Ion-beam mixing in energetic collision cascades: Thermal-spike model and experiments
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Ion-beam mixing in energetic collision cascades: Thermal-spike model and experiments Byungwoo Parka) School of Materials Science and Engineering, Seoul National University, Seoul 151-742, Korea
Hyukjae Lee School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245 (Received 27 May 1997; accepted 30 March 1998)
A phenomenological model of ion-beam mixing during energetic collision cascades is developed, based on the concept of a thermal spike, to correctly predict that the mixing rate Dt depends linearly on nuclear stopping power (instead of a power-law dependence), and is correlated with a heat of mixing (analogous to Darken’s relation). Previous ion-beam mixing experiments from 25 different metallic bilayers agree well with the model’s predictions: mixing rates (Dt)y(ion-dose) , 1 nm4 , and an activation enthalpy of approximately 1 eV for atomic diffusion in liquid-like cascades.
I. INTRODUCTION
The nature of atomic mixing during energetic displacement cascades has been of interest to scientists for over four decades.1–11 For high deposited-energydensity cascades with heavy ions and matrices (Z . 20), various experiments of ion-beam mixing by lowtemperature implantations have suggested correlations between the mixing rate Dt, and a thermodynamic characteristic, the heat of mixing DHmix .7,9 –16 Using the concept of a thermal spike with heat conduction equation and chemical-rate theory (based on Seitz and Koehler’s2 thermal-spike approach), Johnson et al.7 have proposed a model that mixing rates are linearly related to 2DHmix , analogous to Darken’s relationship. However, their model predicted a power-law dependence of the mixing rates on nuclear stopping power e, that is, Dt ~ e 2 , which contradicts a basic concept and numerous experimental results of ion-beam mixing.6,16 While the concept of thermal spike is a fairly old and controversial topic, molecular-dynamics (MD) computer simulations have demonstrated the role of thermal spikes in dense displacement cascades. Local melting in a cascade occurs for several ps ranges, and the majority of atomic mixing occurs by the diffusion in the locally melted region. Diaz de la Rubia et al.8,17,18 performed the MD simulations with 3 and 5 keV Cu1 into Cu at 0 K implantation temperature (to suppress ion-beam enhanced diffusion), with the interatomic forces represented by the Gibson-II Born–Mayer potential for Cu. The central region of cascade shows considerable disorder, and the radial pair-distribution function at 1.1 ps is very similar to that of liquid Cu in equilibrium. The temperature in the center of the a)
e-mail: [email protected] J. Mater. Res., Vol. 14, No. 1, Jan 1999
http://journals.cambridge.org
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cascade decays from initially ,10,000 K (,1 eV) to ,1000 K (,0.1 eV) within 2 ps (with Tm 1000 K). It is found that the majority of the atomic mixing occurs in the melted region (during the thermal spike), and only a relatively small frac
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