Comparisons of atomic thermal motions for graphite at 300 K based on X-ray, neutron, and phonon-spectrum data

Abstract

The mean-square amplitudes of vibration in graphite based on an X-ray charge-density analysis are 0-0032 (2) and 0.0140 (3) /k 2 parallel to and perpendicular to the basal plane, respectively. Values for the parallel vibrations of 0-0031 (6) and 0.0032 A, 2 were derived from temperature-dependent neutron measurements and a calculated phonon spectrum. The neutron measurements and the phonon spectrum both predict lower values 10.0090 (20) and 0.0098 ,~,21 for the out-of-plane vibrations. This small discrepancy may be caused by small changes in the core atomic scattering factors from the free-atom values or by a deficiency in the phonon-spectrum model.

Suppression of intrinsic roughness in encapsulated graphene

“…The 12 ± 5 pmR rms measurement for fully encapsulated graphene is unique: the interior roughness of an encapsulated heterostructure is not accessible by scanning probe techniques. We note that the observed roughness is comparable within experimental error to the measured rms displacement of carbon atoms within bulk graphite [21][22][23]. This could be regarded as somewhat surprising, given that the stacking is performed manually and artificially and considering the lattice mismatch of graphene and hBN.…”

“…The 12 ± 5 pm R rms value is, to our knowledge, the lowest observed to date for graphene, with the roughness of a graphene sheet within a bulk heterostructure measured directly here. This value corresponds within experimental accuracy to the vibrational amplitude of carbon atoms in bulk graphite [21][22][23]. Using density functional theory (DFT) calculations of the hybridized phonon modes in graphene on monolayer hBN and graphene encapsulated by monolayer hBN, we show that the atomic displacements in graphene originate in the lowest-frequency gapped flexural phonon branch and that these decrease when graphene is fully encapsulated by hBN.…”

Temperature evolution of microstructure of turbostratic high melting coal-tar synthetic pitch studied using wide-angle X-ray scattering method

“…The refined mean square atomic displacements (Fig. 8) are higher than the values given in literature [33,34] for graphite hu a 2 i = 3.1 · 10 À5 nm 2 and hu c 2 i = 1.3 · 10 À4 nm 2 . If a part of the refined mean square atomic displacements is contributed to the thermal motions of atoms, similar for graphite and for turbostratic carbon, the difference can be attributed to the static disorder.…”

An energy-dispersive X-ray diffraction study of mean-square atom displacements in highly oriented pyrolytic graphite

“…The error bars of the raw data in Fig. 1 Nicklow et al (1972), we obtain (u2>/AT=3"85 x 10 -5 A 2 K -1 and 6)o=563 K. The Debye temperature from the present work agrees well with the summary of too values as given by Chen & Trucano (1978). Albinet et al (1971) reported a Debye temperature too = 800 K from electron diffraction work.…”

“…Consequently, the vibrational amplitudes of the carbon atoms are expected to be very anisotropic too. These vibrations have been studied by model calculations (Nicklow, Wakabayashi & Smith, 1972;Yoshimori & Kitano, 1956;Biberian, Bienfait & Theeten, 1973;Firey, de Wette, de Rouffignac & Alldredge, 1983) and by experimental methods (Leung, Dresselhaus, Underhill, Krapchev, Dresselhaus & Wuensch, 1981;Chen& Trucano, 1978;Albinet, Biberian & Bienfait, 1971;Ludsteck, 1972). In some of this work the mean-square displacements (m.s.d.)…”