Calculated pre-exponential factors and energetics for adatom hopping on terraces and steps of Cu(100) and Cu(110)

Yıldırım, Handan; Kara, Abdelkader; Durukanoğlu, Sondan; Rahman, Talat S.

doi:10.1016/j.susc.2005.10.055

Cited by 45 publications

(34 citation statements)

References 54 publications

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“…Some examples of thermal quantities that are modified at the nanoscale are lattice specific heat (C v ) [5][6][7][8] , vibrational entropy (S vib ) 2, 4, 9, 10 , atomic mean square displacement (<x 2 >) and Debye temperature (Θ D ) [11][12][13][14][15] , thermal expansion 16,17 , melting temperature 18 , structural phase transitions involving soft phonon modes 28,29 , and thermally activated phenomena described by the pre-exponential factor 30 in Arrhenius-type processes on the surface of NPs (e.g. diffusion and surface chemical reactions 31 ).…”

Section: Introductionmentioning

confidence: 99%

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

et al. 2012

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We have gained insight into the internal degree of atomic disorder in isolated sizeselected Fe nanoparticles (NPs) (~2 -6 nm in size) supported on SiO 2 /Si(111) and Al 2 O 3 (0001) from precise measurements of the low-energy (low-E) part of the phonon density of states [PDOS, g(E)] via 57 Fe nuclear resonant inelastic X-ray scattering (NRIXS), combined with transmission electron microscopy (TEM) measurements. An intriguing size-dependent trend was observed, namely, an increase of the low-E excess density of phonon states (as compared to the PDOS of bulk bcc Fe) with increasing NP size. This is unexpected, since usually the enhancement of the density of low-E phonon modes is attributed to low-coordinated atoms at the NP surface, whose relative content increases with decreasing NP size due to the increase in the surface-to-volume ratio. OurNPs are covered by a Ti coating layer, which essentially restores the local neighbourhood of surface Fe surface atoms towards bulk-like coordination, reducing the surface effect.Our data can be qualitatively explained by the existence of low-coordinated Fe atoms 2 located at grain boundaries or other defects with structural disorder in the interior of the large NPs (~3 -6 nm), while our small NPs (~2 nm) are single-grain and, therefore, characterized by a higher degree of structural order. This conclusion is corroborated by the observation of Debye behaviour at low energy [g(E) ~ E n with n ~ 2] for the small NPs, but non-Debye behaviour (with n ~ 1.4) for the large NPs. The PDOS was used to determine thermodynamic properties of the Fe NPs. Finally, our results demonstrate that, in combination with TEM, NRIXS is a suitable technique to investigate atomic disorder/defects in NPs. We anticipate that our findings are universal for similar NPs with bcc structure.Keywords: Fe, nanoparticle, nuclear resonant inelastic x-ray scattering, atomic force microscopy, transmission electron microscopy, x-ray photoelectron spectroscopy, phonon density of states.

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Section: Introductionmentioning

confidence: 99%

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

et al. 2012

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“…For hopping on the (001), (110), and (111) of Cu, Ag, and Ni, the prefactors are found to be in the range 10 −1 –10 −4 cm 2 s −1 , in line with the value of 10 −3 cm 2 s −1 that is generally used. Yildirim et al demonstrated that for Cu adatom on Cu(110) the prefactor of diffusion is found to be 6.39 × 10 −4 cm 2 s −1 .…”

Section: Resultsmentioning

confidence: 99%

Long jumps contribution to the adatom diffusion process near the step edge: The case of Ag/Cu(110)

Sbiaai

Boughaleb

Kara

et al. 2013

Phys. Status Solidi B

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In this work, the diffusion of a single Ag adatom on a low‐index Cu surface (110) in the presence of a step edge is studied using the embedded‐atom method (EAM). Molecular static simulation is carried out in order to calculate the activation energy of different diffusion processes. Our findings are in a good agreement with results existing in the literature indicating that adatom diffusion via jump process is more favored than the other mechanisms. The activation energy corresponding to diffusing via hopping is found to be 0.25 eV (at 0 K). On the other hand, the activation barrier calculated by molecular dynamics (MD) simulation for a large range of temperature (310–500 K) is found to be around 0.25 eV for both upper and lower position leading to a good agreement between static and dynamic calculations. The prefactor for Ag adatom self‐diffusion via hopping on Cu(110) surface near the step edge is examined. The results show that the prefactors are 2.7 and 3.6 × 104 cm2 s−1 for the upper and lower position, respectively. This is in line with the value of 10−3 cm2 s−1 that is generally adopted. We also found that long jumps occur frequently in this system and their contribution cannot be neglected.

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“…In all our calculations we use the same pre-exponential factor of 10 12 s −1 for all diffusion processes for our KMC simulations, this has been proven to be a good assumption for the systems like the present one 45,46 .…”

Section: Simulation Detailsmentioning

confidence: 99%

Self-learning kinetic Monte Carlo simulations of self-diffusion of small Ag islands on the Ag(111) surface

Shah

Nandipati

Karim

et al. 2015

J. Phys.: Condens. Matter

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The self-diffusion of two-dimensional small Ag islands (containing up to 10 atoms) on Ag(111) surface has been studied using and self-learning kinetic Monte Carlo [J. Phys.: Condens. Matter 24, 354004 (2012)] simulations. A variety of concerted, multi-atom and single-atom processes were automatically revealed in these simulations. The size dependence of the diffusion coefficients, effective energy barriers as well as key diffusion processes responsible for island diffusion are reported. In addition, we have compared activation barriers for concerted diffusion processes with those obtained from Density Functional Theory (DFT) calculations.

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Calculated pre-exponential factors and energetics for adatom hopping on terraces and steps of Cu(100) and Cu(110)

Cited by 45 publications

References 54 publications

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

Long jumps contribution to the adatom diffusion process near the step edge: The case of Ag/Cu(110)

Self-learning kinetic Monte Carlo simulations of self-diffusion of small Ag islands on the Ag(111) surface

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