Is carbon nitride harder than diamond? No, but its girth increases when stretched(negative Poisson ratio)

It has been believed that C3N 4 ceramic would be harder than diamond. Predictions are reported of the mechanical properties based on a force field derived from ab initio quantum mechanics. The predicted structure for oc-C3N 4 is in good agreement with transmission electron diffraction (TED) studies, supporting the identity of the films as ot-C3N 4. The bulk modulus of ot-C3N 4 is calculated to be 189 GPa, significantly less than diamond (436 GPa calculated, 442 GPa experimental). However, ot-C3N 4 is predicted to have a negative Poisson ratio. This may lead to interesting applications. 1. Introduct ion 2. The force field (MSFF) for C3N 4 A great deal of interest was sparked by a recent prediction [1,2] that carbon nitride (13-C3N4, with the same structure as [3-Si3N 4) is even harder than diamond. A number of groups have attempted [3-7] to form thin films of C3N4, and two [3,7] claim to have successfully synthesized ~-C3N 4 thin films. The previous predictions [1,2] were state-of-the-art first principle calculations (local density approximation (LDA)), however several significant assumptions were made that could affect the results. Thus, structures with nonplanar N atom were not considered (in analogy to Si3N 4 which has planar N). In addition, to obtain the compressibility each coordinate was assumed to scale uniformly. * Corresponding author. I Theoretical Division, MSB268, Los Alamos National Laboratory, Los Alamos, VNM 87545, USA. To obtain a force field suitable for predicting mechanical properties, we carried out ab initio calculations [8,9] (Hartree-Fock (HF) wavefunctions, 631G * * basis) on cluster models. Thus for diamond we used adamantane [10,11] ((CH)4(CH2) 6 a cubic molecule), and for C3N 4 we used the analogous hexamethylenetetramine (HMT [12,13], Na(CH2)6). The force field involves two types of terms [14]: (i) Bond stretch (Morse potential), Ebond = D { e x p [ a ( R R e ) ] 1 } 2, where R is the bond length, R e and D are the equilibrium position and depth of the well, and k R = 2Dot 2 is the stretching force constant. (D was not adjusted (standard bond energies were used).) (ii) Angle-bend (harmonic potential), Eangle = 1⁄2ko(O 0~) 2, where 0 is the bond angle, 0 e is the equilibrium angle, and k o is bending force constant. We used the two totally symmetric (A 1) distortions of the nonhydrogen framework of these clusters 0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0009-2614(95)00267-7 Y. Guo, W~A. Goddard 11I/Chemical Physics Letters 237 (1995) 72-76 73 Table 1 Predicted properties of C3N 4 and diamond crystals using the MSFF. Density (p), lattice parameters (a,c), bulk modulus (B), and energy (E) are reported