3.5 Change of interface morphology

3.5.1 Interface sharpening in completely miscible alloys

3.5.1.1 Computer simulations

Using computer simulations, it was shown [12] that, on the nanoscale, for strongly composition-dependent diffusion coefficients, an initially diffuse $A/B$ interface can become chemically abrupt even in ideal (either crystalline or amorphous) systems with complete mutual solubility.

The sharpening can be qualitatively predicted from the classical Fick first law although it is not able to provide correct kinetics on the nanoscale. Since, in ideal systems, $D$ has a positive value, the direction of the flux is always opposite to the direction of the concentration gradient and, for concentration independent diffusion coefficients, this equation should lead to flattening of the interface. However, if $D=D(c)$ (where $D(c)$ is the concentration dependence), the flux $j$ depends not only on the concentration gradient but also on the local composition of the sample. Figure 3.11 illustrates the 'flux distribution' at the interface in the initial state, when the film and the substrate are separated by a wide interface. As the concentration gradient is constant along the interface then, according to Fick's first law, it is only $D$ on which the absolute value of the atomic flux depends. Therefore, in the case of concentration independent $D$ the atomic fluxes, independently of the position, are the same, whereas in case of $D=D(c)$ the 'flux distribution' follows the $D=D(c)$ function.

Figure 3.11: Composition distribution during intermixing in one period of a Mo/V multilayer calculated by KMF (see 2.6.1). The arrows represent schematically the 'flux distribution', i.e. their lengths are proportional to the absolute value of the atomic flux.

We have also shown that sharpening takes place where stress effects intervene. [13]

3.5.1.2 Experiments

We studied Mo/V multilayers.[15] The structures ($20$ bilayers with a modulation length $\approx 5-6$  nm) were produced by magnetron sputtering. The pure Mo and V layers were separated by a roughly $1.5$  nm thick diffuse interface with a constant composition gradient. In order to follow the change of the composition profiles in-situ during heat treatment, x-ray measurements were performed at the KMC2 beamline at the BESSY synchrotron. Symmetrical scans between $53^\circ$ and $66^\circ$ of the scattering angle $2\Theta$ were performed, measuring the scattering intensity around the ($002$ ) Bragg reflection of the Mo/V multilayer structure.

We found from the reconstruction of the diffraction patterns that the interface sharpened during the heat treatment. This conclusion is also supported by the analysis of changes of the intensity ratios during heat treatment. [15]

3.5.2 Dissolution and off-stoichiometric formation of compound layers in solid state reactions

For ordering systems, i.e. in which a new phase forms and grows (solid state reaction) at the interface of a diffusion couple, we have shown that stoichiometric ordered phases at the interface of a bilayer (formed e.g. during sample preparation) may dissolve (even completely) during the annealing process. Later the ordered phase re-forms but highly non-stoichiometrically (Fig. 3.12). [11]

Figure 3.12: Dissolution and off-stoichiometric regrowth of the $AB$ phase in asymmetric diffusion [BCC($100$ )]. Left panel (KMF, 2.6.1): Time evolution ( $t_0 = 0 < t_1 < t_2$ ) of the composition profile. The $AB$ phase dissolves into the $B$ matrix ($t_0$ ,$t_1$ ) and starts to regrow for $t > t_1$ . However the order is not uniform ($t_2$ ). Right panel (KMC, 2.6.2): Atomistic view of the initial state and later when $AB$ is partially dissolved (small part of the KMC cell is shown; lattice planes are detached for better visualisation).