Deformation of graphite lattices by interstitial carbon atoms

Coulson, C. A.; Senent, S.; Herráez, Marta; Leal, Matilde; Santos, Emilio

doi:10.1016/0008-6223(66)90030-3

Cited by 48 publications

(19 citation statements)

References 15 publications

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“…Then, the calculations show the large outward expansion of adjacent layers around the interstitial atoms. [18][19][20][21][22] The calculated volume expansion by an interstitial atom is about 3.3 atomic volume, 21,22 which agrees with the above experimental one.…”

Section: Introductionsupporting

confidence: 80%

“…One is the noncovalent bond model. [17][18][19][20][21][22] The model assumes that the interstitial atom does not form covalent bonds with atoms in the adjacent graphite layers and that their interaction potential consists of a repulsive term and an attractive van der Waals term. Semiempirical calculations on this model estimate that the migration energy of single interstitial atom is 0.02Ϯ 0.01 eV.…”

Section: Introductionmentioning

confidence: 99%

“…Semiempirical calculations on this model estimate that the migration energy of single interstitial atom is 0.02Ϯ 0.01 eV. [18][19][20][21][22] Such a low migration energy suggests that single interstitial atoms can migrate at low temperatures far below room temperature and that the observed low-temperature recoveries are caused by the interaction of migrating interstitials with other interstitials and vacancies. Then, the calculations show the large outward expansion of adjacent layers around the interstitial atoms.…”

Section: Introductionmentioning

confidence: 99%

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Increase in specific heat and possible hindered rotation of interstitialC2molecules in neutron-irradiated graphite

Iwata

Watanabe

2010

Phys. Rev. B

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Irradiation-induced increase in the low-temperature specific heat has been measured in the temperature range of 1.9-43 K in graphite neutron-irradiated to 1.4ϫ 10 20 n / cm 2 ͑E Ͼ 1 MeV͒ around 333 K. The increase of the lattice specific heat is interpreted as due to the hindered rotation of interstitial C 2 molecules in the periodic potential of V͑͒ = ͑V 0 / 2͒͑1 + cos 2͒, where is the angle of rotation and V 0 is 0.040 eV. The first-excited rotational level is 0.0058 eV above the ground state and the rotational frequency is 1.39ϫ 10 12 s −1 . This result shows that C 2 molecules do not form covalent bonds with atoms in the surrounding graphite layers. It is in marked contrast with the result of recent first-principles theoretical calculations that interstitial atoms form strong covalent bonds with atoms in the graphite layers. The concentration of C 2 molecules is estimated to be f = 1.16%. The hole concentration, deduced from the electronic specific heat and the SWMcC band model, suggests that one single vacancy creates one hole and the single vacancy concentration is 2f. Since the measurement of the lattice specific heat gave the concentration of the defects directly, we could evaluate some physical properties for a unit concentration of the defects. The volume changes by a single interstitial atom, an interstitial C 2 molecule, and a single vacancy are deduced to be 2.6Ϯ 0.3, 9.3Ϯ 1.4, and −0.46Ϯ 0.07 atomic volumes, respectively. The formation energy of a Frenkel pair is estimated to be 12.6Ϯ 2.5 eV. The phonon scattering with a reciprocal relaxation time proportional to 1.5 , where is the angular frequency of phonons, is attributed to the scattering of phonons by the disklike strain around interstitial C 2 molecule clusters. A broad dip in the a-axis thermal conductivity observed below room temperature is attributed to the resonance scattering of phonons by the hindered rotation of interstitial C 2 molecules as well as by the vibration of these molecules as rigid units. The positron lifetime of 350 ps is suggested to be the lifetime of positrons trapped in an open space on the periphery of the interstitial clusters of C 2 molecules. The well-known Wigner energy is stored mainly as interstitial C 2 molecules and single vacancies.

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Section: Introductionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Increase in specific heat and possible hindered rotation of interstitialC2molecules in neutron-irradiated graphite

Iwata

Watanabe

2010

Phys. Rev. B

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“…The loss of .ir-electron resonance energy AE, when a single carbon atom is elected from a graphite layer was calculated in the papers of Coulson et al [49,50] (see also [51,52]). The quantities AE, have been termed as localization energy in the theory of chemical reactivity of conjugated hydrocarbons [53].…”

Section: Rr-electron Energy Of Localization Of Frenkel Type Monoradimentioning

confidence: 99%

“…The quantities AE, have been termed as localization energy in the theory of chemical reactivity of conjugated hydrocarbons [53]. The HMO calculations in the papers of Coulson [49,50] were carried out using alternant hydrocarbons (no Clar systems) with DZh symmetry and with numbers of Tcenters (C-atoms) N=10 to 130. The vacancy considered is in the center of the hydrocarbons.…”

Section: Rr-electron Energy Of Localization Of Frenkel Type Monoradimentioning

confidence: 99%

Structure and Energy Spectra of a Class of Polybenzenoid Clar's Hydrocarbons and 1-D Polymers

Dietz

Tyutyulkov

Karabunarliev³

et al. 2000

Polycyclic Aromatic Compounds

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The energy spectra of a class of 2-D polybenzenoid Clar's hydrocarbons with a large number N(N-104) of carbon atoms is studied theoretically. It is shown that at the asymptotic case N -D Z the energy gap (EG) A E (N-m) is different from zero, i.e., the a-systems should possess semiconductor properties. The results for the EG A E ( N -w)#O of the hydrocarbons are in qualitative agreement with the results for the EG calculated for a class of 1-D ladder polymers having the same edge structure as the hydrocarbons. With increasing the number ( M ) of the a-centers of the elementary unit of the polymers, the band gap AE(M+ m) approaches also to a value different from zero. The quantitative results on the equilibria geometries of the hydrocarbons and the polymers correspond to Clar's qualitative characterization of benzenoids composed of disjoint "n-sextets". The energetics of the hydrocarbons with different types of defects and the corresponding Tamm and Frenkel states were also investigated.

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Distortion of the graphite lattice by a vacancy. A two-dimensional model

Nicholson

Bacon

1975

Phys. Stat. Sol. (a)

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The method of lattice statics has been used to calculate the atomic displacements around a vacancy and the vacancy‐vacancy interaction energy in graphite. This was achieved by simulating the vacancy by external forces acting radially on the nearest neighbour atoms, and calculating the lattice Green's function for a two‐dimensional model of the graphite structure. Numerical values for the Green's function are presented, and the leading elastic and lattice terms in its asymptotic expansion are derived. Using a value of the external forces obtained from a molecular‐orbital calculation, it is shown that the distortion of the graphite layer by a vacancy is not small, and the resulting relaxation energy is −3.3 eV. The formation area of a vacancy is −0.14 atomic areas, and the mechanical binding energy of a divacancy is 2.0 eV.

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Deformation of graphite lattices by interstitial carbon atoms

Cited by 48 publications

References 15 publications

Increase in specific heat and possible hindered rotation of interstitialC2molecules in neutron-irradiated graphite

Increase in specific heat and possible hindered rotation of interstitialC2molecules in neutron-irradiated graphite

Structure and Energy Spectra of a Class of Polybenzenoid Clar's Hydrocarbons and 1-D Polymers

Distortion of the graphite lattice by a vacancy. A two-dimensional model

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