Institute of Metals Division - Determination of the Absolute Grain Boundary Energy of Gold at 1300°K

GRAIN boundaries, the interface between adjacent crystals differing only in respective orientation, have been the object of much experimental and moderate theoretical attention for many years. The earlier experimental work was primarily concerned with the effect that grain boundaries have on the physical behavior of metals, while the basic nature of the boundaries themselves drew only secondary attention. A complete turnabout has been witnessed in more recent years, however, as researchers are now undertaking investigations bearing as directly as possible on the character and physical properties of the grain boundary. Quite comprehensive reviews of the past literature on the subject of grain boundaries have been reported on numerous occasions by various authors, and together these references represent a thorough coverage.'-? It becomes evident in these reviews and other papers"" that the properties of grain boundaries can be explained by regarding a grain boundary as a crystalline region of transition between two unmatched grains. Studies show that grain boundaries have a definite interfacial energy. By measuring the geometry about a point where three interfaces meet in equilibrium, the energy of any two boundaries can be measured with respect to the third. If the absolute interfacial energy of one boundary is known, the absolute energy of the other two boundaries can be calculated. This apparently holds true for any system of phases and interfaces.""25 Most studies have been carried out on solid-solid or liquid-solid systems, or systems of both. However, if about the point of intersection one phase is vapor and the other two are disoriented grains, then two interfaces are surfaces, and one is a grain boundary. Investigations leading to relative grain boundary energy for this particular system have been made by Fullman,23 Greenough and King," and Bailey and Watkins." Herring" treats the system mathematically and arrives at an equation, which appears as Eq. 1, in a form consistent with the reference angles indicated in Fig. 1, ( d?1 ?n = x sina + cosa ( ------- 2 ?2 Sinß da + C0Sß (d?2/d As the system of interfaces comes to equilibrium, a groove of angle appears at the intersection of the grain boundary with the surface, an effect first observed by Rosenhain and Humfrey." Eq. 1 is essentially a summation of the vertical components in Fig. 1 set equal to zero, where ?1 and ?2 are surface tension vectors lying along the side of the groove at point 0 in the groove root. The differential vectors represent the forces tending to rotate the surface into a position that will expose a crystal cleavage surface of lowest energy. Chalmers, King, and Shuttleworth- simplify Eq. 1 by assuming the differential vectors equal to zero, ?1 = ?2= ?Surface and arrive at the following equation: ?B = 2?s cos [2] Greenough and King24 use Eq. 2 for determining the grain boundary energy of silver using prepared bi-crystals of known orientation. Bailey and Watkins25 have done the same for copper, as did Chalmers and others on lead. These authors report the grain boundary values as ratios relative to the surface energy. In the above work, the orientation of grains forming the grain boundary in all cases was controlled so