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Author |
Michel, K.H.; Verberck, B. |
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Title |
Rigid-plane phonons in layered crystals |
Type |
A1 Journal article |
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Year  |
2012 |
Publication |
Physica status solidi: B: basic research |
Abbreviated Journal |
Phys Status Solidi B |
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Volume |
249 |
Issue |
12 |
Pages |
2604-2607 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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 |
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Place of Publication |
Berlin |
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Wos |
000312215300072 |
Publication Date |
2012-11-19 |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0370-1972; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.674 |
Times cited |
1 |
Open Access |
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Notes |
; This work has been supported by the Flemish Science Foundation (FWO-Vl) and the Bijzonder Onderzoeksfonds, Universiteit Antwerpen (BOF-UA). ; |
Approved |
Most recent IF: 1.674; 2012 IF: 1.489 |
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Call Number |
UA @ lucian @ c:irua:105992 |
Serial |
2907 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Theory of rigid-plane phonon modes in layered crystals |
Type |
A1 Journal article |
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Year |
2012 |
Publication |
Physical review : B : condensed matter and materials physics |
Abbreviated Journal |
Phys Rev B |
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Volume |
85 |
Issue |
9 |
Pages |
094303-094303,11 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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. |
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Wos |
000301646000006 |
Publication Date |
2012-03-19 |
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Abbreviated Series Title |
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Edition |
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ISSN |
1098-0121;1550-235X; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
3.836 |
Times cited |
38 |
Open Access |
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Notes |
; The authors are indebted to J. Maultzsch for bringing Ref. 20 to their attention. They thank D. Lamoen, F.M. Peeters, B. Trauzettel, and C. Van Haesendonck for useful discussions. This work has been financially supported by the Research Foundation Flanders (FWO). ; |
Approved |
Most recent IF: 3.836; 2012 IF: 3.767 |
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Call Number |
UA @ lucian @ c:irua:97787 |
Serial |
3619 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Theory of phonon dispersions and piezoelectricity in multilayers of hexagonal boron-nitride |
Type |
A1 Journal article |
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Year |
2011 |
Publication |
Physica status solidi: B: basic research |
Abbreviated Journal |
Phys Status Solidi B |
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Volume |
248 |
Issue |
11 |
Pages |
2720-2723 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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. |
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Place of Publication |
Berlin |
Editor |
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Language |
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Wos |
000297517100069 |
Publication Date |
2011-10-18 |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0370-1972; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.674 |
Times cited |
13 |
Open Access |
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Notes |
; Discussions with G. Heger, B. Partoens and F. M. Peeters are gratefully acknowledged. This work has been supported by the Flemish Science Foundation (FWO-Vl) and the Bijzonder Onderzoeksfonds, Universiteit Antwerpen (BOF-UA). ; |
Approved |
Most recent IF: 1.674; 2011 IF: 1.316 |
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Call Number |
UA @ lucian @ c:irua:94034 |
Serial |
3618 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Phonon dispersions and piezoelectricity in bulk and multilayers of hexagonal boron nitride |
Type |
A1 Journal article |
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Year |
2011 |
Publication |
Physical review : B : condensed matter and materials physics |
Abbreviated Journal |
Phys Rev B |
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Volume |
83 |
Issue |
11 |
Pages |
115328-115328,14 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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Abstract |
A unified theory of phonon dispersions and piezoelectricity in bulk and multilayers of hexagonal boron nitride (h-BN) is derived. The dynamical matrix is calculated on the basis of an empirical force constant model of intralayer valence and interlayer van der Waals interactions. Coulomb interactions are calculated by Ewalds method, adapted for the three-dimensional (3D) and the multilayer case. The deformation of the ionic charge distribution with long-wave lattice displacements is taken into account. Special attention is devoted to the nonanalytic long-range Coulomb contribution to the dynamical matrix which is different for the 3D crystal and the multilayer case. Consequently there is a splitting of the transverse optical (TO) and longitudinal optical (LO) phonon branches of E1u symmetry and a discontinuity of the A2u branch at the Γ point in 3D h-BN. No such splitting and discontinuity at Γ are present in multilayer crystals with a finite number N of layers. There a diverging bundle of N overbending optical phonon branches emerges from Γ. Borns long-wave theory is applied and extended for the study of piezoelectricity in layered crystals. While 3D h-BN and h-BN multilayers with an even number of layers (symmetry D6h) are not piezoelectric, multilayers with an uneven number of Nu layers (symmetry D3h) are piezoelectric; the piezoelectric coefficient e1,11 is inversely proportional to Nu. |
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Wos |
000288783700005 |
Publication Date |
2011-03-24 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1098-0121;1550-235X; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
3.836 |
Times cited |
82 |
Open Access |
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Notes |
; Discussions with G. Heger, B. Partoens, and F. M. Peeters are gratefully acknowledged. This work has been supported by the Flemish Science Foundation (FWO-V1) and the Bijzonder Onderzoeksfonds, Universiteit Antwerpen (BOF-UA). ; |
Approved |
Most recent IF: 3.836; 2011 IF: 3.691 |
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Call Number |
UA @ lucian @ c:irua:89602 |
Serial |
2603 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Theoretical phonon dispersions in monolayers and multilayers of hexagonal boron-nitride |
Type |
A1 Journal article |
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Year |
2009 |
Publication |
Physica status solidi: B: basic research |
Abbreviated Journal |
Phys Status Solidi B |
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Volume |
246 |
Issue |
11/12 |
Pages |
2802-2805 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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. |
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Corporate Author |
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Publisher |
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Place of Publication |
Berlin |
Editor |
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Language |
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Wos |
000272904100091 |
Publication Date |
2009-11-12 |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0370-1972; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.674 |
Times cited |
10 |
Open Access |
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Notes |
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Approved |
Most recent IF: 1.674; 2009 IF: 1.150 |
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Call Number |
UA @ lucian @ c:irua:80673 |
Serial |
3609 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Theory of elastic and piezoelectric effects in two-dimensional hexagonal boron nitride |
Type |
A1 Journal article |
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Year |
2009 |
Publication |
Physical review : B : solid state |
Abbreviated Journal |
Phys Rev B |
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Volume |
80 |
Issue |
22 |
Pages |
224301,1-224301,10 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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. |
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Place of Publication |
Lancaster, Pa |
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Wos |
000273228500045 |
Publication Date |
2009-12-21 |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1098-0121;1550-235X; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
3.836 |
Times cited |
96 |
Open Access |
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Notes |
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Approved |
Most recent IF: 3.836; 2009 IF: 3.475 |
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Call Number |
UA @ lucian @ c:irua:80576 |
Serial |
3616 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Theory of the elastic constants of graphite and graphene |
Type |
A1 Journal article |
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Year |
2008 |
Publication |
Physica status solidi: B: basic research |
Abbreviated Journal |
Phys Status Solidi B |
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Volume |
245 |
Issue |
10 |
Pages |
2177-2180 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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. |
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Place of Publication |
Berlin |
Editor |
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Wos |
000260581800066 |
Publication Date |
2008-08-25 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0370-1972; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.674 |
Times cited |
47 |
Open Access |
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Notes |
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Approved |
Most recent IF: 1.674; 2008 IF: 1.166 |
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Call Number |
UA @ lucian @ c:irua:75660 |
Serial |
3621 |
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Author |
Michel, K.H.; Verberck, B. |
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Title |
Theory of the evolution of phonon spectra and elastic constants from graphene to graphite |
Type |
A1 Journal article |
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Year |
2008 |
Publication |
Physical review : B : solid state |
Abbreviated Journal |
Phys Rev B |
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Volume |
78 |
Issue |
8 |
Pages |
085424,1-085424,17 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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. |
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Place of Publication |
Lancaster, Pa |
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Wos |
000259406900106 |
Publication Date |
2008-08-21 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1098-0121;1550-235X; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
3.836 |
Times cited |
72 |
Open Access |
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Notes |
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Approved |
Most recent IF: 3.836; 2008 IF: 3.322 |
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Call Number |
UA @ lucian @ c:irua:76527 |
Serial |
3622 |
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