Pressure-Induced Metallization of Diamond at Room Temperature
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UCTION, STRUCTURE, PROPERTIES
Pressure-Induced Metallization of Diamond at Room Temperature S. M. Sichkar*, † Kurdyumov Institute of Metal Physics, National Academy of Sciences of Ukraine, Kyiv, 03142 Ukraine *e-mail: [email protected] Received March 18, 2019; revised March 25, 2019; accepted March 29, 2019
Abstract—We use four different methods for testing the hypothesis of putative numerical equivalence between the hardness of diamond and the critical pressure of diamond metallization. In modeling crystal distortion by uniaxial compression, the initial calculations of external pressure give the lower limit for the critical pressure: Pm(1) = 213 GPa. This value is compared to semi-empirical findings obtained within Penn’s model for dielectrics, which is Pm(2) = 187.67 GPa. An experimental value for the Vickers hardness, which is HV(1) = 92 GPa, is compared using a semi-empirical approach. A theoretical value for diamond’s hardness calculated within the Penn’s model is HV(2) = 92.22 GPa. Keywords: diamond, metallization, hardness, critical pressure, Penn’s model DOI: 10.3103/S1063457620030089
INTRODUCTION In 1964, Yu. V. Milman [1] was the first to point to the fact that hardness values measured by indentation of homopolar covalent crystals of Si (~120 kbar) and Ge (~80 kbar) are numerically equivalent to the values for critical pressure of transformation into the metallic phases. The latter can be achieved by applying uniform hydrostatic pressure along with an additional uniaxial stress (e.g., in the [001] direction). This transformation changes the crystal lattice symmetry from cubic one to the β-tin tetragonal structure and creates an asymmetrical Z direction. Typically, these conditions can be readily reproduced under an indenter during hardness tests, and Milman proved that dielectric → metal transition occurred in Si and Ge crystals by measuring electrical conductivity under an nonconductive indenter while it was pressed into a sample. Gilman [2] gathered data on Vickers hardness along with values for the critical pressure of transition for around 15 compounds. A good correlation between the measured values can be appreciated in Fig. 1, which shows three dependences: the first line is for homopolar crystals, (e.g. Si and Ge), the second one is for group III–V compounds, and third one is for and group II–VI compounds. Thus, as the ionic character of a compound increases, the transition pressure becomes increasingly higher than its hardness. Does the same numerical relationship between the hardness and the critical pressure that holds for homopolar dielectrics from group IV hold for diamond as well? Of course, we must take into account that each carbon atom in diamond forms purely homopolar bonds with nearest four neighboring atoms in the crystal lattice, and this picture of sp3-hybridized atoms is absolutely identical to that of Si and Ge. Vickers hardness measurements performed for diamond in 2017 found that HV(1) = 92 GPa [3]. In the present work, this value is compared to values for the critical pressure of
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