By Jacob J. Bikerman, Hans G. Wiedemann, Gerhard Bayer, Malcolm B. Huglin
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Additional resources for Inorganic and Physical Chemistry (Topics in Current Chemistry)
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.