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Some directions and planes are defined by symmetry of the crystal system. In monoclinic, trigonal, tetragonal, and hexagonal systems there is one unique axis (sometimes called the principal axis) which has higher rotational symmetry than the other two axes. The basal plane is the plane perpendicular to the principal axis in these crystal ...
The translational invariance of a crystal lattice is described by a set of unit cell, direct lattice basis vectors (contravariant [1] or polar) called a, b, and c, or equivalently by the lattice parameters, i.e. the magnitudes of the vectors, called a, b and c, and the angles between them, called α (between b and c), β (between c and a), and γ (between a and b).
The seesaw geometry occurs when a molecule has a steric number of 5, with the central atom being bonded to 4 other atoms and 1 lone pair (AX 4 E 1 in AXE notation). An atom bonded to 5 other atoms (and no lone pairs) forms a trigonal bipyramid with two axial and three equatorial positions, but in the seesaw geometry one of the atoms is replaced ...
XeF 4, with square planar geometry, has 1 C 4 axis and 4 C 2 axes orthogonal to C 4. These five axes plus the mirror plane perpendicular to the C 4 axis define the D 4h symmetry group of the molecule. For linear molecules, either clockwise or counterclockwise rotation about the molecular axis by any angle Φ is a symmetry operation.
In a molecule that also has an axis of symmetry, a mirror plane that includes the axis is called a vertical mirror plane and is labeled σ v, while one perpendicular to the axis is called a horizontal mirror plane and is labeled σ h. A vertical mirror plane that bisects the angle between two C2 axes is called a dihedral mirror plane, σ d. [6]
If S is the intercept of the plane with the [1 1 0] axis, then i = 1/S. There are also ad hoc schemes (e.g. in the transmission electron microscopy literature) for indexing hexagonal lattice vectors (rather than reciprocal lattice vectors or planes) with four indices. However they do not operate by similarly adding a redundant index to the ...
However, the rhombohedral axes are often shown (for the rhombohedral lattice) in textbooks because this cell reveals the 3 m symmetry of the crystal lattice. The rhombohedral unit cell for the hexagonal Bravais lattice is the D-centered [ 1 ] cell, consisting of two additional lattice points which occupy one body diagonal of the unit cell with ...
The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The electron pairs around a central atom are represented by a formula AX m E n , where A represents the central atom and always has an implied subscript one.