The results which are obtained from the consideration for the known experimental results of the natural agehardening phenomenon of Al-Cu alloys are as follows : Assuming that the exceptional distribution state takes place in the thermal vibration energy being possessed when specimens are quenched,Cu atoms at this district can displace the position in the crystal lattice under the temperature at which the ordinary diffusion occurs and this phenomenon is not on the way of the precipitation, but the special course according to the existence curves.
(1) Atoms at this particular district need less activation energy [ω-F(λ)] than that for the self-diffusion (ω) and F(λ), function of the distance (λ) from the nucleus of migrates, is decreasing in proportion to λ.
(2) The displacement of atoms in this range turns to the center at which F(λ)is the largest.
(3) Assuming that it needs the activation energy (U) when the nuclei ccur, the out-breaking numbers are generally proportional to e-U/kT but in this case the nuclei occur nearly at the position which F(λ)λ=0 is comparatively high.Then this probability is in proportion to the supersaturated Cu atom concentration, moreover F(λ)λ=0 is affected by the conditions of quenching and the concentration of solute atoms.
(4) Supposing the activations energy for the mutual exchange between quenching and aging state as a and θ,ratio of the number of nonmigrated atom's n2 to that of the migrated n1 is calculated from the following formula :n1/n2=ke(θ-ε)/kT, aging velocity V=KNsae-(w-F0)/kT · e-ε/kT,and the hour until finishing of this phenomenon t=gNs-be(w-F0)/kT. Here, F0 is the mean of F(λ) from the nucleus of migration to the farthest point within the migrationable limits and Ns the supersaturated concentration of Cu atoms.
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