© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.3.5.3.2 Cleavage

Jewellers and diamond cutters have known for centuries that diamond has a "perfect cleavage" or "grain" in four directions, parallel to its octahedral crystal faces. After cutting a notch or "kerf" along the grain, a rather dull iron or steel edge is laid athwart the groove and a sharp ~20 microsec blow is struck, forcing apart the groove walls and causing the diamond sample to split along the cleavage plane of structural weakness. Large diamond crystals may be progressively fractured down to near-nanometer scale by this technique. A blade velocity of 500 m/sec should suffice for complete crack penetration through the crystal;⁵³⁶ more energetic cleavage blows give higher fracture velocities which may produce rougher surfaces and even multiple fragmentation. Maximum crack propagation velocity is 1580 m/sec in glass, 4500 m/sec in sapphire, and 7200 m/sec in diamond.⁵³⁶ A large impedance mismatch between the gripper mechanism and the diamond crystal target optimizes pulse reflection at the holding surfaces and maximizes fragmentation. A gripper mechanism made of nylon (failure strength ~10⁹ N/m²; Table 9.3) has an acoustic impedance of 2.9 x 10⁶ kg/m²-sec,⁷⁶³ compared to 6.3 x 10⁷ kg/m²-sec for diamond,⁵³⁶ a huge 22:1 impedance mismatch. A water bath also ensures acoustic reflection because of a large impedance mismatch with diamond (~1.5 x 10⁶ kg/m²-sec for water).

The weakest diamond cleavage plane with the lowest areal bond density is the {111} crystal plane which has a cleavage energy of 10.6 J/m².⁵³⁶ Thus a single cleavage of a 1 micron³ diamond cube requires 10.6 pJ; a striker blade 1 micron long and 10 nm in width must apply a pressure of ~10⁹ N/m² (~10,000 atm) along the contact edge, well below the failure strength of the hardest steel (Table 9.3). As a crude estimate of total cleavage decomposition energy, the progressive fracture of a 1 micron³ diamond cube into one million (10 nm)³ cubes implies a thousandfold increase in surface area and the cleavage of 5.94 x 10⁸ nm² of diamond plane, requiring a minimum energy expenditure of ~6300 pJ to perform the decomposition. The cleavage technique is most applicable to brittle solids and may be less useful in the fragmentation of composite diamondoid materials (Chapter 11).

Last updated on 21 February 2003