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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 |
| | | | | 2,86 |
K | 0.05 | 0.386 | 1 | 0.487 | | |
Na | 0.006 | 0.372 | 0.81 | 0.503 | |
| Li | 0.038 | 0.52 | 9.5 | 0.694 |
| | Ag | 0.055 | 1.77 | 15.1 |
2.35 | | | Au | 0.025 | 1.70 |
0.83 | 2.20 | | | Cu | 0.13 |
2.05 | 4.5 | 2.46 | | 2,03 | Ni |
0.85 | 2.87 | 1350 | 4.15 | | 1,47 |
Pt | 0.034 | 2.64 | 88.6 | 4.05 | | |
V | 0.31 | 3.21 | 2420 | 4.70 | |
| Nb | 0.115 | 3.88 | 65 | 5.21 |
| | Mo | 0.13 | 4.54 | 140 |
5.70 | | | Ta | 0.002 | 3.84 |
1.16 | 4.78 | | | W | 0.13 |
5.62 | 200 | 7.33 | | |
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© H. Föll (Defects - Script)