Symbols 
Meanings 
Examples 
a 
Diameter of the objective aperture 

a 
A lattice or cell parameter: length of a basis vector, length of a cell edge 

a' 
A new basis vector after a transformation of the coordinate system 

a (or ) 
One of the basis vectors of direct lattice 

a* 
Length of a basis vector of reciprocal lattice 

a* 
A basis vector of reciprocal lattice 

A 
Thickness of the crystal in the TEM specimen 
page3769 
A 
Atomic weight of the atoms in the specimen 
page2673 
A(k) 
The aperture function describing the effect of the objective aperture 
page3732 
A(u) 
Aperture function 
page4236 
A_{d} 
Dimensionless atomic mass . 
page2673 
A_{S} 
Surface area of a sphere 
page2671, page4631 
b 
A lattice or cell parameter: length of a basis vector, length of a cell edge 
page3464 
b (or ) 
One of the basis vectors of direct lattice: Burgers vector 

b' 
A new basis vector after a transformation of the coordinate system 

b* 
Length of a basis vector of reciprocal lattice 

b* 
A basis vector of reciprocal lattice 

c (or ) 
One of the basis vectors of direct lattice 

c 
A lattice or cell parameter: length of a basis vector, length of a cell edge 

c' 
A new basis vector after a transformation of the coordinate system 

c* 
Length of a basis vector of reciprocal lattice 

c* 
A basis vector of reciprocal lattice 

C_{c} 
Chromatic aberration coefficient 
page4165 
C_{n} 
Rotation axis in crystallography (1, 2, 3, 4 and 6) 
page1622 
C_{s} 
Spherical aberration of the objective lens 
page1715 
C_{1s} 
Excitation coefficient for plane wave incidence 
page4217 
d 
Diameter of TEM specimen over which the illumination is coherent 
page1708 
D(k) 
Envelope function 
page3879 
d_{hkl} 
Latticeplane spacing of the (hkl) planes, i.e. interplanar distance of neighbouring net planes (hkl) 

e 
Elementary charge 

E_{L2,3} 
Si L_{2,3} energy loss onset of the silicon compounds 
page3441 
E(u) 
Envelope functions, including E_{s} and E_{c} 
page4236 
E_{t}(g) or E_{t}(u) 
Temporalcoherence envelope function 
page4236, page4165 
E_{0} 
Incident electron energy 
page4217 
E_{1s} 
The energy of the lowest energy bound state 
page4217 
E^{n} 
(Euclidean) point space of dimension n 

ΔE 
Energy range of the PEEL spectra 
page3384 
E_{s}(g) 
Spatialcoherence envelope function 
page4236, page4153 
f(θ) 
Atomic scattering factor 
page1421 
f^{e}(s) 
Atomic scattering factor for electrons 

F(g) or F_{hkl} 
Structure factor of the cell, corresponding to the Bragg reflection hkl 

f^{X} 
Atomic scattering factor for xrays 

F 
Fourier transform 

F^{1} 
Inverse Fourier transform 

F(hkl); or F 
Modulus of the structure factor F(hkl) 

g 
Spatial frequency 
page1715 
g 
The spatial frequency 
page3732 
g_{ij} 
Element of metric tensor 

g_{hkl} 
Reciprocalspace vector for the planes with indices hkl 

G 
Metric tensor of direct lattice 

G* 
Metric tensor of reciprocal lattice 

h 
Planck’s constant 

h 
Reciprocallattice vector 

hkl 
Miller indices: indices of the Bragg reflection (Laue indices) from the set of parellel equidistant net planes (hkl) 
page2506 
hkl 
Coordinates of a reciprocallattice point, coefficients of reciprocallattice vector r* 

(hkil) 
BravaisMiller indices: indices of a crystal face, or of a single net plane, for the hexagonal axes a_{1}, a_{2}, a_{3}, c 

(hkl) 
Miller indices: indices of a crystal face, or of a single net plane 
page2506 
{hkl} 
Indices of a set of all symmetrically equivalent crystal faces or net planes, i.e., the family of all the planes that are equivalent to (hkl) by the symmetry of the lattice 
page2506 
{hkil} 
Indices of a set of all symmetrically equivalent crsytal faces or net planes for the hexagonal axes a_{1}, a_{2}, a_{3}, c 

[hkl] 
A direction that denotes the direction in the basis of the direct lattice vectors instead of the reciprocal lattice 
page2506 
<hkl> 
A family of the directions that are equivalent to [hkl] by symmetry 
page2506 
i 
Center of inversion (center of symmetry) 
page1614 
I_{0} 
Objective lens current 
page4165 
I_{0} 
Intensity of the incident electron beam, 
page3769 
k 
The reciprocal space vector 
page3732 
L 
Vector lattice 

m 
Mirror planes in crystals 
page1620 
m 
Relativistic electron mass 

m_{0} 
Electron rest mass 
page4787 
m_{p} 
Proton mass 
page2673 
M 
Symmetry operation or motion 

n 
Dimension of a space 

N 
Atomic density 
page2673 
N_{A} 
Avogadro’s number 
page4475, page2673 
p(r) 
Point spread
function of a system 
page4907 
P_{uvw} 
Probability of seeing a family of zone axes <uvw> 

P(xyz) 
Patterson function at the point x,y,z 

q_{e}(r) 
Specimen transmission function 

Q 
Probability of scattering an electron 
page2673 

Scattering vector 
page1421 
r 
Length of the position vector r (or ) 

r (or ) 
Position vector of a point or an atom: The real space coordinates, threedimensional position vector in direct space 
page3732 
r* 
Reciprocallattice vector 


Position of atom i 
page1421 
s 
g/2 

S 
Illuminating area by the incident electron beam 
page3769 
S 
Point spread function (PSF) of a system 
page2621 
t 
Length of a translation vector t 

t 
Translation vector 

t(r) 
Spread function of the objective lens 

T(u) 
Microscope transfer function 

u 
Spatial frequency 
page3699 
u 
The reciprocal space coordinates 
page3732 
u 
Twodimensional vector in the back focal plane of the objective lens 

u 
Vector with integral coefficients 


Column of integral point coordinates or vector coefficients 

V 
Cell volume of direct lattice 

V_{0} 
Accelerating voltage of the electrons 
page4165 
V_{t} 
The projected potential 
page4173 
V^{n} 
Vector space of dimension n 

V* 
Cell volume of reciprocal lattice 

w 
Weighting factor 

W 
Symmetry operation or motion 

(W,w) 
Symmetry operation W, described by an (n x n) matrix W and an (n x 1) column w 

X 
Point 


Image of a point X after a symmetry operation 


Column of point coordinates or vector coefficients 

xa 
A component of the position vector r (or ) 

X_{kl} 
Complex Fourier coefficient of the pixel at (k, l) 

yb 
A component of the position vector r (or ) 

z 
Crystal thickness 
page4217 
Z 
Average atomic number 
page4476 
zc 
A component of the position vector r (or ) 

r'; x', y', z'; or x_{i}' 
Position vector and point coordinates after a transformation of a coordinate system 


New position vector and point coordinates after a symmetry operation 

u, v, w; or u_{i} 
Integers, coordinates of a (primitive) lattice point; coefficients of vector u 

[uvw] 
Indices of a lattice direction or zone axis 

<uvw> 
Indices of a set of all symmetrically equivalent lattice directions 

x, y, z; or x_{i} 
Coordinates of a point (location of an atom) expressed in units of a, b, c; coordinates of end point of position vector r (or ); coefficients of position vector r (or ).


ξ 
sense vector 
page3461 
ξ_{hkl} 
Extinction distance 
page3769/page4134 
φ(r) 
Electrostatic potential 

Φ_{hkl} 
Fourier coefficients of an electrostatic potential. 
page3880 
Φ_{P} 
Fourier transform of the projected electrostatic potential 

Ψ_{exit} 
Exit wave function from TEM Specimen 
page4217 
ψ_{illum} 
Illumination wave function 
page3732 
ψ_{i}(r) 
Image wave function 
page3732 
ψ_{o}(r) 
Object wave function (in real space) 
page3732 
ψ_{o}(u) 
Object wave function (in reciprocal space) 
page3732 
Ψ_{o,s} 
Wave function of scattered electrons 
page4217 
Φ_{hkl} 
Fourier coefficients of an electrostatic potential 
page3769 
Φ_{1s}(r) 
The lowest energy bound state of the atom column 
page4217 
α 
A lattice or cell parameter: an interaxial (lattice) angle b ^ c 

α 
Electron beam convergence 
page3879 
α* 
An interaxial (lattice) angle of reciprocal lattice b* ^ c* 

α_{max} 
Visibility band halfwidth 

α(hkl); or α 
Phase angle of the structure factor F(hkl) 

ρ 
Density of the material (g/cm3). 
page4475, page2673 
ρ(xyz) 
Electron density at the point x,y,z 

β 
A lattice or cell parameter: an interaxial (lattice) angle c ^ a 

β 
Brightness of electron beam 
page4961 
β 
Collection angle of EELS 
page3384 
β_{2} 
Collection angle (mrad) 
page4476 
β* 
An interaxial (lattice) angle of reciprocal lattice c* ^ a* 

γ 
A lattice or cell parameter: an interaxial (lattice) angle a ^ b 

γ* 
An interaxial (lattice) angle of reciprocal lattice a* ^ b* 

θ 
The scattering angle 
page3732 
σ 
An interaction constant 
page4173 
σ 
Mirror planes in crystals 
page1620 
σ 
Cross section (of an incident electron interacting with an atom) 
page2673 
σ_{T} 
Total scattering cross sectoin (including both elastic and inelastic scatterings, i.e. σ_{elastic} + σ_{inelastic}) for an isolated atom, 
page2673 
Θ, or θ 
Half of the angle between the transmitted and scattered electron beams 
page3769 
ϕ 
Phase 

λ 
Electron wavelength 
page4787 
λ 
Mean free path (of an incident electron interacting with an atom) 
page2673 
χ 
The phase shift from defocus and spherical aberration, phasedistortion function 
page3732 
Δ 
Defocus spread 
page3879 
Δ 
Difference parameter 

Δf 
Objective lens defocus 

Δd_{c} 
Chromatic broadening 
page3384 
ΔE_{L2,3} 
Separation of the L_{3} and L_{2} peak maxima 
page4770 
ΔE_{L2,3} 
Chemical shift of Si L_{2,3} from that of pure silicon 
page3441 
Δf 
Defocus 
page1715 
δE 
Intrinsic energy spread of E_{0} 
page4165 
Ω 
Solid angle subtended by the intersection of two visibility bands 

Γ 
Visibility factor in calculating latticefringe visibility band halfwidths 

δ 
Dirac delta function 

τ 
A relativistic correction factor 
page4476 

into the page 
page4315 
[ ] 
An orientation of a crystal 

[ ] 
A zone axis 

< > 
A group of orientations of a crystal 

( ) 
A crystalline plane 

{ } 
A group of planes of a crystal 

/ 
Indicates parallel symmetry elements 
page2982 
Schoenflies notation 

page1677 