TY - JOUR

T1 - Crystallographic Symmetry

T2 - The Fundamental Feature of Matter Organization Determining the Energy and Space Transformations in Condensed Atomic Systems

AU - Borisov, S. V.

AU - Pervukhina, N. V.

AU - Magarill, S. A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Crystallization proceeds by ordering atomic positions by translational and point symmetry operations. By fixing the symmetrical atomic configuration, this process removes the degrees of freedom from the atoms and thereby minimizes their energy and space volume V* characterizing this configuration. The structure of corundum (Al 2 O 3 ) is crystallographically analyzed and its parameters are compared with those for the other prevalent structures (spinel, garnet, apatite, tourmaline, etc.). The phenomenon of crystallographic symmetry in the space of three coordinates and energy minimizes the number of degrees of freedom, and hence, the energy of atomic systems, unifies their configuration by packing it into a minimum volume-an information cell. An “ideal” construction (stencil) stable with respect to variations in external conditions and atomic compositions forms.

AB - Crystallization proceeds by ordering atomic positions by translational and point symmetry operations. By fixing the symmetrical atomic configuration, this process removes the degrees of freedom from the atoms and thereby minimizes their energy and space volume V* characterizing this configuration. The structure of corundum (Al 2 O 3 ) is crystallographically analyzed and its parameters are compared with those for the other prevalent structures (spinel, garnet, apatite, tourmaline, etc.). The phenomenon of crystallographic symmetry in the space of three coordinates and energy minimizes the number of degrees of freedom, and hence, the energy of atomic systems, unifies their configuration by packing it into a minimum volume-an information cell. An “ideal” construction (stencil) stable with respect to variations in external conditions and atomic compositions forms.

KW - apatite

KW - corundum

KW - crystallographic analysis

KW - degrees of freedom of a structure

KW - garnet

KW - prevalent structure types

KW - spinel

KW - stability conditions

KW - symmetry-stability

KW - tourmaline

UR - http://www.scopus.com/inward/record.url?scp=85064944167&partnerID=8YFLogxK

U2 - 10.1134/S0022476619010104

DO - 10.1134/S0022476619010104

M3 - Article

AN - SCOPUS:85064944167

VL - 60

SP - 75

EP - 80

JO - Journal of Structural Chemistry

JF - Journal of Structural Chemistry

SN - 0022-4766

IS - 1

ER -