A modified “Hole” theory for solute impurity diffusion in liquid metals

Abstract

A modified ''hole'' theory for solute impurity diffusion in liquid metals is presented. The theory calculates an ''effective'' valence for the solute impurities by assuming that the bulk valences of the solvent and solute metals are those given by the Engel-Brewer theory (one for bcc structures, two for cph structures, and three for fcc structures). The effects of balancing the Fermi energy level of the solute with that of the solvent and differences in zero point energy are then considered in calculating the effective valence. The effective valence is then used to calculate a value of diffusional activation energy from a modified Lazarus-LeClaire approach. It is shown that the proposed theory works very well for solute impurity diffusion of a number of solutes in Al, Cu, Ga, Ag, Pb, and Sn, but the paucity of diffusion data is a hindrance to development of theoretical models.

Interdiffusion of Copper and Iron in Liquid Aluminum

“…These values for D 0 and Q 0 from the present investigation are very similar to those obtained by Ejima et al [24] for tracer diffusion of Cu in Al, 1.05 ± 0.15910 À7 m 2 /s and 23,800 ± 1300 J/mole respectively. It is important to note that these values of Q 0 for the diffusion of Cu in Al are close to the value of 24,500 J/mole for pure Al calculated from the phenomenological equation, [1] Q 0 = 3.16 RT m where T m is the melting temperature of Al (933 K). This phenomenological equation also works well for Sn and Sn alloys where 3.16 RT m = 13,300 J/mole and the value of Q 0 for solvent self-diffusion of Sn calculated from six independent investigations (two conducted in microgravity), is Q 0 = 12,100 ± 370 J/mole.…”

“…However, the value of 24,700 J/mole is close to that expected both from the Cu tracer results of Ejima et al [24] and the phenomenological equation for Q 0 . [1] It has been noted that during the diffusion anneal some convective mixing may occur creating scatter in the experimental results but the mixing is localized and convective transport of solute along the length of the capillary is minimal not contributing greatly to the value of the diffusion coefficient. [22] The results of Jiao [27] are also included in Fig.…”

“…[23] Fe dissolved in liquid Al also has a lower valence than Al and therefore would also be a slow diffuser in liquid Al. [1] Included in Fig. 9 are the results of Ejima et al [24] for the tracer diffusion of Ni (2.4910 À4 at.% Ni) and two experimental results for the diffusion of Al-3.5 wt.% Ni alloy into pure Al, one performed in unit gravity [35] and one in microgravity.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] From these models, the temperature dependence of the diffusion coefficient has been given variously as T À5/2 , T 1/2 , T, T 3/2 , T 2 , exp(ÀQ 1 /RT), T 1/2 exp(ÀQ 2 /RT), T exp(ÀQ 3 /RT), and T 2 exp(ÀQ 4 /RT). Several of these theories [1,2,6,13,14,[16][17][18] have been extended to include solute diffusion as well. One of the factors hindering the development of a more inclusive theory for liquid diffusion is the sparcity of reliable experimental results.…”

A sliding cell technique for diffusion measurements in liquid metals

“…3 Despite this effort, current knowledge of diffusion in liquid metals is limited and far from satisfactory. [4][5][6] One of the main reasons for this situation is the lack of accurate and consistent diffusion data. 7 To briefly summarize, there are two common techniques to measure diffusion coefficients in liquid metals: the long capillary (LC) and shear cell (SC) methods.…”