Cited by 2,629Fluid Dynamics and Thin FilmsThermodynamic and Structural Properties of Metals and AlloysSolidification and crystal growth phenomena

The DOI matches its Crossref record.

Theory of Thermal Grooving

Mullins, W. W.·1957·Journal of Applied Physics

DOI 10.1063/1.1722742

Open this paper in CoChat — free account

Abstract

A theory is presented which describes the development of surface grooves at the grain boundaries of a heated polycrystal. The mechanisms of evaporation-condensation and surface diffusion are discussed with the use of the Gibbs-Thompson formula and the assumption that the properties of an interface do not depend on its orientation. For the idealized case in which only one of the mechanisms is operative, the groove profile is shown to have a time-independent shape whose linear dimensions are proportional to t½ for evaporation-condensation, and to t½ for surface diffusion. The proportionality constants are evaluated, and criteria are developed which permit one to estimate which process predominates in practice. Order of magnitude agreement is obtained with estimates of actual grooving speeds and profiles.

Integrity signals

Registry

Crossref · 10.1063/1.1722742

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

No references could be resolved yet.

Research works printed but not linked: 4

1950, Proc. Phys. Soc. B, 63, 350
1949, J. Metals, 1, 169
1948, Proc. Roy. Soc. (London) A, 193, 465
1951, J. Inst. Metals, 79, 415

Sorted by citations

Items 701–800 of 1,002

Phase-field model for grain boundary grooving in multi-component thin films
Bouville, M., Hu, S.-Y. Y., Chen, L.-Q., Chi, D., & Srolovitz, D. (2005) · doi:10.1088/0965-0393/14/3/007 · Cited by 21
Hydrogen pressure dependence of trench corner rounding during hydrogen annealing
Kuribayashi, H., Shimizu, R., Sudoh, K., & Iwasaki, H. (2004) · doi:10.1116/1.1760752 · Cited by 21
Formation, ripening, and stability of epitaxially strained island arrays
Eisenberg, H. R., & Kandel, D. (2002) · doi:10.1103/physrevb.71.115423 · Cited by 21
Grain boundary misorientation and thermal grooving in cube-textured Ni and Ni-Cr tape
Gladstone, T. A., Moore, J., Wilkinson, A., & Grovenor, C. (2001) · doi:10.1109/77.919674 · Cited by 21
Texture inheritance in Al(Cu) interconnect materials
Murray, C., & Rodbell, K. P. (2001) · doi:10.1063/1.1337938 · Cited by 21
Morphological equilibration of rippled and dimpled crystal surfaces: the role of terrace-width fluctuations
Erlebacher, J., & Aziz, M. (1997) · doi:10.1016/s0039-6028(96)01231-9 · Cited by 21
Design of multiscalar metallic multilayer composites for high strength, high toughness, and low CTE mismatch
Srolovitz, D., Yalisove, S., & Bilello, J. (1995) · doi:10.1007/bf02670768 · Cited by 21
Surface energy and surface processes in solids
Geguzin, Y. E., & Ovcharenko, N. N. (1962) · doi:10.1070/pu1962v005n01abeh003403 · Cited by 21
Interfacial Structure and Energy Determine the Heterogeneity in the Electrochemical Metal Dissolution Activity at Grain Boundary
Wang, Y., Li, M., & Ren, H. (2023) · Chemistry of Materials · doi:10.1021/acs.chemmater.3c00220 · Cited by 25
Formation of a single quasicrystal upon collision of multiple grains
Han, I., Wang, K., Cadotte, A., Xi, Z., Parsamehr, H., Xiao, X.-H., Glotzer, S., & Shahani, A. (2021) · Nature Communications · doi:10.1038/s41467-021-26070-9 · Cited by 20
In-situ study of the dewetting behavior of Au/Ni bilayer films supported by a SiO2/Si substrate
Cen, X., Thron, A., & van Benthem, K. (2017) · doi:10.1016/j.actamat.2017.08.027 · Cited by 20
Coarsening of complex microstructures following spinodal decomposition
Park, C.-L., Gibbs, J., Voorhees, P., & Thornton, K. (2017) · doi:10.1016/j.actamat.2017.03.020 · Cited by 20
Structural and electrical characterization of the nickel silicide films formed at 850 °C by rapid thermal annealing of the Ni/Si(100) films
Utlu, G., Artunç, N., Budak, S., & Tari, S. (2010) · doi:10.1016/j.apsusc.2010.03.062 · Cited by 20
Nonthermal Plasma Synthesis of Faceted Germanium Nanocrystals
Cernetti, P., Gresback, R., Campbell, S., & Kortshagen, U. (2007) · doi:10.1002/cvde.200606559 · Cited by 20
Numerical simulation for the formation of nanostructures on the Stranski–Krastanow systems by surface undulation
Chiu, C., & Huang, Z. (2007) · doi:10.1063/1.2743734 · Cited by 20
Numerical Methods for Coupled Surface and Grain Boundary Motion
Pan, Z.-G., & Wetton, B. (2007) · doi:10.48550/arxiv.math/0702503 · Cited by 20
“First proposed by Mullins [13] to model the curvature driven diﬀusion on the surface of a crystal, surface diﬀusion is a diﬀerent evolution law in which the normal velocity of an interface is proportional to the surface Laplacian of mean curvature.”
Thermally stable nanomultilayer films of Cu/Mo
Srinivasan, D., Sanyal, S., Corderman, R., & Subramanian, P. R. (2006) · doi:10.1007/s11661-006-0072-4 · Cited by 20
Film/substrate interface stability in thin films
Krishnamurthy, R., & Srolovitz, D. (2006) · doi:10.1063/1.2173047 · Cited by 20
DNA localization and stretching on periodically microstructured lipid membranes.
Hochrein, M. B., Leierseder, J. A., Golubović, L., & Rädler, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.038103 · Cited by 20
Coupled surface and grain boundary motion : a travelling wave solution
Kanel, J., Novick-Cohen, A., & Vilenkin, A. (2004) · doi:10.1016/j.na.2004.08.014 · Cited by 20
“In line with the philosophy expressed by Mullins in [20, 21, 4], although theoretically the parameter m may vary between 0 and 2, typically, for example in metals, 0 < m < 1/3, and can be taken to be a small parameter.”
BackgroundResult
Oscillating growth of surface roughness in multilayer films
Liu, Z.-J., & Shen, Y.-G. (2004) · doi:10.1063/1.1764598 · Cited by 20
Grain Boundary Grooving Studies of Yttrium Aluminum Garnet (YAG) Bicrystals
Peters, M., & Reimanis, I. (2003) · doi:10.1111/j.1151-2916.2003.tb03390.x · Cited by 20
Interfacial reactions and failure mechanism of Cu/Ta/SiO2/Si multilayer structure in thermal annealing
Latt, K., Lee, Y. K., Osipowicz, T., & Park, H. S. (2002) · doi:10.1016/s0921-5107(02)00093-4 · Cited by 20
The role of particle energy and pulsed particle flux in physical vapor deposition and pulsed–laser deposition
Mayr, S. G., Moske, M., Samwer, K., Taylor, M., & Atwater, H. (1999) · doi:10.1063/1.125546 · Cited by 20
Thermal stability of cobalt silicide stripes on Si (001)
Alberti, A., Via, F. L., Raineri, V., & Rimini, E. (1999) · doi:10.1063/1.371172 · Cited by 20
Rapid liquid metal corrosion along grain boundaries
Fradkov, V. (1994) · doi:10.1016/0956-716x(94)90315-8 · Cited by 20
Atomic structure of grain boundaries in UO2 Bicrystals: A coupled high resolution transmission electron Microscopy/Atomistic simulation approach
Bourasseau, E., Onofri, C., Ksibi, A., Iltis, X., Belin, R., & Lapertot, G. (2022) · doi:10.1016/j.scriptamat.2021.114191 · Cited by 20
Phase-field simulations of faceted Ge/Si-crystal arrays, merging into a suspended film
Salvalaglio, M., Bergamaschini, R., Backofen, R., Voigt, A., Montalenti, F., & Miglio, L. (2017) · doi:10.1016/j.apsusc.2016.05.075 · Cited by 20
“This mechanism was explained by taking into account the thermallyactivated surface diffusion [11, 12], driven by the tendency toward the minimization of the surface energy only.”
Background
High Temperature Oxidation Behaviors of Steels at Initial Stages in Air
Zhong, M., & Webler, B. (2024) · Corrosion Science · doi:10.1016/j.corsci.2024.111838 · Cited by 19
Motion by Crystalline-Like Mean Curvature: A Survey
Giga, Y., & Požár, N. (2021) · Bulletin of Mathematical Sciences · doi:10.1142/s1664360722300043 · Cited by 19
Microstructural evolution of W-10Re alloys due to thermal cycling at high temperatures and its impact on surface degradation
Siller, M., Schatte, J., Gerzoskovitz, S., Knabl, W., Pippan, R., Clemens, H., & Maier-Kiener, V. (2020) · doi:10.1016/j.ijrmhm.2020.105285 · Cited by 19
Microstructural evolution and mechanical properties of hot-rolled Ti-30Zr-5Al-2.5Sn alloy with mixed α and α′ phases
Ma, W., Liu, S.-G., Zhang, X., Chen, B., Wang, F., Zhang, X.-Y., Ma, M., & Liu, R. (2020) · Materials Science & Engineering: A · doi:10.1016/j.msea.2020.139812 · Cited by 19
Pseudoelasticity of Metal Nanoparticles Is Caused by Their Ultrahigh Strength
Sharma, A. S., Gazit, N., Klinger, L. M., & Rabkin, E. (2019) · Advanced Functional Materials · doi:10.1002/adfm.201807554 · Cited by 21
Creep of binary Fe-Al alloys with ultrafine lamellar microstructures
Schmitt, A., Kumar, K., Kauffmann, A., Li, X., Stein, F., & Heilmaier, M. (2017) · doi:10.1016/j.intermet.2017.07.016 · Cited by 19
“thermal grooving [34] and/or d) termination/migration [35].”
Cross-sectional characterization of the dewetting of a Au/Ni bilayer film.
Cen, X., Thron, A., Zhang, X., & van Benthem, K. (2017) · Ultramicroscopy · doi:10.1016/j.ultramic.2016.06.004 · Cited by 19
"Bottom-up" transparent electrodes.
Morag, A., & Jelinek, R. (2016) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2016.07.079 · Cited by 19
Homoepitaxy of germanium by hyperthermal ion irradiation
Chowdhury, D., Ghose, D., & Mollick, S. A. (2014) · doi:10.1016/j.vacuum.2014.03.022 · Cited by 19
Extraction and parametrization of grain boundary networks in glacier ice, using a dedicated method of automatic image analysis
Binder, T., Garbe, C., Wagenbach, D., Freitag, J., & Kipfstuhl, S. (2013) · Journal of Microscopy · doi:10.1111/jmi.12029 · Cited by 19
“The image analysis method may find future applicability for other microstructure image types, for example, using thermal etching (Mullins, 1957), in which information on crystal orientation cannot be utilized for extraction of grains, but instead grain boundaries are mapped directly.”
Method
The Relationship between Grain Boundary Energy, Grain Boundary Complexion Transitions, and Grain Size in Ca-Doped Yttria
Bojarski, S., Knighting, J., Ma, S., Lenthe, W., Harmer, M., & Rohrer, G. (2013) · doi:10.4028/www.scientific.net/msf.753.87 · Cited by 19
“Using Mullins’ [13] analysis it is possible to measure the height and width of a thermal groove and solve for the relative interfacial energy of the grain boundary.”
MethodInfluential
Growth Dynamics of Nanocrystalline Diamond Thin Films Deposited by Hot Filament Chemical Vapor Deposition: Influence of Low Sticking and Re-nucleation Processes
Buijnsters, J. G., & Vázquez, L. (2011) · doi:10.1021/jp201919r · Cited by 19
Strain-induced boundary migration of carbon steel at high temperatures
Yogo, Y., Takeuchi, H., Ishikawa, T., Iwata, N., & Nakanishi, K. (2009) · doi:10.1016/j.scriptamat.2009.08.003 · Cited by 19
Shape Transformation of 4H-SiC Microtrenches by Hydrogen Annealing
Takatsuka, A., Tanaka, Y., Yano, K., Yatsuo, T., Ishida, Y., & Arai, K. (2009) · doi:10.1143/jjap.48.041105 · Cited by 19
Entropy Diagnostics for Fourth Order Partial Differential Equations in Conservation Form
Broadbridge, P. (2008) · Entropy · doi:10.3390/e10030365 · Cited by 19
“Mullins [3] derived the equation for surface diffusion on metals as a fourth order curvature-driven flow, yt = −   1 √ 1 + y2 x   yxx √ 1 + y2 x  ”
Morphological evolution of voids by surface drift diffusion driven by the capillary, electromigration, and thermal-stress gradient induced by the steady state heat flow in passivated metallic thin films and flip-chip solder joints. II. Applications
Ogurtani, T., & Akyildiz, O. (2008) · doi:10.1063/1.2958088 · Cited by 19
Effect of Post-Growth Annealing on Morphology of Ge Mesa Selectively Grown on Si
Park, S., Ishikawa, Y., Tsuchizawa, T., Watanabe, T., Yamada, K., Itabashi, S., & Wada, K. (2008) · IEICE transactions on electronics · doi:10.1093/ietele/e91-c.2.181 · Cited by 19
Electromigration-induced void grain-boundary interactions: The mean time to failure for copper interconnects with bamboo and near-bamboo structures
Ogurtani, T., & Oren, E. (2004) · doi:10.1063/1.1815389 · Cited by 19
The monitoring of grain-boundary grooves in alumina
Munoz, N., Gilliss, S. R., & Carter, C. (2004) · doi:10.1080/09500830310001614487 · Cited by 19
“The profile of the groove in figure 1 pictorially shows the situation where rounded ridges develop, as observed experimentally for this material and proposed by Mullins (1957).”
Background
Theory of discontinuous precipitation: importance of the elastic strain
Brener, E., & Temkin, D. (2003) · doi:10.1016/s1359-6454(02)00471-8 · Cited by 19
Column angle variations in porous chevron thin films
Harris, K., Vick, D., Smy, T., & Brett, M. (2002) · doi:10.1116/1.1517258 · Cited by 19
Evaluating Anisotropic Surface Energies Using the Capillarity Vector Reconstruction Method
Saylor, D., & Rohrer, G. (2001) · doi:10.1023/a:1011262628243 · Cited by 19
Motion by curvature and impurity drag: resolution of a mobility paradox
Cahn, J., & Novick-Cohen, A. (2000) · doi:10.1016/s1359-6454(00)00144-0 · Cited by 19
Capillary instabilities of a catenoidal hole in a solid film
Wong, H., Voorhees, P., Miksis, M., & Davis, S. H. (1997) · doi:10.1063/1.364358 · Cited by 19
Thin film microstructure modelling through line-segment simulation
Friedrich, L., Dew, S., Brett, M., & Smy, T. (1995) · doi:10.1016/0040-6090(95)06672-1 · Cited by 19
Surface Diffusion in MgO and Cr‐Doped MgO
Lytle, S., & Stubican, V. (1982) · doi:10.1111/j.1151-2916.1982.tb10406.x · Cited by 19
In-situ revealing the degradation mechanisms of Pt film over 1000°C
Ma, D.-F., Mao, S.-C., Teng, J., Wang, X., Li, X.-C., Ning, J., Li, Z., Zhang, Q., Tian, Z., Wang, M., et al. (2021) · doi:10.1016/j.jmst.2021.03.064 · Cited by 18
Grain growth stagnation in solid state thin films: A phase-field study
Verma, M., & Mukherjee, R. (2021) · Journal of Applied Physics · doi:10.1063/5.0049027 · Cited by 18
The competing effects of temperature and neutron irradiation on the microstructure and mechanical properties of ITER grade tungsten
Papadakis, D., Dellis, S., Mergia, K., Chatzikos, V., Terentyev, D., Bonny, G., Dubinko, A., Renterghem, W. V., Konstantinović, M., Messoloras, S., et al. (2021) · Fusion engineering and design · doi:10.1016/j.fusengdes.2021.112608 · Cited by 18
Determination of the time-dependent thermal grooving coefficient
Cao, K., Lesnic, D., & Ismailov, M. (2020) · Journal of Applied Mathematics and Computation · doi:10.1007/s12190-020-01388-7 · Cited by 18
Metal hetero-diffusion along the metal-ceramic interfaces: A case study of Au diffusion along the Ni-sapphire interface
Barda, H., & Rabkin, E. (2020) · doi:10.1016/j.actamat.2019.12.051 · Cited by 18
On the Isoperimetric Inequality and Surface Diffusion Flow for Multiply Winding Curves
Miura, T., & Okabe, S. (2019) · doi:10.1007/s00205-020-01591-7 · Cited by 18
“The surface diffusion flow is first introduced by Mullins ( [38]) in 1957 and then studied by many authors.”
Background
Electroplating: Applications in the Semiconductor Industry
Jhothiraman, J. K., & Balachandran, R. (2019) · Advances in Chemical Engineering and Science · doi:10.4236/aces.2019.92018 · Cited by 18
“Dependence of growth velocity during plating to final metal profile has been well established [23] [24].”
Background
Triple Junction at the Triple Point Resolved on the Individual Particle Level.
Chaudhuri, M., Allahyarov, E., Löwen, H., Egelhaaf, S., & Weitz, D. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.128001 · Cited by 18
Capillary-mediated interface perturbations: Deterministic pattern formation
Glicksman, M. (2016) · doi:10.1016/j.jcrysgro.2016.03.031 · Cited by 18
“[46,47], of which the latter investigators formulated species conservation on solid–vapor interfaces subjected to surface diffusion [48,49].”
Background
Effect of hydrogen on the microstructural evolution of a γ-TiAl based alloy
Zong, Y.-Y., Wen, D.-S., Liu, Z.-Y., & Shan, D. (2015) · doi:10.1016/j.matlet.2014.11.139 · Cited by 18
Observation of thermally etched grain boundaries with the FIB/TEM technique
Palizdar, Y., Martín, D., Ward, M., Cochrane, R., Brydson, R., & Scott, A. (2013) · doi:10.1016/j.matchar.2013.07.003 · Cited by 18
“4 has been some debate regarding the pinning effects of mobile grain boundaries and whether such grooves affect their mobility [14,21-24].”
BackgroundInfluential
On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions
Asai, T., & Giga, Y. (2013) · doi:10.4171/ifb/329 · Cited by 18
“The problem stems from an equation proposed by W. W. Mullins (1957) to model formation of surface grooves on the grain boundaries, where the second boundary condition vxxx = 0 is replaced by zero slope condition on the curvature of the graph.”
BackgroundMethodInfluential
Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings
Goray, L., & Lubov, M. (2013) · Journal of Applied Crystallography · doi:10.1107/s0021889813012387 · Cited by 18
“Among the main relaxation mechanisms are surface diffusion, evaporation–condensation and bulk diffusion (Pellicione & Lu, 2007; Mullins, 1957).”
Background
On Well-Posedness, Stability, and Bifurcation for the Axisymmetric Surface Diffusion Flow
LeCrone, J., & Simonett, G. (2012) · SIAM Journal on Mathematical Analysis · doi:10.1137/120883505 · Cited by 18
“The mathematical equations modeling surface diffusion go back to a paper by Mullins [55] from the 1950s, who was in turn motivated by earlier work of Herring [34].”
Result
The thin film equation with backwards second order diffusion
Novick-Cohen, A., & Shishkov, A. (2010) · doi:10.4171/ifb/242 · Cited by 18
Nonlinear Stability of Stationary Solutions for Surface Diffusion with Boundary Conditions
Garcke, H., Ito, K., & Kohsaka, Y. (2008) · SIAM Journal on Mathematical Analysis · doi:10.1137/070694752 · Cited by 18
“The flow (1.1) was first proposed by Mullins [19] in works concerned with thermal grooving.”
BackgroundInfluential
Liquid bridges and black strings in higher dimensions
Miyamoto, U., & Maeda, K. (2008) · doi:10.1016/j.physletb.2008.05.010 · Cited by 18
A size effect in grain boundary migration: A molecular dynamics study of bicrystal thin films
Zhou, L., Zhang, H., & Srolovitz, D. (2005) · doi:10.1016/j.actamat.2005.07.032 · Cited by 18
Niobium nanoclusters studied with In situ transmission electron microscopy
Vystavěl, T., Palasantzas, G., Koch, S., & de Hosson, J. (2003) · doi:10.1063/1.1625789 · Cited by 18
Smooth unique solutions for a modified Mullins-Sekerka model arising in diblock copolymer melts
Escher, J., & Nishiura, Y. (2002) · doi:10.14492/hokmj/1350911774 · Cited by 18
Surface Morphologies: Transient and Equilibrium Shapes
Bonzel, H. (2001) · doi:10.1023/a:1011210627335 · Cited by 18
Three-phase boundary motion by surface diffusion: stability of a mirror symmetric stationary solution
Ito, K., & Kohsaka, Y. (2001) · doi:10.4171/ifb/32 · Cited by 18
“Mullins [24] and it takes the form V = −∆Γ (t) H on Γ (t) for t > 0, (1.”
Directional dependence of surface morphological stability of heteroepitaxial layers
Obayashi, Y., & Shintani, K. (1998) · doi:10.1063/1.368468 · Cited by 18
Equations of motion for epitaxial growth
Zangwill, A., Luse, C., Vvedensky, D., & Wilby, M. (1992) · doi:10.1016/0039-6028(92)90517-a · Cited by 18
Catalytic etching of platinum alloy gauzes
Anderson, D. R. (1988) · doi:10.1016/0021-9517(88)90273-4 · Cited by 18
Surface diffusion of chemisorbed sulfur on nickel (111)
Wood, B., Ablow, C. M., & Wise, H. (1984) · doi:10.1016/0378-5963(84)90086-2 · Cited by 18
Croissance de bicristaux orientés d'oxyde de nickel
Dhalenne, G., Revcolevschi, A., & Gervais, A. (1978) · doi:10.1016/0022-0248(78)90029-5 · Cited by 18
Surface Self‐Diffusion of Ag+ on AgBr by a New Radiotracer Technique
Tan, Y., Perkett, W., & Powell, R. (1971) · doi:10.1063/1.1659850 · Cited by 18
An inverse problem of recovering the heat source coefficient in a fourth-order time-fractional pseudo-parabolic equation
Huntul, M., Tekin, I., Iqbal, M. K., & Abbas, M. (2023) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2023.115712 · Cited by 17
Phase/grain boundary assisted-3D static globularization mechanism of TC17 alloy based on the microstructure reconstruction and in-situ TEM observation
Pang, H., Liu, Y.-G., Luo, J., Li, C.-A., & Li, H. (2023) · Journal of Materials Science & Technology · doi:10.1016/j.jmst.2023.02.043 · Cited by 17
Phase-field simulations of grain boundary grooving under diffusive-convective conditions
Laxmipathy, V. P., Wang, F., Selzer, M., & Nestler, B. (2021) · doi:10.1016/j.actamat.2020.116497 · Cited by 17
An investigation into experimental in situ scanning electron microscope (SEM) imaging at high temperature.
Heard, R., Huber, J., Siviour, C., Edwards, G., Williamson-Brown, E., & Dragnevski, K. (2020) · Review of Scientific Instruments · doi:10.1063/1.5144981 · Cited by 17
Reconstitution reveals how myosin-VI self-organises to generate a dynamic mechanism of membrane sculpting
Rogez, B., Würthner, L., Petrova, A. B., Zierhut, F., Saczko-Brack, D., Huergo, M., Batters, C., Frey, E., & Veigel, C. (2019) · Nature Communications · doi:10.1038/s41467-019-11268-9 · Cited by 17
Solid-state dewetting of single-crystal silicon on insulator: effect of annealing temperature and patch size
Abbarchi, M., Naffouti, M., Lodari, M., Salvalaglio, M., Backofen, R., Bottein, T., Voigt, A., David, T., Claude, J., Bouabdellaoui, M., et al. (2018) · doi:10.1016/j.mee.2018.01.002 · Cited by 17
Dewetting of Au/Ni bilayer films on prepatterned substrates and the formation of arrays of supersaturated Au-Ni nanoparticles
Herz, A., Wang, D., & Schaaf, P. (2014) · doi:10.1116/1.4863320 · Cited by 17
A novel experimental approach to determine the absolute grain boundary energy
Molodov, D., Günster, C., Gottstein, G., & Shvindlerman, L. (2012) · doi:10.1080/14786435.2012.716167 · Cited by 17
Surface Relaxation Below the Roughening Temperature: Some Recent Progress and Open Questions
Kohn, R. (2012) · doi:10.1007/978-3-642-25361-4_11 · Cited by 17
“The thermodynamic viewpoint, which dates back at least to Mullins’ work on grain boundary grooving [20], has long been accepted in connection with motion by surface diffusion above the roughening temperature.”
Background
Surface topography and energy of grain boundary triple junctions in copper tricrystals
Zhao, B., Ziemons, A., Shvindlerman, L., & Gottstein, G. (2012) · doi:10.1016/j.actamat.2011.10.034 · Cited by 17
Normal versus anomalous roughening in electrodeposited Prussian Blue layers
Alamini, M. F., da Silva, R. C., Zoldan, V. C., Isoppo, E., Rodrigues, U. P., Reis, F. D. A. A., Klein, A., & Pasa, A. A. (2011) · doi:10.1016/j.elecom.2011.09.025 · Cited by 17
Fourth Order Geometric Evolution Equations
Wheeler, G. E. (2010) · doi:10.1017/s0004972710001863 · Cited by 17
“The mean curvature flow is motivated initially by the experimental and theoretical work of the physicist Mullins [48, 49], and reads”
Background
Ion irradiation-induced bimodal surface morphology changes in InSb
Perez-Bergquist, A., Li, K.-D., Zhang, Y.-W., & Wang, L.-M. (2010) · Nanotechnology · doi:10.1088/0957-4484/21/32/325602 · Cited by 17
Improving the morphological stability of a polycrystalline tungsten nanowire with a carbon shell
You, G.-F., Gong, H., & Thong, J. (2010) · Nanotechnology · doi:10.1088/0957-4484/21/19/195701 · Cited by 17
Effective Modulation of Ni Silicide Schottky Barrier Height Using Chlorine Ion Implantation and Segregation
Loh, W., Etienne, H., Coss, B., Ok, I., Turnbaugh, D., Spiegel, Y., Torregrosa, F., Banti, J., Roux, L., Hung, P., et al. (2009) · IEEE Electron Device Letters · doi:10.1109/led.2009.2031828 · Cited by 17
“This may help to explain its enhanced thermal stability since NiSi agglomeration has been modeled by the grain boundary grooving model which predicts larger equilibrium groove depth with larger grain size and thinner NiSi thickness [25].”
Background
The surface diffusion flow on rough phase spaces
Escher, J., & Mucha, P. B. (2009) · doi:10.3934/dcds.2010.26.431 · Cited by 17
“[10] J. Escher, G. Simonett, A center Manifold analysis for the Mullins-Sekerka Model, J. Diff.”
Influential
Roughness evolution during chemical vapor deposition
Kajikawa, Y. (2008) · doi:10.1016/j.matchemphys.2008.06.008 · Cited by 17
Tailoring the microstructure and surface morphology of metal thin films for nano-electro-mechanical systems applications
Luber, E. J., Mohammadi, R., Ophus, C., Lee, Z., Nelson-Fitzpatrick, N., Westra, K., Evoy, S., Dahmen, U., Radmilović, V., & Mitlin, D. (2008) · Nanotechnology · doi:10.1088/0957-4484/19/12/125705 · Cited by 17

Authors: Mullins, W. W.
Affiliations: Westinghouse Electric (United States) (US)
Corresponding author: Mullins, W. W.
Venue: Journal of Applied Physics
Publisher: AIP Publishing
Published: 1957-03-01
Volume: 28
Issue: 3
Pages: 333-339
ISSN: 0021-8979 (ISSN-L)
1089-7550
DOI: 10.1063/1.1722742
OpenAlex: W2017334281
Cited by: 2,629
References: 8
Citations by year: 2026: 62 · 2025: 72 · 2024: 73 · 2023: 55 · 2022: 63 · 2021: 102 · 2020: 84 · 2019: 68 · 2018: 57 · 2017: 72 · 2016: 71 · 2015: 57 · 2014: 78 · 2013: 74 · 2012: 71
FWCI: 11.00
Type: journal article
Language: en
Open access: closed
Locations: Journal of Applied Physics (publishedVersion)
Topics: Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Thin Films
Physical Sciences › Materials Science › Metals and Alloys › Thermodynamic and Structural Properties of Metals and Alloys
Physical Sciences › Materials Science › Materials Chemistry › Solidification and crystal growth phenomena
Keywords: thermal grooving, grain boundaries, polycrystalline materials, evaporation and condensation, surface diffusion, Gibbs-Thomson equation, groove profile

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Theory of Thermal Grooving

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Metadata

Record

About these checks