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By Jacob J. Bikerman, Hans G. Wiedemann, Gerhard Bayer, Malcolm B. Huglin

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Example text

In addition, it contains two unknowns (3's and 7sl) and, consequently, can be used only to calculate the difference 3's - 3'sl but not these two quantities separately. To find 3's and 3'sl, each for itself, more hypotheses are needed. In many instances, cos 0 appears to be a linear function of the 3" of the liquid, so that cos 8 = 1 - b ( 3 " - 7c); (72) b and 7e are empirical constants, and 7c is referred to as the "critical surface tension". Elimination of 7 from Eqs. (1) and (72) leads 147) to the relation 7sl = 7s - 7c cos 0 - (cos O/b) + (cos 20/b).

LOt) term fracture mechanics frequently is applied to the corresponding branch o f science. Its findings are outside the scope o f this review. 4. 1. It is reviewed here even more briefly than the surface energy (% or "3"') with which this paper is primarily concerned. In the most popular method of estimating 7t, not this quantity itself but only its ratio to the surface energy, that is, 7t/Ts is determined. Let Fig. 12 be a highly Fig. 12. A grain-boundary groove. The hypothetical tensions OM and ON balance tile hypothetical tension acting along the grain boundary OK.

A second weakness o f the theory lies in the use of l/p2 instead of (1/02) - (1/03); this error may raise the calculated difference T m - Tmr by a factor of, for instance, ten. A third weakness is, that the interface is implied to be perfectly smooth. Surface roughness can be detected even on precision - made ball bearings; thus the assumption of zero roughness on freely solidified solids is not convincing. A fourth defect is caused by the neglect of the crystalline nature of so many solids; a freely growing solid is likely to be bounded by crystallographic planes rather than by smoothly flowing curves.

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