Kinetics of interlayer transport prior to nucleation

Harris, S.

doi:10.1103/physrevb.52.16793

Cited by 13 publications

(17 citation statements)

References 5 publications

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“…This value of ␤ is somewhat higher than was originally reported by Harris et al, 14 0.24, which had made Cross-Fisher scaling 10 appear to hold. However, this report was revised with more accurate measurements to be 0.36 by neutrons 13 and 0.33 by x rays, 15 both consistent with the present results, which we will show leads to a significant deviation from the Cross-Fisher scaling rule. The T c is also obtained for this sample from the fit in Fig.…”

supporting

confidence: 86%

Temperature dependence of the spin-Peierls energy gap and anomalous line shapes in CuGeO3

Martin

Shirane²,

Fujii³

et al. 1996

Phys. Rev. B

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Neutron-scattering measurements on a large single crystal of CuGeO 3 have been used to determine the temperature dependence of the spin-Peierls energy gap. While the power-law behavior of the intensity of structural superlattice peaks is well fit by I(T)ϰ(T c ϪT) 2␤ with an exponent of ␤ϭ0.33, the exponent for the temperature dependence of the energy gap is significantly smaller than expected for conventional spin-Peierls materials. Usual scaling relations relate the energy gap to the superlattice reflection intensity as ⌬(T)ϰI a with aϭ1/3; the present results suggest an exponent of aϷ1/6 for CuGeO 3 . An additional scattering cross section is observed in constant-q and constant-E scans creating a long tail extending to higher energies relating to a proposed scattering continuum. ͓S0163-1829͑96͒50422-4͔

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confidence: 86%

Temperature dependence of the spin-Peierls energy gap and anomalous line shapes in CuGeO3

Martin

Shirane²,

Fujii³

et al. 1996

Phys. Rev. B

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“…where the nucleation rate (21) has been expressed in terms of the coverage using (37). Solving (50) and setting the corresponding coverage to unity yields…”

Section: Deterministic Nucleation and Other Modificationsmentioning

confidence: 99%

Island nucleation in the presence of step-edge barriers: Theory and applications

2000

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We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier ∆ES for descending atoms. The theory is based on the concept of the residence time of an adatom on the island, and yields an expression for the nucleation rate which becomes exact in the limit of strong step edge barriers. This expression differs qualitatively and quantitatively from that obtained using the conventional rate equation approach to nucleation [J. Tersoff et al., Phys. Rev. Lett. 72, 266 (1994)]. We argue that rate equation theory fails because nucleation is dominated by the rare instances when two atoms are present on the island simultaneously. The theory is applied to two distinct problems: The onset of second layer nucleation in submonolayer growth, and the distribution of the sizes of top terraces of multilayer mounds under conditions of strong step edge barriers. Application to homoepitaxial growth on Pt(111) yields the estimate ∆ES ≥ 0.33 eV for the additional energy barrier at CO-decorated steps.

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“…In order to see how the preferred paths for second layer nucleation change with the step crossing probability α, we define the integrated current j n (t) up to t c by J n ≡ tc 0 dt j n (t) = tc 0 dt p n,1 (t)ω n (R(t)) , n ≥ i+1 . (47) This quantity equals the fraction of covered islands at time t c for which the stable nucleus originates from a state possessing exactly n adatoms. Figure 17 shows J n as a function of n for fixed Γ = 10 8 and various α.…”

Section: B Negligible Lifetimes Of Unstable Clustersmentioning

confidence: 99%

Nucleation on top of islands in epitaxial growth

2000

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We develop a theory for nucleation on top of islands in epitaxial growth based on the derivation of lifetimes and rates governing individual microscopic processes. These processes are strongly affected by the additional step edge barrier E_S for descending atoms. If the dissociation times of unstable clusters can be neglected, the theory predicts that for small critical nuclei of size i<=2 the nucleation is governed by fluctuations, during which by chance i+1 atoms are present on the island. For large critical nuclei i>=3 by contrast, the nucleation process can be described in a mean-field type manner, which for large E_S corresponds to the approach developed by Tersoff et al. [Phys. Rev. Lett. 72, 266 (1994)]. In both the fluctuation-dominated and the mean-field case, various scaling regimes are identified, where the typical island size at the onset of nucleation shows a power law in dependence on the adatom diffusion rates, the incoming atom flux, and the step edge crossing probability exp(-E_S/k_B T). For the case where the dissociation rates of metastable clusters enter the problem as additional parameters, we set up a semi-analytical approach based on novel rate equations, which can easily be solved numerically. The results obtained from the theory are in good agreement with Monte Carlo data. Implications for various applications are pointed out.Comment: 24 pages, 10 figure

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Kinetics of interlayer transport prior to nucleation

Cited by 13 publications

References 5 publications

Temperature dependence of the spin-Peierls energy gap and anomalous line shapes in CuGeO3

Temperature dependence of the spin-Peierls energy gap and anomalous line shapes in CuGeO3

Island nucleation in the presence of step-edge barriers: Theory and applications

Nucleation on top of islands in epitaxial growth

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