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“Proton tunneling and nonlinear polarizability effects in hydrogen-bonded ferroelectrics”. Bussmann-Holder A, Michel KH, AIP conference proceedings
T2 –, 5th Williamsburg Workshop on 1st-Principles Calculations for, Ferroelectrics, FEB 01-04, 1998, WILLIAMSBURG, VA , 202 (1998)
Abstract: Hydrogen-bonded ferroelectrics are modelled by a coupled spin/nonlinear lattice (polarizability) interaction Hamiltonian, where specifically the geometry of the hydrogen bond is included. The model leads to a structural phase transition and describes correctly the isotope effect due to the substitution H/D in hydrogen-bonded systems in terms of bond length changes.
Keywords: P1 Proceeding; Condensed Matter Theory (CMT)
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“Quantum charge density fluctuations and the γ-&alpha, phase transition in Ce”. Nikolaev AV, Michel KH, European physical journal : B : condensed matter and complex systems 9, 619 (1999). http://doi.org/10.1007/s100510050806
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.461
Times cited: 19
DOI: 10.1007/s100510050806
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“Rigid-plane phonons in layered crystals”. Michel KH, Verberck B, Physica status solidi: B: basic research 249, 2604 (2012). http://doi.org/10.1002/pssb.201200119
Abstract: The determination of the layer number ${\cal N}$ in nanoscale thin layered crystals is a challenging problem of technological relevance. In addition to innovative experimental techniques, a thorough knowledge of the underlying lattice dynamics is required. Starting from phenomenological atomic interaction potentials we have carried out an analytical study of the low-frequency optical phonon dispersions in layered crystals. At the gamma point of the two-dimensional Brillouin zone the optical phonon frequencies correspond to rigid-plane shearing and compression modes. We have investigated graphene multilayers (GML) and hexagonal boron-nitride multilayers (BNML). The frequencies show a characteristic dependence on ${\cal N}$. The results which are represented in the form of fan diagrams are very similar for both materials. Due to charge neutrality within layers Coulomb forces play no role, only van der Waals forces between nearest neighbor layers are relevant. The theoretical results agree with recent low-frequency Raman results on rigid-layer modes [Tan et al., Nature Mater. 11, 294 (2012)] in GML and double-resonant Raman scattering data on rigid-layer compression modes [Herziger et al., Phys. Rev. B 85, 235447 (2012)] in GML. (C) 2012 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.674
Times cited: 1
DOI: 10.1002/pssb.201200119
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“Sequence of orientational phase transitions in solid C60”. Michel KH, Chemical physics letters 193, 478 (1992). http://doi.org/10.1016/0009-2614(92)85835-X
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.897
Times cited: 14
DOI: 10.1016/0009-2614(92)85835-X
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“Stabilisation of fcc cobalt layers by 0.4 nm thick manganese layers in Co/Mn superlattices”. Michel A, Pierron-Bohnes V, Jay JP, Panissod P, Lefebvre S, Bessière M, Fischer HE, Van Tendeloo G, European physical journal : B : condensed matter and complex systems 19, 225 (2001). http://doi.org/10.1007/s100510170331
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 1.461
Times cited: 8
DOI: 10.1007/s100510170331
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“Stabilization of mercury-based superconductors by foreign cations”. Raveau B, Michel C, Hervieu M, Van Tendeloo G, Maignan A, Annales de chimie (1914)
T2 –, 4th North-African Materials Science Symposium (JMSM 94), NOV 23-24, 1994, CASABLANCA, MOROCCO 19, 487 (1994)
Abstract: The recently discovered superconducting mercury-based cuprates HgBa2Can-1CunO2n+2+delta have proved difficult to synthesize as single phases and are sensitive to environment (CO2, moisture). The present paper gives an overview of new series mercury based superconductors, whose stabilisation is based on the fact that a foreign cation with a higher valency than Hg(II) must be introduced in the mercury layers, in order to fill up partially the oxygen vacancies of these layers. By this method, several new series of superconductors involving strontium instead of barium with critical temperatures ranging from 27 K to 95 K have been isolated : Hg0.5Bi0.5Sr2-xLaxCuO4+delta, Hg(0.5)Bi(0.5)Sr(2)Ca(1-x)R(x)Cu(2)O(6+delta) (R Y, Nd, Pr), Pb0.7Hg0.3Sr2-xLaxCuO4+delta, Pb(0.7)Hg(0.3)Sr(2)Ca(1-x)R(x)Cu(2)O(6+delta) (R = Y, Nd) Hg(1-x)Pr(x)Sr(2)A(1-x')Pr(x') Cu2O6+delta (A = Sr, Ca), Pb0.7Hg0.3Sr2Cu2CO3O7 and Hg1-xCrxSr2CuO4+delta. The behaviour of the praseodymium cuprates that exhibit a rather sharp transition and reach a Tc of 85 K is especially discussed. A method to synthesize new ''Ba-Hg'' superconducting cuprates with the 1212 structure at normal pressure with a Tc up to 110 K is also presented.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Times cited: 2
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“Structural aspects of Bi2-xPbxSr3.5Cu2(CO3)O8-\delta for 0\leq x\leq0.75 : an electron-microscopy study”. Zhang XF, Van Tendeloo G, Amelinckx S, Pelloquin D, Michel C, Hervieu M, Raveau B, Journal of solid state chemistry 113, 327 (1994). http://doi.org/10.1006/jssc.1994.1378
Abstract: The structure and defect structure of Bi2-xPbxSr3.5Cu2 (CO3)O8-delta compounds with 0 less-than-or-equal-to x less-than-or-equal-to 0.75 are carefully investigated by electron diffraction and high-resolution electron microscopy. All compounds have an orthorhombic structure with a almost-equal-to b almost-equal-to 5.4 angstrom and c almost-equal-to 39.5 angstrom. The length of the b-axis decreases monotonically with increasing x. The space group for the basic structure is Abm2. The structure can be considered as an intergrowth of Bi2Sr2CuO6 lamellae with Sr2CuO2 (CO3) lamellae along the c-axis. CO3 groups behave as bridges connecting the CuO6 octahedra. In the x = 0 compound the carbon atoms are shifted away from their symmetry positions; the orientational ordering of the CO3 groups (or the carbon shift) in successive CO planes alternates along +b and -b. Typical Bi-type and Pb-type modulations are found along the b-axis up to a Pb content x = 0.5. Electron beam irradiation destroys the ordering of the CO3 groups and alters the modulated structure. (C) 1994 Academic press, inc.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 2.133
Times cited: 8
DOI: 10.1006/jssc.1994.1378
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“Structural characteristics of the 40K superconductor Bi2Sr5Cu3(CO3)2O10: a HREM study”. Hervieu M, Pelloquin D, Michel C, Van Tendeloo G, Raveau B, Journal of solid state chemistry 112, 139 (1994)
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 2.133
Times cited: 5
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“Structural investigations of recently discovered high Tc superconductors”. Van Tendeloo G, Krekels T, Amelinckx S, Babu TGN, Greaves C, Hervieu M, Michel C, Raveau B, Microscopy research and technique 30, 102 (1995). http://doi.org/10.1002/jemt.1070300203
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 1.154
Times cited: 4
DOI: 10.1002/jemt.1070300203
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“Substitution of mercury for thallium in the 2223 cuprate: the 130K superconductor Tl1.6Hg0.4Ba2Cu3O10-x”. Goutenoire F, Maignan A, Van Tendeloo G, Martin C, Michel C, Hervieu M, Raveau B, Solid state communications 90, 47 (1994)
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 1.897
Times cited: 16
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“Superconductivity up to 110K in the 1212-Hg based cuprate Nd1-xCaxBa2Hg1-xCu2+xO6+y”. Maignan A, Michel C, Van Tendeloo G, Hervieu M, Raveau B, Physica: C : superconductivity 216, 1 (1993)
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 0.942
Times cited: 32
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“Superexchange and electron correlations in alkali fullerides AC60, A=K, Rb, Cs”. Nikolaev AV, Michel KH, The journal of chemical physics 122, 064310 (2005). http://doi.org/10.1063/1.1844491
Abstract: Superexchange interactions in alkali fullerides AC(60) are derived for C-60 molecular ions separated by interstitial alkali-metal ions. We use a multiconfiguration approach which comprises the lowest molecular orbital states of the C-60 molecule and the excited s and d states of the alkali-metal atom A. Interactions are described by the valence bond (Heitler-London) method for a complex (C-60 – A – C-60) – with two valence electrons. The electronic charge transfer between the alkali-metal atom and a neighboring C-60 molecule is not complete. The occupation probability of excited d and s states of the alkali atom is not negligible. In correspondence with the relative positions of the C-60 molecules and A atoms in the polymer crystal, we consider 180degrees and 90degrees (angle) superexchange pathways. For the former case the ground state is found to be a spin singlet separated from a triplet at similar to20 K. For T < 20 K there appear strong spin correlations for the 180degrees superexchange pathway. The results are related to spin lattice relaxation experiments on CsC60 in the polymerized and in the quenched cubic phase. (C) 2005 American Institute of Physics.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.965
Times cited: 11
DOI: 10.1063/1.1844491
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“Superposition of quantum and classical rotational motions in Sc2C2@C84 fullerite”. Michel KH, Verberck B, Hulman M, Kuzmany H, Krause M, The journal of chemical physics 126, 064304 (2007). http://doi.org/10.1063/1.2434175
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.965
Times cited: 14
DOI: 10.1063/1.2434175
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“Symmetry lowering at the structural phase transitions in NpO2 and UO2”. Nikolaev AV, Michel KH, Physical review : B : condensed matter and materials physics 68, 054112 (2003). http://doi.org/10.1103/PhysRevB.68.054112
Abstract: The structural phase transitions with electric-quadrupole long-range order in NpO2 (Fm (3) over barm-->Pn (3) over barm) and UO2 (Fm (3) over barm-->Pa (3) over bar) are analyzed from a group theoretical point of view. In both cases, the symmetry lowering involves three quadrupolar components belonging to the irreducible representation T-2g (Gamma(5)) of O-h and condensing in a triple-q structure at the X point of the Brillouin zone. The Pa (3) over bar structure is close to Pn (3) over barm, but allows for oxygen displacements. The Pa (3) over bar ordering leads to an effective electrostatic attraction between electronic quadrupoles while the Pn (3) over barm ordering results in a repulsion between them. It is concluded that the Pn (3) over barm structure can be stabilized only through some additional process such as strengthening of the chemical bonding between Np and O. We also derive the relevant structure-factor amplitudes for Pn (3) over barm and Pa (3) over bar, and the effect of domains on resonant x-ray scattering experiments.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 15
DOI: 10.1103/PhysRevB.68.054112
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“Synthesis and characterization of mercury based “1222&rdquo, cuprates (Hg1-xMx)(Sr,Ba)2Pr2Cu2O9-\delta (M = Pr, Pb, Bi, Tl)”. Hervieu M, Van Tendeloo G, Michel C, Martin C, Maignan A, Raveau B, Journal of solid state chemistry 115, 525 (1995). http://doi.org/10.1006/jssc.1995.1169
Abstract: Five new layered cuprates, with a 1222-type structure, have been synthesized according to the formula (Hg(1-x)M(x))(Sr,Ba)(2) Pr2Cu2O9-delta with M = Pr, Pb, Pi, and Tl. They crystallize in a tetragonal cell with a approximate to a(p) and c approximate to 29.5 Angstrom; their structure consists in a triple intergrowth of oxygen-deficient perovskite, rock-salt-and fluorite-type layers. They are characterized by a mixed [Hg(1-x)M(x)O(1-delta)] layer in the rock-sail-type slice. The ED and HREM studies show that Tl, Bi, and Pb are statistically distributed in the mixed [Hg(1-x)M(x)O(1-delta)] layer, contrary to Pr which involves an ordering phenomenon along a. Different stacking defects are observed and discussed as well as the cleavage mode of the crystals. (C) 1995 Academic Press, Inc.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 2.133
Times cited: 5
DOI: 10.1006/jssc.1995.1169
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“The C60 molecules in (C60)N@SWCNT peapods: crystal field, intermolecular interactions and dynamics”. Verberck B, Michel KH, Nikolaev AV, Fullerenes, nanotubes, and carbon nanostructures 14, 171 (2006). http://doi.org/10.1080/15363830600663529
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.35
Times cited: 10
DOI: 10.1080/15363830600663529
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“The isotope effect in hydrogen-bonded systems”. Bussmann-Holder A, Michel KH, International journal of modern physics: B: condensed matter physics, statistical physics, applied physics
T2 –, 1st International Conference on New Theories, Discoveries, and, Applications of Superconductors and Related Materials (New3SC-1), FEB 19-24, 19 12, 3406 (1998). http://doi.org/10.1142/S021797929800274X
Abstract: The giant isotope effect on the ferro- and antiferroelectric transition temperature upon deuteration of hydrogen-bonded systems is well known experimentally since various decades. Yet, theoretically only recently a microscopic understanding of this effect has been achieved which, specifically, took into account the geometry of the O ... H ... O bond. The implications of this modeling are multiple as numerous hydrogen-bonded organic systems show the same effects as ferro- and antiferroelectrics, i.e., cooperative proton tunneling at a well-defined temperature.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 0.736
DOI: 10.1142/S021797929800274X
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“Theoretical model for the structural phase transition and the metal-insulator transition in polymerized KC60”. Verberck B, Nikolaev AV, Michel KH, Fullerenes, nanotubes, and carbon nanostructures
T2 –, 6th Biennial International Workshop on Fullerenes and Atomic Clusters, JUN 30-JUL 04, 2003, St Petersburg, RUSSIA 12, 243 (2004). http://doi.org/10.1081/FST-120027164
Abstract: The recently discovered structural phase transition in Polymerized KC60 at about 50K leads to a doubling of the unit cell volume and is accompanied by a metal-insulator transition. Here, we show that the ((a) over right arrow + (c) over right arrow, (b) over right arrow, (a) over right arrow – (c) over right arrow) superstructure results from orientational charge density waves along the polymer chains and correlated displacements of the K+ ions. The presented model can also account for the metal-insulator transition. The effect is specific for the space group Pmnn of KC60 and is absent in both Rb- and CsC60 (space group 12/m), in agreement with the present experimental knowledge of these compounds.
Keywords: A1 Journal article; Engineering sciences. Technology; Condensed Matter Theory (CMT)
Impact Factor: 1.35
DOI: 10.1081/FST-120027164
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“Theoretical model for the structural phase transition at the metal-insulator transition in polymerized KC60”. Verberck B, Nikolaev AV, Michel KH, Physical Review B 66, 165425 (2002). http://doi.org/10.1103/PhysRevB.66.165425
Abstract: The recently discovered structural transition in polymerized KC60 at about 50 K results in a doubling of the unit cell volume and accompanies the metal-insulator transition. Here we show that the ((a) over right arrow+(c) over right arrow,(b) over right arrow,(a) over right arrow-(c) over right arrow) superstructure results from small orientational charge density waves along the polymer chains and concomitant displacements of the surrounding K+ ions. The effect is specific for the space group Pmnn of KC60 and is absent in RbC60 and CsC60 (space group I2/m). The mechanism is relevant for the metal-insulator transition.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 10
DOI: 10.1103/PhysRevB.66.165425
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“Theoretical phonon dispersions in monolayers and multilayers of hexagonal boron-nitride”. Michel KH, Verberck B, Physica status solidi: B: basic research 246, 2802 (2009). http://doi.org/10.1002/pssb.200982307
Abstract: Starting from an empirical force constant model of valence interactions and calculating by Ewald's method the electrostatic force constants, we derive the dynamical matrix for a monolayer and for multilayer systems of hexagonal boron nitride (h-BN). Solution of the secular problem leads to the corresponding phonon dispersion relations. The interplay between valence forces and Coulomb forces is discussed. A comparison with previous results on graphene and graphene multilayers is made. Our spectra on the h-BN monolayer are rather similar to previous ab initio theory results. Comparison is also made with Raman and infrared experimental results.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.674
Times cited: 10
DOI: 10.1002/pssb.200982307
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“Theory of crystal structures of polymerized C60-fullerite and fullerides AC60, A=K, Rb, Cs”. Michel KH, Nikolaev AV, Verberck B s.l. (2001).
Keywords: H1 Book chapter; Condensed Matter Theory (CMT)
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“Theory of distinct crystal structures of polymerized fullerides AC60, A=K, Rb, Cs: the specific role of alkalis”. Michel KH, Nikolaev AV, Physical review letters 85, 3197 (2000). http://doi.org/10.1103/PhysRevLett.85.3197
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 8.462
Times cited: 16
DOI: 10.1103/PhysRevLett.85.3197
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“Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride”. Michel KH, Verberck B, Physical review : B : solid state 80, 224301 (2009). http://doi.org/10.1103/PhysRevB.80.224301
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.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 96
DOI: 10.1103/PhysRevB.80.224301
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“Theory of phonon dispersions and piezoelectricity in multilayers of hexagonal boron-nitride”. Michel KH, Verberck B, Physica status solidi: B: basic research 248, 2720 (2011). http://doi.org/10.1002/pssb.201100084
Abstract: Taking into account covalent, Coulomb and van der Waals interactions, we construct the dynamical matrix and calculate the phonon dispersion relations for multilayer crystals of hexagonal boron-nitride. Coulomb interactions account for a strong overbending of optical phonons. Applying and extending Born's long-wave theory to the case of multilayer crystals, we calculate the piezoelectric stress constant equation image as a function of the number of layers equation image. In agreement with group theory, we find that equation image for equation image even; for an uneven number equation image of layers we obtain equation image, i.e. the piezoelectric constant decreases as equation image.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.674
Times cited: 13
DOI: 10.1002/pssb.201100084
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“Theory of rigid-plane phonon modes in layered crystals”. Michel KH, Verberck B, Physical review : B : condensed matter and materials physics 85, 094303 (2012). http://doi.org/10.1103/PhysRevB.85.094303
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.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 38
DOI: 10.1103/PhysRevB.85.094303
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“Theory of the elastic constants of graphite and graphene”. Michel KH, Verberck B, Physica status solidi: B: basic research 245, 2177 (2008). http://doi.org/10.1002/pssb.200879604
Abstract: Born's long wave method is used to study the elastic properties of graphite and graphene. Starting from an empirical force constant model derived from full inplane phonon dispersions of graphite [Mohr et al., Phys. Rev. B 76, 035439 (2007)] we calculate the tension coefficients of graphene. Extending the model by interplanar interactions, we calculate the elastic constants of graphite. The agreement of our theoretical values with inelastic x-ray scattering results on elastic constants of graphite [Bosak et al., Phys. Rev. B 75, 153408 (2007)] is very satisfactory.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.674
Times cited: 47
DOI: 10.1002/pssb.200879604
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“Theory of the evolution of phonon spectra and elastic constants from graphene to graphite”. Michel KH, Verberck B, Physical review : B : solid state 78, 085424 (2008). http://doi.org/10.1103/PhysRevB.78.085424
Abstract: We present a unified theory of the phonon dispersions and elastic properties of graphene, graphite, and graphene multilayer systems. Starting from a fifth-nearest-neighbor force-constant model derived from full in-plane phonon dispersions of graphite [Mohr et al., Phys. Rev. B 76, 035439 (2007)], we use Born's long-wave method to calculate the tension and bending coefficients of graphene. Extending the model by interplanar interactions, we study the phonon dispersions and the elastic constants of graphite, and the phonon spectra of graphene multilayers. We find that the inner displacement terms due to sublattice shifts between inequivalent C atoms are quantitatively important in determining the elastomechanical properties of graphene and of graphite. The overall agreement between theory and experiment is very satisfactory. We investigate the evolution from graphene to graphite by studying the increase in the rigid plane optical mode as a function of the number of layers N. At N=10 the graphite value B2g1127 cm−1 is attained within a few percent.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 72
DOI: 10.1103/PhysRevB.78.085424
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“Translation-rotation coupling, phase transitions and elastic phenomena in orientationally disordered crystals”. Lynden-Bell RM, Michel KH, Reviews of modern physics 66, 721 (1994). http://doi.org/10.1103/RevModPhys.66.721
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 29.604
Times cited: 128
DOI: 10.1103/RevModPhys.66.721
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“Theory of anharmonic phonons in two-dimensional crystals”. Michel KH, Costamagna, Peeters FM, Physical review : B : condensed matter and materials physics 91, 134302 (2015). http://doi.org/10.1103/PhysRevB.91.134302
Abstract: Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semiempirical model for anharmonic couplings of third and fourth orders, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Gruneisen parameters, the thermal tension and the thermal expansion coefficients as a function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions, we obtain the renormalization and decay rate of in-plane and flexural phonons as a function of temperature, wave vector, and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There, we find that the transition temperature T-alpha from negative to positive thermal expansion is lowered with smaller system size. Renormalization of the flexural mode has the opposite effect and leads to values of T-alpha approximate to 300 K for systems of macroscopic size. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of normal and umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 38
DOI: 10.1103/PhysRevB.91.134302
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“Theory of thermal expansion in 2D crystals”. Michel KH, Costamagna, Peeters FM, Physica status solidi: B: basic research 252, 2433 (2015). http://doi.org/10.1002/pssb.201552286
Abstract: The thermal expansion alpha(T) in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to alpha(T) is due to anharmonic couplings between in-plane stretching modes and out-of-plane bending (flexural modes). Genuine in-plane anharmonicities give a positive contribution to alpha(T). The competition between these two effects can lead to a change of sign (crossover) from a negative value of alpha(T) in a temperature (T) range T <= T-alpha to a positive value of alpha(T) for T > T-alpha in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two-dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in-plane and out-of-plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature T-alpha. Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.674
Times cited: 21
DOI: 10.1002/pssb.201552286
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