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 901–1,000 of 1,002

Finite element analysis of the splitting and cylinderization processes of damage microcracks
Huang, P.-Z., Li, Z.-H., & Sun, J. (2001) · doi:10.1088/0965-0393/9/3/306 · Cited by 14
“migration, a thermal groove develops along the boundary to establish a static equilibrium between the surface tensions and the boundary tension [ 59 ], and the triple point is then characterized by the equilibrium angle θ (in figure 7, 2 sin θ = γb/γs).”
Background
Sintering of regular two-dimensional arrays of particles surface and grain boundary diffusion
Zhang, W., Schneibel, J., & Hsueh, C.-H. (1994) · doi:10.1080/01418619408242952 · Cited by 14
Autodiffusion superficielle du nickel en presence d'ha logenes adsorbes
Oda, O., & Rhead, G. E. (1979) · doi:10.1016/0036-9748(79)90189-3 · Cited by 14
Surface diffusion measurements in nickel using a modified relaxation technique
Azzerri, N., & Colombo, R. (1976) · doi:10.1016/0026-0800(76)90049-5 · Cited by 14
Morphology of thermally etched basal surfaces of cadmium selenide
Munir, Z., Seacrist, L., & Hirth, J. P. (1971) · doi:10.1016/0039-6028(71)90049-5 · Cited by 14
Grain boundary diffusion in compositionally complex alloys: A comprehensive review
Yadav, B., Muralikrishna, G., Vaidya, M., Wilde, G., & Divinski, S. (2025) · International Materials Reviews · doi:10.1177/09506608251390882 · Cited by 13
Grain Boundary Grooving by Surface Diffusion in Nickel Bicrystals
Haremski, P., Epple, L., Wieler, M., Lupetin, P., Klinger, L., Rabkin, E., & Hoffmann, M. (2022) · Social Science Research Network · doi:10.2139/ssrn.4101125 · Cited by 13
Self-Detachment and Subsurface Densification of Dealloyed Nanoporous Thin Films
Henkelmann, G., Waldow, D., Liu, M.-W., Lührs, L., Li, Y., & Weissmüller, J. (2022) · Nano letters (Print) · doi:10.1021/acs.nanolett.2c02666 · Cited by 13
Morphological evolution via surface diffusion learned by convolutional, recurrent neural networks: Extrapolation and prediction uncertainty
Lanzoni, D., Albani, M., Bergamaschini, R., & Montalenti, F. (2022) · Physical Review Materials · doi:10.1103/physrevmaterials.6.103801 · Cited by 7
Stress-Induced Acceleration and Ordering in Solid-State Dewetting.
Boccardo, F., Rovaris, F., Tripathi, A., Montalenti, F., & Pierre-Louis, O. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.026101 · Cited by 13
DC electric field‐assisted hot pressing of zirconia: Methodology, phenomenology, and sintering mechanism
Xu, J.-K., Liu, Z.-T., Xie, Z.-P., He, S., & Xi, X.-Q. (2021) · Journal of The American Ceramic Society · doi:10.1111/jace.17963 · Cited by 13
On the role of interfacial elasticity in morphological instability of a heteroepitaxial interface
Shuvalov, G., & Kostyrko, S. (2021) · Continuum Mechanics and Thermodynamics · doi:10.1007/s00161-021-01010-6 · Cited by 13
“The application of Mullins–Sekerka model to problems differ from crystal growth was discussed in numerous works [32,54,80,82,102].”
Background
Effect of transport mechanism on the coarsening of bicontinuous structures: A comparison between bulk and surface diffusion
Andrews, W., Elder, K., Voorhees, P., & Thornton, K. (2020) · doi:10.1103/physrevmaterials.4.103401 · Cited by 13
“In coarsening via both bulk and surface diffusion, mass transport is driven by differences in chemical potential within the structure [6, 29].”
BackgroundInfluential
Enabling silicon-on-silicon photonics with pedestalled Mie resonators
Garin, M., Sola, M. A., Julian, A. G., & Ortega, P. (2018) · Nanoscale · doi:10.1039/c8nr02259c · Cited by 13
Relaxation of low-angle grain boundary structure by climb of the constituent dislocations
Gu, Y.-J., Xiang, Y., & Srolovitz, D. (2016) · doi:10.1016/j.scriptamat.2015.11.016 · Cited by 13
Ni silicide study at the atomic scale: Diffusing species, relaxation and grooving mechanisms
Kousseifi, M. E., Hoummada, K., & Mangelinck, D. (2015) · doi:10.1016/j.actamat.2014.10.029 · Cited by 13
Grain growth, anomalous scaling, and grain boundary grooving in polycrystalline CdTe thin films
Kwon, D., Shim, Y., Amar, J., & Compaan, A. (2014) · doi:10.1063/1.4901068 · Cited by 13
Evolution of (001) and (111) facets for selective epitaxial growth inside submicron trenches
Jiang, S., Merckling, C., Guo, W., Waldron, N., Caymax, M., Vandervorst, W., Seefeldt, M., & Heyns, M. (2014) · doi:10.1063/1.4861416 · Cited by 13
Continuum modeling of particle redeposition during ion-beam erosion
Diddens, C., & Linz, S. J. (2013) · European Physical Journal B : Condensed Matter Physics · doi:10.1140/epjb/e2013-40555-7 · Cited by 13
Surface pattern formation and scaling described by conserved lattice gases.
Ódor, G., Liedke, B., & Heinig, K. (2009) · Physical review. E, Statistical, nonlinear, and soft matter physics · doi:10.1103/physreve.81.051114 · Cited by 13
Guided assembly of nanostructures via elastic interactions
Lou, Y., & Bassani, J. (2008) · doi:10.1016/j.jmps.2008.08.009 · Cited by 13
“The mass flux, J, is assumed to be proportional to the gradient of chemical potential, μ , that is defined by variations in local free 1 Boldface symbols denote tensor variables. energy density with respect to compositional variations (Mullins, 1957).”
Background
Effect of grain shape on the agglomeration of polycrystalline thin films
Bouville, M. (2006) · doi:10.1063/1.2454452 · Cited by 13
Variational formulation of irreversible thermodynamics of surfaces and interfaces with grain-boundary triple-junction singularities under the capillary and electromigration forces in anisotropic two-dimensional space
Ogurtani, T. (2006) · doi:10.1103/physrevb.73.235408 · Cited by 13
Pinch off of nanopipes under electron irradiation in GaN
Pailloux, F., Colin, J., Barbot, J., & Grilhé, J. (2005) · doi:10.1063/1.1894591 · Cited by 13
On the mechanism of annealing effect in electrical resistivity of sub-100 nm Ag (1% W) films
Glickman, E., Inberg, A., Bogush, V., Aviram, G., Croitoru, N., & Shacham-Diamand, Y. (2004) · doi:10.1016/j.mee.2004.07.052 · Cited by 13
Formation and structure of misfit dislocations at the La2Zr2O7-Y2O3 -stabilized ZrO2 (001) reaction front during vapour-solid reaction
Lu, C.-J., Senz, S., & Hesse, D. (2002) · doi:10.1080/09500830110118058 · Cited by 13
“The domainboundary grooving occurs by surface diŒusion because of the higher strain ®eld at domain boundaries (Mullins 1957, 1960).”
Background
Surface Morphological Evolution of Thin Films Under Stress and Capillary Forces
Genin, F. (2001) · doi:10.1023/a:1011231131878 · Cited by 13
Theory of feature broadening in direct-write optical lithography
Bradley, R. M., Eschmann, A., & Lee, S. A. (2000) · doi:10.1063/1.1289475 · Cited by 13
Evolution of vesicles subject to adhesion
Rosso, R., Sonnet, A., & Virga, E. (2000) · Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2000.0574 · Cited by 13
“It is known that for the motion by surface di¬usion (Mullins 1957) a curve can fail to remain convex during the evolution (Coleman et al .”
Background
A comparison of theoretical and experimental profiles for thermally-induced grain-boundary grooving
Lee, K.-Y., & Case, E. (1999) · doi:10.1051/epjap:1999247 · Cited by 13
Junction Line Disclinations: Characterisation and Observations
Dimitrakopulos, G., Komninou, P., Karakostas, T., & Pond, R. (1999) · doi:10.1023/a:1008713124286 · Cited by 13
The thermal stability of deformed Al-CuAl2 eutectic
Ho, E., & Weatherly, G. (1977) · doi:10.1179/msc.1977.11.4.109 · Cited by 13
Solving the Annealing of Mo Interconnects for Next‐Gen Integrated Circuits
Erofeev, I., Hartanto, A. W., Saidov, K., Aabdin, Z., Pacco, A., Philipsen, H., Tjiu, W., Hui, H. K., Holsteyns, F., & Mirsaidov, U. (2024) · Advanced Electronic Materials · doi:10.1002/aelm.202400035 · Cited by 12
Coalescence as a key process in wafer-scale diamond heteroepitaxy
Lebedev, V., Kustermann, J., Engels, J., Weippert, J., Cimalla, V., Knittel, P., Kirste, L., Giese, C., Quellmalz, P., Graff, A., et al. (2024) · Journal of Applied Physics · doi:10.1063/5.0189631 · Cited by 12
Observation of Uniaxial Magnetic Anisotropy and Out-of-Plane Coercivity in W/Co20Fe60B20/W Structures with High Thermal Stability
Saravanan, L., Gupta, N. K., Pandey, L., Kokila, I. P., Therese, H. A., & Chaudhary, S. (2021) · Journal of Alloys and Compounds · doi:10.1016/j.jallcom.2021.162600 · Cited by 12
Wetting of YSZ by molten Sn–8Zr, Sn–4Zr–4Ti, and Sn–8Ti alloys at 800–900 °C
Lin, Q., Tan, K., Wang, L., & Sui, R. (2021) · Ceramics International · doi:10.1016/j.ceramint.2021.09.112 · Cited by 12
Nanoparticle formation through dewetting of a solid-state thin film on a substrate: A phase-field study
Verma, M., & Mukherjee, R. (2020) · doi:10.1016/j.jallcom.2020.155163 · Cited by 12
Mapping hot-pressed Li6.25Al0.25La3Zr2O12(LLZO) grains and grain boundaries through a simple thermal grooving technique
Sato, M., García-Méndez, R., & Sakamoto, J. S. (2020) · Journal of Asian Ceramic Societies · doi:10.1080/21870764.2020.1789286 · Cited by 13
Recent developments in ion beam-induced nanostructures on AIII-BV compound semiconductors
Trynkiewicz, E., Jany, B., Janas, A., & Krok, F. (2018) · Journal of Physics: Condensed Matter · doi:10.1088/1361-648x/aacc45 · Cited by 12
Destabilisation of nanoporous membranes through GB grooving and grain growth
Joshi, C., Abinandanan, T., Mukherjee, R., & Choudhury, A. (2017) · doi:10.1016/j.commatsci.2017.07.026 · Cited by 12
Grain boundaries effects on hole morphology and growth during solid state dewetting of thin films
Derkach, V., Novick-Cohen, A., & Rabkin, E. (2017) · doi:10.1016/j.scriptamat.2017.02.046 · Cited by 12
Blazed diffraction gratings produced by ion bombardment of pre-patterned solid surfaces
Harrison, M. P., & Bradley, R. M. (2017) · doi:10.1063/1.4975352 · Cited by 12
One-minute deposition of micrometre-thick porous Si-Cu anodes with compositional gradients on Cu current collectors for lithium secondary batteries
Lee, J., Hasegawa, K., Momma, T., Osaka, T., & Noda, S. (2015) · doi:10.1016/j.jpowsour.2015.04.024 · Cited by 12
A Self-Scanned Active-Matrix Tactile Sensor Realized Using Silicon-Migration Technology
Zeng, F., & Wong, M. (2015) · Journal of microelectromechanical systems · doi:10.1109/jmems.2014.2344025 · Cited by 12
“However, the migration time required to reach equivalent topological states is scaled by λ4 [13].”
Background
Analysis of mirror soft-x-ray-EUV scattering using generalized continuous growth model of multiscale reliefs.
Goray, L., & Lubov, M. (2015) · Optics Express · doi:10.1364/oe.23.010703 · Cited by 12
Modeling of Microstructure Evolution in Metallic Multilayers with Immiscible Constituents
Wan, H., Shen, Y., He, X., & Wang, J. (2013) · JOM · doi:10.1007/s11837-012-0547-2 · Cited by 12
Fabrication of metallic nanoparticles by spinodal dewetting of thin films: A high-throughput approach
Michalak, W., Miller, J. B., Yolcu, C., & Gellman, A. (2012) · doi:10.1016/j.tsf.2012.07.041 · Cited by 12
Grain Growth and the Puzzle of its Stagnation in Thin Films a Detailed Comparison of Experiments and Simulations
Barmak, K., Eggeling, E., Sharp, R., Roberts, S., Shyu, T. C., Sun, T., Yao, B., Ta'asan, S., Kinderlehrer, D., Rollett, A., et al. (2012) · doi:10.4028/www.scientific.net/msf.715-716.473 · Cited by 12
Surface effect on the coalescence of Pt clusters: A molecular dynamics study
Kayhani, K., Mirabbaszadeh, K., Nayebi, P., & Mohandesi, A. (2010) · doi:10.1016/j.apsusc.2010.05.010 · Cited by 12
The effect of kinetics in the surface evolution of thin crystalline films
Stöcker, C., & Voigt, A. (2007) · doi:10.1016/j.jcrysgro.2006.11.246 · Cited by 12
Melting of alloys along the inter-phase boundaries in eutectic and peritectic systems
Brener, E., & Temkin, D. (2006) · doi:10.1016/j.actamat.2006.12.016 · Cited by 12
Roughening kinetics of thin films in the presence of both stress and Ehrlich–Schwobel barrier
Liu, Z.-J., & Shen, Y.-G. (2003) · doi:10.1063/1.1637448 · Cited by 12
Stress distributions and energetics in the laterally ordered systems of buried pyramidal Ge/Si(001) islands: An atomistic simulation study
Makeev, M., Yu, W.-B., & Madhukar, A. (2003) · doi:10.1103/physrevb.68.195301 · Cited by 12
Evolution of penny-shaped microcracks by interface migration
Huang, P., Sun, J., & Li, Z.-H. (2003) · doi:10.1016/s0020-7683(03)00022-2 · Cited by 12
Morphological instability of pores and tubules
Kirill, D., Davis, S. H., Miksis, M., & Voorhees, P. (2002) · doi:10.4171/ifb/66 · Cited by 12
“The seminal work on evolution by surface diffusion, Mullins [11], formulates the equations for surface energy-driven diffusion.”
Background
Models of void electromigration
Cummings, L., Richardson, G., & Amar, M. B. B. (2001) · European journal of applied mathematics · doi:10.1017/s0956792501004326 · Cited by 12
“(A derivation of this law of motion by surface diffusion, which was first introduced by Mullins [21], is given in Davi & Gurtin [5]; see Elliott & Garcke [7] and the references therein for”
Method
Thermal grooving at the interface between alumina and monazite
Marshall, D. B., Waldrop, J., & Morgan, P. E. D. (2000) · doi:10.1016/s1359-6454(00)00233-0 · Cited by 12
Organometallic chemical vapor deposition of V-groove InGaAs/GaAs quantum wires incorporated in planar Bragg microcavities
Constantin, C., Martinet, E., Rudra, A., Leifer, K., Lelarge, F., Biasiol, G., & Kapon, E. (1999) · doi:10.1016/s0022-0248(99)00361-9 · Cited by 12
Surface morphologies of sputter-deposited aluminum films studied using a high-resolution phase-measuring laser interferometric microscope.
Furukawa, M., Yamamoto, Y., Ikakura, H., Tanaka, N., Hashimoto, M., Sano, A., & Shingubara, S. (1996) · Applied Optics · doi:10.1364/ao.35.000701 · Cited by 12
The growth dynamics of thick sputtered copper coatings under the influence of surface diffusion: A quantitative atomic force microscopy study
Eisenmenger-Sittner, C., Bergauer, A., Bangert, H., & Bauer, W. (1995) · doi:10.1063/1.359778 · Cited by 12
Evolution of phases and microstructure in optical waveguides of lithium niobate
Mccoy, M., Dregia, S., & Lee, W. E. (1994) · doi:10.1557/jmr.1994.2040 · Cited by 12
Evolution of structural and magnetic properties in Ta/Ni81Fe19 multilayer thin films
Hashim, I., Atwater, H., Kung, K., & Valletta, R. (1993) · doi:10.1063/1.355252 · Cited by 12
Hillock and island formation during annealing of gold films
Khan, M. S. R. (1987) · doi:10.1007/bf02744393 · Cited by 12
Thermal etching of silver
Rhead, G., & Mykura, H. (1962) · doi:10.1016/0001-6160(62)90206-7 · Cited by 12
Stability Enhancement of the Platinum Thin-Film Temperature Detector up to 1400 °C by Printing Al₂O₃ Protective Layer
Wang, H.-G., Liu, Z., Wang, B., Kong, M.-Y., Xu, D., Gao, L., Li, Q., Zhao, Z., Lu, W., Zhao, X., et al. (2024) · IEEE Sensors Journal · doi:10.1109/jsen.2024.3387085 · Cited by 11
“In the equilibrium state, the angle between the grain boundary and the free surface is the equilibrium angle θ [18], [41], [42] where γ g and γ s are the grain boundary energy and surface energy of Pt grains, respectively.”
Background
Finite element schemes with tangential motion for fourth order geometric curve evolutions in arbitrary codimension
Deckelnick, K., & Nürnberg, R. (2024) · Numerische Mathematik · doi:10.1007/s00211-025-01477-4 · Cited by 11
“Curves endowed with a geometric energy, and gradient flows related to these energies, are of interest in differential geometry, materials science, continuum mechanics, biological applications, microelectronics and computer vision, [34, 32, 29, 39, 20].”
Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus
Gennaro, D. D., Diana, A., Kubin, A., & Kubin, A. (2023) · Mathematische Annalen · doi:10.1007/s00208-024-02863-3 · Cited by 11
“It has been proposed in the physical literature by Mullins [37] to model surface dynamics for phase interfaces when the evolution is governed by mass diffusion in the interface.”
Engineering Epitaxy and Condensation: Fabrication of Ge Nanolayers, Mechanism and Applications
Berbezier, I., Bouabdellaoui, M., Bollani, M., Salvalaglio, M., Assaf, E., Favre, L., Abel, M., Ronda, A., Gourhant, O., Deprat, F., et al. (2023) · Social Science Research Network · doi:10.2139/ssrn.4343371 · Cited by 11
In-situ observation of the incipient melting of borides and its effect on the hot-workability of Ni-based superalloys
Schulz, B., Leitner, T., & Primig, S. (2023) · Journal of Alloys and Compounds · doi:10.1016/j.jallcom.2023.170324 · Cited by 11
Rigid Body Motion of Multiple Particles in Solid-State Sintering
Wakai, F., & Okuma, G. (2022) · Social Science Research Network · doi:10.2139/ssrn.4073477 · Cited by 11
Grain boundary grooving in a polycrystalline thin film: A phase-field study
Mukherjee, R., & Abinandanan, T. (2022) · Computational materials science · doi:10.1016/j.commatsci.2021.111076 · Cited by 11
Anomalous strain-energy-driven macroscale translation of grains during nonisothermal annealing
Higgins, M., Kang, J., Huang, G., Montiel, D., Lu, N., Liu, H., Shen, Y.-F., Staublin, P., Park, J.-S., Almer, J., et al. (2021) · PHYSICAL REVIEW MATERIALS · doi:10.1103/physrevmaterials.5.l070401 · Cited by 11
On Self-Limiting Rotation and Diffusion Mechanisms during Sintering of Silver Nanowires
Jahangir, M. N., Devaraj, H., & Malhotra, R. (2020) · doi:10.1021/acs.jpcc.0c05716 · Cited by 11
Influence of melt convection on the morphological evolution of seaweed structures: Insights from phase-field simulations
Laxmipathy, V. P., Wang, F., Selzer, M. A., Nestler, B., & Ankit, K. (2019) · Computational Materials Science · doi:10.1016/j.commatsci.2019.109196 · Cited by 12
Evolution of sorptive and textural properties of CaO-based sorbents during repetitive sorption/regeneration cycles: Part II. Modeling of sorbent sintering during initial cycles
Bazaikin, Y., Derevschikov, V., Malkovich, E. G., Lysikov, A., & Okunev, A. G. (2019) · Chemical Engineering and Science · doi:10.1016/j.ces.2018.12.065 · Cited by 11
Reshaping and sintering of 3D fcc metal nanoclusters: Stochastic atomistic modeling with realistic surface diffusion kinetics
Lai, K. C., & Evans, J. (2019) · PHYSICAL REVIEW MATERIALS · doi:10.1103/physrevmaterials.3.026001 · Cited by 11
Dynamic spheroidisation behaviour of the lamellar Ti–22Al–25Nb alloy during hot compression
Yang, J.-L., Wang, G.-F., Jiao, X.-Y., Li, Y.-T., & Zhang, K.-F. (2018) · doi:10.1080/02670836.2017.1415013 · Cited by 11
“The equilibrium equation (Equation (1)), proposed by Mullins [31], is suitable over a wide range to describe the spheroidisation process: γO−O γO−B2 = 2 cos θ (1) where γO−B2 and γO−O are the surface energies of the O-B2 and O-O phases, respectively, and 2θ is the angle between γO−B2 and γO−O.”
Background
Topography evolution of germanium thin films synthesized by pulsed laser deposition
Schumacher, P., Mayr, S. G., & Rauschenbach, B. (2017) · doi:10.1063/1.4981800 · Cited by 11
Modified Young's equation for equilibrium dihedral angles of grain boundary grooves in thin films at the nanoscale
Lin, S.-C., Liu, M.-W., Gururajan, M., & Wu, K.-A. (2016) · doi:10.1016/j.actamat.2015.09.037 · Cited by 11
Stability of a Lamellar Structure – Effect of the True Interlamellar Spacing on the Durability of a Pearlite Colony / Stabilność Struktury Płytkowej – Wpływ Rzeczywistej Odległości Międzypłytkowej Na Trwałość Kolonii Perlitu
Czarski, A., Skowronek, T., & Matusiewicz, P. (2015) · doi:10.1515/amm-2015-0405 · Cited by 11
Synergetic Light-Harvesting and Near-Field Enhancement in Multiscale Patterned Gold Substrates
Hernández, L. A. G., Millone, M. A. D., Cortés, E., Castez, M. F., Auguié, B., Vela, M., Salvarezza, R., & Fainstein, A. (2015) · doi:10.1021/acsphotonics.5b00345 · Cited by 11
Theoretical and Experimental Study of Metallic Dot Agglomeration Induced by Thermal Dewetting
Yoshino, M., Li, Z.-X., & Terano, M. (2015) · doi:10.1115/1.4029685 · Cited by 11
Microstructural evolution and mechanism of grain growth in magnesia ceramics prepared by high pressure and temperature with ultra-high heating rate
Liu, J.-H., Fu, Z., Wang, W.-M., Zhang, J.-Y., Wang, H., Wang, Y., Lee, S.-W., & Niihara, K. (2014) · Science China Technological Sciences · doi:10.1007/s11431-014-5518-0 · Cited by 11
Modeling dewetting of ultra-thin solid films
Chame, A., & Pierre-Louis, O. (2013) · doi:10.1016/j.crhy.2013.06.004 · Cited by 11
Grain boundary grooving in bi-crystal thin films induced by surface drift-diffusion driven by capillary forces and applied uniaxial tensile stresses
Akyildiz, Ö., Ören, E. E., & Oǧurtani, T. Ö. (2011) · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · doi:10.1080/14786435.2011.634850 · Cited by 11
Anisotropic surface energy formulations and their effect on stability of a growing thin film
Korzec, M., Münch, A., & Wagner, B. (2012) · doi:10.4171/ifb/291 · Cited by 11
“x; y; t/ based on Mullins’ surface diffusion equation [31, 39] ht D p”
Background
Domain Matching Epitaxy of Mg-Containing Ag Contact on p-Type GaN
Song, Y., Son, J., Yu, H.-K., Lee, J.-H., Jung, G., Lee, J. Y., & Lee, J.-L. (2011) · doi:10.1021/cg200323h · Cited by 11
Evolution of a fractal system with conserved order parameter under thermal annealing
Bahadur, J., Mazumder, S., Sen, D., & Ramanathan, S. (2010) · Journal of Physics: Condensed Matter · doi:10.1088/0953-8984/22/19/195107 · Cited by 11
Dynamic scaling in thin-film growth with irreversible step-edge attachment.
Reis, F. D. A. A. (2010) · doi:10.1103/physreve.81.041605 · Cited by 11
HOMOGENEOUS STATIONARY SOLUTION FOR BCF MODEL DESCRIBING CRYSTAL SURFACE GROWTH
Fujimura, H., & Yagi, A. (2009) · doi:10.32219/isms.69.3_295 · Cited by 11
“[11] W. W. Mullins, Theory of thermal grooving, J. Applied Phys.”
BackgroundInfluential
Nanometer-scale patterning of alkali halide surfaces by ion bombardment
Saeed, S., Sinha, O. P., Krok, F., & Szymoński, M. (2008) · doi:10.1016/j.apsusc.2008.06.043 · Cited by 11
Persistence and survival in equilibrium step fluctuations
Constantin, M., Dasgupta, C., Sarma, S. S. S., Dougherty, D. B., & Williams, E. D. (2007) · doi:10.1088/1742-5468/2007/07/p07011 · Cited by 11
Numerical study of the stability of (111) and (331) microfacets on Au, Pt, and Ir (110) surfaces
Ndongmouo, U. T., Hontinfinde, F., & Ferrando, R. (2005) · doi:10.1103/physrevb.72.115412 · Cited by 11
On the Grain Boundary Grooving in Thin Filaments
Klinger, L., & Rabkin, E. (2005) · doi:10.4028/www.scientific.net/ddf.249.213 · Cited by 11
Hydrogen-mediated quenching of strain-induced surface roughening during gas-source molecular beam epitaxy of fully-coherent Si0.7Ge0.3 layers on Si(001)
Spila, T., Desjardins, P., Vailionis, A., Kim, H., Taylor, N., Cahill, D., Greene, J., Guillon, S., & Masut, R. (2002) · doi:10.1063/1.1448680 · Cited by 11
Surface molecular diffusion in latex films observed by atomic force microscopy
Song, M., Hourston, D. J., Zhang, H.-X., Hammiche, A., & Pollock, H. M. (2001) · doi:10.1016/s0032-3861(01)00021-0 · Cited by 11
Finite-element simulation of the diffusive growth of grain boundary voids
Huang, P.-Z., Li, Z.-H., & Sun, J. (2000) · doi:10.1088/0965-0393/8/6/306 · Cited by 11
Using the tensile stress field to control quantum dot arrangements
Jin, Z., Wang, B.-Z., Peng, Y.-H., Zhao, F.-H., Chen, W.-Y., Liu, S.-Y., & Gao, C.-X. (1999) · doi:10.1016/s0039-6028(98)00934-0 · Cited by 11
Capillary instabilities in polycrystalline metallic foils: Experimental observations of thermal pitting in nickel
Genin, F., Mullins, W., & Wynblatt, P. (1994) · doi:10.1016/0956-7151(94)90167-8 · Cited by 11
Self-citation
The inclination dependence of the energy of Cu 19a grain boundaries
Schmelzle, R., Muschik, T., Gust, W., & Predel, B. (1991) · doi:10.1016/0956-716x(91)90339-3 · Cited by 11

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