Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Strasse 1, Düsseldorf 40237, Germany.
J Mech Behav Biomed Mater. 2013 Apr;20:296-304. doi: 10.1016/j.jmbbm.2013.01.030. Epub 2013 Feb 13.
We employ ab initio calculations and investigate the single-crystalline elastic properties of (Ca,Mg)CO3 crystals covering the whole range of concentrations from pure calcite CaCO3 to pure magnesite MgCO3. Studying different distributions of Ca and Mg atoms within 30-atom supercells, our theoretical results show that the energetically most favorable configurations are characterized by elastic constants that nearly monotonously increase with the Mg content. Based on the first principles-derived single-crystalline elastic anisotropy, the integral elastic response of (Ca,Mg)CO3 polycrystals is determined employing a mean-field self-consistent homogenization method. As in case of single-crystalline elastic properties, the computed polycrystalline elastic parameters sensitively depend on the chemical composition and show a significant stiffening impact of Mg atoms on calcite crystals in agreement with the experimental findings. Our analysis also shows that it is not advantageous to use a higher-scale two-phase mix of stoichiometric calcite and magnesite instead of substituting Ca atoms by Mg ones on the atomic scale. Such two-phase composites are not significantly thermodynamically favorable and do not provide any strong additional stiffening effect.
我们采用从头算方法研究了（Ca，Mg）CO3 晶体的单晶弹性性质，涵盖了从纯方解石 CaCO3 到纯菱镁矿 MgCO3 的整个浓度范围。通过研究 30 原子超晶胞内 Ca 和 Mg 原子的不同分布，我们的理论结果表明，能量上最有利的构型具有与 Mg 含量几乎单调增加的弹性常数。基于第一性原理导出的单晶弹性各向异性，采用平均场自洽均匀化方法确定（Ca，Mg）CO3 多晶的整体弹性响应。与单晶弹性性质一样，计算得到的多晶弹性参数对化学成分非常敏感，并表现出 Mg 原子对方解石晶体的显著增强效应，与实验结果一致。我们的分析还表明，在原子尺度上用化学计量的方解石和菱镁矿的更高尺度两相混合物代替 Ca 原子而不是用 Mg 原子代替 Ca 原子并不具有优势。这种两相复合材料在热力学上并不具有优势，也不会提供任何强烈的额外增强效果。
