['The', 'particular', 'phase', 'field', 'model', 'we', 'employ', 'is', 'an', 'extension', 'of', '[', '6', ']', ',', 'and', 'is', 'based', 'on', 'the', 'three', 'dimensional', 'thermal', 'phase', 'field', 'model', 'of', '[', '7', ']', 'and', 'two', 'dimensional', 'thermal', '-', 'solutal', 'phase', 'field', 'model', 'of', '[', '8', ']', '.']