Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Physical Sciences Reviews

Ed. by Giamberini, Marta / Jastrzab, Renata / Liou, Juin J. / Luque, Rafael / Nawab, Yasir / Saha, Basudeb / Tylkowski, Bartosz / Xu, Chun-Ping / Cerruti, Pierfrancesco / Ambrogi, Veronica / Marturano, Valentina / Gulaczyk, Iwona

Online
ISSN
2365-659X
See all formats and pricing
More options …

Multi-facets of kinetic roughening of interfaces

Palash Nath
  • Department of Physics, Kaliyaganj College, Kaliyaganj, Uttar Dinajpur -733129, West Bengal, India
  • This work was initiated at National Institute of Science Education and Research, Bhubaneswar, Orissa - 752050, India
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Debnarayan Jana
Published Online: 2018-11-24 | DOI: https://doi.org/10.1515/psr-2017-0109

Abstract

In this review, the authors are going to explore the intriguing aspects of kinetic roughening of interfaces. Interface roughness dynamics connected with various physical processes have been studied through novel microscopic models in connection with experiments. The statistical properties of such rough interfaces appearing in wide range of physical systems are observed to belong to different universality classes characterized by the scaling exponents. With the advancement of characterization techniques, the scaling exponents of thin-film surface (or the morphological evolution of amorphous surfaces eroded by ion bombardment) are easily computed even in situ during the growing (erosion) conditions. The relevant key physical parameters during the dynamics crucially control the overall scaling behaviour as well as the scaling exponents. The non-universal nature of scaling exponents is emphasized on the variations of the physical parameters in experimental studies and also in theoretical models. Overall, this review containing both theoretical and experimental results will unfold some novel features of surface morphology and its evolution and shed important directions to build an appropriate theoretical framework to explain the observations in systematic and consistent experiments.

Keywords: kinetic roughening; scaling exponents; interface growth; discrete models; continuum models

References

  • [1]

    Gupta S, Majumdar SN, Sihcr G. Fluctuating interfaces subject to stochastic resetting. Phys Rev Lett. 2014;112:220601 (4pp).PubMedGoogle Scholar

  • [2]

    Carter RWG, Woodroffe CD, editors. Coastal evolution, late quarternary shoreline morphodynamics. Cambridge: Cambridge University Press, 1994.Google Scholar

  • [3]

    Sapoval B, Baldassarri A, Gabrielli A. Self-stabilized fractality of seacoasts through damped erosion. Phys Rev Lett. 2004;93:098501 (4pp).PubMedGoogle Scholar

  • [4]

    Family F, Vicsek T. Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model. J Phys A: Math Gen. 1985;18:L75 (4pp).Google Scholar

  • [5]

    Kim JM, Kosterlitz JM. Growth in a restricted solid-on-solid model. Phys Rev Lett. 1989;62:2289–92.CrossrefGoogle Scholar

  • [6]

    Mandal PK, Jana D. Multifractal behavior of the surfaces evolved with surface relaxation. Phys Rev E. 2008;77:061604 (6pp).Google Scholar

  • [7]

    Mandal PK, Jana D. Non-universal finite-size scaling of rough surfaces. J Phys A: Math Theor. 2009;42:485004 (15pp).Google Scholar

  • [8]

    Miranda AM, Menezes-Sobrinho IL, Couto MS. Spontaneous imbibition experiment in newspaper sheets. Phys Rev Lett. 2010;104:086101 (4pp).PubMed

  • [9]

    Mandal PK, Nath P, Jana D. Experimental evidence of multiaffinity of pinned interfaces. Eur Phys J B. 2013;86:132 (6pp).Google Scholar

  • [10]

    Kumar PBS, Jana D. Imbibition: experiment and simulation Physica A. 1996;224:199–206.Google Scholar

  • [11]

    Zhang J, Zhang YC, Astrøm P, Levinsen MT. Modeling forest fire by a paper-burning experiment, a realization of the interface growth mechanism. Physica A. 1992;189:383–9.CrossrefGoogle Scholar

  • [12]

    Czirók A, Somafai E, Vicsek T. Self-affine roughening in a model experiment on erosion in geomorphology. Physica A. 1994;205:355–66.CrossrefGoogle Scholar

  • [13]

    Somafai E, Czirók A, Vicsek T. Power-law distribution of landslides in an experiment on the erosion of a granular pile. J Phys A: Math Gen. 1994;27:L757–64.CrossrefGoogle Scholar

  • [14]

    Mello BA, Chaves AS, Oliveira FA, Fernando A. Discrete atomistic model to simulate etching of a crystalline solid. Phys Rev E. 2001;63:041113 (8pp).Google Scholar

  • [15]

    Barabási AL, Stanley HE. Fractal concepts in surface growth. Cambridge, New York: Cambridge University Press, 1995.

  • [16]

    Meakin P. The growth of rough surfaces and interfaces. Phys Rep. 1993;235:189–289.CrossrefGoogle Scholar

  • [17]

    Healy TH, Zhang YC. Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics. Phys Rep. 1985;254:215–414.Google Scholar

  • [18]

    Jana D. On a simple yet interesting experiment in complex system. Phys Teach. 1998;40:161–6.Google Scholar

  • [19]

    Kardar M, Parisi G, Zhang YC. Dynamic scaling of growing interfaces. Phys Rev Lett. 1986;56:889–92.CrossrefPubMedGoogle Scholar

  • [20]

    Edwards SF, Wilkinson DR. The surface statistics of a granular aggregate. Proc R Soc Lond. 1982;A381:17–31.Google Scholar

  • [21]

    Wolf DE, Kertész J. Surface width exponents for three- and four-dimensional Eden growth. Europhys Lett. 1987;4:651–7.CrossrefGoogle Scholar

  • [22]

    Kim Y. Growth equation for a simple vapor deposition model. Prog Theo Phys. 2000;104:495 (10pp).Google Scholar

  • [23]

    Jullien R, Botet R. Scaling properties of the surface of the Eden model in d=2, 3, 4. J Phys A. 1985;18:2279–88.CrossrefGoogle Scholar

  • [24]

    Sarma SD, Tamborenea P. A new universality class for kinetic growth: One-dimensional molecular-beam epitaxy. Phys Rev Lett. 1991;66:325–8.CrossrefPubMedGoogle Scholar

  • [25]

    Horowitz CM, Monetti RA, Albano EV. Competitive growth model involving random deposition and random deposition with surface relaxation. Phys Rev E. 2001;63:066132 (6pp).Google Scholar

  • [26]

    Pellegrini YP, Jullien R. Roughening transition and percolation in random ballistic deposition. Phys Rev Lett. 1990;64:1745–8.PubMedCrossrefGoogle Scholar

  • [27]

    Silveira FA, Aar ao Reis FDA. Surface and bulk properties of deposits grown with a bidisperse ballistic deposition model. Phys Rev E. 2007;75:061608 (7pp).Google Scholar

  • [28]

    Kolakowska A, Novotny MA. Comment on “Dynamic properties in a family of competitive growing models”. Phys Rev E. 2010;81:033101 (2pp).Google Scholar

  • [29]

    Alava M, Dubé M, Rost M. Imbibition in disordered media. Adv Phys. 2004;53:83–175.CrossrefGoogle Scholar

  • [30]

    Cuerno R, Castro M, Cuerno R, Castro M, Munoz-GarcÍa J, Gago R, et al. Universal non-equilibrium phenomena at submicrometric surfaces and interfaces. Euro Phys J Special Topics. 2007;146:427–41.CrossrefGoogle Scholar

  • [31]

    Ramasco JJ, Lopez JM, Rodriguez MA. Generic dynamic scaling in kinetic roughening. Phys Rev Lett. 2000;84:2199 (4pp).PubMedGoogle Scholar

  • [32]

    Juknevicius V, Ruseckas J, Armaitis J. Large scale spatio-temporal behaviour in surface growth scaling and dynamics of slow height variations in generalized two-dimensional Kuramoto-Sivashinsky equations. Eur Phys J. B 2017;90:163 (12pp).Google Scholar

  • [33]

    Garca-Carranco SM, Bory-Reyes J, Balankin AS. The crude oil price bubbling and universal scaling dynamics of price volatility. Physica A. 2016;452:60–8.CrossrefGoogle Scholar

  • [34]

    Buldyrev SV, Barabási AL, Caserta F, Havlin S, Stanley HE, Vicsek T. Anomalous interface roughening in porous media: experiment and model. Phys Rev A. 1992;45:R8313–6.CrossrefGoogle Scholar

  • [35]

    Nath P, Mandal PK, Jana D. Kardar-Parisi-Zhang universality class of a discrete erosion model. Int J Mod Phys C. 2015;26:1550049 (11pp).Google Scholar

  • [36]

    Nath P, Jana D. Observation of nonuniversal scaling exponent in a novel erosion model. Int J Mod Phys C. 2015;26:1550115 (13pp).Google Scholar

  • [37]

    Chan WL, Chason E. Making waves: kinetic processes controlling surface evolution during low energy ion sputtering. J Appl Phys. 2007;101:121301 (46pp).Google Scholar

  • [38]

    Nabiyouni G, Jalali Farahani B. Anomalous scaling in surface roughness evaluation of electrodeposited nanocrystalline Pt thin films. Appl Surf Sci. 2009;256:674–82.CrossrefGoogle Scholar

  • [39]

    Yadava RP, Dwivedi S, Mittal AK, Kumar M, Pandey AC. Fractal and multifractal analysis of LiF thin film surface. Appl Surf Sci. 2012;261:547–53.CrossrefGoogle Scholar

  • [40]

    Gredig T, Silverstein EA, Byrne MP. Height–Height correlation function to determine grain size in iron phthalocyanine thin films. J Phys Conf Series. 2013;417:012069 (5pp).Google Scholar

  • [41]

    Kolanek K, Tallarida M, Michling M, Schmeisser D. In situ study of the atomic layer deposition of HfO2 on Si. J Vac Sci Technol. 2012;30:01A143(15pp); Kolanek K, Tallarida M, Schmeisser D. Height distribution of atomic force microscopy images as a tool for atomic layer deposition characterization. J Vac Sci Technol. 2013;31:01A104 (13pp); Characterization of HfO2/La2 O3 layered stacking deposited on Si substrate. J Vac Sci Technol B. 2013;31:01A113 (5pp).Google Scholar

  • [42]

    Chanphana R, Chatraphorn P, Dasgupta C. Healing time for the growth of thin films on patterned substrates. Physica A. 2014;407:160–74.CrossrefGoogle Scholar

  • [43]

    Cureno R, Vazquez L. Advances in condensed matter and statistical physics, edited by E. Korutcheva and R. Cuerno. New York: Nova Science Publishers, 2004:237–59.

  • [44]

    Krug J. Origins of scale invariance in growth processes. Adv Phys. 1997;46:139–282.CrossrefGoogle Scholar

  • [45]

    Meakin P. Fractals, scaling and growth far from equilibrium. Cambridge: Cambridge University Press, 1998.

  • [46]

    Krug J. Turbulent interfaces. Phys Rev Lett. 1994;72:2907–10.CrossrefPubMedGoogle Scholar

  • [47]

    Krug J, Spohn H. Solids far from equilibrium, edited by C. Godréche. Cambridge: Cambridge University Press, 1992.

  • [48]

    Krim J, Palasantzas G. Experimental observation of self–affine scaling and kinetic roughening at sub–micron lengthscales. Int J Mod Phys B. 1995;9:599–632.CrossrefGoogle Scholar

  • [49]

    Gokhale S, Nagamanasa KH, Santosh V, Sood AK, Ganpathy R. Directional grain growth from anisotropic kinetic roughening of grain boundaries in sheared colloidal crystals. PNAS. 2012;109:20314–9.CrossrefPubMedGoogle Scholar

  • [50]

    Malcai O, Lidar DA, Biham O, Avnir D. Scaling range and cutoffs in empirical fractals. Phys Rev E. 1997;56:2817–28.CrossrefGoogle Scholar

  • [51]

    Ojeda F, Cuerno R, Salvarezza R, Vázquez L. Dynamics of rough interfaces in chemical vapor deposition: experiments and a model for silica films. Phys Rev Lett. 2000; 84:3125–8;Ojeda F, Cuerno R, Salvarezza R, Agulló–Rueda F, Vázquez L. Modeling heterogeneity and memory effects on the kinetic roughening of silica films grown by chemical vapor deposition. Phys Rev B. 2003;67:245416 (13pp).Google Scholar

  • [52]

    Gago R, Vázquez L, Cuerno R, Varela M, Ballesteros C, Albella JM. Production of ordered silicon nanocrystals by low–energy ion sputtering. Appl Phys Lett. 2001;78:3316–8.CrossrefGoogle Scholar

  • [53]

    Henkel M, Noh JD, Pleimling M. Phenomenology of aging in the Kardar–Parisi–Zhang equation. Phys Rev E. 2012;85:030102 (5pp).Google Scholar

  • [54]

    Allegra N, Fortin JY, Henkel M. Boundary crossover in semi-infinite non-equilibrium growth processes. J Stat Mech. 2014;2014:P02018.Google Scholar

  • [55]

    Imamura T, Sasamoto T. Exact solution for the stationary Kardar–Parisi–Zhang equation. Phys Rev Lett. 2002;108:190603 (5pp).Google Scholar

  • [56]

    Calabrese P, Doussal PL. Exact solution for the Kardar–Parisi–Zhang equation with flat initial conditions. Phys Rev Lett. 2011;106:250603 (4pp).PubMedGoogle Scholar

  • [57]

    Santalla SN, Lagura JR, Gatta TL, Cuerno R. Random geometry and the Kardar-Parisi-Zhang (KPZ) universalility class. New J Phys. 2015;17:033018(13pp); Crdoba-Torres P, Santalla SN, Cuerno R, Rodrguez-Laguna R. Kardar-Parisi-Zhang Universality in first-passage percolation: the role of geodesic degeneracy. ArXiV:1802.05253.

  • [58]

    Sasamoto T, Spohn H. Point–interacting Brownian motions in the KPZ universality class. Electr J Probab. 2015;20:1 (28pp).Google Scholar

  • [59]

    Hairer M, Quastel J. A class of growth models rescaling to KPZ. ArXiV:1512.07845v1.

  • [60]

    Wio HS, Rodrguez MA, Gallego R, Deza RR, Revelli JA. KPZ dynamics from a variational perspective: potential landscape, time behavior, and other issues. ArXiV:1511.03727v1.

  • [61]

    Takenchi KA, Sano M, Sasamoto T, Spohn H. Growing interfaces uncover universal fluctuations behind scale invariance. Sci Rep. 2011;1:34 (5 pp).PubMedGoogle Scholar

  • [62]

    Huergo MAC, Pasquale MA, González PH, Bolzán AE, Arvia AJ. Growth dynamics of cancer cell colonies and their comparison with noncancerous cells. Phys Rev E. 2012;85:011918 (9pp).Google Scholar

  • [63]

    Khanin K, Nechaev S, Oshanin G, Sobolevski A, Vasilyev O. Ballistic deposition patterns beneath a growing Kardar–Parisi–Zhang interface. Phys Rev E. 2010;82:061107 (10pp).Google Scholar

  • [64]

    Wolf DE, Villain J. Growth with surface diffusion. Europhys Lett. 1990;13:389–94.CrossrefGoogle Scholar

  • [65]

    Alves SG, Moreira JG. Transitions in a probabilistic interface growth model. J Stat Mech. 2011;P04022 (9pp).Google Scholar

  • [66]

    Anspach N, Linz SJ. Modeling particle redeposition in ion-beam erosion processes under normal incidence. J Stat Mech. 2010;P06023 (27pp).Google Scholar

  • [67]

    Kim JM, Sarma SD. Growth in a restricted–curvature model. Phys Rev E. 1993;48:2599–602.CrossrefGoogle Scholar

  • [68]

    Jeong HC, Kim JM. Restricted curvature model with suppression of extremal height. Phys Rev E. 2002;66:051605 (5pp).Google Scholar

  • [69]

    Jeong HC, Kim JM, Choi H, Kim Y. Anomaly of the height–height correlation functions in self–flattening surface growth. Phys Rev E. 2003;67:046117 (4pp).Google Scholar

  • [70]

    Pagnani A, Parisi G. Multisurface coding simulations of the restricted solid–on–solid model in four dimensions. Phys Rev E. 2013;87:010102 (4pp).Google Scholar

  • [71]

    Oliveira TJ, Aar ao Reis FDA. Roughness exponents and grain shapes. Phys Rev E 2011;83:041608 (7pp).Google Scholar

  • [72]

    Lita AE, Sanchez JE. Effects of grain growth on dynamic surface scaling during the deposition of Al polycrystalline thin films. Phys Rev B. 2000;61:7692–9.CrossrefGoogle Scholar

  • [73]

    Kleinke MU, Davalos J, da Fonseca CP, Gorenstein A. Scaling laws in annealed LiCoOx films. Appl Phys Lett. 1999;74:1683–5.CrossrefGoogle Scholar

  • [74]

    Vasco E, Polop C, Ocal C. Growth atomic mechanisms of pulsed laser deposited La modified PbTiO3 perovskites. Eur Phys J B. 2003;35:49.CrossrefGoogle Scholar

  • [75]

    Ehrlich G, Hudda FG. Atomic view of surface self-diffusion: tungsten on tungsten. J Chem Phys. 1966;44:1039–49.CrossrefGoogle Scholar

  • [76]

    Schwoebel RL. Step motion on crystal surfaces. J Appl Phys. 1966;37:3682–6.CrossrefGoogle Scholar

  • [77]

    Politi P, Grenet G, Marty A, Ponchet A, Villain J. Instabilities in crystal growth by atomic or molecular beams. Phys Rep. 2000;324:271–406.CrossrefGoogle Scholar

  • [78]

    Pierre-Louis O, DOrsogna MR, Einstein TL. Edge diffusion during growth: the Kink Ehrlich-Schwoebel effect and resulting instabilities. Phys Rev Lett. 1998;82:3661–4.Google Scholar

  • [79]

    Kaufmanna NAK, Lahourcadea L, Hourahineb B, Martina D, Grandjean N. Critical impact of EhrlichSchwbel barrier on GaN surface morphology during homoepitaxial growth. J Cryst Growth. 2016;433:36–42.CrossrefGoogle Scholar

  • [80]

    Leal FF, Ferreira SC, Ferreira SO. Modelling of epitaxial film growth with an EhrlichSchwoebel barrier dependent on the step height. J Phys: Condens Matter. 2011;23:292201 (6pp).PubMedGoogle Scholar

  • [81]

    Gianfrancesco AG, Tselev A, Baddorf AP, Kalinin SV, Vasudevan RK. The EhrlichSchwoebel barrier on an oxide surface: a combined Monte-Carlo and in situ scanning tunneling microscopy approach. Nanotechnology. 2015;26:455705.PubMedCrossrefGoogle Scholar

  • [82]

    Gerlach R, Maroutian T, Douillard L, Martinotti D, Ernst HJ. A novel method to determine the EhrlichSchwoebel barrier. Surf Sci. 2001;480:97–102.CrossrefGoogle Scholar

  • [83]

    Li SC, Han Y, Jia JF, Xue QK, Liu F. Determination of the Ehrlich-Schwoebel barrier in epitaxial growth of thin films. Phys Rev B. 2006;74:195428.CrossrefGoogle Scholar

  • [84]

    Banerjee K, Shamanna J, Ray S. Surface morphology of a modified ballistic deposition model. Phys Rev E. 2014;90:022111 (7pp).Google Scholar

  • [85]

    Mal B, Ray S, Shamanna J. Revisiting surface diffusion in random deposition. Eur Phys J B. 2011; 82:341(7pp); Mal B, Ray S, Shamanna J. Surface properties and scaling behavior of a generalized ballistic deposition model. Phys Rev E. 2016;93:022121 (6pp).Google Scholar

  • [86]

    Horowitz CM, Albano EV. Dynamic scaling for a competitive growth process: random deposition versus ballistic deposition. J Phys A. 2001;34:357.CrossrefGoogle Scholar

  • [87]

    Horowitz CM, Albano EV. Dynamic properties in a family of competitive growing models. Phys Rev E. 2006;73:031111 (8pp).Google Scholar

  • [88]

    Robledo A, Grabill CN, Kuebler SM, Dutta A, Heinrich H, Bhattacharya A. Morphologies from slippery ballistic deposition model: a bottom–up approach for nanofabrication. Phys Rev E. 2011;83:051604 (9pp).Google Scholar

  • [89]

    Lehnen C, Lu TM. Morphological evolution in ballistic deposition. Phys Rev B. 2010;82:085437 (4pp).Google Scholar

  • [90]

    Family F. Scaling of rough surfaces: effects of surface diffusion. J Phys A. 1986;19:L441–6.CrossrefGoogle Scholar

  • [91]

    Topic N, Pöschel T. Steepest descent ballistic deposition of complex shaped particles. J Comput Phys. 2016;308:421–37.CrossrefGoogle Scholar

  • [92]

    Efraim Y, Taitelbaum H. Can Ising model and/or QKPZ equation properly describe reactive–wetting interface dynamics? Cent Eur J Phys. 2009;7:503 (6pp).Google Scholar

  • [93]

    Corberi F, Lippiello E, Zannetti M. Roughening of an interface in a system with surface or bulk disorder. J Phys A (UK). 2016;49:185001 (16pp).Google Scholar

  • [94]

    Mullins WW. Theory of thermal grooving. J Appl Phys. 1957;28:333–9;Herring C. The physics of powder metallurgy, edited W. E. Kingston. New York; McGraw-Hill, 1951.

  • [95]

    Villain J. Continuum models of crystal growth from atomic beams with and without desorption. J Phys I France. 1991;1:19–42.CrossrefGoogle Scholar

  • [96]

    Lai ZW, Sarma SD. Kinetic growth with surface relaxation: continuum versus atomistic models. Phys Rev Lett. 1991;66:2348–51.CrossrefPubMedGoogle Scholar

  • [97]

    Chen YJ, Zapperi S, Sethna JP. Crossover behavior in interface depinning. Phys Rev E. 2015;92:022146 (7pp).Google Scholar

  • [98]

    Vivo E, Nicoli M, Engler M, Michely T, Vázquez L, Cuerno R. Surface anisotropy in surface kinetic roughening: analysis and experiments. Phys Rev E. 2012;86:245427 (8pp).Google Scholar

  • [99]

    Vivo E, Nicoli M, Cuerno R. Strong anisotropy in two dimensional surfaces with generic scale invariance: gaussian and related models. Phys Rev E. 2012;86:051611 (12pp).Google Scholar

  • [100]

    Vivo E, Nicoli M, Cuerno R. Strong anisotropy in two dimensional surfaces with generic scale invariance: non–linear effects. Phys Rev E. 2014;89:042407 (21pp).Google Scholar

  • [101]

    Garg SK, Cuerno R, Kanjilal D, Som T. Anomalous behavior in temporal evolution of ripple wavelength under medium energy Ar+ ion bombardment on Si: a case of initial wavelength selection. J Appl Phys USA. 2016;119:225301 (7pp).Google Scholar

  • [102]

    Sperlin BA, Abelson JR. Kinetic roughening of amorphous silicon during hot–wire chemical vapor deposition at low temperature. J Appl Phys. 2007;101:024915 (7pp).Google Scholar

  • [103]

    Aurongzeb D, Washinton E, Basavaraj M, Berg JM, Temkin H, Holtz M. Nanoscale surface roughening in ultrathin aluminum films. J Appl Phys. 2006;100:114320 (4pp).Google Scholar

  • [104]

    Pal A, Ghosh R, Giri PK. Early stages of growth of Si nanowires by metal assisted chemical etching: a scaling study. Appl Phys Lett. 2015;107:072104 (5pp).Google Scholar

  • [105]

    Drotar JT, Zhao YP, Lu TM, Wang GC. Surface roughening in shadowing growth and etching in 2 + 1 dimensions. Phys Rev B. 2000;62:2118–25.CrossrefGoogle Scholar

  • [106]

    Yao JH, Guo H. Shadowing instability in three dimensions. Phys Rev E. 1993;47:1007–11.CrossrefGoogle Scholar

  • [107]

    Pelliccione M, Karabacak T, Gaire C, Wang GC, Lu TM. Mound formation in surface growth under shadowing. Phys Rev B 2006;74:125420 (10pp).Google Scholar

  • [108]

    Wang L, Walker G, Chai J, Iacopi A, Fernandes A, Dimitrijev S. Kinetic surface roughening and wafer bow control in heteroepitaxial growth of 3C–SiC on Si(111) substrates. Sci Rep. 2015;5:15423 (8pp).PubMedGoogle Scholar

  • [109]

    Bouchbinder E, Procaccia I, Santucci S, Vaenl L. Fracture surfaces as multiscaling graphs. Phys Rev Lett. 2006;96:055509 (4pp).PubMedGoogle Scholar

  • [110]

    Bouchbinder E, Mathiesen J, Procaccia I. Roughening of fracture surfaces: the role of plastic deformation. Phys Rev Lett. 2004;92:245505 (4pp).PubMedGoogle Scholar

  • [111]

    Bak P, Tang C, Wiesenfeld K. Self-organized criticality: an explanation of the 1/f noise. Phys Rev Lett. 1987;59:381–4.PubMedCrossrefGoogle Scholar

  • [112]

    Chowdhury D, Ghose D, Mollick SA, Satpati B, Bhattacharya SR. Nanorippling of ion irradiated GaAs (001) surface near the sputter-threshold energy. Phys Stat Solidi (B) 2015;252:811–5.CrossrefGoogle Scholar

  • [113]

    Brú A, Albertos S, Garc&’ıa-Asenjo JAL, Brú I. Pinning of tumoral growth by enhancement of the immune response. Phys Rev Lett. 2004;92:238101 (4pp).PubMedGoogle Scholar

  • [114]

    Barness D, Efraim Y, Taitelbaum H, Sinvani M, Shaulov A, YeshurunY. Kinetic roughening of magnetic flux fronts in Bi2Sr2CaCu2O8+δ crystals with columnar defects. Phys Rev B. 2012;85:174516 (5pp).Google Scholar

  • [115]

    Tang LH, Kardar M, Dhar D. Driven depinning in anisotropic media. Phys Rev Lett. 1995;74:920–3.PubMedCrossrefGoogle Scholar

  • [116]

    Zhao YP. Kinetic roughening in polymer film growth by vapor deposition. Phys Rev Lett. 2000;85:3229–32.CrossrefPubMedGoogle Scholar

  • [117]

    Lai ZW, Sarma SD. Kinetic growth with surface relaxation: continuum versus atomistic models. Phys Rev Lett. 1991;66:2348–51.CrossrefPubMedGoogle Scholar

  • [118]

    d’Affara G, Caldore I. (Communita Mountana Centro Caldore, Cortina, 1990).

  • [119]

    Verma P, Mager MD, Melosh MA. Rough-smooth-rough dynamic interface growth in supported lipid bilayers. Phys Rev E. 2014;89:012404 (5pp).Google Scholar

  • [120]

    Straumal BB, Kogenkova OA, Gornakova AS, Sursaeva VG, Baretzky B. Review: garin boundary faceting-roughening phenomena. J Mater Sci 2016;54:382–404.Google Scholar

  • [121]

    Straumal BB, Semenov VN, Kogenkova OA, Watanabe T. Pokrovsky-Talapov critical behavior and rough-to-rough ridges of the ∑3 coincidence tilt boundary in Mo. Phys Rev Lett. 2004;92:19610 (4pp).Google Scholar

  • [122]

    Andreed AF. Faceting phase transitions of crystals. Sov Phys JETP. 1981;53:1063–9.Google Scholar

  • [123]

    Pokrovsky VL, Talapov AL. Ground state, spectrum and phase diagram of two-dimensional incommensurate crystals. Phys Rev Lett. 1979;42:65 (4pp).Google Scholar

  • [124]

    Straumal BB, Gornakova AS, Sursaeva VG, Yashoniko VP. Second order faceting-foughening of teh tilt grain boundary in zinc. Int J Mater Res. 2009;100:525–9.CrossrefGoogle Scholar

  • [125]

    Nasehnejad M, Nabiyouni G, Shahraki MG. Thin film growth by 3D multi-particle diffusion limited aggregation model: anomalous roughening and fractal analysis. Physica A. 2018;493:135–47.CrossrefGoogle Scholar

  • [126]

    Nasehnejad M, Shahraki MG, Nabiyouni G. Atomic force microscopy study, kinetic roughening and multifractal analysis of electrodeposited silver films. Appl Surf Sci. 2016;389:735–41.CrossrefGoogle Scholar

  • [127]

    Schneider NM, Park JH, Grogan JM, Steingart DA, Bau HH, Ross FM. Nanoscale evolution of interface morphology during electrodeposition. Nat Commun. 2017;8:2174 (10pp).PubMedGoogle Scholar

  • [128]

    Townsend ER, Enckevort WJP, Meijer JAM, Vlieg E. Additive enhanced creeping of sodium chloride crystals. Cryst Growth Des. 2017;17:3107–15.PubMedCrossrefGoogle Scholar

  • [129]

    Hsu C-L, Juang M-Y, Lin P-W, Liaw B-R, Shih C-T. Temperature-dependent morphology and characteristic parameters of annealed gold nanolayers. Phys Status Solidi B. 2017;254:1600855 (5pp).Google Scholar

  • [130]

    Harel M, Taitelbaum H. Effect of temperature on the dynamics and geometry of reactive-wetting interfaces around room temperature. Phys Rev E. 2017;96:062801 (7pp).PubMedGoogle Scholar

  • [131]

    Olafson KN, Rimer JD, Vekilov PG. Early onset of kinetic roughening due to a finite step width in hematin crystallization. Phys Rev Lett. 2017;119:198101 (4pp).PubMedGoogle Scholar

  • [132]

    Mondal S, Chowdhury D, Barman P, Bhattacharyya SR. Growth dynamics of copper thin film deposited by soft-landing of size selected nanoclusters. Eur Phys J. D 2017;71:327 (5pp).Google Scholar

  • [133]

    Santalla SN, RodrÍguez-Laguna J, Abad JP, MarÍn I, Espinosa MM, Muñoz-GarcÍa J. et al. Non-universality of front fluctuations for compact colonies of non-motile bacteria. arXiv:1702.03903.Google Scholar

  • [134]

    Orrillo PA, Santalla SN, Cuerno R,Vzquez L, Ribotta SB, Gassa LM, et al. Morphological stabilization and KPZ scaling by electrochemically induced co-deposition of nanostructured NiW alloy films. Sci Rep. 2017;7:17997(12pp).PubMedGoogle Scholar

  • [135]

    Castro M, Cuerno R, Nicoli M, Vzquez L, Buijnsters JG. Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants. New J Phys. 2012;14:103039 (15pp).Google Scholar

  • [136]

    Cuerno R, Castro M. Transients due to instabilities hinder Kardar-Parisi-Zhang scaling: a unified derivation for surface growth by electrochemical and chemical vapor deposition. Phys Rev Lett. 2001;87:236103 (4pp).Google Scholar

  • [137]

    Nicoli M, Castro M, Cuerno R. Unified moving-boundary model with fluctuations for unstable diffusive growth. Phys Rev E. 2008;78:021601 (17pp).Google Scholar

About the article

Published Online: 2018-11-24


Citation Information: Physical Sciences Reviews, Volume 4, Issue 4, 20170109, ISSN (Online) 2365-659X, DOI: https://doi.org/10.1515/psr-2017-0109.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in