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
Melting Point
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
Activation enthalpy H1
Activation enthalpy H1
[eV] D1(1)
Activation enthalpy H1
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 With frame as PDF

go to 3.2.2 Self-Diffusion

go to Exercise 3.2-1 Crystal Identity

© H. Föll (Defects - Script)