A difference equation for the growth of large grains in a grain-dispersed alloy model, where a large amount of uniform fine grains and an extremely small amount of large grains {the initial sizes (diameter) are
dF,0 and
dL,0, respectively.
dL,0⁄
dF,0≥2} are dispersed in the liquid phase was derived on the assumption that the rate-determining step of Ostwald ripening is the interface reaction. Next, the numerical calculation of the size (
dL,3.6) of WC large grains after the sintering of 1673 K-3.6 ks in the fine grained WC-10 mass%Co hardmetal with the addition of VC (5 mass% in Co) which is most effective among the well-known grain growth inhibitors and with two kinds of grain sizes was carried out to estimate the values of
dF,0 and
dL,0 where abnormal grain growth (
dL,3.6⁄
dL,0≥2) becomes to occur.
The results obtained were as follows: (1) The equation derived is
dL,t+Δt=
dL,t+(81⁄32)
K(1⁄
dF,0−1⁄
dL,t)
Δt, where
K is the same as in the well-known grain growth equation of \bar
dt2−\bar
d02=
Kt. (2) The calculation by using the differential equation, in which the measured
K value (2.18×10
−2 μm
2/ks or 2.18×10
−14 m
2/ks) of the hardmetal with the same chemical composition but usual grain size distribution was substituted, showed the following; (2-1) The abnormal grain growth occurs irrespective of
dL,0, for example, in the case of
dF,0≤0.1 μm. The abnormal grain growth in this case was considered to be a substantial phenomenon. (2-2) The abnormal grain growth does not occur irrespective of
dL,0 in the case of
dF,0≥0.3 μm. These indicate that the present design criterion of commercial fine grained hardmetal that the average grain size, i.e.,
dF,0 is fixed near 0.5 μm in minimum is rational from the viewpoint of the stable production. (3) The value of
K necessary for inhibiting the abnormal grain growth even in the case of
dF,0=0.1 μm is calculated to be less than 0.336×10
−2 μm
2/ks.
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