Linear-parabolic transition in reactive diffusion – A concept of kinetic modelling

Tomán, János J.; Schmitz, Guido; Erdélyi, Zoltán

doi:10.1016/j.commatsci.2017.06.009

Cited by 5 publications

(7 citation statements)

References 21 publications

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“…Since the activation energy of the interface barriers is higher, they become more effective at lower temperatures. This finding agrees with the theoretical concepts on interface barriers [38].…”

supporting

confidence: 92%

“…Nevertheless, after sufficiently large reaction thickness, diffusion through the silicide must become the rate limiting factor, a transition towards a parabolic growth shall be observed. The relation between the layer thickness (w) and the time (t) may be described by the following formula [36][37][38]:…”

mentioning

confidence: 99%

“…First, a fast transformation of the amorphous mixed layer [18,19] and the neighboring regions takes place, leading to a Cu 3 Si layer of 10-20 nm thickness. At these low temperatures, the atomic jumps across the interface are hindered significantly [38]. This leads to an interface-controlled linear growth regime until a relatively large thickness of the silicide is reached.…”

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confidence: 99%

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The transition from linear to-parabolic growth of Cu3Si phase in Cu/a-Si system

et al. 2018

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The solid state reaction between Cu and a-Si films was investigated at 150-200°C by depth profiling with secondary neutral mass spectrometry. Intermixing was observed leading to the formation of a homogeneous Cu 3 Si layer at the interface. The growth of the crystalline silicide follows a parabolic law at 165°C and 200°C. At 150°C a transition from linear to parabolic kinetics is observed. Combining with our previous experimental results showing linear kinetics at 135°C [Acta Materialia, 61 (2013) 7173-7179], the temperature dependence of the linear and parabolic coefficients as well as the transition length can be estimated.

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confidence: 92%

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confidence: 99%

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confidence: 99%

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The transition from linear to-parabolic growth of Cu3Si phase in Cu/a-Si system

et al. 2018

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“…[13,14] Such interface-controlled transport results in a slow linear growth of the intermetallic/hydride phase in the initial stages of atomic transport (see ref. [35] ) rather than a faster parabolic growth. [10,12] To allow for such linear growth, we describe the temporal evolution of the width of the Li-rich rock salt phase by Equation (1):…”

Section: Growth Kinetics Of the Rock Salt Phase: A Linear To Parabolic Transitionmentioning

confidence: 98%

“…which is inspired by the work of Gösele and Tu, [36] and Tomán et al [35] and further derived in the supplementary information. The variable t denotes the time, cR is the maximum concentration (atomic fraction of Li on the octahedral sites) of the rock salt phase which equals 1.…”

Section: Growth Kinetics Of the Rock Salt Phase: A Linear To Paraboli...mentioning

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Slow‐Moving Phase Boundary in Li_4/3+_xTi_5/3O₄

2021

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the material was first explored by Murphy et al. in 1983, [3] but only in 1995 Ohzuku et al. demonstrated its use in lithium-ion battery application and reported a nearly constant dis-/charge voltage of 1.55 V versus Li/Li + . [4] The constant voltage for de-/intercalation is indicative of a phase transformation during lithium insertion/ removal. However, the existence of a twophase reaction at room temperature and on a macroscopic scale has been debated in the past, with reports suggesting solidsolution [5] and/or nano-domains [6] in an equilibrium condition. Nevertheless, the existence of the two phases was confirmed by direct imaging individual phases using high-resolution transmission electron microscopy (TEM). [7] A cubic unit-cell of Li 4/3 Ti 5/3 O 4 has 8 formula units with 32 oxygen atoms located at the 32e sites, 1/3rd of the lithium and all of the titanium atoms are occupying 16d sites (octahedral positions) and the remaining 8 atoms of lithium are at 8a sites (tetrahedral positions). [8] During the phase transformation to Li 7/3 Ti 5/3 O 4 upon lithium insertion, the atoms of lithium at the 8a sites shift to the neighboring 16c position (octahedral position) and the insertion of eight additional lithium atoms takes place in the remaining 16c positions thus filling up all of the octahedral sites. [4,8] This reordering and insertion of lithium atoms, is accompanied by a huge change in the electronic [8] and the optical properties. [9] However, structurally, there is a mere 0.2% change in the volume of the unit-cell (hence the term "zero-strain" phase transformation was coined). [4] The fast dis-/charge ability of LTO (practically achieved by surface modification and reducing particle size) [2] must be governed by the transport properties of lithium and the kinetics of phase propagation in the electrode, provided, the electronic conductivity is sufficient. Ganapathy et al., [16] using first-principle calculations, addressed the migration across the phase boundary and its movement during the phase transformation to explain the fast dis-/charging ability of this material. Their calculation suggests that a fast migration in and out of the phase boundary enables the phase boundary to move almost like a "liquid." This would be in contrast to some silicon-based [10][11][12] and hydrogen-based systems [13,14] where the interface between structurally different phases is known to hinder the migration of atoms. Such hindrance at the phase boundary would lead to a deviation from a normal diffusion-controlled parabolic growth to a slower interface-controlled linear growth of the silicide or hydride phase in the initial stages of atomic transport. This study is aimed at experimentally determining the migration of Lithium titanate is one of the most promising anode materials for high-power demands but such applications desire a complete understanding of the kinetics of lithium transport. The poor diffusivity of lithium in the completely lithiated and delithiated (pseudo spinel) phases challenges to explain the highr...

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Machine learning-assisted measurement of lithium transport using operando optical microscopy

Kerner,

Joshi,

Mead

et al. 2024

Acta Materialia

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Linear-parabolic transition in reactive diffusion – A concept of kinetic modelling

Cited by 5 publications

References 21 publications

The transition from linear to-parabolic growth of Cu3Si phase in Cu/a-Si system

The transition from linear to-parabolic growth of Cu3Si phase in Cu/a-Si system

Slow‐Moving Phase Boundary in Li_4/3+_xTi_5/3O₄

Machine learning-assisted measurement of lithium transport using operando optical microscopy

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Linear-parabolic transition in reactive diffusion – A concept of kinetic modelling

Cited by 5 publications

References 21 publications

The transition from linear to-parabolic growth of Cu3Si phase in Cu/a-Si system

The transition from linear to-parabolic growth of Cu3Si phase in Cu/a-Si system

Slow‐Moving Phase Boundary in Li4/3+xTi5/3O4

Machine learning-assisted measurement of lithium transport using operando optical microscopy

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Product

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Slow‐Moving Phase Boundary in Li_4/3+_xTi_5/3O₄