Adsorption of H 2 O, NH 3, CO, NO 2, and NO on graphene: A first-principles study
|
|
- Audra Marshall
- 6 years ago
- Views:
Transcription
1 Asorption of H 2 O, NH 3, CO, NO 2, an NO on graphene: A first-principles stuy O. Leenaerts,* B. Partoens, an F. M. Peeters Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium Receive 26 July 2007; revise manuscript receive 20 February 2008; publishe 17 March 2008 Motivate by the recent realization of graphene sensors to etect iniviual gas molecules, we investigate the asorption of H 2 O, NH 3,CO,NO 2, an NO on a graphene substrate using first-principles calculations. The optimal asorption position an orientation of these molecules on the graphene surface is etermine an the asorption energies are calculate. Molecular oping, i.e., charge transfer between the molecules an the graphene surface, is iscusse in light of the ensity of states an the molecular orbitals of the asorbates. The efficiency of oping of the ifferent molecules is etermine an the influence of their magnetic moment is iscusse. DOI: /PhysRevB PACS number s : h, Hb, Bc, Uw I. INTRODUCTION The synthesis of monolayer graphite i.e., graphene 1 an the experimental observation of Dirac charge carriers in this system 2,3 have awakene an enormous interest in this twoimensional material. The unusual properties of carriers in graphene are a consequence of the gapless an approximately linear electron ispersion at the vicinity of the Fermi level at two inequivalent points of the Brillouin zone. In the low-energy limit, the quasiparticles in these systems are escribe in terms of massless chiral relativistic fermions governe by the Dirac equation. The goo sensor properties of carbon nanotubes are alreay known for some time, 4 but recently, the possibility to use graphene as a highly sensitive gas sensor was also reporte. 5 It was shown that the increase in graphene charge carrier concentration inuce by asorbe gas molecules can be use to make highly sensitive sensors, even with the possibility of etecting iniviual molecules. The sensor property is base on changes in the resistivity ue to molecules asorbe on the graphene sheet that act as onors or acceptors. The sensitivity of NH 3, CO, an H 2 Oupto1ppb parts per 10 9 was emonstrate, an even the ultimate sensitivity of an iniviual molecule was suggeste for NO 2. These excellent sensor properties of graphene are ue to two important facts: i graphene is a two-imensional crystal with only a surface an no volume, which maximizes the effect of surface opants, an ii graphene is highly conuctive an shows metallic conuctance even in the limit of zero carrier ensity. To fully exploit the possibilities of graphene sensors, it is important to unerstan the interaction between the graphene surface an the asorbate molecules. We perform in this letter first-principles calculations for the molecules NH 3,NO 2, NO, CO, an H 2 O asorbe on graphene. We etermine their exact orientation on the surface an their preferential bining site by calculating their bining energy. Their charge transfer to the graphene surface is investigate in orer to etermine the onor or acceptor character of the molecular opant. use for the stuy of molecular asorbates on single-walle carbon nanotubes SWNT All our DFT calculations were carrie out with the ABINIT coe, 11 within the generalize graient approximation GGA of Perew Burke Ernzerhof. 12 The avantage of GGA over the local ensity approximation LDA in this work is that the GGA will not lea to a strong boning of the molecules as in LDA. So, if the molecules bin in GGA, they will efinitely bin in a real system an in LDA too. The istance between asorbate an the graphene surface, however, will be somewhat overestimate an consequently the bining energy will be unerestimate. We use a plane wave basis set with a cutoff energy of 816 ev an pseuopotentials of the Troullier Martins type. 14 For the asorption of the molecules NH 3, CO, an H 2 O, we use non-spin-polarize calculations, while for NO 2 an NO, we use spin-polarize ones. The total system consists of a 4 4 graphene supercell 32 C atoms with a single molecule asorbe to it Fig. 1 an with a istance of 16 Å between ajacent graphene layers. The sampling of the Brillouin zone is one using a Monkhorst Pack 15 gri, which is teste to give converge results for all the properties we calculate. For the calculation of the ensity of states DOS, weusea Monkhorst Pack gri an a Gaussian smearing of 0.14 ev. Charge transfers are calculate base on the Hirshfel charge analysis. 16 The atomic charge Q A for each atom is obtaine by with r the calculate ensity an A 0 r the electron ensity compute for the isolate atom A an taken from Ref. 11 II. COMPUTATIONAL DETAILS The first-principles calculations are performe using ensity functional theory DFT which has been successfully FIG. 1. Color online H 2 O on graphene. 4 4 supercell of graphene with asorbe H 2 O molecule /2008/77 12 / The American Physical Society
2 LEENAERTS, PARTOENS, AND PEETERS Q A = 0 A r A 0 A r r r, from which the charge transfer is euce. From this result we etermine whether or not the asorbate acts as an acceptor or a onor. It shoul be note that the size of the charge transfer is slightly epenent on the metho use to calculate it. The istance from the asorbate to the graphene surface is calculate from the ifference in weighte averages of the ifferent atoms of the molecule an the carbon atoms of the graphene sheet, where we use the atomic number Z of the atoms as the weight factor. III. RESULTS For each asorbate, three asorption sites are consiere, namely, on top of a carbon atom T, the center of a carbon hexagon C, an the center of a carbon-carbon bon B see Fig. 1. For these positions, ifferent orientations of the molecules are examine an the asorption energy is calculate for all of them. The asorption energy is the energy of the isolate graphene sheet an isolate molecule minus the energy of the fully relaxe graphene sheet with the molecule asorbe to it. We i not correct these energies for the ipole-ipole interactions which occur ue to the finite size of the supercells. However, these energies mainly cancel, resulting in corrections of the orer of 2 mev in the worst cases H 2 O an NH 3. This has no influence on any of our conclusions, so we ecie to neglect them. The strength of the molecular oping is iscusse in light of the ensity of states an the highest occupie molecular orbital HOMO an lowest unoccupie molecular orbital LUMO of the asorbate. The position of these orbitals, visible as peaks in the DOS, is practically inepenent of the orientation an asorption site of the molecule, so we only show the total DOS for one geometry per molecule. We can now istinguish two charge transfer mechanisms: i a charge transfer can occur ue to the relative position in the DOS of the HOMO an LUMO of the asorbate. If the HOMO is above the Fermi level of pure graphene the Dirac point, there is a charge transfer to graphene. If the LUMO is below the Dirac point, charge will transfer to the molecule. ii The charge transfer between asorbate an graphene is also partially etermine by the mixing of the HOMO an LUMO with the graphene orbitals hybriization. This mixing scales with the overlap of the interacting orbitals an the inverse of their energy ifference. It is more ifficult to iscuss the asorption energy in this way because of the large amount of possible interacting orbitals present in graphene. Our investigation starts with the nonmagnetic molecules H 2 O, NH 3, an CO, followe by the paramagnetic ones, NO 2 an NO. We iscuss the molecules in the orer of increasing complexity of their charge transfer mechanism. A. H 2 O on graphene We examine the following orientations of the H 2 O molecule with respect to the graphene surface: starting from the TABLE I. H 2 O on graphene: the asorption energy, the istance of H 2 O above the graphene surface, an the charge transfer from the molecule to graphene for ten ifferent B u T u C u B n T n C n B T C C v O atom the H-O bons pointing up u, own, or parallel to the graphene surface n. Another orientation v was suggeste in a theoretical stuy, base on an empirical metho, of the asorption of H 2 O on graphite. 13 This orientation has one O-H bon parallel to the surface an the other one pointing to the surface. All properties were foun to be almost invariant with respect to rotations aroun the axis perpenicular to the surface an through the oxygen atom, an therefore, we will not iscuss this orientation. The results of the calculations are given in Table I. From Table I, we learn that all the asorption energies are small, which is partially a consequence of the calculation metho. This is not very important because the asorption energies are only use to compare the ifferent geometries an to fin the best position an orientation of the molecule for which we nee only relative values. Table I also shows that the asorption energy is primarily etermine by the orientation u,, n, an v an to a lesser egree by the position C, B, an T of the molecule. The energy ifferences are 5 6 mev with respect to the orientation, but they vary with about 1 2 mev when changing the position. This ifference in importance of position an orientation is even more pronounce when we look at the charge transfers. If the O atom points to the graphene surface, there is a small charge transfer to graphene, but if the H atoms point to the surface, there is a small charge transfer to the water molecule. This is a consequence of the form of the HOMO an LUMO of H 2 O an their relative position with respect to the Dirac point see Fig. 2. The HOMO 1b 1 is completely locate on the O atom, but the LUMO 4a 1 is mostly locate on the H atoms. In the u orientation, the HOMO plays the ominant role an onates, through a small mixing with graphene orbitals above the Fermi level, some charge to graphene. There is also a stronger mixing with the orbitals below the Dirac point because they are closer in energy, but this oes not inuce any charge transfer because all these orbitals are fille. In the an v orientations, the LUMO of H 2 O interacts stronger with the surface an is able, through a small mixing with the
3 ADSORPTION OF H 2 O, NH 3,CO,NO 2, AND FIG. 2. Color online H 2 O on graphene. Inset: a the HOMO an b the LUMO of H 2 O the H atoms are white an the oxygen atom is re; green an yellow inicate ifferent signs of the orbital wave function. Main panel: DOS of H 2 O on graphene. The blue otte lines show the positions of the molecular orbitals of H 2 O. graphene orbitals below the Dirac point, to accept some charge from graphene. There is also a stronger mixing with orbitals above the Dirac point now, but this oes not inuce any charge transfer because all these orbitals are empty. In the n orientation, it is again the HOMO that will interact stronger, but now there is also some interaction with the LUMO. There will be a charge transfer from the molecule to graphene, but because of the interaction with the LUMO, it will be smaller. Experimentally, 5 one fins that H 2 O acts as an acceptor on graphene which is in accorance with our theoretical results where we fin that the acceptor character C, v is energetically favore on perfect graphene. B. NH 3 on graphene Two orientations of the ammonia molecule were investigate, one with the H atoms pointing away from the surface u an the other with the H atoms pointing to the surface. All properties were again foun to be almost invariant to rotations aroun the axis perpenicular to the surface an through the nitrogen atom. The results of the calculations are given in Table II. The asorption site an the orientation are now seen to be of the same importance for the asorption energy. The charge transfer, however, is solely etermine by the orientation of the NH 3 molecule. TABLE II. NH 3 on graphene: the asorption energy, the istance of NH 3 above the graphene surface, an the charge transfer from the molecule to graphene for six ifferent B u T u C u B T C FIG. 3. Color online NH 3 on graphene. Inset: a the HOMO an b the LUMO of NH 3 the N atom is blue an the H atoms are white. Main panel: DOS of NH 3 on graphene. There is a small charge transfer from the molecule to the graphene surface of 0.03e in the u orientation an there is almost no charge transfer in the orientation. We can see how this comes about by looking at the HOMO 3a 1 an LUMO 4a 1 of the NH 3 molecule Figs. 3 a an 3 b. In the u orientation, the HOMO is the only orbital that can have a significant overlap with the graphene orbitals an thus can cause charge transfer. As a consequence, the NH 3 molecule will act as a onor. In the orientation, both HOMO an LUMO can cause charge transfers which are similar in magnitue but in opposite irections. The net charge transfer is therefore close to 0. The u orientation is energetically favore which explains the onor character as observe experimentally. 5 We also performe LDA calculations for the asorption of NH 3 on graphene. The results of these are similar for the charge transfer, but the asorption energy is much larger 100 mev. The real asorption energy is known to lie between the two approximate values obtaine through GGA an LDA. This is consistent with the experimental observation 5 that the asorbates can be remove from the surface by annealing at 150 C. C. CO on graphene Three ifferent orientations were use for the CO molecule. Two with the molecule perpenicular to the surface, with the O atom above the C atom u an the other way aroun, an one parallel to the surface n. From Table III, we notice that the CO molecule always acts as a onor. The size of the charge transfer only epens on the orientation of the molecule with respect to the surface Fig. 4. The ifferences in charge transfer are ue to ifferences in orbital overlap between the HOMO 5 of the CO molecule an graphene. The LUMO 2 seems to play no important role in the oping process although it is closer to the Dirac point than the HOMO. To unerstan this, we have to take into account the symmetry of this orbital an the graphene orbitals. The DOS below an close 3 ev to the Dirac point originates from mostly boning combinations of the p z atomic orbitals of the C atoms of graphene. The DOS above the Dirac point is mostly ue to antiboning combinations. The completely antisymmetric LUMO will
4 LEENAERTS, PARTOENS, AND PEETERS TABLE III. CO on graphene: the asorption energy, the istance of CO above the graphene surface, an the charge transfer from the molecule to graphene for seven ifferent B u T u C u T C B n C n therefore mostly interact with the DOS above the Dirac point which oes not cause any oping. The HOMO is thus the more important orbital an the charge transfer is consequently always to graphene. Because the HOMO is mainly locate on the C atom, the charge transfer is largest when the C atom is closest to the surface u orientation, smallest when the O atom is closer to the surface orientation, an intermeiate when both atoms are at an almost equal istance from the surface n orientation. FIG. 5. Color online NO 2 on graphene. Inset: HOMO an LUMO of NO 2 the N atom is blue an the O atom is re. Main panel: spin-polarize DOS of NO 2 on graphene. smaller than the first one but it is still noticeable in the strength of the magnetic moment of the system. The total magnetic moment of graphene an asorbate in, e.g., the B, orientation is B. The charge transfer from graphene M =0 B to NO 2 M =1 B is 0.099e, so the orbital mixing causes a charge transfer of 0.039e to graphene. D. NO 2 on graphene In Ref. 17, it was state that asorbates with a magnetic moment in general result in a larger oping. Therefore, we will now turn our attention to paramagnetic molecules. The first one is NO 2 which has, in a spin-polarize calculation, an energy that is 0.4 ev smaller as compare to an unpolarize one an therefore is paramagnetic. We examine three ifferent orientations of the NO 2 molecule: starting from the N atom, the N-O bons pointing up u, own, or parallel to the graphene surface n. The LUMO 6a 1, of NO 2 is locate 0.3 ev below the Dirac point Fig. 5. This inuces a large charge transfer to the molecule. However, there are also some NO 2 orbitals close enough to the Dirac point to cause some charge transfer in the opposite irection through orbital mixing especially the HOMO 6a 1, Table IV. The latter charge transfer is E. NO on graphene To test whether or not there is always strong oping by paramagnetic molecules, we will investigate another one. For NO, a spin-polarize calculation gives an energy that is 0.3 ev lower than a non-spin-polarize one, so NO is inee a paramagnetic molecule. We investigate the same orientations an use the same notations as for the CO molecule replace C with N. Contrary to the claim mae in Ref. 17, we i not fin that NO inuces any strong oping. The charge transfers are an orer of magnitue smaller than in the case of the NO 2 molecule see Table V which is comparable to the nonmagnetic molecules. Physically, we can unerstan this if we compare the DOS of the asorbates NO Fig. 6 an NO 2 on graphene. For NO 2 asorbe on graphene, the LUMO is situate 0.3 ev below the Dirac point of graphene. TABLE IV. NO 2 on graphene: the asorption energy, the istance of NO 2 above the graphene surface, an the charge transfer from the molecule to graphene for six ifferent FIG. 4. Color online CO on graphene. Inset: a the HOMO an b the LUMO of CO the C atom is black an the O atom is re. Main panel: DOS of CO on graphene. B T C B u T u C n
5 ADSORPTION OF H 2 O, NH 3,CO,NO 2, AND TABLE V. NO on graphene: the asorption energy, the istance of NO above the graphene surface, an the charge transfer from the molecule to graphene for six ifferent TABLE VI. Summary of results. Asorbate Theory Expt. a C u T u C T C n B n H 2 O Acceptor Acceptor NH 3 Donor Donor CO Donor Donor NO 2 Acceptor Acceptor NO Donor a Reference 5. This inuces a strong oping. In the case of NO Fig. 6, the HOMO is egenerate 2 x,2 y an is half fille so it is also the LUMO an lies only 0.1 ev below the Dirac point. This inuces a very small charge transfer from graphene to NO, but ue to its small strength, it can be over compensate by orbital mixing. The HOMO an/or LUMO, of NO can, because it is half fille, cause charge transfer in both irections by mixing with the graphene orbitals below an above the Dirac point. However, as in the case of the LUMO of CO, it interacts mostly with the latter ue to symmetry reasons. So, the orbital mixing leas to charge transfer to graphene. We see from Table V that the charge transfer ue to orbital mixing always overcompensates the small transfer ue to the position of the HOMO an/or LUMO, so NO always act as a onor. We notice that there are large ifferences in an in the istance. They are obviously correlate because a smaller istance between asorbate an graphene leas to a larger orbital overlap an consequently to more orbital mixing i.e., a larger charge transfer. The ifferences in the istance can be explaine by the overlap of the 5 orbital. The position of this orbital is very close in energy to that part of the graphene DOS that originates from the boning combinations of carbon p z orbitals aroun the point. Mixing of these orbitals inuces a net energy shift upwar so they repel each other strongly. The geometry of the 5 orbital gives a large overlap in the u orientation, a smaller overlap in the orientation, an the smallest overlap in the n orientation. This gives a simple explanation for all the ifferences foun from our calculations. IV. SUMMARY AND CONCLUSIONS The charge transfer between the consiere asorbates an graphene is foun to be almost inepenent on the asorption site but it oes epen strongly on the orientation of the asorbate with respect to the graphene surface. We compare two paramagnetic molecules, NO 2 an NO, an foun that NO 2 inuces a relatively strong oping 0.1e, but NO oes not 0.02e. This is in contrast to Ref. 17 where it was claime that paramagnetic molecules are strong opants which we foun inee to be the case for NO 2 but not so for NO. For the consiere asorbates, the sign of the charge transfer agrees with what was foun experimentally see Table VI in Ref. 5. We showe that these charge transfers can be unerstoo from two charge transfer mechanisms. In NO 2 on graphene, it is mainly ue to the position of the LUMO below the Dirac point for all the other stuie asorbates it is cause by the mixing of the HOMO or LUMO orbitals with the orbitals of graphene. The strength of this hybriization can be euce from the geometrical orientation of the HOMO an LUMO orbitals with respect to the graphene surface. The strength of the charge transfer an the bining energies must be seen in light of the use approximations GGA an the metho of calculation Hirshfel metho, which probably lea to an unerestimation. The trens an relative values, on the other han, are much more trustworthy. Our results are also in goo agreement with theoretical stuies of the asorption of molecules on large SWNTs in, e.g., Ref. 6. This suggests that some of the knowlege of asorption on nanotubes shoul be transferable to graphene. ACKNOWLEDGMENTS FIG. 6. Color online NO on graphene. Inset: a 5 orbital an b HOMO/LUMO of NO the N atom is blue an the O atom is re. Main panel: spin-polarize DOS of NO on graphene. This work was supporte by the Flemish Science Founation FWO-Vl, by the NOI-BOF of the University of Antwerp, an by the Belgian Science Policy IAP
6 LEENAERTS, PARTOENS, AND PEETERS 1 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, an A. A. Firsov, Science 306, K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, an A. A. Firsov, Nature Lonon 438, Y. Zhang, Y.-W. Tan, H. L. Stormer, an P. Kim, Nature Lonon 438, J. Kong, N. R. Franklin, C. Zhou, M. G. Chapline, S. Peng, K. Cho, an H. Dai, Science 287, F. Schein, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, an K. S. Novoselov, Nat. Mater. 6, J. Zhao, A. Bulum, J. Han, an J. P. Lu, Nanotechnology 13, S. Santucci, S. Picozzi, F. Di Gregorio, L. Lozzi, C. Cantalini, L. Valentini, J. M. Kenny, an B. Delley, J. Chem. Phys. 119, J. A. Robinson, E. S. Snow, S. C. Baescu, T. L. Reinecke, an F. K. Perkins, Nano Lett. 6, S. Peng an K. Cho, Nanotechnology 11, S. Peng an K. Cho, Nano Lett. 3, J. P. Perew, K. Burke, an M. Ernzerhof, Phys. Rev. Lett. 77, B. S. González, J. Hernánez-Rojas, J. Bretón, an J. M. Gomez Llorente, J. Phys. Chem. C 111, N. Troullier an J. L. Martins, Phys. Rev. B 43, H. J. Monkhorst an J. D. Pack, Phys. Rev. B 13, F. L. Hirshfel, Theor. Chim. Acta 44, T. O. Wehling, K. S. Novoselov, S. V. Morozov, E. E. Vovin, M. I. Katsnelson, A. K. Geim, an A. I. Lichtenstein, Nano Lett. 8,
arxiv: v1 [cond-mat.mtrl-sci] 9 Oct 2007
Adsorption of H 2 O, NH 3, CO, NO 2, and NO on graphene: A first-principles study O. Leenaerts, B. Partoens, and F. M. Peeters Universiteit Antwerpen, Departement Fysica, Groenenborgerlaan 171, B-2020
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 15 Mar 2007
Molecular Doping of Graphene arxiv:cond-mat/79v1 [cond-mat.mes-hall] 15 Mar 7 T. O. Wehling, 1 K. S. Novoselov, S. V. Morozov, E. E. Vdovin, M. I. Katsnelson, 4 A. K. Geim, and A. I. Lichtenstein 1 1 I.
More informationFrom graphene to graphite: Electronic structure around the K point
PHYSICL REVIEW 74, 075404 2006 From graphene to graphite: Electronic structure around the K point. Partoens* and F. M. Peeters Universiteit ntwerpen, Departement Fysica, Groenenborgerlaan 171, -2020 ntwerpen,
More informationOutline. Introduction: graphene. Adsorption on graphene: - Chemisorption - Physisorption. Summary
Outline Introduction: graphene Adsorption on graphene: - Chemisorption - Physisorption Summary 1 Electronic band structure: Electronic properties K Γ M v F = 10 6 ms -1 = c/300 massless Dirac particles!
More informationAdsorption of H 2 O, CO 2, O 2, Ti and Cu on Graphene: A molecular modeling approach
International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:12 No:06 234 Adsorption of H 2 O, CO 2, O 2, Ti and Cu on Graphene: A molecular modeling approach Hilal S Wahab a,*, Salam H. Ali b, Adi
More informationBilayer Heterosystem
Journal of Physics: Conference Series PAPER OPEN ACCESS First-Principles Stuy of Asorption of Halogen Molecules on Graphene-MoS 2 Bilayer Heterosystem To cite this article: S. Lamichhane et al 2016 J.
More informationFirst-principles Studies of Formaldehyde Molecule Adsorption on Graphene Modified with Vacancy, -OH, -CHO and -COOH Group
2017 Asia-Pacific Engineering and Technology Conference (APETC 2017) ISBN: 978-1-60595-443-1 First-principles Studies of Formaldehyde Molecule Adsorption on Graphene Modified with Vacancy, -OH, -CHO and
More informationEnhanced stability of hydrogen atoms at the graphene/graphane interface of. nanoribbons
Enhanced stability of hydrogen atoms at the graphene/graphane interface of nanoribbons Z. M. Ao, 1, A. D. Hernández-Nieves, 2,3, F. M. Peeters, 2 and S. Li 1 1. School of Materials Science and Engineering,
More informationElectronic properties of aluminium and silicon doped (2, 2) graphyne nanotube
Journal of Physics: Conference Series PAPER OPEN ACCESS Electronic properties of aluminium and silicon doped (2, 2) graphyne nanotube To cite this article: Jyotirmoy Deb et al 2016 J. Phys.: Conf. Ser.
More informationExtinction, σ/area. Energy (ev) D = 20 nm. t = 1.5 t 0. t = t 0
Extinction, σ/area 1.5 1.0 t = t 0 t = 0.7 t 0 t = t 0 t = 1.3 t 0 t = 1.5 t 0 0.7 0.9 1.1 Energy (ev) = 20 nm t 1.3 Supplementary Figure 1: Plasmon epenence on isk thickness. We show classical calculations
More informationBohr Model of the Hydrogen Atom
Class 2 page 1 Bohr Moel of the Hyrogen Atom The Bohr Moel of the hyrogen atom assumes that the atom consists of one electron orbiting a positively charge nucleus. Although it oes NOT o a goo job of escribing
More informationLecture 2 Lagrangian formulation of classical mechanics Mechanics
Lecture Lagrangian formulation of classical mechanics 70.00 Mechanics Principle of stationary action MATH-GA To specify a motion uniquely in classical mechanics, it suffices to give, at some time t 0,
More informationDETECTION OF NO 2 ADSORBED ON GRAPHYNE NANOTUBES
DETECTION OF NO 2 ADSORBED ON GRAPHYNE NANOTUBES A.R. KARAMI 1, R. MAJIDI 2 1 Department of Chemistry, Shahid Rajaee Teacher Training University, Lavizan, 16788-15811 Tehran, Iran, E-mail: ar_karami@srttu.edu,
More informationThe electric field as a novel switch for uptake/release of hydrogen storage in nitrogen. doped graphene
The electric field as a novel switch for uptake/release of hydrogen storage in nitrogen doped graphene Z. M. Ao, 1,* A. D. Hernández-Nieves, 2,3 F. M. Peeters 3 and S. Li 1 1 School of Materials Science
More informationreversible hydrogenation
Strain engineering on graphene towards tunable and reversible hydrogenation Zhiping Xu 1,* and Kun Xue 2 1 Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge
More informationProblem Set 2: Solutions
UNIVERSITY OF ALABAMA Department of Physics an Astronomy PH 102 / LeClair Summer II 2010 Problem Set 2: Solutions 1. The en of a charge rubber ro will attract small pellets of Styrofoam that, having mae
More informationStrong anomalous optical dispersion of graphene: complex refractive index measured by Picometrology
Strong anomalous optical ispersion of graphene: complex refractive inex measure by Picometrology Xuefeng Wang, Yong P. Chen an Davi D. Nolte* Department of Physics, Purue University, West Lafayette, N
More informationQuasibound states of quantum dots in single and bilayer graphene
PHYSICAL RIW B 77, 115423 8 Quasibound states of quantum dots in single and bilayer graphene A. Matulis 1,2, * and F. M. Peeters 1, 1 Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171,
More informationTable of Common Derivatives By David Abraham
Prouct an Quotient Rules: Table of Common Derivatives By Davi Abraham [ f ( g( ] = [ f ( ] g( + f ( [ g( ] f ( = g( [ f ( ] g( g( f ( [ g( ] Trigonometric Functions: sin( = cos( cos( = sin( tan( = sec
More informationAB INITIO STUDY OF NANO STRUCTURED FUNCTIONALIZED GRAPHENE WITH 30C ATOMS
International Journal of Science, Environment and Technology, Vol. 1, No 3, 2012, 108-112 AB INITIO STUDY OF NANO STRUCTURED FUNCTIONALIZED GRAPHENE WITH 30C ATOMS Naveen Kumar* and Jyoti Dhar Sharma Deptt.
More informationHow the potentials in different gauges yield the same retarded electric and magnetic fields
How the potentials in ifferent gauges yiel the same retare electric an magnetic fiels José A. Heras a Departamento e Física, E. S. F. M., Instituto Politécnico Nacional, México D. F. México an Department
More informationELECTRON DIFFRACTION
ELECTRON DIFFRACTION Electrons : wave or quanta? Measurement of wavelength an momentum of electrons. Introuction Electrons isplay both wave an particle properties. What is the relationship between the
More informationarxiv:cond-mat/ v1 [cond-mat.other] 14 Dec 2005
Managing the supercell approximation for charge efects in semiconuctors: finite size scaling, charge correction factors, the bangap problem an the ab initio ielectric constant. arxiv:con-mat/52v [con-mat.other]
More informationHydrogen Peroxide Adsorption on Graphene with Stone-Wales Defect
JNS 4 (2014) 1-8 Hydrogen Peroxide Adsorption on Graphene with Stone-Wales Defect R. Majidi a, *, A. R. Karami b a Department of Physics, Shahid Rajaee Teacher Training University, Lavizan, 16788-15811
More informationBand structure engineering of graphene by strain: First-principles calculations
Band structure engineering of graphene by strain: First-principles calculations Gui Gui, Jin Li, and Jianxin Zhong* Laboratory for Quantum Engineering and Micro-Nano Energy Technology, Xiangtan University,
More informationSurface Science 609 (2013) Contents lists available at SciVerse ScienceDirect. Surface Science
Surface Science 69 () 47 Contents lists available at SciVerse ScienceDirect Surface Science journal homepage: www.elsevier.com/locate/susc Scanning tunneling spectroscopy an ensity functional calculation
More informationAb initio study of CNT NO 2 gas sensor
Chemical Physics Letters 387 (2004) 271 276 www.elsevier.com/locate/cplett Ab initio study of CNT NO 2 gas sensor Shu Peng a, *, Kyeongjae Cho a, Pengfei Qi b, Hongjie Dai b a Department of Mechanical
More informationinflow outflow Part I. Regular tasks for MAE598/494 Task 1
MAE 494/598, Fall 2016 Project #1 (Regular tasks = 20 points) Har copy of report is ue at the start of class on the ue ate. The rules on collaboration will be release separately. Please always follow the
More informationDensity functional theory calculations of atomic hydrogen adsorption on graphenes with vacancy defects
Density functional theory calculations of atomic hydrogen adsorption on graphenes with vacancy defects Shunfu Xu Institute of Architecture and Engineering, Weifang University of Science and Technology,
More informationOptimization of Geometries by Energy Minimization
Optimization of Geometries by Energy Minimization by Tracy P. Hamilton Department of Chemistry University of Alabama at Birmingham Birmingham, AL 3594-140 hamilton@uab.eu Copyright Tracy P. Hamilton, 1997.
More informationTheory of doping graphene
H. Pinto, R. Jones School of Physics, University of Exeter, EX4 4QL, Exeter United Kingdom May 25, 2010 Graphene Graphene is made by a single atomic layer of carbon atoms arranged in a honeycomb lattice.
More informationensembles When working with density operators, we can use this connection to define a generalized Bloch vector: v x Tr x, v y Tr y
Ph195a lecture notes, 1/3/01 Density operators for spin- 1 ensembles So far in our iscussion of spin- 1 systems, we have restricte our attention to the case of pure states an Hamiltonian evolution. Toay
More informationAnalytic Scaling Formulas for Crossed Laser Acceleration in Vacuum
October 6, 4 ARDB Note Analytic Scaling Formulas for Crosse Laser Acceleration in Vacuum Robert J. Noble Stanfor Linear Accelerator Center, Stanfor University 575 San Hill Roa, Menlo Park, California 945
More informationTransport properties through double-magnetic-barrier structures in graphene
Chin. Phys. B Vol. 20, No. 7 (20) 077305 Transport properties through double-magnetic-barrier structures in graphene Wang Su-Xin( ) a)b), Li Zhi-Wen( ) a)b), Liu Jian-Jun( ) c), and Li Yu-Xian( ) c) a)
More informationTEST 2 (PHY 250) Figure Figure P26.21
TEST 2 (PHY 250) 1. a) Write the efinition (in a full sentence) of electric potential. b) What is a capacitor? c) Relate the electric torque, exerte on a molecule in a uniform electric fiel, with the ipole
More informationMath Notes on differentials, the Chain Rule, gradients, directional derivative, and normal vectors
Math 18.02 Notes on ifferentials, the Chain Rule, graients, irectional erivative, an normal vectors Tangent plane an linear approximation We efine the partial erivatives of f( xy, ) as follows: f f( x+
More informationThermal conductivity of graded composites: Numerical simulations and an effective medium approximation
JOURNAL OF MATERIALS SCIENCE 34 (999)5497 5503 Thermal conuctivity of grae composites: Numerical simulations an an effective meium approximation P. M. HUI Department of Physics, The Chinese University
More informationarxiv: v1 [cond-mat.mes-hall] 13 Feb 2012
Controlling Band Gap in Silicene Monolayer Using External Electric Field C. Kamal 1 arxiv:1202.2636v1 [cond-mat.mes-hall] 13 Feb 2012 1 Indus Synchrotrons Utilization Division, Raja Ramanna Centre for
More informationVectors in two dimensions
Vectors in two imensions Until now, we have been working in one imension only The main reason for this is to become familiar with the main physical ieas like Newton s secon law, without the aitional complication
More informationarxiv: v2 [cond-mat.mtrl-sci] 2 Mar 2013
Quasiparticle ban structures an optical properties of straine monolayer MoS an WS Hongliang Shi 1, Hui Pan 1, Yong-Wei Zhang 1, an Boris I. Yakobson 1 Institute of High Performance Computing, A*STAR, Singapore
More informationSimplified model for the energy levels of quantum rings in single layer and bilayer graphene
PHYSICAL REVIEW B 81, 51 1 Simplified model for the energy levels of quantum rings in single layer and bilayer graphene M. Zarenia, 1 J. Milton Pereira, A. Chaves, F. M. Peeters, 1,, * and G. A. Farias
More informationPhysics 505 Electricity and Magnetism Fall 2003 Prof. G. Raithel. Problem Set 3. 2 (x x ) 2 + (y y ) 2 + (z + z ) 2
Physics 505 Electricity an Magnetism Fall 003 Prof. G. Raithel Problem Set 3 Problem.7 5 Points a): Green s function: Using cartesian coorinates x = (x, y, z), it is G(x, x ) = 1 (x x ) + (y y ) + (z z
More informationPhysics 2212 GJ Quiz #4 Solutions Fall 2015
Physics 2212 GJ Quiz #4 Solutions Fall 215 I. (17 points) The magnetic fiel at point P ue to a current through the wire is 5. µt into the page. The curve portion of the wire is a semicircle of raius 2.
More informationExperiment I Electric Force
Experiment I Electric Force Twenty-five hunre years ago, the Greek philosopher Thales foun that amber, the harene sap from a tree, attracte light objects when rubbe. Only twenty-four hunre years later,
More informationEnergy band of graphene ribbons under the tensile force
Energy band of graphene ribbons under the tensile force Yong Wei Guo-Ping Tong * and Sheng Li Institute of Theoretical Physics Zhejiang Normal University Jinhua 004 Zhejiang China ccording to the tight-binding
More informationStates near Dirac points of a rectangular graphene dot in a magnetic field
States near Dirac points of a rectangular graphene dot in a magnetic field S. C. Kim, 1 P. S. Park, 1 and S.-R. Eric Yang 1,2, * 1 Physics Department, Korea University, Seoul, Korea 2 Korea Institute for
More informationAPPROXIMATE SOLUTION FOR TRANSIENT HEAT TRANSFER IN STATIC TURBULENT HE II. B. Baudouy. CEA/Saclay, DSM/DAPNIA/STCM Gif-sur-Yvette Cedex, France
APPROXIMAE SOLUION FOR RANSIEN HEA RANSFER IN SAIC URBULEN HE II B. Bauouy CEA/Saclay, DSM/DAPNIA/SCM 91191 Gif-sur-Yvette Ceex, France ABSRAC Analytical solution in one imension of the heat iffusion equation
More informationTransition Metals. d-block
Transition Metals The transition metals are -block metals. Sometimes the term is use to refer to all -block elements (all of which are metals), though more strictly it inclues those that are in the transition
More informationarxiv: v2 [cond-mat.mtrl-sci] 24 Dec 2014
Defect in Phosphorene arxiv:1411.6986v2 [cond-mat.mtrl-sci] 24 Dec 2014 Wei Hu 1, 2, 3, and Jinlong Yang 1 Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
More informationPCCP PAPER. 1 Introduction. A. Nenning,* A. K. Opitz, T. M. Huber and J. Fleig. View Article Online View Journal View Issue
PAPER View Article Online View Journal View Issue Cite this: Phys. Chem. Chem. Phys., 2014, 16, 22321 Receive 4th June 2014, Accepte 3r September 2014 DOI: 10.1039/c4cp02467b www.rsc.org/pccp 1 Introuction
More informationThe Electronic Properties of SiC Graphene-Like: Doped and No-Doped Case
Copyright 2011 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational and Theoretical Nanoscience Vol. 8, 1 5, 2011 The Electronic Properties
More informationQuantum transport through graphene nanostructures
Quantum transport through graphene nanostructures S. Rotter, F. Libisch, L. Wirtz, C. Stampfer, F. Aigner, I. Březinová, and J. Burgdörfer Institute for Theoretical Physics/E136 December 9, 2009 Graphene
More informationStrain-induced programmable half-metal and spin-gapless semiconductor in an edge-doped boron nitride nanoribbon
Strain-induced programmable half-metal and spin-gapless semiconductor in an edge-doped boron nitride nanoribbon Shuze Zhu 1, Teng Li 1 Department of Mechanical Engineering, University of Maryland, College
More informationLecture Notes: March C.D. Lin Attosecond X-ray pulses issues:
Lecture Notes: March 2003-- C.D. Lin Attosecon X-ray pulses issues: 1. Generation: Nee short pulses (less than 7 fs) to generate HHG HHG in the frequency omain HHG in the time omain Issues of attosecon
More informationwater adding dye partial mixing homogenization time
iffusion iffusion is a process of mass transport that involves the movement of one atomic species into another. It occurs by ranom atomic jumps from one position to another an takes place in the gaseous,
More informationConservation Laws. Chapter Conservation of Energy
20 Chapter 3 Conservation Laws In orer to check the physical consistency of the above set of equations governing Maxwell-Lorentz electroynamics [(2.10) an (2.12) or (1.65) an (1.68)], we examine the action
More informationTorque OBJECTIVE INTRODUCTION APPARATUS THEORY
Torque OBJECTIVE To verify the rotational an translational conitions for equilibrium. To etermine the center of ravity of a rii boy (meter stick). To apply the torque concept to the etermination of an
More informationComparative Approaches of Calculation of the Back Water Curves in a Trapezoidal Channel with Weak Slope
Proceeings of the Worl Congress on Engineering Vol WCE, July 6-8,, Lonon, U.K. Comparative Approaches of Calculation of the Back Water Curves in a Trapezoial Channel with Weak Slope Fourar Ali, Chiremsel
More informationInorganic Nanoribbons with Unpassivated Zigzag Edges: Half Metallicity and Edge Reconstruction
Nano Res. 2011, 4(2): 233 239 ISSN 1998-0124 233 DOI 10.1007/s12274-010-0074-9 CN 11-5974/O4 Research Article Inorganic Nanoribbons with Unpassivated Zigzag Edges: Half Metallicity and Edge Reconstruction
More informationElectric Potential. Slide 1 / 29. Slide 2 / 29. Slide 3 / 29. Slide 4 / 29. Slide 6 / 29. Slide 5 / 29. Work done in a Uniform Electric Field
Slie 1 / 29 Slie 2 / 29 lectric Potential Slie 3 / 29 Work one in a Uniform lectric Fiel Slie 4 / 29 Work one in a Uniform lectric Fiel point a point b The path which the particle follows through the uniform
More informationGas adsorption on MoS 2 monolayer from first-principles calculations
Gas adsorption on MoS 2 monolayer from first-principles calculations Shijun Zhao, 1,2 Jianming Xue 1,2,* and Wei Kang 2 1 State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking
More informationConductors & Capacitance
Conuctors & Capacitance PICK UP YOUR EXAM;; Average of the three classes is approximately 51. Stanar eviation is 18. It may go up (or own) by a point or two once all graing is finishe. Exam KEY is poste
More informationDefects in TiO 2 Crystals
, March 13-15, 2013, Hong Kong Defects in TiO 2 Crystals Richard Rivera, Arvids Stashans 1 Abstract-TiO 2 crystals, anatase and rutile, have been studied using Density Functional Theory (DFT) and the Generalized
More informationGas molecule adsorption in carbon nanotubes and nanotube bundles
INSTITUTE OF PHYSICS PUBLISHING Nanotechnology 13 () 195 Gas molecule adsorption in carbon nanotubes and nanotube bundles NANOTECHNOLOGY PII: S957-8()35-X Jijun Zhao 1, Alper Buldum 1, Jie Han and Jian
More informationPhysics 2212 K Quiz #2 Solutions Summer 2016
Physics 1 K Quiz # Solutions Summer 016 I. (18 points) A positron has the same mass as an electron, but has opposite charge. Consier a positron an an electron at rest, separate by a istance = 1.0 nm. What
More informationResearch Article Mass Transport Induced by Heat Current in Carbon Nanotubes
Nanomaterials Volume 2013, Article ID 386068, 4 pages http://x.oi.org/10.1155/2013/386068 Research Article Mass Transport Inuce by Heat Current in Carbon Nanotubes Wei-Rong Zhong, 1 Zhi-Cheng Xu, 1 Ming-Ming
More informationNUMERICAL METHODS FOR QUANTUM IMPURITY MODELS
NUMERICAL METHODS FOR QUANTUM IMPURITY MODELS http://www.staff.science.uu.nl/~mitch003/nrg.html March 2015 Anrew Mitchell Utrecht University Quantum impurity problems Part 1: Quantum impurity problems
More informationIn the usual geometric derivation of Bragg s Law one assumes that crystalline
Diffraction Principles In the usual geometric erivation of ragg s Law one assumes that crystalline arrays of atoms iffract X-rays just as the regularly etche lines of a grating iffract light. While this
More informationStructural, electronic and magnetic properties of vacancies in single-walled carbon nanotubes
Structural, electronic and magnetic properties of vacancies in single-walled carbon nanotubes W. Orellana and P. Fuentealba Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653,
More informationNonlinear optical conductance in a graphene pn junction in the terahertz regime
University of Wollongong Research Online Faculty of Engineering - Papers (Archive) Faculty of Engineering and Information Sciences 2010 Nonlinear optical conductance in a graphene pn junction in the terahertz
More informationElectronic Structure of ABC-stacked Multilayer Graphene and Trigonal Warping:A First Principles Calculation
Journal of Physics: Conference Series PAPER OPEN ACCESS Electronic Structure of ABC-stacked Multilayer Graphene and Trigonal Warping:A First Principles Calculation To cite this article: Celal Yelgel 2016
More informationLagrangian and Hamiltonian Mechanics
Lagrangian an Hamiltonian Mechanics.G. Simpson, Ph.. epartment of Physical Sciences an Engineering Prince George s Community College ecember 5, 007 Introuction In this course we have been stuying classical
More informationRSC Advances.
This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after
More informationElectric Charge and Electrostatic Force
PHY 049 Lecture Notes Chapter : Page 1 of 8 Electric Charge an Electrostatic Force Contemporary vision: all forces of nature can be viewe as interaction between "charges", specific funamental properties
More informationUniversity of Chinese Academy of Sciences, Beijing , People s Republic of China,
SiC 2 Siligraphene and Nanotubes: Novel Donor Materials in Excitonic Solar Cell Liu-Jiang Zhou,, Yong-Fan Zhang, Li-Ming Wu *, State Key Laboratory of Structural Chemistry, Fujian Institute of Research
More informationThe Limits of Multiplexing
Article type: Focus Article The Limits of Multiplexing Dan Shen,, D.P. Dittmer 2, an J. S. Marron 3 Keywors Multiplexing, Genomics, nanostring TM, DASL TM, Probability Abstract We were motivate by three
More informationDelocalization of boundary states in disordered topological insulators
Journal of Physics A: Mathematical an Theoretical J. Phys. A: Math. Theor. 48 (05) FT0 (pp) oi:0.088/75-83/48//ft0 Fast Track Communication Delocalization of bounary states in isorere topological insulators
More informationChapter 24: Magnetic Fields and Forces Solutions
Chapter 24: Magnetic iels an orces Solutions Questions: 4, 13, 16, 18, 31 Exercises & Problems: 3, 6, 7, 15, 21, 23, 31, 47, 60 Q24.4: Green turtles use the earth s magnetic fiel to navigate. They seem
More informationDiophantine Approximations: Examining the Farey Process and its Method on Producing Best Approximations
Diophantine Approximations: Examining the Farey Process an its Metho on Proucing Best Approximations Kelly Bowen Introuction When a person hears the phrase irrational number, one oes not think of anything
More informationRFSS: Lecture 4 Alpha Decay
RFSS: Lecture 4 Alpha Decay Reaings Nuclear an Raiochemistry: Chapter 3 Moern Nuclear Chemistry: Chapter 7 Energetics of Alpha Decay Geiger Nuttall base theory Theory of Alpha Decay Hinrance Factors Different
More informationQuantum mechanical approaches to the virial
Quantum mechanical approaches to the virial S.LeBohec Department of Physics an Astronomy, University of Utah, Salt Lae City, UT 84112, USA Date: June 30 th 2015 In this note, we approach the virial from
More informationPrep 1. Oregon State University PH 213 Spring Term Suggested finish date: Monday, April 9
Oregon State University PH 213 Spring Term 2018 Prep 1 Suggeste finish ate: Monay, April 9 The formats (type, length, scope) of these Prep problems have been purposely create to closely parallel those
More informationHydrogenated Bilayer Wurtzite SiC Nanofilms: A Two-Dimensional Bipolar Magnetic Semiconductor Material
5 Hydrogenated Bilayer Wurtzite SiC Nanofilms: A Two-Dimensional Bipolar Magnetic Semiconductor Material Long Yuan, Zhenyu Li, Jinlong Yang* Hefei National Laboratory for Physical Sciences at Microscale,
More informationSpectral Flow, the Magnus Force, and the. Josephson-Anderson Relation
Spectral Flow, the Magnus Force, an the arxiv:con-mat/9602094v1 16 Feb 1996 Josephson-Anerson Relation P. Ao Department of Theoretical Physics Umeå University, S-901 87, Umeå, SWEDEN October 18, 2018 Abstract
More informationProf. Dr. Ibraheem Nasser electric_charhe 9/22/2017 ELECTRIC CHARGE
ELECTRIC CHARGE Introuction: Orinary matter consists of atoms. Each atom consists of a nucleus, consisting of protons an neutrons, surroune by a number of electrons. In electricity, the electric charge
More informationA Simple Model for the Calculation of Plasma Impedance in Atmospheric Radio Frequency Discharges
Plasma Science an Technology, Vol.16, No.1, Oct. 214 A Simple Moel for the Calculation of Plasma Impeance in Atmospheric Raio Frequency Discharges GE Lei ( ) an ZHANG Yuantao ( ) Shanong Provincial Key
More informationEquations of lines in
Roberto s Notes on Linear Algebra Chapter 6: Lines, planes an other straight objects Section 1 Equations of lines in What ou nee to know alrea: The ot prouct. The corresponence between equations an graphs.
More informationOn the number of isolated eigenvalues of a pair of particles in a quantum wire
On the number of isolate eigenvalues of a pair of particles in a quantum wire arxiv:1812.11804v1 [math-ph] 31 Dec 2018 Joachim Kerner 1 Department of Mathematics an Computer Science FernUniversität in
More informationSurvey Sampling. 1 Design-based Inference. Kosuke Imai Department of Politics, Princeton University. February 19, 2013
Survey Sampling Kosuke Imai Department of Politics, Princeton University February 19, 2013 Survey sampling is one of the most commonly use ata collection methos for social scientists. We begin by escribing
More informationarxiv: v1 [cond-mat.mes-hall] 28 Aug 2014
Electric field control of spin-resolved edge states in graphene quantum nanorings arxiv:1408.6634v1 [cond-mat.mes-hall] 28 Aug 2014 R. Farghadan 1, and A. Saffarzadeh 2, 3 1 Department of Physics, University
More informationGoal of this chapter is to learn what is Capacitance, its role in electronic circuit, and the role of dielectrics.
PHYS 220, Engineering Physics, Chapter 24 Capacitance an Dielectrics Instructor: TeYu Chien Department of Physics an stronomy University of Wyoming Goal of this chapter is to learn what is Capacitance,
More informationSupporting Information
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2015. Supporting Information for Adv. Funct. Mater., DOI: 10.1002/adfm.201503131 Tuning the Excitonic States in MoS 2 /Graphene van
More information4. Important theorems in quantum mechanics
TFY4215 Kjemisk fysikk og kvantemekanikk - Tillegg 4 1 TILLEGG 4 4. Important theorems in quantum mechanics Before attacking three-imensional potentials in the next chapter, we shall in chapter 4 of this
More informationChapter 6: Energy-Momentum Tensors
49 Chapter 6: Energy-Momentum Tensors This chapter outlines the general theory of energy an momentum conservation in terms of energy-momentum tensors, then applies these ieas to the case of Bohm's moel.
More informationQubit channels that achieve capacity with two states
Qubit channels that achieve capacity with two states Dominic W. Berry Department of Physics, The University of Queenslan, Brisbane, Queenslan 4072, Australia Receive 22 December 2004; publishe 22 March
More informationTuning the Electronic Structure of Graphene by an Organic Molecule
Letter Subscriber access provided by NATIONAL UNIV OF SINGAPORE Tuning the Electronic Structure of Graphene by an Organic Molecule Y. H. Lu, W. Chen, Y. P. Feng, and P. M. He J. Phys. Chem. B, 2009, 113
More informationarxiv: v2 [cond-mat.stat-mech] 11 Nov 2016
Noname manuscript No. (will be inserte by the eitor) Scaling properties of the number of ranom sequential asorption iterations neee to generate saturate ranom packing arxiv:607.06668v2 [con-mat.stat-mech]
More informationChapter 2 Governing Equations
Chapter 2 Governing Equations In the present an the subsequent chapters, we shall, either irectly or inirectly, be concerne with the bounary-layer flow of an incompressible viscous flui without any involvement
More informationRaman Imaging and Electronic Properties of Graphene
Raman Imaging and Electronic Properties of Graphene F. Molitor, D. Graf, C. Stampfer, T. Ihn, and K. Ensslin Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland ensslin@phys.ethz.ch
More informationSelf-compensating incorporation of Mn in Ga 1 x Mn x As
Self-compensating incorporation of Mn in Ga 1 x Mn x As arxiv:cond-mat/0201131v1 [cond-mat.mtrl-sci] 9 Jan 2002 J. Mašek and F. Máca Institute of Physics, Academy of Sciences of the CR CZ-182 21 Praha
More information