Debye model

About: Debye model is a research topic. Over the lifetime, 7462 publications have been published within this topic receiving 133987 citations.

Dark-field transmission electron microscopy and the Debye-Waller factor of graphene

Abstract: Graphene's structure bears on both the material's electronic properties and fundamental questions about long range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multi-layer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multi-layer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary.

Pressure-volume-temperature equation of state of tungsten carbide to 32 GPa and 1673 K

Abstract: We have obtained pressure-volume-temperature (P-V-T) equation of state for hexagonal tungsten carbide (α-WC) up to 32 GPa and 1673 K using synchrotron x-ray diffraction in a multianvil apparatus at the SPring-8 facility. MgO and Au were used as pressure calibrants. A least-squares fit of the P-V-T-data to a high-temperature Birch–Murnaghan equation of state yielded V0=20.750±0.002 A3, KT=384±4 GPa, K′=4.65±0.32, temperature derivative of the bulk modulus (∂KT/∂T)P=−0.014±0.002 GPa/K, and thermal expansion α=a0+a1T with a0=0.96(±0.05)×10−5 K−1 and a1=0.48(±0.05)×10−8 K−2. The data showed an anisotropic nature of compressibility, with the a-axis (KTa=341±6 GPa) more compressible than the c-the axis (KTc=506±12 GPa) as well as an anisotropic temperature dependence of KT. The estimated thermal Gruneisen parameters are 1.44–1.64 and the Debye temperature is calculated to be 1220 K, which is different from previous estimates.

Molecular motions in liquid. I. Rotation of water and small alcohols studied by deuteron relaxation

Abstract: The deuteron spin lattice relaxation time T1 of CH3OD, C2H5OD, (CH3)2CHOD, and (CH3)3CHOD is reported as a function of temperature and frequency. The deuteron T1 of the alcohols in dilute benzene solutions was also measured at 25°C. A detailed analysis of the experimental results and other magnetic and dielectric relaxation data from the literature was made. Based upon the analysis, it is suggested that the success of the Debye model in explaining the dielectric and magnetic relation behavior of water and small alcohols may be purely coincidental. It seems that the error in applying Stokes law for the rotation of a macroscopic sphere to small molecules in liquid and the error in assuming that water and alcohols rotate as monomers largely cancel each other, yielding much better apparent agreement between calculated and experimental data than those for nonassociating liquids. The deuteron T1’s for the alcohols are further analyzed in terms of anisotropic rotation.