# Values for the Formation Enthalpy of Vacancies

| In this module a collection of vacancy data will be built up.
|  | There might be several values for one and the same quantity, sometimes wildly different. Some colleagues would criticize the "uncritical" inclusion in a table like this.
|  | Well, discussing incompatible values, always culminating at the conclusion that one's own measurements are superior to the measurements of the others, is one of the joys in the life of a scientist. And of course, there is only one value that can be correct within the basic assumptions (e.g. that we have just vacancies, not doing anything in particular except for migrating around a bit). So maybe some measurements were not so good, some evaluations relied on faulty assumptions - or, maybe, the basic premise of single vacancies is wrong.
|  | Who knows - now. Eventually we will find out what is really going on. This is the way science works and students should be aware of this. The same comment made for the self-diffusion data in Si applies.
|  | In Si, for example, the emerging point of view now (July 2001) seems to be that you cannot simply consider just having vacancies, or vacancies and interstitials, but you must consider a complex system of Si vacancies, interstitials, oxygen interstitials, C substitutional atoms, and all kinds of recombination, pair formation and agglomeration phenomena that interact strongly and couple the point defect concentrations (oxygen precipitation, e.g. produces Si interstitial, C precipitation eats 'em up). Since the exact situation depends on many parameters, experiments may measure quite different values of just a single parameter - and those measurements were perfectly correct!
Element | cV at Tm × 10-4 Various techniques | HF [eV] from Dl/l - Da/a | HF [eV] from positron annihilation | HF [eV] from Thermopower |
Ag | 1,7 - 5,2 17 - 24 | Dl TE | 0,99 | 1.31 0,89 | L M | 1,0 | TP
Al | 3 - 11 20 11 - 22 6 | Dl TE C E | 0,65 | 0,68 0,66 | L M |  |
Au | 7,2 14 40 7 5 - 20 3 | Dl TE C Q E QM | 0,92 | 0,89 0,89 | L M |  |
Cd | 5 -6,2 24 40 | D TE Q |  | 0,52 | D |  |
Cu | 2 - 7,6 13 50 | D TE C | 1,04 | 1,42 1,28 | L M |  |
Co |  |  |  | 1,34 | A |  |
Cr |  |  |  | 2,0 | D |  |
In |  |  |  | 0,56 0,55 | L A |  |
Kr | 3 |  |  |  |  |  |
La |  |  |  |  |  | 0,98 | TD
Li | 4 |  |  |  |  |  |
Mg |  |  |  | 0,9 | M |  |
Mo | 190 290 - 430 | TE C |  | 3,6 3,0 3,0 | L M D |  |
Na | 7 |  |  |  |  |  |
Nb |  |  |  | 2,65 | D |  |
Ni |  |  |  | 1,78 | D |  |
Pb | 1,7 20 - 23 | Dl TE C | 0,5 | 0,65 0,50 | L A |  |
Pd |  |  |  | 1.,85 | D | 1,7 1,5 | TC TD
Pt | 70 - 80 100 26 3 | TE C Q QM |  | 1,35 1,32 | L D | 1,45 1,45 | TP TC
Ru |  |  |  |  |  | 1,75 | TD
Si |  |  | no values obtained | no values obtained |  |  |
Sn | <0,3 6 - 14 13 | Dl TE C |  | 0,54 | D |  |
Ta |  |  |  | 2,9 2,8 | M D |  |
Tl |  |  |  | 0,46 | M |  |
V |  |  |  | 2,07 | D |  |
W | 230 210 - 340 1 - 3 | TE C QM |  | 4,6 4,1 4,0 3,67 | L M D QM |  |
Zn |  |  |  | 0,54 | A |  |

| Some remarks
|  | There are more ways to obtain the formation enthalpy of vacancies from positron annihilation than just measuring the life time. In particular, measurements of Angular correlations between the emitted g-rays (abbreviated "A") Doppler broadening (abbreviated "D") complement the lifetime measurements which also can be done in two modes (lifetime spectroscopy "L"; and mean life time measurements "M" Values given are from the compilation in Kraftmakhers book..
|  | Vacancies influence thermal conductivity "TC", thermopower "TP" and thermal diffusivity "TD" of metals, Clever measurements allow to deduce the vacancy formation enthalpy. Values given are from Kraftmakhers book.
|  | Vacancy concentrations at the melting point can be measured with various techniques. The abbreviations refer to D l = D l - D a method E = stored enthalpy DC = differential calorimetry Q = quenching QM = microscopic observations of quenched samples SH = specific heat TE = thermal expansion.

With frame

2.1.1 Simple Vacancies and Interstitials

Formation Enthalpies and Entropies for Vacnacies an Self-Interstitials

4.1.1 Experimental Techniques for Studying Point Defects

Self-Diffusion in Si

© H. Föll (Defects - Script)