Application of the square root diffusivity to diffusion in Ni-Cr-Al-Mo alloys
- PDF / 439,023 Bytes
- 5 Pages / 597 x 774 pts Page_size
- 111 Downloads / 180 Views
I.
INTRODUCTION
I T has been shown that the models involving the "square root diffusivity" can be used to measure the diffusivity of ternary alloys and to predict their interdiffusion behavior, t~] Theory suggests that a similar approach can be applied to quaternary and higher order alloys as well. [2,3J In the present work, the square root diffusivity of a quatemary Ni-Cr-AI-Mo alloy was measured, and the results were compared with previous work on a related ternary Ni-Cr-AI alloy. The objective was to demonstrate that such measurements are possible, that the diffusivities obtained can be used to predict multicomponent behavior, and to show how Mo affects the interdiffusion of Cr and A1 in Ni alloys. II.
BACKGROUND
Except for studies of quaternary alloys by Dayananda and co-workers, t4,51 previous efforts to measure diffusivities of higher order systems with diffusion couples have focused on ternary systems. [6] Ternary couples can be analyzed with a variation of the well-known BoltzmannMatano analysis, tT] Although it can be applied to measuring the 2 • 2 diffusivity matrix [D] of a ternary alloy, it cannot be used to calculate all elements of the 3 • 3 diffusivity matrix of a quaternary alloy.[4.s] Alternate analyses have been suggested for measuring [D] in quatemary and higher order systems, t3,Sj but they assume that the diffusivity is constant (e.g., that it does not vary with composition). This assumption is valid in principle when the concentration differences across a diffusion couple approach zero. [6] However, accurate results may be obtained with finite concentration differences as well. For example, it has been shown for binary alloys that errors due to linear variations of the diffusivity with concentration tend to cancel when "symmetric pairing of data "[9] is used.
Recent work l~] on ternaries has shown that averaging data and applying a constant diffusivity analysis lead to accurate results as well. In that work, the "square root diffusivity" [r] was determined from diffusion couple data taken from Ni-Cr-A1 alloys. It was found that, within experimental error, the [D] obtained from the identity [D] = [r] [r]
was the same as that obtained directly from the BoltzmannMatano analysis. Also, it was shown for a series of seven different diffusion couples that the concentration profiles could be predicted to within -+0.1 at. pet when initial concentration differences were on the order of 5 at. pet or less. In preparation for the current work, a theoretical study was made of the various types of concentrations profiles that can occur in quaternary diffusion couples. [1~ Five types of concentration profiles were identified, but only three types are likely to be observed. These are the same three types possible in ternary diffusion couples. 1~11 Therefore, ternary and quaternary data will normally appear similar and can be treated in a similar way. The square root diffusivity analysis for quaternary systems is based on linear equations that have the following form:12]
Si
=
- V t / T r (r, ,AC~ + r~2
Data Loading...
