Theoretical Analysis of the Graphitization of a Nanodiamond
- PDF / 469,768 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 48 Downloads / 127 Views
1039-P15-10
Theoretical Analysis of the Graphitization of a Nanodiamond S. Joon Kwon, and Jae-Gwan Park Nano Science and Technology Division, Korea Institute of Science and Technology, HawolkokDong, Seongbuk-Gu, Seoul, 130-650, Korea, Republic of ABSTRACT A theoretical analysis of the nanodiamond graphitization was presented. Thermodynamic analysis of the nanodiamond showed three kinds of phase-diagram; smaller nanodiamond, nanodiamond-graphite, and larger nanodiamond. In the theoretical analysis, the most probable and the maximum volume fractions of graphite in the nanodiamond were 0.76 and 0.84, respectively regardless of the annealing temperature and the initial radius of the nanodiamond. The highest graphitization probability decreased with increasing annealing temperature. INTRODUCTION Nanodiamond has attracted interests due to its important properties for industrial application. It can be transformed into graphite by annealing at a relatively low temperature and under atmospheric pressure. Graphitization results in the variation in the surface-dependent physical properties of the nanodiamond. In this study, a theoretical analysis elucidating the phase-diagram of the nanodiamond and graphite is presented. The analysis also shows that the most probable and the maximum volume fractions of graphite in the nanodiamond have constant values respectively, without reference to the annealing temperature and the nanodiamond size. THEORY Determination of a threshold critical size of a nanodiamond for the graphitization Graphitization occurs at the surface of the nanodiamond of initial radius of r. The nanodiamond is in the metastable state in the region defined by the process temperature range of 713-1273 K and the process pressure range of 81-200 MPa [1]. Since the size is small enough, the surface tension in capillary effect considered in the Laplace-Young equation plays an important role to determine the thermodynamic stability of the nanodiamond. Schematic graphitization of the nanodiamond is shown in figure 1(a). If the graphitization is an
energetically favorable process, the free energy of the nanodiamond coated with graphite, ∆Gg, should be lower than that of the initial nanodiamond, ∆Gd. The free energy difference, ∆G =∆Gg - ∆Gd at the annealing temperature T can be expressed as ∆G = ∆Gg − ∆Gd = 4π r 2 (γ g − γ d ) +
4π∆Vm 3 2γ ⎞ ⎛ (r − r '3 ) ⎜ A − P − d ⎟ , 3Vmg r' ⎠ ⎝
(1)
where r’ is the radius of the residual core diamond after the graphitization, A is the phaseequilibrium-line pressure in the bulk state of the graphite and diamond, which can be written as A = 2.01×106T + 2.02×109 (Pa) [2], Vmg is the molar volume of graphite (Vmg = 5.187×10-6 m3mol-1), ∆Vm is the molar volume difference between diamond (Vmd = 3.417×10-6 m3mol-1) and graphite, P is the reaction pressure that is assumed to be atmospheric pressure, γg is the surface free energy of graphite (γg = 0.55 Jm-2), and γd is the surface free energy of diamond (γd = 3.7 Jm2 ) [2]. Experimental data for the surface energies of the materials are res
Data Loading...
