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650 19 PROCESSES AT SOLID SURFACES
Assume that on the surface the atoms are centred on a square grid of side a0,
the lattice spacing, with the atoms in contact (a face of a simple cubic lattice). It
follows that the radius of each atom is half the lattice spacing r = a0/2. Hence,
the area, A, of a single surface atom is approximated by A = πr2 = π( 12 a0)
2 =
1
4πa20 .
For p = 100 kPa, the number of collisions made with a single surface atom in
each second by oxygen is
ncol = AZw∆t = 1
4πZwa20∆t
= 1
4π × (2.68... × 1027 m−2 s−1) × (291 × 10−12 m)2 × (1 s) = 1.79 × 108
For p = 1.00 Pa, the number of collisions is reduced by a factor of 105 compared
to the calculation just made: AZw = 1.79 × 103 .
P19A.4 Using Bragg’s law, λ = 2d sin θ, it is observed that for a given wavelength,
the greater the separation d of atomic layers within a lattice, the smaller the
scattering angle θ.�erefore, in terms of the LEED pattern, the farther apart
the atoms responsible for the pattern, the closer the spots appear in the LEED
pattern.
�erefore, tripling the horizontal separation between the atoms corresponds
to the spot separation reducing to a third of the original separation between
the spots. �e vertical separation between atoms is unchanged, therefore the
vertical separation of LEED spots in that dimension remains unchanged. �e
result is shown in Fig. 19.1.
Original LEED pattern Reconstruction LEED pattern
Figure 19.1
19B Adsorption and desorption
Answers to discussion questions
D19B.2 �e assumptions made in deriving the Langmuir isotherm are: