Ion Implantation and Synthesis of Materials - Studium

188 13 Ion-Induced Atomic Intermixing at the Interface: Ion Beam MixingTable 13.1. Heat of mixing and stopping in bilayer systemsbilayer system ∆H mix (kJ (gram-atom) −1 dE/dx (eV nm −1 )Au/Cu −9 31.0W/Cu +36 32.2Hf/Ni −62 32.9Hf/Ti 0 23.5dE/dx from SRIM. ∆H mix after de Boer et al. (1989)themselves. The enthalpy difference, ∆H mix , results from the chemical joining of Aand B atoms and the formation of A–B bonds during alloying. The more negativethe heat of mixing, the greater the tendency to form A–B alloys.In bilayer systems with negative heats of mixing, there is a driving force toform interface alloys during ion irradiation. Although it would seem that ion beamirradiation would intermix layered structures, thermodynamic effects canoverwhelm ballistic processes. If heats of mixing are positive and the sampletemperature is sufficiently low, ion irradiation can cause intermixing. However,when the sample temperature is increased, the mixed layer back-segregates into itscomponents, a process known as demixing.The mixing rate in bilayer systems is expressed as the derivative expressiond(4 Dt ) / dφ, where the variable D is the chemical interdiffusion coefficient. InFig. 13.7, d(4 Dt ) / dφis plotted for several metal bilayer systems as a function ofthe systems’ heat of mixing (heat of mixing data is taken at the 50 atomic %composition). Figure 13.7 shows that the mixing rate is thermodynamicallybiased. When thermodynamic driving forces are important, the mixing rateequation for bilayer mixing can be expressed as4Dtφ4Dto⎛= ⎜1−φ ⎝2 ∆HkTBmix⎞⎟⎠(13.7)where4 Dt / φ is the ballistic-induced mixing term, defined aso24 D ot FD〈 r 〉= 0.268φNEd(13.8)Equation (13.7) is a linear expression with ∆H mix , with a slope defined by24 D ot 2 FD〈 r 〉= 0.536φ kT NEkTBdB(13.9)