# Numbers for Self-Diffusion

| Here a few numbers for self diffusion
|  | 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.
|  | 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.
| First some not-so-simple crystals:
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
| Now some metals; the values are form Neumann and Toelle (1986, 1990) as compiled by Kraftmakher
|  | You will find two pre-exponential factors D0 and two activation enthalpies H in tke left part of the table.
|  | 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.
|  | 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.
|  | 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).
| However - the numbers you get are quite different for fits with one or two sets.
|  | This serves as another example for how difficult it is to obtain unambiguos, air-tight data in the business!
Crystal | Fitting with two sets | Fitting with one set
--- | --- | ---
D0(1) cm2s–1 | Activation enthalpy H1 [eV] | D0(2) cm2s–1 | Activation enthalpy H1 [eV] D1(1) cm2s–1 | D0 cm2s–1 | 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 |  |

With frame

3.2.2 Self-Diffusion

Exercise 3.2-1 Crystal Identity

© H. Föll (Defects - Script)