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Theoretical Investigation of Binary Eutectic Alloy Nanoscale Phase Diagrams


Recently, embedded binary eutectic alloy nanostructures (BEANs) have drawn some attention. A previously calculated equilibrium structure map predicts four possible nanocrystal alloy morphologies: phase-separated, bi-lobe, core-shell and inverse coreshell

governed by two dimensionless interface energy parameters. The shape of the bilobe nanoparticles is obtained by nding the surface area of all interfaces that minimizes the overall energy, while also maintaining mechanical equilibrium at the triple point.

Two representative alloy systems displaying eutectic phase diagrams and negligible solid solubility were chosen: GeSn and AuGe. GeSn samples were prepared by sequential implantation of Ge and Sn into SiO2. AuGe samples were prepared by implanting Ge within Au-doped silica lms. Transmission electron microscopy images revealed bi-lobe nanocrystals in both samples. Therefore, the interface energies in both systems must be such that the dimensionless parameters lie in the region of bi-lobe stability.

Careful analysis of the bi-lobe structure leads to the determination of two dimensionless length scales, which describe the bi-lobe independent of the size of the nanoparticle. These two parameters, eta 1 and eta 2 can be used to calculate contours of equal eta 1 and eta 2 over the entire range of bi-lobe stability. Experimental measurement and comparison to predicted structures leads to determination of acting dimensionless interface energies. Experimentally available wetting data is then used to calculate the remaining interface energies in the system. gamma Ge(s)/SiO2 was found to be between 0.82-0.99 J/m2 . gamma Ge0.22Sn0.78(l)/SiO2 and gamma Au0.53Ge0.47(l)/SiO2 are determined to be 1.20 and 0.94 J/m2 , respectively.

To investigate the possibility of size eects at the nanoscale, size dependent phase diagrams for the AuGe and GeSn system are determined. This is done by the theoretical approach rst outlined byWeissmueller et al., which takes into account the energy contribution of the various morphologies listed above. Results from this calculation are compared to those using the tangent line construction approach. The composition dependent surface energies of binary alloy liquids required in this calculation are determined using Butler's equation.

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