1.18.2.1 Anthony’s Experiments

RIS was predicted by Anthony,18 in 1969, a few years before the first experimental observations: a rare case in the field of radiation effects. The prediction stemmed from an analogy with nonequilibrium seg­regation observed in aluminum alloys quenched from high temperature. Between 1968 and 1970, in a pio­neering work in binary aluminum alloys, Anthony and coworkers18-22 systematically studied the non­equilibrium segregation ofvarious solute elements on the pyramidal cavities formed in aluminum after quenching from high temperature. They explained this segregation by a coupling between the flux of excess vacancies toward the cavities and the flux
of solute (Figure 1). Nonequilibrium segregation had been previously observed by Kuczynski eta/.23 during the sintering of copper-based particles and by Aust eta/.24 after the quenching of zone refined metals.

Anthony suggested that similar coupling should produce nonequilibrium segregation in alloys under irradiation.18,19 He predicted that the segregation should be much stronger than after quenching because under irradiation, the excess vacancy con­centration and the resulting flux can be sustained for very long times.19,25 As for the cavities formed by vacancy condensation in alloys under irradiation, which result in the swelling phenomenon (Chapter 1.03, Radiation-Induced Effects on Microstruc­ture and Chapter 1.04, Effect of Radiation on Strength and Ductility of Metals and Alloys), he pointed out that with solute and solvent atoms of different sizes, segregation should generate strains around the voids.25 Finally, he predicted intergranu­lar corrosion in austenitic steels and zirconium alloys, resulting from possible solute depletion near grain

boundaries.25

Anthony also presented a detailed discussion on nonequilibrium segregation mechanisms, in the framework of the TIP,18-21 showing that the nonequi­librium tendencies are controlled by the phenomeno­logical coefficients Lj of the Onsager matrix, which can be — in principle — computed from vacancy jump frequencies (see below Section 1.18.3). Clarifying previous discussions on nonequilibrium segregation mechanisms,23,24 he considered two limiting cases for the coupling between solute and vacancy fluxes in an A-B alloy (at the time, he did not apparently consider the coupling between solute and interstitial fluxes and its possible contribution to RIS). In both cases, the total flux of atoms must be equal and in the direction oppo­site to the vacancy flux:

(a) (b)

Figure 2 Radiation-induced segregation mechanisms due to coupling between point defect and solute fluxes in a binary A-B alloy. (a) An enrichment of B occurs if dBV < dAV and a depletion if dBV > dAV. (b) When the vacancies drag the solute, an enrichment of B occurs. (c) An enrichment of B occurs when dBI > dAI.

1. If both A and B fluxes are in the direction opposite to the vacancy flux (Figure 2(a)), one can expect a depletion of B near the vacancy sinks if the vacancy diffusion coefficient of B is larger than that of A (dBV > dV); in the opposite case (dBV < dAV), one can expect an enrichment of B (it is worth noting that this was essentially the explanation proposed by Kuczynski eta/23 in 1960).

2. But A and B fluxes are not necessarily in the same direction. If the B solute atoms are strongly bound to the vacancies and if a vacancy can drag a B atom without dissociation, the vacancy and solute fluxes can be in the same direction (Figure 2(b)): this was the explanation proposed by Aust et at24 In such a case, an enrichment of B is expected, even if dBV > dAV.