TY  - CONF
AU  - Hadžijojić, Milivoje
AU  - Ćosić, Marko
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12420
AB  - We present the results of our theoretical study of 5 keV proton transmission through two-dimensional crystals. Proton trajectories were obtained by numerical solving Newton's equations of motion. Obtained trajectories are subsequently used to construct the proton angular yield. Singularities of a function that maps initial proton positions to the set of scattering angles form lines in the scattering angle plane along which the angular yield is significantly larger. These lines are named rainbow lines in analogy with optical rainbow scattering. It is shown that the rainbow pattern determines the shape of the angular distribution of transmitted protons. Change in the interaction potential, due to reorientation of the crystal relative to the direction of the incident beam or by varying model parameters, induces nontrivial transformation of the rainbow pattern. We have conducted a thorough study of these transfigurations, which led to the development of the morphological analysis of rainbow scattering. The developed analysis technique is based on the study of shape, not the exact particle count or position of the rainbow line, which makes it insensitive to noise. An established morphological method was used for studying graphene thermal motion. The Debye theory and Molecular Dynamics were used to calculate the covariance matrix of atomic thermal vibrations. It was shown that the outer part of the rainbow pattern can be modeled by ellipses, whose parameters are dependent on the structure of the covariance matrix. A numerical procedure was developed to extract the covariance matrix from the corresponding outer rainbow lines. Furthermore, it was shown that the outer rainbows' size could be used to characterize the atomic composition of two-dimensional crystals. We have investigated the influence of a crystal structure on the rainbow pattern by studying the transmission of protons through graphene containing different point defects. It was shown that each defect type produces a distinctive rainbow pattern, which then could be used to determine the unknown densities of the different defect types present in the same sample.
C3  - SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts
T1  - Analysis of Two-Dimensional Crystals Via Rainbow Scattering
SP  - 60
EP  - 60
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12420
ER  - 

@conference{
author = "Hadžijojić, Milivoje and Ćosić, Marko",
year = "2023",
abstract = "We present the results of our theoretical study of 5 keV proton transmission through two-dimensional crystals. Proton trajectories were obtained by numerical solving Newton's equations of motion. Obtained trajectories are subsequently used to construct the proton angular yield. Singularities of a function that maps initial proton positions to the set of scattering angles form lines in the scattering angle plane along which the angular yield is significantly larger. These lines are named rainbow lines in analogy with optical rainbow scattering. It is shown that the rainbow pattern determines the shape of the angular distribution of transmitted protons. Change in the interaction potential, due to reorientation of the crystal relative to the direction of the incident beam or by varying model parameters, induces nontrivial transformation of the rainbow pattern. We have conducted a thorough study of these transfigurations, which led to the development of the morphological analysis of rainbow scattering. The developed analysis technique is based on the study of shape, not the exact particle count or position of the rainbow line, which makes it insensitive to noise. An established morphological method was used for studying graphene thermal motion. The Debye theory and Molecular Dynamics were used to calculate the covariance matrix of atomic thermal vibrations. It was shown that the outer part of the rainbow pattern can be modeled by ellipses, whose parameters are dependent on the structure of the covariance matrix. A numerical procedure was developed to extract the covariance matrix from the corresponding outer rainbow lines. Furthermore, it was shown that the outer rainbows' size could be used to characterize the atomic composition of two-dimensional crystals. We have investigated the influence of a crystal structure on the rainbow pattern by studying the transmission of protons through graphene containing different point defects. It was shown that each defect type produces a distinctive rainbow pattern, which then could be used to determine the unknown densities of the different defect types present in the same sample.",
journal = "SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts",
title = "Analysis of Two-Dimensional Crystals Via Rainbow Scattering",
pages = "60-60",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12420"
}

Hadžijojić, M.,& Ćosić, M.. (2023). Analysis of Two-Dimensional Crystals Via Rainbow Scattering. in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts, 60-60.
https://hdl.handle.net/21.15107/rcub_vinar_12420

Hadžijojić M, Ćosić M. Analysis of Two-Dimensional Crystals Via Rainbow Scattering. in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts. 2023;:60-60.
https://hdl.handle.net/21.15107/rcub_vinar_12420 .

Hadžijojić, Milivoje, Ćosić, Marko, "Analysis of Two-Dimensional Crystals Via Rainbow Scattering" in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts (2023):60-60,
https://hdl.handle.net/21.15107/rcub_vinar_12420 .

TY  - CONF
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12349
AB  - The main goal of our analysis is to show that the shape of the angular distributions can be used to study 2D materials. For this kind of systems, angular distributions contain lines along which large yield dominantly determine their shape. We focus on the relationship between the reduced interaction potential and the shape of the rainbow pattern. Metamorphoses of the rainbow pattern in the impact parameter plane were investigated and attributed to the bifurcations of the critical points of the rainbow line curvature. It will be shown that the impact parameter rainbow vertices are connected with the corresponding cusps of rainbows in the scattering angle plane, and their bifurcations will be analyzed in detail.
C3  - ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings
T1  - The Morphological analysis of the rainbow scattering effect in proton transmission through graphene
SP  - 115
EP  - 120
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12349
ER  - 

@conference{
author = "Ćosić, Marko and Hadžijojić, Milivoje",
year = "2023",
abstract = "The main goal of our analysis is to show that the shape of the angular distributions can be used to study 2D materials. For this kind of systems, angular distributions contain lines along which large yield dominantly determine their shape. We focus on the relationship between the reduced interaction potential and the shape of the rainbow pattern. Metamorphoses of the rainbow pattern in the impact parameter plane were investigated and attributed to the bifurcations of the critical points of the rainbow line curvature. It will be shown that the impact parameter rainbow vertices are connected with the corresponding cusps of rainbows in the scattering angle plane, and their bifurcations will be analyzed in detail.",
journal = "ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings",
title = "The Morphological analysis of the rainbow scattering effect in proton transmission through graphene",
pages = "115-120",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12349"
}

Ćosić, M.,& Hadžijojić, M.. (2023). The Morphological analysis of the rainbow scattering effect in proton transmission through graphene. in ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings, 115-120.
https://hdl.handle.net/21.15107/rcub_vinar_12349

Ćosić M, Hadžijojić M. The Morphological analysis of the rainbow scattering effect in proton transmission through graphene. in ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings. 2023;:115-120.
https://hdl.handle.net/21.15107/rcub_vinar_12349 .

Ćosić, Marko, Hadžijojić, Milivoje, "The Morphological analysis of the rainbow scattering effect in proton transmission through graphene" in ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings (2023):115-120,
https://hdl.handle.net/21.15107/rcub_vinar_12349 .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10615
AB  - We have investigated long-time dynamics of the transverse resonant states occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. This was done by a detailed analysis of quantum carpet, generated by the interference of the resonant states. We found that structure of the carpet depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Close to every fractional revival additional repeated and inverted reconstructed patterns were observed which do not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately, and conclude that dynamics, in this case, is quasi-periodic. This peculiar behavior was traced back to the level of coordination between fluctuations of resonances amplitude and phase functions.
T2  - Chaos, Solitons and Fractals
T1  - Nonlinear dynamics of positron resonances in a carbon nanotube
VL  - 166
SP  - 112898
DO  - 10.1016/j.chaos.2022.112898
ER  - 

@article{
author = "Ćosić, Marko and Hadžijojić, Milivoje",
year = "2023",
abstract = "We have investigated long-time dynamics of the transverse resonant states occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. This was done by a detailed analysis of quantum carpet, generated by the interference of the resonant states. We found that structure of the carpet depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Close to every fractional revival additional repeated and inverted reconstructed patterns were observed which do not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately, and conclude that dynamics, in this case, is quasi-periodic. This peculiar behavior was traced back to the level of coordination between fluctuations of resonances amplitude and phase functions.",
journal = "Chaos, Solitons and Fractals",
title = "Nonlinear dynamics of positron resonances in a carbon nanotube",
volume = "166",
pages = "112898",
doi = "10.1016/j.chaos.2022.112898"
}

Ćosić, M.,& Hadžijojić, M.. (2023). Nonlinear dynamics of positron resonances in a carbon nanotube. in Chaos, Solitons and Fractals, 166, 112898.
https://doi.org/10.1016/j.chaos.2022.112898

Ćosić M, Hadžijojić M. Nonlinear dynamics of positron resonances in a carbon nanotube. in Chaos, Solitons and Fractals. 2023;166:112898.
doi:10.1016/j.chaos.2022.112898 .

Ćosić, Marko, Hadžijojić, Milivoje, "Nonlinear dynamics of positron resonances in a carbon nanotube" in Chaos, Solitons and Fractals, 166 (2023):112898,
https://doi.org/10.1016/j.chaos.2022.112898 . .

TY  - JOUR
AU  - Hadžijojić, Milivoje
AU  - Ćosić, Marko
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11092
AB  - We have studied the transmission of 5 keV protons through graphene. Proton dynamics was modeled by classical theory. Proton trajectories define a mapping of the set of initial proton positions to the set of scattering angles. Singularities of the Jacobian associated with the introduced mapping form curves known as the rainbow lines. The differential cross section is infinite along the rainbow lines, making the proton count significantly larger along the rainbow pattern. Hence, rainbows dominantly determine the shape and size of the angular distribution of transmitted protons. It was found that reorientation of the graphene with respect to the incident beam direction and deformation of the graphene crystal lattice induce the transformation of the proton rainbow pattern. We thoroughly studied the morphological properties of the proton rainbow pattern. It was shown that angular distribution and the corresponding rainbow pattern could be used to determine the covariance matrix of atomic thermal displacements and to characterize point defects present in graphene. Graphical abstract: [Figure not available: see fulltext.] © 2023, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.
T2  - European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics
T1  - Study of graphene by proton rainbow scattering
VL  - 77
IS  - 5
SP  - 86
DO  - 10.1140/epjd/s10053-023-00664-y
ER  - 

@article{
author = "Hadžijojić, Milivoje and Ćosić, Marko",
year = "2023",
abstract = "We have studied the transmission of 5 keV protons through graphene. Proton dynamics was modeled by classical theory. Proton trajectories define a mapping of the set of initial proton positions to the set of scattering angles. Singularities of the Jacobian associated with the introduced mapping form curves known as the rainbow lines. The differential cross section is infinite along the rainbow lines, making the proton count significantly larger along the rainbow pattern. Hence, rainbows dominantly determine the shape and size of the angular distribution of transmitted protons. It was found that reorientation of the graphene with respect to the incident beam direction and deformation of the graphene crystal lattice induce the transformation of the proton rainbow pattern. We thoroughly studied the morphological properties of the proton rainbow pattern. It was shown that angular distribution and the corresponding rainbow pattern could be used to determine the covariance matrix of atomic thermal displacements and to characterize point defects present in graphene. Graphical abstract: [Figure not available: see fulltext.] © 2023, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.",
journal = "European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics",
title = "Study of graphene by proton rainbow scattering",
volume = "77",
number = "5",
pages = "86",
doi = "10.1140/epjd/s10053-023-00664-y"
}

Hadžijojić, M.,& Ćosić, M.. (2023). Study of graphene by proton rainbow scattering. in European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics, 77(5), 86.
https://doi.org/10.1140/epjd/s10053-023-00664-y

Hadžijojić M, Ćosić M. Study of graphene by proton rainbow scattering. in European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics. 2023;77(5):86.
doi:10.1140/epjd/s10053-023-00664-y .

Hadžijojić, Milivoje, Ćosić, Marko, "Study of graphene by proton rainbow scattering" in European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics, 77, no. 5 (2023):86,
https://doi.org/10.1140/epjd/s10053-023-00664-y . .

TY  - CONF
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12285
AB  - We have investigated long-time dynamics of the quantum carpets occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. We found that the carpet structure depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Additional inverted revived patterns were observed close to fractional revival, which does not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately and conclude that dynamics, in this case, is quasi-periodic.
C3  - 9th International Conference "Charged & Neutral Particles Channeling Phenomena"
T1  - The structure of quantum carpets in a carbon nanotube
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12285
ER  - 

@conference{
author = "Ćosić, Marko and Hadžijojić, Milivoje",
year = "2023",
abstract = "We have investigated long-time dynamics of the quantum carpets occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. We found that the carpet structure depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Additional inverted revived patterns were observed close to fractional revival, which does not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately and conclude that dynamics, in this case, is quasi-periodic.",
journal = "9th International Conference "Charged & Neutral Particles Channeling Phenomena"",
title = "The structure of quantum carpets in a carbon nanotube",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12285"
}

Ćosić, M.,& Hadžijojić, M.. (2023). The structure of quantum carpets in a carbon nanotube. in 9th International Conference "Charged & Neutral Particles Channeling Phenomena".
https://hdl.handle.net/21.15107/rcub_vinar_12285

Ćosić M, Hadžijojić M. The structure of quantum carpets in a carbon nanotube. in 9th International Conference "Charged & Neutral Particles Channeling Phenomena". 2023;.
https://hdl.handle.net/21.15107/rcub_vinar_12285 .

Ćosić, Marko, Hadžijojić, Milivoje, "The structure of quantum carpets in a carbon nanotube" in 9th International Conference "Charged & Neutral Particles Channeling Phenomena" (2023),
https://hdl.handle.net/21.15107/rcub_vinar_12285 .

TY  - JOUR
AU  - Hadžijojić, Milivoje
AU  - Ćosić, Marko
AU  - Rymzhanov, Ruslan
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9968
AB  - We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.
T2  - Journal of Physical Chemistry C
T1  - Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene
VL  - 125
IS  - 38
SP  - 21030
EP  - 21043
DO  - 10.1021/acs.jpcc.1c05971
ER  - 

@article{
author = "Hadžijojić, Milivoje and Ćosić, Marko and Rymzhanov, Ruslan",
year = "2021",
abstract = "We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.",
journal = "Journal of Physical Chemistry C",
title = "Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene",
volume = "125",
number = "38",
pages = "21030-21043",
doi = "10.1021/acs.jpcc.1c05971"
}

Hadžijojić, M., Ćosić, M.,& Rymzhanov, R.. (2021). Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene. in Journal of Physical Chemistry C, 125(38), 21030-21043.
https://doi.org/10.1021/acs.jpcc.1c05971

Hadžijojić M, Ćosić M, Rymzhanov R. Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene. in Journal of Physical Chemistry C. 2021;125(38):21030-21043.
doi:10.1021/acs.jpcc.1c05971 .

Hadžijojić, Milivoje, Ćosić, Marko, Rymzhanov, Ruslan, "Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene" in Journal of Physical Chemistry C, 125, no. 38 (2021):21030-21043,
https://doi.org/10.1021/acs.jpcc.1c05971 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
AU  - Rymzhanov, Ruslan
AU  - Petrović, Srđan M.
AU  - Bellucci, Stefano
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8022
AB  - The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.
T2  - Carbon
T1  - Investigation of the graphene thermal motion by rainbow scattering
VL  - 145
SP  - 161
EP  - 174
DO  - 10.1016/j.carbon.2019.01.020
ER  - 

@article{
author = "Ćosić, Marko and Hadžijojić, Milivoje and Rymzhanov, Ruslan and Petrović, Srđan M. and Bellucci, Stefano",
year = "2019",
abstract = "The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.",
journal = "Carbon",
title = "Investigation of the graphene thermal motion by rainbow scattering",
volume = "145",
pages = "161-174",
doi = "10.1016/j.carbon.2019.01.020"
}

Ćosić, M., Hadžijojić, M., Rymzhanov, R., Petrović, S. M.,& Bellucci, S.. (2019). Investigation of the graphene thermal motion by rainbow scattering. in Carbon, 145, 161-174.
https://doi.org/10.1016/j.carbon.2019.01.020

Ćosić M, Hadžijojić M, Rymzhanov R, Petrović SM, Bellucci S. Investigation of the graphene thermal motion by rainbow scattering. in Carbon. 2019;145:161-174.
doi:10.1016/j.carbon.2019.01.020 .

Ćosić, Marko, Hadžijojić, Milivoje, Rymzhanov, Ruslan, Petrović, Srđan M., Bellucci, Stefano, "Investigation of the graphene thermal motion by rainbow scattering" in Carbon, 145 (2019):161-174,
https://doi.org/10.1016/j.carbon.2019.01.020 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
AU  - Rymzhanov, Ruslan
AU  - Petrović, Srđan M.
AU  - Bellucci, Stefano
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8031
AB  - The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.
T2  - Carbon
T1  - Investigation of the graphene thermal motion by rainbow scattering
VL  - 145
SP  - 161
EP  - 174
DO  - 10.1016/j.carbon.2019.01.020
ER  - 

@article{
author = "Ćosić, Marko and Hadžijojić, Milivoje and Rymzhanov, Ruslan and Petrović, Srđan M. and Bellucci, Stefano",
year = "2019",
abstract = "The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.",
journal = "Carbon",
title = "Investigation of the graphene thermal motion by rainbow scattering",
volume = "145",
pages = "161-174",
doi = "10.1016/j.carbon.2019.01.020"
}

Ćosić, M., Hadžijojić, M., Rymzhanov, R., Petrović, S. M.,& Bellucci, S.. (2019). Investigation of the graphene thermal motion by rainbow scattering. in Carbon, 145, 161-174.
https://doi.org/10.1016/j.carbon.2019.01.020

Ćosić M, Hadžijojić M, Rymzhanov R, Petrović SM, Bellucci S. Investigation of the graphene thermal motion by rainbow scattering. in Carbon. 2019;145:161-174.
doi:10.1016/j.carbon.2019.01.020 .

Ćosić, Marko, Hadžijojić, Milivoje, Rymzhanov, Ruslan, Petrović, Srđan M., Bellucci, Stefano, "Investigation of the graphene thermal motion by rainbow scattering" in Carbon, 145 (2019):161-174,
https://doi.org/10.1016/j.carbon.2019.01.020 . .