of two or more identical Bravais space lattices the one thrust within the other, not coincident with it, but either moved parallel to some axis or rotated 180 degrees, 120 degrees, 90 degrees or 60 degrees around this axis, or with both motions.
Finally, von Federow, Schonfliess and Barlow (1890-94) showed that other arrange ments of points not identical but similar could be added which "faced the opposite way,' that is, were like the mirror repetitions of the pre ceding groupings. In this way 165 types were
added, making in all some 230 "space groups' or types of homogeneous crystal structure each with the symmetry of some one of the 32 crys tal classes and for the first time representing all these crystal classes.
The Nature of the Structural Haily in 1784 advanced the theory that crystals were built up of little paralleloptpeda constant in shape in any one substance but differing in different substances and closely fitted together without interstices.
From that date until comparatively recently, the view has been widely held that the struc tural unit of the space lattice was an aggre gation of chemical molecules called the physical molecule, and that for instance polymorphic sub stances were due to differences in number of chemical molecules constituting the physical molecule.
This View is definitely abandoned as a re salt of the increasing knowledge as to the close relations which exist (see CHEMICAL CRYSTAL LOGRAPHY) between the crystal structure and the composition. Whether the unit is the chemical molecule in which the position of the atoms is definitely fixed or whether the chemical mole cule is not present in the crystallized compound and the unit is merely a group of atoms in equilibrium is not yet quite agreed upon, but later researches indicate that each atom consti tutes a point in a space lattice, fixed under one set of conditions and of definite volume but susceptible of change under changed conditions giving different structures and therewith new physical characters. For instance, Bragg's re searches indicate that for halite, NaCI, the structure is composed of two intersecting face centred cubic spaced lattices, the sodium atoms on one, the chlorine atoms on the other, while for fluorite, CaF,, the calcium atoms are ar ranged on a face centred cubic lattice and the fluorine atoms are at the centres of the small cubes.