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 . .