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Crystal Systems and General Chemistry B. D. Sharma California State University, Los Angeles, Los Angeles, CA 90032 and Los Angeles Pierce College, Woodland Hills, CA 91371
Crystal chemistry is a subject of great importance (1,2) and, with good reasons. some asvects of this tooic are included in
chemistry. The of thi; subject invariably includes either a table or eraohics of cmta l svswms alone with axial length and interaxial angle relatfouships. In the a&ence of svmmetrv considerations. the relationshiv of axial leneths and interaxial angles for each crystal system can he ;is- leading.
We present the definitions of each crystal system from the point of minimum symmetry inherent in each crystal system relating the packing of the chemical motif in the three-di- mensional array and the consequence of the same toward the interaxial angles and axial length ratios. For detailed and precise discussion from a crystallographic point of view the reader is referred to texts on crystallography and physical chemistry ( 3 , 4 , 5 ) . Tricllnlc System
The symmetry of a triclinic system is either just onefold rotation axis or just center of symmetw. These svmmetrv elements place no restrictionson~either
Cubic System The minimum symmetry requirements are four body di-
agonals of the parallelepiped intersecting each other at angles of 70' 32' and 109' 28' and have the characteristics of three- fold rotation. These automaticallv lead to three mutually perpendicular rwufold rotation axes which in turn intersect the threefold rutution axes a t an nnrlc uiSJ0 44'. This leads to a unit cell with a = b = e and a =-p = r = 90. It is worth emphasizing that a unit cell defining a cube does not neces- sarily belong to the cubic system even though a crystal be- longing to the cubic system has a unit cell that is a cube, which may or may not have fourfold rotation axes as a part of the symmetry required for a cubic system.
Therefore, we wish to emphasize that axial ratios and in- teraxial angles of unit cells for crystal systems are the conse-
quence of symmetry inherent in the crystal that relates the chemical motif in a three-dimensional array, along with the nature of the chemical motif.
In the tnhle on the previous page we presmt il ct~rrrct re- Iationshiu of interaxial angles and axial leneth ratios fur the seven cr&al systems, an&e keep in mindihe symmetry of each crystal system. Literature Cited (1) Psuling, I. .. "The Nature of the Chemical Bond." 3rd Ed.. Comell University Press,
Ithses, 1960. (21 Gmy. H. B., "Chemical Bonds." W. A. Benjamin lnc, 1973, pp. 181-222. (31 '"International Tables for X-rsr Cwtsllograph~: Kymoch P r e , Binngham, England, 19R9,ValI. (41 Glurker, J. P. and T~eblmd. K. N.. ''Crystal Stmctm Anal* k Primer" Oxfad
Univenity Preas,N.Y., 1912. (51 Mwre. W. J., "Physid Chemistry,' 4th Ed.. hontice-Hall lnc., Englewuod CIiW, New
Jersey. 1972. pp. &?3-837.
Volume 59 Number 9 September 1982 743