Anomalous Lattice Dynamics in AgC4N3: Insights From Inelastic Neutron Scattering and Density Functional Calculations

Abstract

We have performed temperature dependent inelastic neutron scattering measurements to study the anharmonicity of phonon spectra of AgC₄N₃. The analysis and interpretation of the experimental spectra is done using ab-initio lattice dynamics calculations. The calculated phonon spectrum over the entire Brillouin zone is used to derive linear thermal expansion coefficients. The effect of van der Waals interaction on structure stability has been investigated using advanced density functional methods. The calculated isothermal equation of states implies a negative linear compressibility along the c-axis of the crystal, which also leads to a negative thermal expansion along this direction. The role of elastic properties inducing the observed anomalous lattice behavior is discussed.

Keywords: 63.20.-e; 65.40.-b; 78.70.Nx; ab-initio; density functional theory; inelastic neutron scattering; lattice dynamics; linear compressibility; negative thermal expansion; phonon.

Figure 1

(Left) The crystal structure of AgC₄N₃ projected in the ab plane. (Right) The building block consisting of 18 interpenetrating membered rings, and forming the ab plane of the structure. Key: C-Green, N-Red, and Ag-Blue.

Figure 2

(Left) Comparison of DFT calculation, and experimental phonon density of states of AgC₄N₃. For clarity, the experimental spectra are shift vertically. (Right: Top) The calculated neutron-weighted total density of states and the partial contributions from various atoms of AgC₄N₃. The calculated neutron spectra have been broadened corresponding to the experimental resolution. (Right: Bottom) The calculated partial density of states from various atoms of AgC₄N₃, showing the full energy range to account for the C-N modes bending and stretch.

Figure 3

The calculated phonon dispersion curves along the high symmetry directions in the Brillouin zone AgC₄N₃. The Bradley-Cracknell notation is used for the high-symmetry points; Γ(0, 0, 0), S(1/2, 0, 0), R(0, 1/2, 0), T(1/2 0 0), W(1/4, 1/4, 1/4), and X(1/2, −1/2, 1/2).

Figure 4

The calculated (solid lines) pressure dependence of unit cell lattice parameters of AgC₄N₃ compared with the experimental data (circles). The experimental data is available from 1 to 6 kbar. The data was extrapolated to 0 kbar and used for estimation of l/l₀.

Figure 5

The displacement vectors corresponding to the difference (× 35) in atomic coordinates of (Left) experimental structures at 1.18 and 6.15 kbar, and (Right) calculated structures at 0.0 and 5.0 kbar. The ambient pressure experimental data is not available in the high pressure setup of the experiment. So we have used experimental structures at 1.18 and 6.15 kbar for plotting the displacement vectors. Key: C-Green, N-Red, and Ag-Blue.

Figure 6

The calculated anisotropic mode Grüneisen parameters Γ_a, Γ_b, and Γ_c, averaged over phonon modes in the entire Brillouin zone, as a function of phonon energy, on application of anisotropic pressure along a-, b-, and c-axes, respectively.

Figure 7

(Left) The calculated and experimental temperature dependence of unit cell parameters of AgC₄N₃. (Right) The calculated temperature dependence of linear thermal expansion coefficients of AgC₄N₃.

Figure 8

The calculated eigenvectors of the zone center phonon at 13.7 meV, giving rise to a negative thermal expansion behavior along the c-axis in AgC₄N₃. The corresponding mode Grüneisen values are Γ_a = 2.39, Γ_b = 0.10, Γ_c = −2.99. Key: C-Green, N-Red, and Ag-Blue.