Pith. sign in

REVIEW 4 major objections 5 minor 44 references

Accelerated recrystallization of nanocrystalline films as a manifestation of the inner size effect of the diffusion coefficient

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that recrystallization in 100 nm copper and silver films is driven by grain-boundary diffusion that runs 6 to 9 orders of magnitude faster than bulk self-diffusion, an 'inner size effect' caused by excess grain-boundary…

desk verdict Credible microscopy of accelerated recrystallization in 100 nm Cu and Ag films, but the headline 6–9 orders diffusion-enhancement claim rests on a rate constant that the paper itself says is not an atomic diffusion coefficient. read the letter →

arxiv 2502.01422 v1 pith:3FQJ6MXS submitted 2025-02-03 cond-mat.mtrl-sci physics.bio-ph

S. Petrushenko , S. Dukarov , M. Fijalkowski , V. Sukhov This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.bio-ph PACS 68.55.-a66.30.-h61.72.Mm
keywords nanocrystallinefilmsrecrystallizationgrain-boundarydiffusioninnersizeeffectcoppersilverbimodalgraindistributionself-annealing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports that 100-nm-thick polycrystalline copper and silver films recrystallize far faster than bulk diffusion would allow. By tracking the shift of the most probable crystallite size during short anneals at 250°C, the authors estimate a grain-boundary diffusion coefficient of about $10^{-17}$–$10^{-18}$ m$^2$/s, which is 6 to 9 orders of magnitude above the bulk self-diffusion coefficients of silver and copper. They interpret this acceleration as an 'inner size effect': internal grain boundaries carry excess free energy that intensifies diffusion, in analogy to how free surfaces drive size effects in nanoparticles. Because the film thickness is large enough to suppress ordinary surface-related size effects, the authors argue the enhancement must come from the internal nanocrystalline structure. If correct, the result means macroscopic polycrystalline films can behave like nanomaterials kinetically, with recrystallization finishing in minutes or seconds at modest temperatures.

What carries the argument

The paper's central object is the 'inner size effect': the idea that grain boundaries and other internal interfaces, because they carry excess free energy, play for a bulk polycrystal the role that free surfaces play for a nanoparticle, intensifying diffusion and accelerating recrystallization. The quantitative workhorse is the conditional grain-boundary diffusion coefficient $D_r$, estimated from the relation $D_r = x^2/(2t)$, where $x$ is the shift of the most probable crystallite radius (the low-size histogram peak) and $t$ is the annealing time. This coefficient carries the argument: comparing $D_r$ with tabulated bulk self-diffusion coefficients is what yields the claimed 6–9 orders-of-magnitude acceleration. A second structural element is the two-population model for Cu films, where grains in the main film and grains confined to mushroom-shaped protrusions evolve independently, which is used to explain why the bimodal size distribution persists instead of collapsing into a single lognormal peak.

What would settle it

Prepare Cu and Ag films with the same columnar grain structure at 50, 100, and 200 nm thickness and anneal them identically. If the inferred $D_r$ changes across thicknesses, then surface or interface diffusion contributes and the observed acceleration cannot be assigned purely to inner grain-boundary effects; if $D_r$ stays constant, the internal-boundary interpretation is supported.

Watch

Extended reading notes

Core claim

The central claim is that short-term annealing of 100 nm nanocrystalline Cu and Ag films produces accelerated recrystallization governed by a conditional grain-boundary diffusion coefficient $D_r$ of about $10^{-17}$–$10^{-18}$ m$^2$/s, determined from the displacement of the most probable crystallite radius using $D_r = x^2/(2t)$. This is about 6 orders of magnitude above bulk self-diffusion in silver and 9 orders above bulk self-diffusion in copper. The authors observe that as-deposited Cu films have a bimodal crystallite size distribution with peaks near 15 and 35 nm that persists during annealing, which they attribute to two independent grain populations: normal grains with full access to surrounding material and grains inside 'mushroom-shaped' surface elements with limited substance supply. Ag films contain micron-sized, highly defective grains formed by self-annealing as well as a nanoscale fraction that grows from about 25 nm to 50 nm after annealing at 250°C. Because the films are 100 nm thick, the authors exclude conventional external size effects and assign the acceleration to the excess energy of internal grain boundaries, i.e., an inner size effect that lowers the activation barrier for diffusion. They also note the estimate is a lower bound, since resistance measurements indicate the main recrystallization stage finishes in tens of seconds, well within the 2–5 minute anneal.

Load-bearing premise

The interpretation rests on the assumption that a 100 nm film is thick enough for ordinary external size effects to be negligible, so the observed acceleration can be attributed entirely to internal grain-boundary energy.

Editorial extensions

If this is right

  • Short anneals of minutes at 250°C are enough to coarsen grains in 100 nm Cu and Ag films, so recrystallization engineering of such films can rely on grain-boundary transport rather than bulk diffusion.
  • The inferred $D_r$ of $10^{-17}$–$10^{-18}$ m$^2$/s is 6 (Ag) and 9 (Cu) orders of magnitude above bulk self-diffusion, and about a factor of 10 and 1000–10000 above the conditional coefficient expected from classical grain-boundary diffusion.
  • Because the first intensive recrystallization stage is complete within about two minutes, and resistance changes within tens of seconds, the reported diffusion coefficients are lower bounds on the acceleration, not upper bounds.
  • The persistence of bimodal grain size distributions in Cu films during annealing shows that classical primary recrystallization models, which predict a single lognormal peak, are insufficient for films containing morphological elements with restricted mass supply.
  • Films thick enough to be considered macroscopic can still exhibit nanoscale-like diffusion kinetics when their internal boundary energy is high, implying that inner size effects are a general route to enhanced mass transport in bulk nanocrystalline metals.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the inner size effect is generic, similar acceleration should appear in other bulk nanocrystalline metals and in multilayers, with the magnitude scaling with grain-boundary energy density; comparing metals with different boundary energies, such as Ni versus Cu, would separate the thermodynamic driving force from the atomic transport mechanism.
  • The thickness-exclusion argument could be tested directly: applying the same deposition and annealing to 50-, 100-, and 200-nm films with matched grain size would show whether $D_r$ is thickness-independent (supporting the inner size effect) or thickness-dependent (pointing to surface or interface diffusion).
  • A sharper test of the mechanism would be to measure grain-boundary tracer diffusion in free-standing 100 nm films and compare it with the $D_r$ inferred from grain growth, since the paper's estimate is indirect and mixes boundary migration kinetics with atomic diffusion.
  • The resistance-drop timescale of 10–30 s suggests that electrical resistivity during first annealing could serve as a fast, inexpensive probe for inner size effects in other metal films, because the irreversible drop tracks the same recrystallization process.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript reports TEM and FESEM observations of recrystallization in 100 nm thick polycrystalline Cu and Ag films during short annealing at 250 °C. The authors find bimodal crystallite size distributions in Cu that persist after annealing, and a bimodal distribution in Ag with a nanosized fraction that coarsens from 25 to 50 nm. Using Eq. (2), Dr = x^2/(2t), they estimate a conditional grain-boundary diffusion coefficient Dr ≈ 10^-18 m2/s and conclude that diffusion in these nanocrystalline films is enhanced by 6–9 orders of magnitude relative to bulk self-diffusion, attributing this to an 'inner size effect' associated with grain-boundary energy.

Significance. The microstructural data—particularly the >2000-grain statistics and the dark-field TEM analysis—provide a useful experimental description of recrystallization in nanocrystalline Cu and Ag films, and the observation that the bimodal distribution in Cu is preserved during annealing is an interesting empirical finding. If the quantitative claim were sound, it would have implications for the thermal stability of nanocrystalline metal films. However, the central quantitative inference is currently not supported as stated: Dr from Eq. (2) is a boundary-migration rate constant, not an atomic diffusion coefficient, and the comparison with bulk self-diffusion omits the more relevant grain-boundary diffusion baseline. The qualitative observation of accelerated recrystallization is credible, but the paper does not establish a size-dependent diffusion coefficient in its present form.

major comments (4)
  1. [Results and discussion, Eq. (2) and Conclusions] The quantity Dr = x^2/(2t) is a grain-boundary migration rate constant rather than an atomic diffusion coefficient, and the text itself concedes that 'direct identification of Dr with the atomic diffusion coefficient is impossible' (paragraph after Eq. (2)). Nevertheless, the Conclusions state that the 'diffusion coefficient increases by a factor of 10–10000' and is '6 and 9 orders of magnitude higher than the bulk diffusion coefficient.' These statements are internally inconsistent: a rate constant that encodes both driving force and mobility cannot be compared with tracer or self-diffusion coefficients. The conclusions should be reframed in terms of an effective boundary mobility or migration rate, with comparisons made to the appropriate grain-boundary diffusion baseline.
  2. [Results and discussion, Eq. (2)] The value Dr ≈ 10^-18 m2/s is presented without any uncertainty estimate. The most probable radii are read from histograms with no reported confidence intervals, and the annealing time is taken as 200–300 s while the resistivity data cited in the same section indicate that the irreversible resistance drop occurs within 10–30 s. If t = 30 s rather than 200 s, Dr increases by nearly an order of magnitude, which materially changes the claimed enhancement range. Propagation of these uncertainties is required before the '6–9 orders' statement can be supported.
  3. [Results and discussion, comparison with bulk diffusion] The comparison baseline is inappropriate. For recrystallization, the relevant transport pathway is grain-boundary diffusion, which for Ag and Cu at 523 K is already many orders of magnitude above volume self-diffusion. The manuscript states (citing [35]) that Dr is typically about 100 times higher than the grain-boundary diffusion coefficient, but the Conclusions compare only with the bulk coefficient. Comparing Dr with bulk D therefore overstates any size effect; the authors should compare with published grain-boundary diffusion coefficients or justify why bulk D is the correct baseline.
  4. [Experimental section and Discussion, thickness argument] The claim that a 100 nm thickness is sufficient for the samples to be considered bulk in the context of size effects is not established. Cited works [38–40] report diffusion size effects in films of 5–135 nm thickness, including a 2–3 order reduction of hydrogen diffusion in 22 nm Pd films and a roughly one-order reduction at 46 nm. Surface and interface diffusion can also contribute at 100 nm, and the authors do not provide a control experiment with thicker films or a quantitative assessment of surface-diffusion contributions. The attribution of the observed acceleration solely to the 'inner size effect' is therefore not uniquely determined.
minor comments (5)
  1. [Figure numbering] Two figures are labeled Fig. 14: one showing mushroom-shaped copper grains and another showing a silver film curling under the electron beam. These should be renumbered sequentially.
  2. [References] References [29] and [30] are incomplete URLs without titles, journal names, or full bibliographic information; they should be completed.
  3. [Acknowledgment] The Acknowledgment contains a typo: 'the those of the author(s)' should read 'those of the author(s)'.
  4. [Introduction] There are several English-language issues, for example 'films are widely used in applied, the behavior of which...' in the first paragraph; the manuscript would benefit from a thorough language edit.
  5. [Introduction, terminology] The term 'inner size effect' is used throughout without a precise definition. It would help to define it operationally in the Introduction and to connect it with established concepts such as grain-boundary excess energy and its contribution to the free energy of nanocrystalline materials.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: Dr is computed from measured grain-radius shifts via a textbook formula and is not fitted to a target; self-citations to the 'inner size effect' framework are interpretive and not load-bearing for the numerical result.

full rationale

The central quantitative estimate uses Eq. (2), Dr = x^2/(2t), with x taken as the measured change in the most probable crystallite radius during annealing and t as the anneal time. This is a direct, parameter-free estimate from the histograms in Fig. 9; the paper does not fit any parameter to a target value and does not use Dr to regenerate the observed grain sizes. The comparisons of Dr with tabular bulk self-diffusion coefficients in the Conclusions are arithmetic consequences of the estimate, not quantities that were put into the estimate. The 'inner size effect' attribution rests on the thickness argument (100 nm films treated as bulk, with external size effects documented only for much thinner films) and on the excess free energy of grain boundaries; the self-citations [1,44] supply the terminology and prior melting-point analogues but are not load-bearing for the measured Dr value or the grain-growth data. The paper explicitly concedes that 'direct identification of Dr with the atomic diffusion coefficient is impossible,' so the physical interpretation is qualified; that is a correctness caveat rather than a circular derivation. The only mild self-referential element is the authors' own 'inner size effect' concept, which is used as an interpretive framework rather than as an input that forces the reported enhancement.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central quantitative claim relies on a small number of modeling choices: the use of the phenomenological relation Dr = x^2/(2t), the identification of grain-size peak shift with boundary displacement, an assumed annealing time of about 200 s, and the premise that 100 nm films are bulk-like with respect to external size effects. No new entities are introduced. The comparison with tabular bulk diffusion coefficients is the basis for the claimed 6-9 order enhancement.

free parameters (1)
  • Annealing time t in Dr = x^2/(2t) = 200 s (assumed from 2-5 min anneal)
    The reported Dr depends linearly on 1/t; the authors later note recrystallization completes within 10-30 s per resistance data, so the assumed time sets a lower bound on the inferred enhancement.
assumptions (5)
  • domain assumption Eq (2), Dr = x^2/(2t), adequately describes grain-boundary motion during recrystallization.
    Introduced from Ref [35] without derivation; the central quantitative result depends on this phenomenological relation.
  • domain assumption The change in the most probable crystallite radius between as-deposited and annealed states equals the boundary displacement x.
    Stated in Results: 'Accepting that x in our case is equal to the difference of the most probable radii...' This ignores distribution width and shape changes.
  • domain assumption 100 nm film thickness is large enough to exclude conventional external size effects, so any enhancement is due to internal boundaries.
    Argued in Experimental and Discussion: 'the selected thickness is already sufficient for the samples to be considered bulk...' No direct measurement of thickness-dependent diffusion was made.
  • domain assumption Excess grain-boundary energy lowers diffusion activation energy and drives accelerated self-diffusion.
    Borrowed from Refs [41-43] and the authors' prior 'inner size effect' papers; not tested by the present experiments.
  • domain assumption Tabulated bulk self-diffusion coefficients for Cu and Ag are the correct reference values for comparison.
    Used to compute the claimed 6-9 order-of-magnitude enhancement; values are not cited in detail.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Accelerated recrystallization of nanocrystalline films as a manifestation of the inner size effect of the diffusion coefficient." pith.science (2026). https://pith.science/paper/3FQJ6MXS

@misc{pith2026250201422,
  author       = {Pith},
  title        = {Pith review of: Accelerated recrystallization of nanocrystalline films as a manifestation of the inner size effect of the diffusion coefficient},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3FQJ6MXS}},
  note         = {Machine review of arXiv:2502.01422}
}
read the original abstract

This paper is devoted to studying the recrystallization of 100 nm thick polycrystalline films of copper and silver. It is found that in copper films deposited by the thermal evaporation method onto a substrate at room temperature, a bimodal crystallite size distribution with maxima at 15 and 35 nm is observed. The bimodal distribution in copper films is preserved during annealing, which leads to a shift of both peaks of the crystallite size distribution histograms to the larger sizes region. In contrast to Cu, micron-sized crystallites are present even in as-deposited Ag films besides the nanosized fraction. These grains are formed due to the phenomenon of self-annealing and weakly evolve during heating owing to grain growth stagnation. The nanosized fraction in as-deposited Ag films is represented by crystallites with the most probable size of 25 nm, which increases to 50 nm as a result of short-term annealing at the temperature of 250{\deg}C. The grain-boundary diffusion coefficient was determined, which is more than 10-18 m2/s for both films of metals. The obtained value indicates a multiple intensification of self-diffusion processes in films, the thickness of which allows us to refer them to macroscopic sample

Figures

Figures reproduced from arXiv: 2502.01422 by the authors.

Figure 4
Figure 4. Bright field (a) and dark-field (b) TEM images of the as-deposited Ag film. Arrows show twinning planes, which are one of the defects of as-deposited silver films [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 10
Figure 10. Apart from diffraction reflections from crys [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. The electron diffraction pattern of as-deposited copper film and the photometric plot of its central part obtained after background subtraction. The relative brightness of the lines indicated in the right part of the graph is obtained by integrating the sections of the photometric curve corresponding to the diffraction peaks. According to classical concepts, recrystallization observed in thin films is divided into p… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 42 canonical work pages

  1. [35]

    Gorelick, S. S. (2005). Recrystallization of metals and alloys. MISiS. 2005, 432 p (In Russian)

    work page 2005

  2. [1]

    I., Dukarov, S

    Petrushenko, S. I., Dukarov, S. V., Sukhov, V. N., & Churilov, I. G. (2015). Inner size effect in the polycrystalline metal films of fusible metals. Journal of Nano-& Electronic Physics, 7(2), 02033

    work page 2015

  3. [2]

    V., Petrushenko, S

    Dukarov, S. V., Petrushenko, S. I., Sukhov, V. M., & Churilov, I. G. (2019). Formation of Island Structures During Melting Process of Tin Films on Amorphous Carbon Substrate. Metallofizika i Novejsie Tehnologii, 41(4). 10.15407/mfint.41.04.0445

    work page doi:10.15407/mfint.41.04.0445 2019

  4. [3]

    O., Bohomaz, V

    Nevgasimov, O. O., Bohomaz, V. V., Petrushenko, S. I., & Dukarov, S. V. (2022). Morphology of island structures formed by self-organization processes during melting of lead films. Materials Today: Proceedings, 62, 5787-5795. 10.1016/j.matpr.2022.03.491

    work page doi:10.1016/j.matpr.2022.03.491 2022

  5. [4]

    Reiss, G., Vancea, J., & Hoffmann, H. (1986). Grain-boundary resistance in polycrystalline metals. Physical review letters, 56(19), 2100. 10.1103/PhysRevLett.56.2100

    work page doi:10.1103/physrevlett.56.2100 1986

  6. [5]

    H., Wei, C

    Zhang, Z. H., Wei, C. W., Cao, H. J., Han, J. J., & Zhang, Y. (2019). Structure -induced metastable phase transformation in Cu6Sn5 intermetallics. Materials Letters, 249, 124-127. 10.1016/j.matlet.2019.04.083

    work page doi:10.1016/j.matlet.2019.04.083 2019

  7. [6]

    Y., Jeon, Y

    Yoo, E., Samardak, A. Y., Jeon, Y. S., Samardak, A. S., Ognev, A. V., Komogortsev, S. V., & Kim, Y. K. (2020). Composition-driven crystal structure transformation and magnetic properties of electrode posited Co–W alloy nanowires. Journal of Alloys and Compounds, 843, 155902. 10.1016/j.jallcom.2020.155902

    work page arXiv 2020

  8. [7]

    Zhao, Z., Shang, J., Hu, A., & Li, M. (2016). The effects of Sn solder grain size on the morphology and evolution of Cu6Sn5 in the aging process. Materials Letters, 185, 92-95. 10.1016/j.matlet.2016.08.115

    work page doi:10.1016/j.matlet.2016.08.115 2016

Show all 44 references
  1. [8]

    Han, H., Lee, C., Kim, Y., Lee, J., Yoon, S., & Yoo, B. (2022). The self-annealing phenomenon of electrodeposited nano-twin copper with high defect density. Frontiers in Chemistry, 10, 1056596. 10.3389/fchem.2022.1056596

    2022

  2. [9]

    V., Petrushenko, S

    Dukarov, S. V., Petrushenko, S. I., & Sukhov, V. N. (2021). Supercooling during crystallisation and thermal dispergation of thin In-Pb films located between molybdenum layers. Thin Solid Films, 734, 138867. 10.1016/j.tsf.2021.138867

    2021

  3. [10]

    V., Petrushenko, S

    Dukarov, S. V., Petrushenko, S. I., & Sukhov, V. N. (2018). Supercooling during crystallization of a fusible component in Cu/(Bi–Sn) multilayer films. Materials Research Express, 6(1), 016403. 10.1088/2053- 1591/aae0c7

    2018 doi

  4. [11]

    P., & Dehm, G

    Bishara, H., Langenohl, L., Zhou, X., Gault, B., Best, J. P., & Dehm, G. (2023). Decoupling the electrical resistivity contribution of grain boundaries in dilute Fe-alloyed Cu thin films. Scripta Materialia, 230, 115393. 10.1016/j.scriptamat.2023.115393

    2023

  5. [12]

    I., Dukarov, S

    Petrushenko, S. I., Dukarov, S. V., & Sukhov, V. N. (2017). Effect of lead on the thermal dispersion of continuous polycrystalline copper films. Vacuum, 142, 29-36. 10.1016/j.vacuum.2017.04.037

    2017 doi

  6. [13]

    S. I. Petrushenko, S. V. Dukarov, and V. N. Sukhov, Growth of Through Pores and Thermal Dispersion of Continuous Polycrystalline Films of Copper, Metallofizika i Novejsie Tehnologii, 38, No. 10: 1351—1366 (2016) (in Ukrainian) 10.15407/mfint.38.10.1351

    2016 doi

  7. [14]

    R., & Rabkin, E

    Almog, E., Derkach, V., Sharma, A., Novick-Cohen, A., Greer, J. R., & Rabkin, E. (2021). Thermal stability of thin Au films deposited on salt whiskers. Acta Materialia, 205, 116537. https://doi.org/10.1016/j.actamat.2020.116537

    2021

  8. [15]

    H., Liu, H

    Tseng, H. H., Liu, H. C., Yu, M. H., Ong, J. J., Tran, D. P., & Chen, C. (2023). Epitaxial growth of (111) nanotwinned Ag on (111) nanotwinned Cu films for low-temperature Cu–Cu bonding. Crystal Growth & Design, 23(8), 5519-5527. 10.1021/acs.cgd.3c00157

    2023 doi

  9. [16]

    Y., Li, J

    Zhang, M., Gao, L. Y., Li, J. J., Sun, R., & Liu, Z. Q. (2023). Characterization of Cu -Cu direct bonding in ambient atmosphere enabled using (111)-oriented nanotwinned-copper. Materials Chemistry and Physics, 306, 128089. 10.1016/j.matchemphys.2023.128089

    2023

  10. [17]

    T., Liu, Y

    Wang, Y., Huang, Y. T., Liu, Y. X., Feng, S. P., & Huang, M. X. (2022). Thermal instability of nanocrystalline Cu enables Cu-Cu direct bonding in interconnects at low temperature. Scripta Materialia, 220, 114900. 10.1016/j.scriptamat.2022.114900

    2022

  11. [18]

    A., Vorob’ev, Y

    Chebotkevich, L. A., Vorob’ev, Y. D., Samardak, A. S., & Ognev, A. V. (2003). Effect of the crystal structure and interlayer exchange coupling on the coercive force in Co/Cu/Co films. Physics of the Solid State, 45, 907-910. 10.1134/1.1575333

    2003 doi

  12. [19]

    Y., Samardak, A

    Samardak, V. Y., Samardak, A. Y., Borisov, S. A., Antonov, V. A., Mushtuk, P. S., Shtarev, D. S., ... & Ognev, A. V. (2023). Investigation of the composition, structure and magnetic properties of the Nd2Fe14B ceramics dependence on the initial powder characteristics and spark ...

    2023

  13. [20]

    R., & Zöllner, D

    Rios, P. R., & Zöllner, D. (2018). Critical assessment 30: Grain growth–Unresolved issues. Materials Science and Technology, 34(6), 629-638. 10.1080/02670836.2018.1434863

    2018

  14. [21]

    Mukherjee, R., & Abinandanan, T. A. (2022). Grain boundary grooving in a polycrystalline thin film: A phase-field study. Computational Materials Science, 203, 111076. 10.1016/j.commatsci.2021.111076

    2022

  15. [22]

    Verma, M., & Mukherjee, R. (2021). Grain growth stagnation in solid state thin films: A phase -field study. Journal of Applied Physics, 130(2). 10.1063/5.0049027

    2021 doi

  16. [23]

    Rabkin, E., & Srolovitz, D. J. (2020). Grain growth stagnation in thin films due to shear-coupled grain boundary migration. Scripta Materialia, 180, 83-87. 10.1016/j.scriptamat.2020.01.019

    2020 doi

  17. [24]

    Xia, Y., Zuo, J., Yang, C., Wu, K., Liu, G., & Sun, J. (2023). Influence of thermal annealing on the microstructure evolution, fracture and fatigue behavior of nanocrystalline Cu films. Materials Today Communications, 36, 106793. 10.1016/j.mtcomm.2023.106793

    2023

  18. [25]

    E., Muster, T

    Lau, D., Hughes, A. E., Muster, T. H., Davis, T. J., & Glenn, A. M. (2010). Electron-beam-induced carbon contamination on silicon: Characterization using Raman spectroscopy and atomic force microscopy. Microscopy and Microanalysis, 16(1), 13-20. 10.1017/S1431927609991206

    2010 doi

  19. [26]

    Hugenschmidt, M., Adrion, K., Marx, A., Müller, E., & Gerthsen, D. (2023). Electron -beam-induced carbon contamination in STEM-in-SEM: Quantification and mitigation. Microscopy and Microanalysis, 29(1), 219-234. 10.1093/micmic/ozac003

    2023 doi

  20. [27]

    K., Rauch, E

    Kiss, Á. K., Rauch, E. F., Pécz, B., Szívós, J., & Lábár, J. L. (2015). A tool for local thickness determination and grain boundary characterization by CTEM and HRTEM techniques . Microscopy and Microanalysis, 21(2), 422-435. 10.1017/S1431927615000112

    2015 doi

  21. [28]

    S., & Weatherly, G

    Jin, Q., Wilkinson, D. S., & Weatherly, G. C. (1998). Determination of grain-boundary film thickness by the fresnel fringe imaging technique. Journal of the European Ceramic Society, 18(15), 2281-2286. 10.1016/S0955-2219(98)00140-X

    1998 doi

  22. [29]

    https://doi.org/10.1016/0254-0584(95)01515-9

    doi

  23. [30]

    https://doi.org/10.1116/1.568682

    doi

  24. [31]

    Thompson, C. V. (1990). Grain growth in thin films. Annual review of materials science, 20(1), 245-268. 10.1146/annurev.ms.20.080190.001333

    1990

  25. [32]

    Zöllner, D. (2021). Topological evolution of thin films during grain growth. Computational Materials Science, 200, 110803. 10.1016/j.commatsci.2021.110803

    2021

  26. [33]

    Y., Chu, Y

    Chang, S. Y., Chu, Y. C., Tu, K. N., & Chen, C. (2021). Effect of anisotropic grain growth on improving the bonding strength of< 111>-oriented nanotwinned copper films. Materials Science and Engineering: A, 804, 140754. 10.1016/j.msea.2021.140754

    2021

  27. [34]

    L., Shen, Y

    Lu, T. L., Shen, Y. A., Wu, J. A., & Chen, C. (2019). Anisotropic grain growth in (111) nanotwinned Cu films by DC electrodeposition. Materials, 13(1), 134. 10.3390/ma13010134

    2019 doi

  28. [36]

    A., Kremer, J

    Beck, P. A., Kremer, J. C., Demer, L. J. and Holzworth, M. L., Trans. AIME, 1948, 175, 372400

    1948

  29. [37]

    Gollapudi, S., & Soni, A. K. (2020). Understanding the effect of grain size distribution on the stability of nanocrystalline materials: an analytical approach. Materialia, 9, 100579. 10.1016/j.mtla.2019.100579

    2020

  30. [38]

    A., Bogatyrenko, S

    Minenkov, A. A., Bogatyrenko, S. I., Sukhov, R. V., & Kryshtal, A. P. (2014). Size dependence of the activation energy of diffusion in multilayer Cu-Ni films. Physics of the Solid State, 56(4), 823-826

    2014

  31. [39]

    Bogatyrenko, S., Kryshtal, A., Kruk, A., & Skryl, O. (2020). Mixing of Immiscible Compon ents by the Size Effect: A Case Study of Au–Ni Nanostructures. The Journal of Physical Chemistry C, 124(47), 25805- 25811. 10.1021/acs.jpcc.0c06800

    2020 doi

  32. [40]

    Li, Y., & Cheng, Y. T. (1996). Hydrogen diffusion and solubility in palladium thin films. International journal of hydrogen energy, 21(4), 281-291. 10.1016/0360-3199(95)00094-1

    1996 doi

  33. [41]

    Darken, L. S. (1948). Diffusion, mobility and their interrelation through free energy in binary metallic systems. Trans. Aime, 175, 184-201

    1948

  34. [42]

    C., Heine, V., Needs, R

    Milman, V., Payne, M. C., Heine, V., Needs, R. J., Lin, J. S., & Lee, M. H. (1993). Free energy and entropy of diffusion by ab initio molecular dynamics: Alkali ions in silicon. Physical review letters, 70(19), 2928. 10.1103/PhysRevLett.70.2928

    1993 doi

  35. [43]

    V., Sidorenkov, A

    Kolesnikov, S. V., Sidorenkov, A. V., & Saletsky, A. M. (2020). Simulation of the Inte raction of Graphene with a Copper Surface Using a Modified Morse Potential. JETP Letters, 111, 116-120. 10.1134/S0021364020020083

    2020 doi

  36. [44]

    Dukarov, S., Petrushenko, S., Sukhov, V., Churilov, I., Samsonik, A., & Skryl, O. (2018). Inner size effect in layered films with eutectic interaction of components. Acta Physica Polonica A, 133(5), 1186-1190. 10.12693/APhysPolA.133.1186

    2018 doi

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.