Estimates of internal stress and related mosaicity in solution grown crystals: proteins

Abstract

The concept of microscopic stress centers is applied to evaluate macroscopic lattice rotation in a striation layer. The centers are trapped by the growing crystals replacing normal molecules; they are characterized by strain tensor ε ̂ o and induce lattice distortions. The lattice rotation in striation layer is found to occur around axes parallel to the growing face, rotation angle being proportional to the center stress tensor and variation of the center concentration. Estimates for lysozyme give rotation in the order of arcmin for impurity volume fraction of ∼10 −2 and ε o≃3×10 −2. Impurities are known to induce cracks, mosaic blocks or splitting in inorganic salts growing at high supersaturation, probably via adsorption, making the nuclei-to-substrate binding weaker and thus facilitating appearance of the misoriented 2D or 3D nuclei. Here, 2D nucleation is addressed. An average mosaic misorientation 〈 ω〉 1/2 due to randomly misoriented 2D nuclei was estimated for lysozyme. The calculated mosaicity is shown to steeply increase with supersaturation. At the chosen reasonable parameters, 〈 ω〉 1/2 is also of the order of arcmin at the supersaturation range Δ μ/kT≃0.5–3 where Δ μ is the difference in chemical potentials between the protein molecules in solution and in crystal and kT is thermal energy.