The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
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Chemists often make use of the observed shapes of crystals to help in their identification. The description of the shapes of crystals is the subject of the science of crystallography. Every crystal can be classified in one of the following six crystal systems:
Cubic. Three axes are at right angles and a re of equal length.
Hexagonal. Three equal lateral axes are intersecting at angles of 60o and vertical axis of variable length are at right angles (as in the hexagonal prism).
Tetragonal. All three axes are at right angles and the two lateral axes are equal.
Orthorhombic. Three unequal axes are at right angles to each other.
Monoclinic. Three unequal axes that have only one oblique intersection.
Triclinic. Three unequal axes that intersect at oblique angles.
Five-fold symmetry was ignored for a long period of time in science, especially in crystallography. This was because of a proof of the impossibility of a five-fold symmetry axis in a crystal medium. Only one-, two-, three-, four-, and six-fold symmetry axes are possible. Three-dimensional structures with five-fold symmetry cannot be packed to fill all available space and cover a surface without gaps. This was an official understanding until 1985 when Kroto/Smalley (1996 Nobel Prize in Chemistry) research team discovered the carbon-60 (C60) molecule--a truncated icosahedron with 12 pentagons, 20 hexagons, 60 vertices, and 90 edges. Its discovery opened a new branch in crystallography.
The basic physical properties of C-60 are: density 1.67 g/cm3, diameter 0.71 nm, lattice constant 1.42 nm, ionization potential 7.6 eV (12.16x10-19J). In the crystal state (central-cubic), it shows only rotation. Experimental results strongly indicate that rotation in crystal is faster than in solution (rotational diffusion constant is 3x1010 vs. 1.8x1010 per second).