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Here a few numbers for self
diffusion |
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Numbers like this always should be taken with a
grain of salt; they are often to a bit of doubt. It is not uncommon that newer
measurements or new interpretations of old measurements give quite different
results. |
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You may wonder a bit yourself, what
self-diffusion in crystasl with two or more different atoms means, and how it
relates to the prevalent defetc type, e.g.
Schottky defects in
NaCl. |
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First some not-so-simple
crystals: |
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Crystal |
Diffusing
Particle |
Melting Point
[oC] |
Activation enthalpy H
[eV]
(= HM,V + HF,V) |
H2 |
H2 |
- 259 |
0,016 |
Ar |
Ar |
- 189 |
0,18 |
H2O |
H2O |
100 |
0,58 |
NaCl |
Cl |
801 |
2,3 |
NaCl |
Na |
801 |
0,86 |
Ge |
Ge |
940 |
2,94 |
Si |
Si |
1412 |
5,11 |
GaAs |
Ga |
1238 |
5,54 |
GaAs |
As |
1238 |
9,96 |
Al |
Al |
660 |
1,47 |
Cu |
Cu |
1083 |
2,03 |
Ni |
Ni |
1455 |
2,86 |
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Now some metals; the values are form
Neumann and Toelle (1986, 1990) as compiled by
Kraftmakher |
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You will find two pre-exponential factors
D0 and two
activation enthalpies H in tke left part of the table. |
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That is, because according to Neumann and Toelle,
the self-diffusion data taken over a large region of temperatures do not form a straight line in an Arrhenius plot and
therefore cannot be fitted with just one
exponential. |
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So you fit with two exponentials, and it is
anyone's guess what the second set (with the higher activation energy) actually
describes. A common explanation is that you see the influence of double
vacancies. While the formation energy is almost twice that of a single vacancy,
the mgration energy canbe substantially lower - the sum thus may weel be
relavant for self-diffusion. |
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But you could also argue that you see the
influence of self-interstitials, or that this is all baloney; and that any
curvature of the Arrhenius plots, if there is indeed some, is due to some
temperature dependence of the formation/migration entrpopies and enthalpies
(which could exist on theoretical reasons). |
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However - the numbers you get are
quite different for fits with one or two sets. |
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This serves as another example for how difficult
it is to obtain unambiguos, air-tight data in the business! |
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Crystal |
Fitting with two sets |
Fitting with one set |
D0(1)
cm2s1 |
Activation enthalpy H1
[eV] |
D0(2)
cm2s1 |
Activation enthalpy H1
[eV] D1(1)
cm2s1 |
D0
cm2s1 |
Activation enthalpy H1
[eV] |
Al |
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2,86 |
K |
0.05 |
0.386 |
1 |
0.487 |
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Na |
0.006 |
0.372 |
0.81 |
0.503 |
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Li |
0.038 |
0.52 |
9.5 |
0.694 |
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Ag |
0.055 |
1.77 |
15.1 |
2.35 |
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Au |
0.025 |
1.70 |
0.83 |
2.20 |
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Cu |
0.13 |
2.05 |
4.5 |
2.46 |
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2,03 |
Ni |
0.85 |
2.87 |
1350 |
4.15 |
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1,47 |
Pt |
0.034 |
2.64 |
88.6 |
4.05 |
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V |
0.31 |
3.21 |
2420 |
4.70 |
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Nb |
0.115 |
3.88 |
65 |
5.21 |
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Mo |
0.13 |
4.54 |
140 |
5.70 |
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Ta |
0.002 |
3.84 |
1.16 |
4.78 |
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W |
0.13 |
5.62 |
200 |
7.33 |
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© H. Föll