a, b, c; or ai |
Basis vectors of the direct lattice |
a, b, c |
Lengths of basis vectors, lengths of cell edges |
Lattice or cell parameters |
α, β, γ |
Interaxial (lattice) angles , , ![[{\bf a} \wedge {\bf b}]](/teximages/abch1o1/abch1o1fi4.svg) |
V |
Cell volume of the direct lattice |
G |
Matrix of the geometrical coefficients (metric tensor) of the direct lattice |
![[g_{ij}]](/teximages/abch1o1/abch1o1fi5.svg) |
Element of metric matrix (tensor) G |
r; or x |
Position vector (of a point or an atom) |
r |
Length of the position vector r |
xa, yb, zc |
Components of the position vector r |
x, y, z; or ![[x_{i}]](/teximages/abch1o1/abch1o1fi6.svg) |
Coordinates of a point (location of an atom) expressed in units of a, b, c; coordinates of end point of position vector r; coefficients of position vector r |
![[{\bi x} = \pmatrix{x\cr y\cr z\cr} = \pmatrix{x_{1}\cr x_{2}\cr x_{3}\cr}]](/teximages/abch1o1/abch1o1fi7.svg) |
Column of point coordinates or vector coefficients |
t |
Translation vector |
t |
Length of the translation vector t |
; or ![[t_{i}]](/teximages/abch1o1/abch1o1fi9.svg) |
Coefficients of translation vector t |
![[{\bi t} = \pmatrix{t_{1}\cr t_{2}\cr t_{3}\cr}]](/teximages/abch1o1/abch1o1fi10.svg) |
Column of coefficients of translation vector t |
u |
Vector with integral coefficients |
u, v, w; or ![[u_{i}]](/teximages/abch1o1/abch1o1fi11.svg) |
Integers, coordinates of a (primitive) lattice point; coefficients of vector u |
![[{\bi u} = \pmatrix{u\cr v\cr w\cr} = \pmatrix{u_{1}\cr u_{2}\cr u_{3}\cr}]](/teximages/abch1o1/abch1o1fi12.svg) |
Column of integral point coordinates or vector coefficients |
o |
Zero vector |
o |
Column of zero coefficients |
a′, b′, c′; or ![[{\bf a}_{i}']](/teximages/abch1o1/abch1o1fi13.svg) |
New basis vectors after a transformation of the coordinate system (basis transformation) |
r′; or x′; x′, y′, z′; or ![[x_{i}']](/teximages/abch1o1/abch1o1fi14.svg) |
Position vector and point coordinates after a transformation of the coordinate system (basis transformation) |
; or ; , , ; or ![[\tilde{x}_{i}]](/teximages/abch1o1/abch1o1fi20.svg) |
New position vector and point coordinates after a symmetry operation (motion) |