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Sticking coefficient : ウィキペディア英語版
Sticking coefficient
Sticking coefficient is the term used in surface physics to describe the ratio of the number of adsorbate atoms (or molecules) that adsorb, or "stick", to a surface to the total number of atoms that impinge upon that surface during the same period of time.〔(sticking coefficient ) ''IUPAC Compendium of Chemical Terminology'' 2nd Edition (1997), Accessed 30 September 2008〕 Sometimes the symbol Sc is used to denote this coefficient, and its value is between 1 (all impinging atoms stick) and 0 (no atoms stick). The coefficient is a function of surface temperature, surface coverage (θ) and structural details as well as the kinetic energy of the impinging particles.
==Derivation==
When arriving at a site of a surface, an adatom has three options. There is a probability that it will adsorb to the surface (P_a), a probability that it will migrate to another site on the surface (P_m), and a probability that it will desorb from the surface and return to the bulk gas (P_d). For an empty site (θ=0) the sum of these three options is unity.
: P_a + P_m + P_d=1
For a site already occupied by an adatom (θ>0), there is no probability of adsorbing, and so the probabilities sum as:
: P_d'+P_m'=1
For the first site visited, the P of migrating overall is the P of migrating if the site is filled plus the P of migrating if the site is empty. The same is true for the P of desorption. The P of adsorption, however, does not exist for an already filled site.
: P_=P_m(1-\theta)+P_m'(\theta)
: P_=P_d(1-\theta)+P_d'(\theta)
: P_=P_m(1-\theta)
The P of migrating from the second site is the P of migrating from the first site ''and then'' migrating from the second site, and so we multiply the two values.
: P_=P_ \times P_=P_^2
Thus the sticking probability ( s_c ) is the P of sticking of the first site, plus the P of migrating from the first site ''and then'' sticking to the second site, plus the P of migrating from the second site ''and then'' sticking at the third site etc.
: s=P_a(1-\theta)+P_P_a(1-\theta)+P_^2P_a(1-\theta)...
: s=P_a(1-\theta)\sum_^ P_^n
There is an identity we can make use of.
:\sum_^ x^n =\frac\forall x<1
:\therefore s=P_a(1-\theta)\frac=P_a+P_d
: s_0=\frac
: \frac=\frac
If we just look at the P of migration at the first site, we see that it is certainty minus all other possibilities.
: P_m1=1-P_d(1-\theta)-P_d'(\theta)-P_a(1-\theta)
Using this result, and rearranging, we find:
: \frac=()^
: \frac=()^
: K\overset}\frac

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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