We conducted Vickers indentation tests on Fe-free (Mg2SiO4) and Fe-bearing (Mg1.8Fe0.2SiO4) olivine single crystals and high-density polycrystalline material with average grain sizes ranging from 170 to 890 nm. The Vickers microhardness (Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document}) of the Fe-free polycrystalline material with the finest grain size is ~ 17 GPa at a load of 0.1 N, while that of the Fe-bearing single crystal is ~ 8 GPa at the largest load applied. Overall, Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document} decreases with increasing grain size, load (indentation depth), and the presence of Fe. For each grain size, Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document} is well characterized by a power law of the form Hv/Hv0∝l-x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}} /H_{{\text{v}}}^{0} \propto l^{ - x}$$\end{document}, where Hv0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}^{0}$$\end{document} is the depth-independent value of Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document}, l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document} represents either grain size or indentation depth, and x is 0.09. Despite the small exponent value for each size effect, the nonlinear interaction of the two size effects results in large variations of Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document} in our samples. We show that our semi-empirically derived relationship as a function of grain size and indentation depth explains the Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document} of both polycrystalline and single-crystal olivine at any indentation conditions. Indentation fracture toughness of the finest-grained material is 0.8 MPam1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{MPa}}\;{\text{m}}^{1/2}$$\end{document}, which increases slightly to 1.1 MPam1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{MPa}}\;{\text{m}}^{1/2}$$\end{document} with increasing grain size, while the toughness of the single crystals varies from 0.5 to 0.8 MPam1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{MPa}}\;{\text{m}}^{1/2}$$\end{document} depending on the crystallographic orientation of the fracture planes.

中文翻译：

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橄榄石的维氏压痕测试：尺寸效应

我们对无铁 (Mg2SiO4) 和含铁 (Mg1.8Fe0.2SiO4) 橄榄石单晶和高密度多晶材料进行了维氏压痕测试，平均晶粒尺寸为 170 至 890 nm。维氏显微硬度 (Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength {\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document}) 具有最细晶粒尺寸的无铁多晶材料在约 17 GPa 0.1 N 的载荷，而含 Fe 单晶的载荷在最大载荷下约为 8 GPa。全面的，Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} {-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document} 随着晶粒尺寸、载荷（压痕深度）和 Fe 的存在而减小。对于每个粒度，l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} {-69pt} \begin{document}$$l$$\end{document} 表示颗粒大小或压痕深度，x 为 0.09。尽管每个尺寸效应的指数值很小，但两种尺寸效应的非线性相互作用导致 Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{ amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document在我们的示例中。我们表明，我们作为粒度和压痕深度函数的半经验推导关系解释了 Hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \ usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\text{v}}}$$\end{document}任何压痕条件下的多晶和单晶橄榄石。最细粒度材料的压痕断裂韧度为 0.8 MPam1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{ mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{MPa}}\;{\text{m}}^{1/2}$$\end {document}，它略微增加到 1。