Abstract: Starting from our previous work in which we obtained a system of coupled integrodifferential equations for acoustic sound waves and phonon density fluctuations in two-dimensional (2D) crystals, we derive here the corresponding hydrodynamic equations, and we study their consequences as a function of temperature and frequency. These phenomena encompass propagation and damping of acoustic sound waves, diffusive heat conduction, second sound, and Poiseuille heat flow, all of which are characterized by specific transport coefficients. We calculate these coefficients by means of correlation functions without using the concept of relaxation time. Numerical calculations are performed as well in order to show the temperature dependence of the transport coefficients and of the thermal conductivity. As a consequence of thermal tension, mechanical and thermal phenomena are coupled. We calculate the dynamic susceptibilities for displacement and temperature fluctuations and study their resonances. Due to the thermomechanical coupling, the thermal resonances such as the Landau-Placzek peak and the second-sound doublet appear in the displacement susceptibility, and conversely the acoustic sound wave doublet appears in the temperature susceptibility, Our analytical results not only apply to graphene, but they are also valid for arbitrary 2D crystals with hexagonal symmetry, such as 2D hexagonal boron nitride, 2H-transition-metal dichalcogenides, and oxides.

Abstract: Starting from a Hamiltonian with anharmonic coupling between in-plane acoustic displacements and outof-plane (flexural) modes, we derived coupled equations of motion for in-plane displacements correlations and flexural mode density fluctuations. Linear response theory and time-dependent thermal Green's functions techniques are applied in order to obtain different response functions. As external perturbations we allow for stresses and thermal heat sources. The displacement correlations are described by a Dyson equation where the flexural density distribution enters as an additional perturbation. The flexural density distribution satisfies a kinetic equation where the in-plane lattice displacements act as a perturbation. In the hydrodynamic limit this system of coupled equations is at the basis of a unified description of elastic and thermal phenomena, such as isothermal versus adiabatic sound motion and thermal conductivity versus second sound. The general theory is formulated in view of application to graphene, two-dimensional h-BN, and 2H-transition metal dichalcogenides and oxides.

Abstract: The elastic constant C-11 and piezoelectric stress constant e(1),(11) of two-dimensional (2D) dielectric materials comprising h-BN, 2H-MoS2, and other transition-metal dichalcogenides and dioxides are calculated using lattice dynamical theory. The results are compared with corresponding quantities obtained with ab initio calculations. We identify the difference between clamped-ion and relaxed-ion contributions with the dependence on inner strains which are due to the relative displacements of the ions in the unit cell. Lattice dynamics allows us to express the inner-strain contributions in terms of microscopic quantities such as effective ionic charges and optoacoustical couplings, which allows us to clarify differences in the piezoelectric behavior between h-BN and MoS2. Trends in the different microscopic quantities as functions of atomic composition are discussed.

Abstract: The crystal field in the orientationally disordered phase of C90-fullerite is derived from an intermolecular potential model, which takes into account the geometric difference between double bonds and single bonds. The molecules are modelled as rigid bodies, atoms and single bonds are treated as single interaction centers, while double bonds are described by a distribution of interaction centers along the bond. The crystal field is expanded in terms of cubic rotator functions. The calculated expansion coefficients are compared with empirical values derived from diffraction data. The angular dependence of the crystal field, resulting from an anticlockwise rotation of the molecule around the [111] axis, exhibits an absolute and a secondary minimum at angles of 98-degrees and 38-degrees respectively. The self interaction of the molecule in a deformable lattice is investigated.

Abstract: The electronic properties of boron nitride nanoribbons (BNNRs) doped with a line of carbon atoms are investigated using density functional calculations. By replacing a line of alternating B and N atoms with carbons, three different configurations are possible depending on the type of the atoms which bond to the carbons. We found very different electronic properties for these configurations: (i) the NCB arrangement is strongly polarized with a large dipole moment having an unexpected direction, (ii) the BCB and NCN arrangements are nonpolar with zero dipole moment, (iii) the doping by a carbon line reduces the band gap regardless of the local arrangement of the borons and the nitrogens around the carbon line, and (iv) the polarization and energy gap of the carbon-doped BNNRs can be tuned by an electric field applied parallel to the carbon line. Similar effects were found when either an armchair or zigzag line of carbon was introduced.

Abstract: The lattice dynamics of low-frequency rigid-plane modes in metallic (graphene multilayers, GML) and in insulating (hexagonal boron-nitride multilayers, BNML) layered crystals is investigated. The frequencies of shearing and compression (stretching) modes depend on the layer number N and are presented in the form of fan diagrams. The results for GML and BNML are very similar. In both cases, only the interactions (van der Waals and Coulomb) between nearest-neighbor planes are effective, while the interactions between more distant planes are screened. A comparison with recent Raman scattering results on low-frequency shear modes in GML [Tan et al., Nat. Mater., in press, doi: 10.1038/nmat3245, (2012)] is made. Relations with the low-lying rigid-plane phonon dispersions in the bulk materials are established. Master curves, which connect the fan diagram frequencies for any given N, are derived. Static and dynamic thermal correlation functions for rigid-layer shear and compression modes are calculated. The results might be of use for the interpretation of friction force experiments on multilayer crystals.

Abstract: Using time-differential perturbed angular correlation spectroscopy we have measured the electric field gradient (EFG) at 111Cd probe nuclei in solid Ce in a pressure range up to 8 GPa. Covering various allotropic phases of Ce, we find that the value of the EFG in the cubic α phase is almost four times larger than in the cubic γ phase and close to values in the noncubic phases α′ and α″. These results together with the differences in time modulation of the spectra are interpreted as evidence for quadrupolar electronic charge-density ordering and symmetry lowering at the γ→α transition while the lattice remains face-centered cubic

Abstract: Starting from an empirical force constant model of valence interactions and calculating by Ewalds method the ion-ion force constants, we derive the dynamical matrix for a monolayer crystal of hexagonal boron nitride (h-BN). The phonon dispersion relations are calculated. The interplay between valence and Coulomb forces is discussed. It is shown by analytical methods that the longitudinal and the transverse optical (LO and TO) phonon branches for in-plane motion are degenerate at the Γ point of the Brillouin zone. Away from Γ, the LO branch exhibits pronounced overbending. It is found that the nonanalytic Coulomb contribution to the dynamical matrix causes a linear increase of the LO branch with increasing wave vector starting at Γ. This effect is general for two-dimensional (2D) ionic crystals. Performing a long-wavelength expansion of the dynamical matrix, we use Borns perturbation method to calculate the elastic constants (tension coefficients). Since the crystal is noncentrosymmetric, internal displacements due to relative shifts between the two sublattices (B and N) contribute to the elastic constants. These internal displacements are responsible for piezoelectric and dielectric phenomena. The piezoelectric stress constant and the dielectric susceptibility of 2D h-BN are calculated.

Abstract: The orientation of a C(70) fullerene molecule encapsulated in a single-walled carbon nanotube (SWCNT) depends on the tube radius. First we confirm that chirality effects do not affect the orientation as well by comparing discrete atomistic calculations with the results of a continuous tube approximation for a variety of SWCNTs. The molecular and the tube symmetry are exploited by using symmetry-adapted rotator functions. We accurately determine the optimal molecular orientation as a function of the tube radius; for low (less than or similar to 7 A) and high (greater than or similar to 7.2 A) tube radii, lying and standing molecular orientations are recovered, respectively. In between, we observe a transition regime. In addition, we consider off-axis positions. We perform a one-dimensional liquid description of a chain of on-axis C(70) molecules inside a SWCNT. All results agree well with recent x-ray diffraction experiments.

Abstract: A theoretical model is presented for the description of the metal-insulator transition which accompanies the structural phase transition at T approximate to 50 K in polymerized KC60. The model involves orientational charge density waves (along the C-60 polymer chains) which were introduced previously for a description of the structural phase transition. A satisfactory qualitative and quantitative understanding is obtained when the three-dimensionality of the crystal and the presence of the K+ counterions is properly taken into account.