Cleaving the Halqeh-ye-nur diamonds: a dynamic fracture analysis

The degree of surface roughness and clarity with which a surface in a brittle material can be formed via fracture is known to be related to the speed of the propagating crack. Cracks traversing a brittle material at low speed produce very smooth surfaces, while those propagating faster create less reflective and rough surfaces (Buehler MJ, Gao H. 2006 Nature 439, 307-310 (doi:10.1038/nature04408)). The elastic wave speeds (c(l)≈18 000 m s(-1), c(s)≈11 750 m s(-1)) in diamond are fast (Willmott GR, Field JE. 2006 Phil. Mag. 86, 4305-4318 (doi:10.1080/14786430500482336)) and present a particular problem in creating smooth surfaces during the cleaving of diamond-a routine operation in the fashioning of diamonds for gemstone purposes--as the waves are reflected from the boundaries of the material and can add a tensile component to the propagating crack tip causing the well-known cleavage steps observed on diamond surfaces (Field JE. 1971 Contemp. Phys. 12, 1-31 (doi:10.1080/00107517108205103); Field JE. 1979 Properties of diamond, 1st edn, Academic Press; Wilks EM. 1958 Phil. Mag. 3, 1074-1080 (doi:10.1080/14786435808237036)). Here we report an analysis of two diamonds, having large dimensions and high aspect ratio, which from a gemological analysis are shown to have been cleaved from the same 200 carat specimen. A methodology for their manufacture is calculated by an analysis of a model problem. This takes into account the effect of multiple reflections from the sample boundaries. It is suggested that the lapidary had an intuitive guide to how to apply the cleavage force in order to control the crack speed. In particular, it is shown that it is likely that this technique caused the fracture to propagate at a lower speed. The sacrifice of a large diamond with the intention of creating thin plates, rather than a faceted gemstone, demonstrates how symbolism and beliefs associated with gemstones have changed over the centuries (Harlow GE. 1998 The nature of diamonds, Cambridge University Press). The scientific insights gained by studying these gemstones suggest a method of producing macroscale atomically flat and stress-free surfaces on other brittle materials.