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 | Photons. Interact weakly with matter, can penetrate relatively deeply and can be used to probe surfaces at high pressures. |
| Electrons, ions. Interact strongly due to the Coulomb force. They generally penetrate less than photons and techniques based on their use are more surface sensitive. |
Units we use:
1 eV = 1.60 x 10-19 Joules
since 1 mole contains 6.023 x 10-19 molecules
1 eV/molecule = 23.069 kcal/mole = 96.478 kJ/mol
The meV range is the thermal energy often used for vibrational energies (kT at 20 C is 25 meV).
The 0.1 - 25 eV range is the range where most of the chemistry occur. Energies for dissociation, adsorption, ionization, are in this range. The soft UV - visible - near infrared change is 1-4 eV (Energy of photon = 1.2 x 104 eV/l where l is the wavelength in Å).
The 0.1-10 keV range is the one you will commonly find is the energy of X-rays, electrons, and ions used for surface analysis. This is also the energy range where electrons are bound in most atomic core levels used in electron spectroscopy for surface analysis.
0.1-3 MeV range is the range of ion energies used in probing surface structure and composition by Rutherford scattering.
Coulomb Force between charges q1q2 separated a distance r in a medium of dielectric constant e
F = q1q2/(4pee0 r2)
where e0 is the permittivity of vacuum
eo= 8.854x10-14 coulomb volt-1 cm-1
From now on we are going to assume vacuum, e = 1. If the charges are given in units of the (positive) elementary charge (e = 1.6 x 10-19 Coulomb) and r is given in Å.
F(eV/Å) = 14.4 q1q2/r2
The potential energy of a charge q1 at a distance r from a charge q2 in vacuum is given by:
U(eV) = 14.4 q1q2/r
In a material, this energy must be divided by the dielectric constant e. A dipole potential is created by a pair of charges +q and -q separated a distance d (dipole moment P = qd) and aligned along the z-axis. The potential energy of a charge q1 in this dipole field is:
U(eV) = 14.4 q1P cosq /r2
where q is the angle from the axis of the dipole and P is in units of eÅ. P is usually given in Debyes (D).
1 D = 3.336 x 10-28 Coulomb cm = 0.2085 eÅ.
Symmetrical molecules like H2, O2, N2, CO2, CCl4 have zero dipole moments. The values of P for some common asymmetric molecules are P(CO) = 0.1 D, P(HCl) = 1.0 D, P(H2O) = 1.84 D.
The force between a charge and a dipole decays like 1/r4, much faster than the Coulomb force. The force between two dipoles decays even faster, like 1/r7. Remember that the force is proportional to the derivative of the potential, so the potential falls like 1/r6 for a dipole-dipole interaction.
Although an atom or molecule may not have a dipole moment, an induced dipole will be formed in the presence of an electric field, such as that near a surface or one generated by a single charge. The electron cloud is polarized, and the interaction is given by the polarization potential:
U = -2a e2/2r4
where a is called the polarizability, a measure of how easily the molecule is deformed by the electric field. Some values of a in Å3 are 0.21 (He), 0.81 (H2),1.57 (O2), 1.64 (Ar), 10.2 (CCl4).
Particles behave, statistically, as if they were waves of wavelength
l = h/p = h/(2mE)1/2
where h is Planck's constant, p is the momentum of the particle, m its mass and E its energy. For electrons, the de Broglie wavelength is:
l(Å) = (150 eV/E)1/2
or of the order of lattice or intermolecular spacings for valence electrons which have kinetic energies of several eV (the kinetic energy of an electron in the hydrogen atom is 13.6 eV, in the Fermi level of Aluminum is about 11 eV.)
For atoms, the wavelength is usually much smaller than interatomic dimensions, so their motion can be treated classically, except for very light atoms at very low temperatures. For a Helium atom,
l(Å) = (0.02 eV/E)1/2
or about 2 Å at 30 K.
The probability of finding an electron at a distance r from the proton is given by the square of the wavefunction. The probability decreases exponentially, as exp(-r/a0) where a0 is 0.8853 Å. The electron moves in the Coulomb potential so the centripetal and centrifugal forces are in balance:
ke2/r2 = mv2/r
where k is the constant for the Coulomb potential, m the mass of the electron and v its velocity. The velocity for r =a0 is the Bohr velocity, v0 = 2.19 x 108 cm/s or 137 times smaller than c, the speed of light. The velocity decreases with r; at small r it may become comparable with c and relativistic corrections are needed.
Excited states are characterized by the principal quantum number n and the angular momentum L, which is quantized.
L = m v r = l h
where l is an integer. States with l =0, 1, 2, 3, 4 are called s, p, d, f. g.
Last updated: Sept. 7, 2000
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Copyright 2002, by Raúl Baragiola, University of Virginia. All rights reserved. |