Etude par Sonde Atomique Tomographique de la formation de nano ...

tel-00751814, version 1 - 14 Nov 2012
Appendixes
Appendix 3. 3DAP data treatment methods
The procedure for the data treatment is similar for all materials and consists of several
steps. The assumption of a random distribution of solute atoms is tested by methods discussed
below.
a) Statistical tests
3DAP technique is used to check fine scale variations of composition in materials. If there
are slight variations of chemical compositions, the so called frequency distribution (FD) may
reveal microstructural features that are not visible (by eyes) on 3D pictures.
When atoms are randomly distributed a binomial distribution (BD) of the local
concentrations is expected. If precipitation, clustering or segregation occurs in the material, the
FD becomes broader than the BD or even shows well separated peaks corresponding to
different phases.
In order to construct the FD, the APT data are divided into blocks, usually containing
equal number of atoms (Nbox), called the sampling block size (typically 50…500 atoms).
However, the shape of the FD may vary with the chosen block size. For those cases, data
should be analysed in a more careful way.
A convenient and straightforward test is suggested by Thuvander et al [5]. It is usually
used when small variations of composition or ordering are of interest. The random or non
random distribution of solute atoms is tested by comparing the value of the standard error (s)
calculated from experimental data and standard deviation (σ) of the binomial distribution
calculated from the experimental data set.
The mean concentration, c0, of element A is calculated using the experimental data. Then
the standard error, s, is calculated for every block size in a range, typically 100-500 atoms,
using the expression:
1 ��
n
2
b
2
s � ( c � c )
(1)
i 0
n �1
i 1
b
where nb is the total number of blocks and ci is the concentration of element A in block i. With
increasing of block size, s generally decreases. The experimentally obtained s is compared with
the standard deviation, σ, of the BD:
200