Elasticity aragonite

Biocoral is composed of crystaUine calcium carbonate or aragonite, the metastable form of calcium carbonate. The compressive strength of Biocoral varies from 26 (50% porous) to 395 MPa (dense) and depends on the porosity of the ceramic. Likewise, the modulus of elasticity (Young s Modulus) of Biocoral varies from 8 (50% porous) to 100 GPa (dense) [Biocoral, 1989]. 

Related to the idea of hierarchy is the use of modular stmeture building up materials through the assembly of identical smaller units. The stepwise unfolding of the muscle protein titin is due to a kind of modular domain stmeture and gives it a sawtooth stress—strain curve, very dilTerent from a purely elastic filament. Similar force curves were measured for the polymeric filaments that are pulled out from the organic binder between the aragonite plates of nacre as the plates are separated (Fig. This... 

Fig. 5 The proteinaceous filaments that arc pulled out cf the organic binding layer between separated sheets of aragonite in nacre (a) extend in a stepwise manner, as revealed by force measurements with the atomic force microscope (b). The sawtooth stress-strain curve creates a greater work of fracture (area below the curve) than that for either a short, stiff adhesive strand or a long, smoothly elastic one. (After Ref. [26].) View this art in color at www.dekker.com.)...

The energy parameters were fitted to equilibrium structural data (cell constants and atomic fractional coordinates), elastic constants, vibrational frequencies at the centre of the Brillouin zone (wave vector K=0) and, for the SM case only, dielectric tensor components, using the THBFIT program[24]. The input data are all the experimental quantities referred to above, and initial trial values for the energy parameters to be optimized. At first specific potentials were fitted in this way separately on calcite and aragonite then some of them were used to compute properties of the other polymorph, so as to check their generality and transferability. 

This simplified equilibration process holds strictly for a cubic crystal in a general non-cubic case, the volume, static pressure and bulk modulus have to be replaced by the strain components (related to unit-cell parameters), stress components and elastic constants, respectively. The computer program PARAPOCS[17] performs the lattice-dynamical, thermodynamical and quasi-harmonic calculations in the general tensorial formalism, and has been used to obtain all results reported below for calcite and aragonite. 

TABLE 13. Experimental unit-cell data (De Villiers, 1971) and elastic constants[45] of aragonite compared to values calculated by RIMl and RIM2 (optimized on aragonite) and RIM (optimized on ealcite) potentials. Quantities with asterisks were not included in the fitting of RIMl and RIM2. 

Pavese, A., Catti, M.,Price, G.D.,and Jackson, R.A.(1992) Interatomic potentials for CaCOs polymorphs (calcite and aragonite), fitted to elastic and vibrational data,... 

Yamamoto, A., Shiro, Y., and Murata, H. (1974) Optioally-aotive vibrations and elastic constants of calcite and aragonite, Bull. Chem. Soc. Japan 47, 2(>5-2Ti. Salje, E. and Viswanathan, K. (1976) The phase diagram calcite- aragonite as derived from the crystallographic properties, Contrib. Mineral. Petrol. 55, 55-67. Dovesi, R., Saunders, V.R.S., and Roetti, C. (1992) CRYSTAL92. User s Manual, Gruppo di Chimioa Teorica, Universitd di Torino. 

Pavese A, Catti M, Price GD, Jackson RA (1992) Interatomic potentials for the CaCOs polymorphs (calcite and aragonite) fitted to elastic and vibrational data. Phys Chem Miner 19 80-87 Perram JW, Petersen HG, Leenw SW de (1988) An algorithm for the simulation of condensed matter which grows as the 3/2 power of the nurnber of particles. Mol Phys 65 875-893 Petersen HG, Soelvason D, Perram JW, Smith ER (1994) The very fast multipole method. J Chem Phys 101 8870-8876... 

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