The formation of three-grain junctions during solidification. Part II: theory

Abstract

<jats:title>Abstract</jats:title><jats:p>We provide a simple geometric theory of crystal growth which predicts the shape and final dihedral angle of three-grain junctions of an augite crystal with two plagioclase grains. The predicted dihedral angle <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Delta $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> depends on the initial impingement angle <jats:inline-formula><jats:alternatives><jats:tex-math>$$\psi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> formed by the plagioclase grains, and also on the relative growth rates of the augite and the plagioclase, and shows reasonable agreement with data obtained from natural samples. We show that the two augite-plagioclase grain boundaries will normally curve towards each other, which is consistent with the first two types of junction described in the companion paper. However, the third type, the eagle’s beak, is formed by the meeting of grain boundaries which curve in the same direction. Although it is possible to account for this type of junction by invoking the localised dissolution of one of the plagioclase grains, this is unlikely to occur. A more plausible explanation involves the late impingement of the two plagioclase grains, consistent with the observation that eagles’ beaks are common in gabbros and strongly orthocumulate troctolites, in which the plagioclase framework has not been established by the time augite is growing in substantial quantities. An observed flattening of the curve of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Delta $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> values at high values of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\psi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> can be explained by taking into account the importance of interfacial energy in late-stage crystallisation.</jats:p>