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Zone axis, a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to ''any'' direction referenced to the direct lattice (as distinct from the reciprocal lattice) of a crystal in three dimensions. It is therefore indexed with direct lattice-indices, instead of with Miller-indices. High-symmetry zone axes through a crystal lattice, in particular, often lie in the direction of tunnels through the crystal between planes of atoms. This is because, as we see below, such zone axis directions generally lie within more than one plane of atoms in the crystal. == Zone-axis indexing == Crystal-lattice translational-invariance〔J. M. Ziman (1972 2nd ed) ''Principles of the theory of solids'' (Cambridge U. Press, Cambridge UK).〕〔Zbigniew Dauter and Mariusz Jaskolski (2010) "How to read (and understand) Volume A of International Tables for Crystallography: an introduction for nonspecialists", ''J. Appl. Cryst.'' 43, 1150-1171 (pdf )〕 is described by a set of unit-cell direct-lattice (contra-variant〔George Arfken (1970) ''Mathematical methods for physicists'' (Academic Press, New York).〕 or polar) basis-vectors a, b, c, or in essence by the magnitudes of these vectors (the lattice parameters a, b and c) and the angles between them (namely α between b and c, β between c and a, and γ between a and b). Direct lattice-vectors have components measured in distance units, like meters or Ångstroms. These lattice-vectors are ''indexed'' by listing one (often integral) multiplier for each basis-triplet component, generally to be placed between either square , () and () because each of these vectors is symmetrically equivalent. The term zone-axis, more specifically, refers to only the ''direction'' of a direct-space lattice-vector. For example, since the () and () lattice-vectors share a common direction, their orientations ''both'' correspond the ()-zone of the crystal. Just as a set of lattice-planes in direct-space corresponds to a reciprocal-lattice vector in the complementary-space of spatial-frequencies and momenta, a "zone" is defined〔E. W. Nuffield (1966) ''X-ray diffraction methods'' (John Wiley, NY).〕〔B. E. Warren (1969) ''X-ray diffraction'' (Addison-Wesley, paperback edition by Dover Books 1990) ISBN 0-486-66317-5.〕 as a set of reciprocal-lattice planes in frequency-space that corresponds to a lattice-vector in direct-space. The reciprocal-space analog to zone-axis is "lattice-plane normal" or "g-vector direction". Reciprocal-lattice (one-form〔cf. Charles W. Misner, Kip S. Thorne and John Archibald Wheeler (1973) ''Gravitation'' (W. H. Freeman, San Francisco CA).〕 or axial) vectors are ''Miller-indexed'' using the reciprocal-lattice basis-triplet (a *, b *, c *) instead, generally between either round () or curly \, || || reciprocal space e.g. () ||co-variant or axial |- |} A useful and quite general rule of crystallographic "dual vector spaces in 3D" is that the condition for a direct lattice-vector () to have a direction (or zone-axis) perpendicular to the reciprocal lattice-vector () is simply hu+kv+lw = 0. This is true even if, as is often the case, the basis-vector set used to describe the lattice is not Cartesian. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Zone axis」の詳細全文を読む スポンサード リンク
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