Studies of a Phenomenological Model of Ion Mixing
- PDF / 280,344 Bytes
- 6 Pages / 420.48 x 639 pts Page_size
- 99 Downloads / 177 Views
STUDIES OF A PHENOMENOLOGICAL MODEL OF ION MIXING Y.-T. Cheng,* T. W. Workman, M-A. Nicolet, and W. L. Johnson CaliforniaInstitute of Technology, Pasadena,CA 91125
ABSTRACT The phenomenological model of ion mixing based on the concept of a thermal spike and chemically biased diffusion is further developed. Experimental results available to date are compared with the model.
INTRODUCTION In an effort to obtain a quantitative description of ion mixing phenomena, a series of experiments has been performed to clarify the mechanisms of ion mixing induced by dense collisional cascades [1,2,31. It was observed that a chemical effect due to the heat of mixing of binary alloys contributes significantly to ion mixing: With all else being equal, metallic bilayers with a large negative heat of mixing mix more effectively than those with a zero or positive heat of mixing [1]. This effect is not accounted for by the ballistic models of ion mixing [4,5,6]. However, it can be explained using Darken's description of chemically biased diffusion [1]. Furthermore, the characteristic kinetic energy of moving particles was estimated to be on the order of I eV/particle [1], indicating the possibility of a thermal spike. Later experiments demonstrated the effect of the thermal spike, such as the influence of cohesive energy on ion mixing [2]. A phenomenological model was then developed based on the concept of thermal spikes and chemically biased diffusion [3]. In the following, we shall provide another derivation of the phenomenological equation of ion mixing obtained earlier and compare the model with additional experimental results.
FROM VINEYARD'S THERMAL SPIKE TO A PHENOMENOLOGICAL MODEL OF ION MIXING The thermal spike idea has been discussed now for over 30 years [7,8,9,10]. A spike or a high density cascade can be described as a local volume in which essentially all the atoms are simultaneously in motion [9]. A thermal spike is a spike in which the velocity distribution of moving particles resembles the Maxwell-Boltzmann distribution [7,8]. Thus, the concept of a local temperature can be introduced through the use of the law of equipartition of energy. Desired physical parameters can be obtained for a system experiencing a thermal spike if their behavior as a function of temperature is known. The * Present address: Physical Chemistry Department, General Motors Research Laboratories, Warren, Michigan 48090-9055.
Mat. Res. Soc. Symp. Proc. Vol. 74. c 1987 Materials Research Society
420
temperature can be calculated simply by solving the thermal diffusion equation under specified boundary conditions. During the last 15 years a significant amount of experimental evidence on spike effects has been obtained from sputtering and ion implantation studies [8]. Vineyard's Thermal Spike We shall follow Vineyard's approach [10] to cylindrical thermal spikes because his solution entails a simple analytic form, which can be easily extended to include the heat of mixing effect. The equation of heat conduction in an isotropic, uniform medium w
Data Loading...
