Towards multiscale modelling of localised corrosion

Abstract

Localised corrosion is a cause of unanticipated and sometimes catastrophic failures of equipment, transport vessels and infrastructures. Therefore, the development of modern corrosion-resistant materials and inhibitors by design is both technically and economically attractive. In the coming decades, industrial components will be engineered from molecular structures. This prospect provides the designer with a truly enormous range of choices in design, which is a situation that demands predictive tools that can link molecular structures with the final component performance. In particular, the development of alloys and inhibitors can replace the use of toxic compounds in protecting metal surfaces. To execute a tailored design programme, it is necessary to understand how corrosion and the associated processes occur from the molecular level to the component level and how the overall system behaviour emerges because of the inherent links among different scales. Therefore, in the present work, the literature on theoretical modelling of localised corrosion and related experimentation are reviewed from a multiscale viewpoint. The review addresses (a) the challenges in the theoretical formulation of the important phenomena that influence localised corrosion and (b) the hurdles facing computational methods. It is shown that (i) the existing models lack the resolution to design effective corrosion-resistant systems, (ii) the numerical strategies for linking the scales are in a state of evolution and (iii) there are gaps in the experimental characterisation of the corrosion system, particularly at the lower end of the scales. Suggestions are provided towards the construction of a multiscale model (MSM) for localised corrosion.

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References

Kutz

(ed.): ‘Handbook of environmental degradation of materials’; 2005, Norwich, NY, USA, William Andrew, Inc.

Ahmed

: ‘Principles of corrosion engineering and corrosion control’; 2006, Oxford, UK, Butterworth-Heinamann.

Zhang

: ‘Building from the bottom up’, Mater. Today, 2003, 6, (5), 20–27.

Azmat

N. S.

Ralston

K. D.

Muster

T. H.

Muddle

B. C.

and Cole

I. S.

: ‘A high-throughput test methodology for atmospheric corrosion studies’, J. Electrochem. Soc., 2011, 14, (6), C9–C11.

Elliot

J. A.

: ‘Novel approaches to multiscale modelling in materials science’, Int. Mater. Rev., 2011, 56, (4), 207–225.

Cole

I. S.

Azmat

N. S.

Kanta

and Venkatraman

: ‘What really controls the atmospheric corrosion of zinc? Effect of marine aerosols on atmospheric corrosion of zinc’, Int. Mater. Rev., 2009, 54, (3), 117–133.

Maurice

and Marcus

: ‘Passive films at the nanoscale’, Electrochim. Acta., 2012, 84, 129–138.

Franco

A. A.

and Gerard

: ‘Multiscale model of carbon corrosion in a PEFC: coupling with electrocatalysis and impact on performance degradation’, J. Electrochem. Soc., 2008, 155, (4), B367–B384.

Ingram

G. D.

Cameron

I. T.

and Hangos

K. M.

: ‘Classification and analysis of integrating frameworks in multiscale modelling’, Chem. Eng. Sci., 2004, 59, 2171–2187.

10.

Rafii-Tabar

and Chirazi

: ‘Multi-scale computational modelling of solidification phenomena’, Phys. Rep., 2002, 365, 145–249.

11.

C.-J.

: ‘Atomistic simulations for material processes within multiscale method’; 2009, Aachen, Rheinisc-Westfalischen Technischen Hochschule Aachen.

12.

Tan

: Combined atomistic and continuum simulation of fracture and corrosion, in ‘Comprehensive structural integrity’ volume 8: ‘Interfacial and nanoscale fracture’, Editors-in-Chief: I. Milne, R. O. Ritchie, and B. Karihaloo, 2003, Oxford, UK, Pergamon, 413–451.

13.

Frankel

G. S.

and Stratmann

: ‘Meeting report: future perspectives of corrosion science’, Corros. Eng., Sci. and Technol., 2009, 44, (5), 328–331.

14.

Shifler

D. A.

: ‘Factors that influence corrosion of materials and how modeling may predict these effects’, 2005 Tri-Service Corrosion Conf., November 14–18, 2005, Orlando, FL, NACE.

15.

Anderko

: ‘Modeling of aqueous corrosion’, in ‘Shreir’s corrosion’, (eds. T. Richardson, et al.), 4th edn, 1585–1629; 2010, Toronto, ON, ChemTec Publishing Inc.

16.

Cubicciotti

: ‘Potential-pH diagrams for alloy-water systems under LWR conditions’, J. Nucl. Mater., 1993, 201, 176–183.

17.

Bouzoubaa

Costa

Diawara

Audiffern

and Marcus

: ‘Insight of DFT and atomistic thermodynamics on the adsorption and insertion of halides onto the hydroxylated NiO(111) surface’, Corros. Sci., 2010, 52, 2643–2652.

18.

Bouzoubaa

Diawara

Maurice

Minot

and Marcus

: ‘Ab initio modeling of localized corrosion: study of the role of surface steps in the interaction of chlorides with passivated nickel surfaces’, Corros. Sci., 2009, 51, 2174–2182.

19.

Chakraborty

and Truhlar

D. G.

: ‘Quantum mechanical reaction rate constants by vibrational configuration interaction: the OH+H2 –> H2O + H reaction as a function of temperature’, PNAS, 2005, 102, (19), 6744–6749.

20.

Costa

Sharkas

Islam

M. M.

and Marcus

: ‘A realistic ab initio model of the passive film formed on stainless steels’; Workshop Report, 2009, Trinity College, Dublin.

21.

Hendy

S. C.

Laycock

N. J.

and Ryan

M. P.

: ‘Atomistic modeling of cation transport in the passive film on iron and implications for models of growth kinetics’, J. Electrochem. Soc., 2005, 152, (8), B271–B276.

22.

Agarwal

A. S.

Landau

and Payer

J. H.

: ‘Modeling the current distribution in thin electrolyte films with applications to crevice corrosion’, J. Electrochem. Soc., 2010, 157, C9–C17.

23.

Cole

I. S.

and Paterson

D. A.

: Corros. Eng., Sci. Technol., 2004, 39, (2), 125–130.

24.

Cottis

R. A.

: ‘Introduction to the modeling of corrosion’, in ‘Shreir’s corrosion’, (eds. T. Richardson et al.), 4th edn, 1581–1584; 2010, Toronto, ChemTec Publishing Inc.

25.

Laycock

N. J.

Moayed

M. H.

and Newman

J. S.

: ‘Metastable pitting and the critical pitting temperature’, J. Electrochem. Soc., 1998, 145, (8), 2622–2628.

26.

Macdonald

D. D.

: ‘The point defect model for the passive state’, J. Electrochem. Soc., 1992, 139, (12), 3434–3449.

27.

Mansfeld

and Oldham

K. B.

: ‘A modification of the Stern-Geary linear polarization equation’, Corros. Sci., 1971, 11, 787–796.

28.

Marcus

Maurice

and Strehblow

H.-H.

: ‘Localized corrosion (pitting): a model of passivity breakdown including the role of the oxide layer nanostructure’, Corros. Sci., 2008, 50, 2698–2704.

29.

Scheiner

and Hellmich

: ‘Finite volume model for diffusion- and activation- controlled pitting corrosion of stainless steel’, Comput. Methods Appl. Mech. Eng., 2009, 198, 2898–2910.

30.

Sharland

S. M.

Jackson

C. P.

and Diver

A. J.

: ‘A finite element model of the propagation of corrosion crevices and pits’, Corros. Sci., 1989, 29, (9), 1149–1166.

31.

Vautrin-Ul

Taleb

Stafiej

Chausse

and Badiali

J. P.

: ‘Reprint of “Mesoscopic modelling of corrosion phenomena: coupling between electrochemical and mechanical processes, analysis of the deviation from the Faraday law”’, Electrochim. Acta, 2007, 52, 7802–7810.

32.

Reigada

Sagues

and Costa

J. M.

: ‘A Monte Carlo simulation of localized corrosion’, J. Chem. Phys., 1994, 101, (3), 2329–2337.

33.

Alamilla

J. L.

and Sosa

: ‘Stochastic modelling of corrosion damage propagation in active sites from field inspection data’, Corros. Sci., 2008, 50, 1811–1819.

34.

Baroux

: ‘The kinetics of pit generation on stainless steels’, Corros. Sci., 1988, 28, (10), 969–986.

35.

Valor

Caleyo

Alfonso

Rivas

and Hallen

J. M.

: ‘Stochastic modeling of pitting corrosion: a new model for initiation and growth of multiple corrosion pits’, Corros. Sci., 2007, 49, 559–579.

36.

Williams

D. E.

Westcott

and Fleischmann

: ‘Stochastic models of pitting corrosion of stainless steels’, J. Electrochem. Soc., 1985, 132, (8), 1804–1811.

37.

Scully

J. R.

and Hudson

J. L.

: ‘Cooperative stochastic behavior in localized corrosion’, J. Electrochem. Soc., 1997, 144, (5), 1614–1619.

38.

Gabrielli

Huet

Keddam

and Oltra

: ‘A review of the probabilistic aspects of localized corrosion’, Corrosion, 1990, 46, 266–278.

39.

J. V.

: ‘Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes’ J. Clin. Epidemiol., 1996, 49, (11), 1225–1231.

40.

Bailey

R. A.

Pidaparti

R. M.

Jayanti

and Palakal

M. J.

: ‘Corrosion prediction in aging aircraft materials using neural networks’, 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., 2000, Atlanta, GA.

41.

Cavanaugh

M. K.

Buchheit

R. G.

and Birbilis

: ‘Modeling the environmental dependence of pit growth using neural network approaches’, Corros. Sci., 2010, 52, (9), 3070–3077.

42.

Colorado-Garrido

Ortega-Toledo

D. M.

Hernández

J. A.

González-Rodríguez

J. G.

and Uruchurtu

: ‘Neural networks for Nyquist plots prediction during corrosion inhibition of a pipeline steel’, J. Solid State Electrochem., 2009, 13, 1715–1722.

43.

Pidarparti

R. M.

: ‘Structural corrosion health assessment using computational intelligence models’, Struct. Health Monit., 2007, 6, (3), 245–259.

44.

Svintradze

D. V.

and Pidarparti

R. M.

: ‘A theoretical model for metal corrosion degradation’, Int. J. Corros., 2010, 2010, 1–7.

45.

Cottis

R. A.

: ‘Neural network methods for corrosion data reduction’, in ‘Shreir’s corrosion’, (eds. T. Richardson, et al.), 4th edn, 1680–1692; 2010, Toronto, ChemTec Publishing Inc.

46.

Engelhard

M. H.

and Macdonald

D. D.

: ‘Unification of the deterministic and statistical approaches for predicting localized corrosion damage. I. Theoretical foundation’, Corros. Sci., 2004, 46, 2755–2780.

47.

Laycock

N. J.

Noh

J. S.

White

S. P.

and Krouse

D. P.

: ‘Computer simulation of pitting potential measurements’, Corros. Sci., 2005, 47, 3140–3177.

48.

Turnbull

McCartney

L. N.

and Zhou

: ‘A model to predict the evolution of pitting corrosion and the pit-to-crack transition incorporating statistically distributed input parameters’, Corros. Sci., 2006, 48, 2084–2105.

49.

Suter

Webb

E. G.

Bohni

and Alkire

R. C.

: ‘Pit initiation on stainless steels in 1 M NaCl with and without mechanical stress’, J. Electrochem. Soc., 2001, 148, (5), B174–B185.

50.

Birbilis

and Buchheit

R. G.

: ‘Investigation and discussion of characteristics for intermetallic phases common to aluminum alloys as a function of solution pH’, J. Electrochem. Soc., 2008, 155, (3), C117–C126.

51.

Ingram

G. D.

and Cameron

I. T.

: ‘Formulation and comparison of alternative multiscale models for drum granulation’, Comput. Aided Chem. Eng., 2005, 20, 481–486.

52.

Rountree

C. L.

Kalia

R. K.

Lidorikis

Nakano

Van Brutzel

and Vashishta

: ‘Atomistic aspects of crack propagation in brittle materials: multimillion atom molecular dynamics simulations’, Annu. Rev. Mater. Res., 2002, 32, 377–400.

53.

Chen

Lee

J. D.

and Eskandarian

: ‘Meshless methods in solid mechanics’; 2006, New York, Springer.

54.

Daphalapurkar

N. P.

Coker

and Komanduri

: ‘Simulation of dynamic crack growth using the Generalized Interpolation Material Point (GIMP) method’, Int. J. Fract., 2007, 143, 79–102.

55.

Das

and Cleary

P. W.

: ‘Effect of rock shapes on brittle fracture using Smoothed particle hydrodynamics’, Theor. Appl. Fract. Mech., 2010, 23, 47–60.

56.

Liu

G. R.

and Liu

M. B.

: ‘Smoothed particle hydrodynamics: a mesh-free particle method’; 2003, Singapore, World Scientific Publishing Co. Pte. Ltd.

57.

Frankel

G. S.

: ‘Pitting corrosion’, in ‘Metals handbook’, (eds. S. D. Cramer, et al.); 2003, Materials Park OH, ASM International.

58.

Marcus

(ed.): ‘Corrosion mechanisms in theory and practice’; 2012, Boca Raton, FL, CRC Press.

59.

Roberge

P. R.

: ‘Handbook of corrosion engineering’; 2000, New York, McGraw-Hill.

60.

Szklarska-Smialowska

: ‘Pitting corrosion of metals’; 1986, Houston, NACE.

61.

Zhang

X. G.

: ‘Corrosion and electrochemistry of zinc’; 1996, New York, Plenum Press.

62.

Sharland

S. M.

: ‘A review of the theoretical modelling of crevice and pitting corrosion’, Corros. Sci., 1987, 27, (3), 289–325.

63.

Kennell

G. F.

Evitts

R. W.

and Heppner

K. L.

: ‘A critical crevice solution and IR drop crevice corrosion model’, Corros. Sci., 2008, 50, 1716–1725.

64.

Venkatraman

M. S.

Cole

I. S.

Gunasegaram

D. R.

and Emmanuel

: ‘Modelling corrosion of a metal under an aerosol droplet’, Mater. Sci. Forum, 2010, 654–656, 1650–1653.

65.

Barnard

N. C.

and Brown

S. G. R.

: ‘Modelling the relationship between microstructure of Galfan-type coated steel and cut-edge corrosion resistance incorporating diffusion of multiple species’, Corros. Sci., 2008, 50, 2846–2857.

66.

Brown

S. G. R.

and Barnard

N. C.

: ‘3D computer simulation of the influence of microstructure on the cut edge corrosion behaviour of a zinc aluminium alloy galvanized steel’, Corros. Sci., 2006, 48, 2291–2303.

67.

Jakab

M. A.

Little

D. A.

and Scully

J. R.

: ‘Experimental and modelling studies of the oxygen reduction reaction on AA2024-T3’, J. Electrochem. Soc., 2005, 152, (8), B311–B320.

68.

Zhang

Ruan

Wolfe

D. A.

and Frankel

G. S.

: ‘Statistical model for intergranular corrosion growth kinetics’, Corros. Sci., 2003, 45, 353–370.

69.

Cavanaugh

M. K.

Buchheit

R. G.

and Birbilis

: ‘Evaluation of a simple microstructural-electrochemical model for corrosion damage accumulation in microstructurally complex aluminum alloys’, Eng. Fract. Mech., 2009, 76, 641–650.

70.

Zhou

Luo

Hashimoto

Hughes

A. E.

and Thompson

G. E.

: ‘Study of localized corrosion in AA2024 aluminium alloy using electron tomography’, Corros. Sci., 2012, 58, 299–306.

71.

Rappaz

and Gandin

C. A.

: ‘Probabilistic modeling of microstructure formation in solidification processes’, Acta Metall. Mater., 1993, 41, 345–360.

72.

Hao

Liu

W. K.

Moran

Vernery

F. J.

and Olson

G. B.

: ‘Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels’, Comput. Methods Appl. Mech. Eng., 2004, 193, 1865–1908.

73.

Vernery

F. J.

Liu

W. K.

Moran

and Olson

: ‘A micromorphic model for the multiple scale failure of heterogeneous materials’, J. Mech. Phys. Solids, 2008, 56, 1320–1347.

74.

Lee

P. D.

Chirazi

Atwood

R. C.

and Wang

: ‘Multiscale modelling of solidification microstructures, including microsegregation and microporosity, in an Al–Si–Cu alloy’, Mater. Sci. Eng. A, 2004, 365, 57–65.

75.

Wang

Allison

and Lee

P. D.

: ‘Multiscale modeling of the influence of Fe content in a Al–Si–Cu alloy on the size distribution of intermetallic phases and micropores’, J. Appl. Phys., 2010, 107, 061804-1–061804-11.

76.

Wang

J. S.

and Lee

P. D.

: ‘Simulating tortuous 3D morphology of microporosity formed during the solidification of Al-Si-Cu alloys’, Int. J. Cast Met. Res., 2007, 20, (3), 151–158.

77.

Tan

Sridharan

and Allen

T. R.

: ‘Altering corrosion response via grain boundary engineering’, Mater. Sci. Forum, 2008, 595–598, 409–418.

78.

Bombac

: ‘Atomistic simulations of precipitation kinetics in multicomponent interstitia/substitutional alloys’, DSc thesis, University of Ljubljana, Ljubljana, 2012.

79.

Kempf

Vignal

Martin

and Virtanen

: ‘Relationships between strain, microstructures and oxide growth at the nano- and microscale’, Surf. Interface Anal., 2008, 40, 43–50.

80.

Osada

: ‘Electron Probe Microanalysis (EPMA) measurement of aluminum oxide film thickness in the nanometer range on aluminum sheets’, X-Ray Spectrom., 2005, 34, 92–95.

81.

Thomas

J. K.

and Ondrejcin

R. S.

: ‘Aluminum oxide film thickness and emittance (U)’; 1991, Aiken SC 29808, Savannah River Laboratory.

82.

Graedel

T. E.

: ‘Corrosion mechanisms for zinc exposed to the atmosphere’, J. Electrochem. Soc., 1989, 136, (4), 193C–203C.

83.

Strehblow

H.-H.

(ed.): ‘Passivity of metals’, (eds. R. C. Alkire et al.), 271–374; 2003, Weinheim, Wiley-VCH.

84.

Jeurgens

L. P. H.

Sloof

W. G.

Tichelaar

F. D.

and Mittemeijer

E. J.

: ‘Thermodynamic stability of amorphous oxide films on metals: application to aluminum oxide films on aluminum substrates’, Phys. Rev. B, 2000, 62, (7), 4707–4719.

85.

Cole

I. S.

Muster

T. H.

Furman

S. A.

Wright

and Bradbury

: ‘Products formed during the interaction of seawater droplets with zinc surfaces: I. Results from 1- and 2·5-day exposures’, J. Electrochem. Soc., 2008, 155, (5), C244–C255.

86.

Lau

Glenn

A. M.

Hughes

A. E.

Scholes

F. H.

Muster

T. H.

and Hardin

S. G.

: ‘Factors influencing the deposition of Ce-based conversion coatings, Part II: the role of localised reactions’, Surf. Coat. Technol., 2009, 203, 2937–2945.

87.

Sziraki

Cziraki

Vertesy

and Kiss

: ‘A kinetic model of the spontaneous passivation and corrosion of zinc in near neutral Na2SO4 solutions’, Electrochim. Acta, 1998, 43, (1–2), 175–186.

88.

Szklarska-Smialowska

: ‘Pitting corrosion of aluminum’, Corros. Sci., 1999, 41, 1743–1767.

89.

Hughes

A. E.

Scholes

F. H.

Glenn

A. M.

Lau

Muster

T. H.

and Hardin

S. G.

: ‘Factors influencing the deposition of Ce-based conversion coatings, part I: the role of Al3+ ions’, Surf. Coat. Technol., 2009, 203, 2927–2936.

90.

White

P. A.

Hughes

A. E.

Furman

S. A.

Sherman

Lau

Muster

T. H.

Corrigan

P. A.

Glenn

A. M.

Harvey

T. G.

Hardin

S. G.

Mardel

Garcia-Espallargas

S. J.

Kwakernaak

and Mol

J. M. C.

: ‘High through-put channel arrays for inhibitor testing: proof of concept for AA024-T3’, Corros. Sci., 2009, 51, 2279–2290.

91.

Macdonald

D. D.

: ‘Kinetic stability diagrams’, ECS Transactions, Cancun, Mexico, 403–418; 2007, Pennington, NJ, The Electrochemical Society.

92.

Zhou

Birbilis

and Macdonald

D. D.

: ‘Kinetic stability of aluminium’, Proc. Conf. on ‘Corrosion and prevention ‘10, Adelaide, Australia, 2010, ACA, Paper 102.

93.

Wang

M.-H.

and Hebert

K. R.

: ‘Metal and oxygen ion transport during ionic conduction in amorphous anodic oxide films’, J. Electrochem. Soc., 1999, 146, (10), 3741–3749.

94.

Vago

E. R.

Calvo

E. J.

and Stratmann

: ‘Electrocatalysis of oxygen reduction at well-defined iron oxide electrodes’, Electrochim. Acta, 1994, 39, (11/12), 1655–1659.

95.

Chen

Z. Y.

Cui

and Kelly

R. G.

: ‘Calculations of the cathodic current delivery capacity and stability of crevice corrosion under atmospheric environments’, J. Electrochem. Soc., 2008, 155, (7), C360–C368.

96.

Mansfeld

and Kenkel

J. V.

: ‘Laboratory studies of galvanic corrosion: I. Two-metal couples’, Corrosion, 1975, 31, 298–302.

97.

Venkatraman

M. S.

Cole

I. S.

and Emmanuel

: ‘Corrosion under a porous layer: a porous electrode model and its implications for self-repair’, Electrochim. Acta, 2011, 56, (24), 8192–8203.

98.

Rodney

Tanguy

and Vandermbroucq

: ‘Modeling the mechanics of amorphous solids at different length scale and time scale’, Modell. Simul. Mater. Sci. Eng., 2011, 19, 083001.

99.

Williams

D. E.

Kilburn

M. R.

Cliff

and Waterhouse

G. I. N.

: ‘Composition changes around sulphide inclusions in stainless steels, and implications for the initiation of pitting corrosion’, Corros. Sci., 2010, 52, 3702–3716.

100.

Kim

D.-H.

Lee

G.-W.

and Kim

Y.-C.

: ‘Interaction of zinc interstitial with oxygen vacancy in zinc oxide: an origin of n-type doping’, Solid State Commun., 2012, 152, 1711–1714.

101.

Diawara

Beh

Y.-A.

and Marcus

: ‘Atomistic simulation of the passivation of iron-chromium alloys using calculated local diffusion activation barriers’, in ‘Passivation of metals and semiconductors and properties of thin oxide’, (ed. P. Marcus), 2006, Amsterdam, Elsevier, 651–657.

102.

Renner

F. U.

Stierle

Dosch

Kolb

D. M.

Lee

T.-L.

and Zegenhagen

: ‘Initial corrosion observed on the atomic scale’, Nature, 2006, 439, (9), 707–710.

103.

Seyeux

Maurice

Klein

L. H.

and Marcus

: ‘Initiation of localized corrosion at the nanoscale by competitive dissolution and passivation of nickel surfaces’, Electrochim. Acta, 2008, 54, 540–544.

104.

Macdonald

D. D.

: ‘Passivity- the key to our metal-based civilization’, Pure Appl. Chem., 1999, 71, (6), 951–978.

105.

Zavadil

K. R.

Ohlhausen

J. A.

and Kotula

P. G.

: ‘Nanoscale void nucleation and growth in the passive oxide on aluminum as a prepitting process’, J. Electrochem. Soc., 2006, 153, (8), B296–B303.

106.

Anon. : ‘A deterministic model for corrosion and activity incorporation in nuclear power plants’, www.vtt.fi/liitetiedostot/muut/ANTIOXI%20AB%20060207%20VTT.ppt 2007 [viewed 5 September 2013].

107.

Ding

and Hihara

L. H.

: ‘Corrosion initiation and anodic-cathodic alteration of localized corrosion of SiC-reinforced aluminum matrix composites in NaCl solution’, ECS Trans., 2007, 3, 237–247.

108.

Toth

(ed.): ‘Adsorption theory, modeling and analysis’; 2002, New York, Marcel Dekker.

109.

Anderko

Sridhar

Yang

L. T.

Grise

S. L.

Saldanha

B. J.

and Dorsey

M. H.

: ‘Validation of localised corrosion model using real time corrosion monitoring in a chemical plant’, Corros. Eng., Sci. Technol., 2005, 40, (1), 33–42.

110.

Farrow

L. A.

Graedel

T. E.

and Leygraf

: ‘Gildes model studies of aqueuos chemistry. II. The corrosion of zinc in gaseous exposure chamber’, Corros. Sci., 1996, 38, 2181.

111.

Franck

U. F.

and FitzHugh

: ‘Periodische Electrodenprozesse und ihre Beschreibung duschen Mathematische Moodell’, Z. Electrochemie, 1961, 65, 156.

112.

Hoar

T. P.

and Jacob

W. R.

: ‘Breakdown of passivity of stainless steel by halide Ions’, Nature, 1967, 216, 1299–1301.

113.

McCafferty

: ‘Sequence of steps in the pitting of aluminum by chloride ions’, Corros. Sci., 2003, 45, (7), 1421–1438.

114.

Okada

: ‘Considerations of the stability of pit repassivation during pitting corrosion of passive metals’, J. Electrochem. Soc., 1984, 131, (5), 1026–1032.

115.

Frankel

G. S.

and Sridhar

: ‘Understanding localized corrosion’, Materials Today, 2008, 11, 38–44.

116.

Macdonald

D. D.

: ‘On the existence of our metals-based civilization I. Phase-space analysis’, J. Electrochem. Soc., 2006, 153, B213.

117.

Krishnamurthy

White

R. E.

and Ploehn

H. J.

: ‘Simplified point defect model for growth of anodic passive films on iron’, Electrochim. Acta, 2002, 47, 3375–3381.

118.

Gece

: ‘The use of quantum chemical methods in corrosion inhibitor studies’, Corros. Sci, 2008, 50, (11), 2981–2992.

119.

Gece

and Bilgic

: ‘Molecular-level understanding of the inhibition efficiency of some inhibitors of zinc corrosion by quantum chemical approach’, Ind. Eng. Chem. Res., 2012, 51, (43), 14115–14120.

120.

Sholl

D. S.

and Steckel

J. A.

: ‘Density functional theory: a practical introduction’; 2009, Hoboken, NJ, John Wiley & Sons Inc.

121.

Taylor

C. D.

: ‘Atomistic modeling of corrosion events at the interface between a metal and its environment’, Int. J. Corros., 2012, 2012, 1–13.

122.

Gece

: ‘The use of quantum chemical methods in corrosion inhibitor studies’, Corros. Sci., 2008, 50, 2981–2992.

123.

Goulart

C. M.

Esteves-Souza

Martinez-Huitle

C. A.

Rodrigues

C. J. F.

Maciel

M. A. M.

and Echevarria

: ‘Experimental and theoretical evaluation of semicarbazones and thiosemicarbazones as organic corrosion inhibitors’, Corros. Sci., 2013, 67, 281–291.

124.

Janik

M. I.

Taylor

C. D.

and Neurock

: ‘First-principles analysis of the initial electroreduction steps of oxygen over pt(111)’, J. Electrochem. Soc., 2009, 156, B126–B135.

125.

Khaled

K. F.

: ‘Studies of iron corrosion inhibition using chemical, electrochemical and computer simulation techniques’, Electrochim. Acta, 2010, 55, 6523–6532.

126.

Kokalj

Peljhan

Finsgar

and Milosev

: ‘What determines the inhibition effectiveness of ATA, BTAH and BTAOH corrosion inhibitors on copper?’, J. Am. Chem. Soc., 2010, 132, 16657–16668.

127.

Musa

A. Y.

: ‘Corrosion inhibition of mild steel in 1·0 M HCl by amino compound: electrochemical and DFT studies’, Metall. Mater. Trans. A, 2012, 43A, 3379–3386.

128.

Soler

J. M.

Artacho

Gale

J. D.

Garcia

Junquera

Ordejon

and Sanchez-Portal

: ‘The SIESTA method for ab initio order-N materials simulation’, J. Phys.: Condens. Matter, 2002, 14, 2745–2779.

129.

Yeh

K. Y.

: ‘Density functional theory-based electrochemical models for the oxygen reduction reaction: comparison of modeling approaches for electric field and solvent effects’, J. Comput. Chem., 2011, 32, 3399–3408.

130.

Abodi

L. C.

DeRose

J. A.

Van Damme

Demeter

Suter

and Deconinck

: ‘Modeling localized aluminum alloy corrosion in chloride solutions under non-equilibrium conditions: steps toward understanding pitting initiation’, Electrochim. Acta, 2012, 63, 169–178.

131.

Harvey

T. G.

Hardin

S. G.

Hughes

A. E.

Muster

T. H.

White

P. A.

Markley

T. A.

Corrigan

P. A.

Mardel

Garcia

S. J.

Mol

J. M. C.

and Glenn

A. M.

: ‘The effect of inhibitor structure on the corrosion of AA2024 and AA7075’, Corros. Sci., 2011, 53, 2184–2190.

132.

Arslan

Kandemirli

Ebenso

E. E.

Love

and Alemu

: ‘Quantum chemical studies on the corrosion inhibition of some sulphonamides on mild steel in acidic medium’, Corros. Sci., 2009, 51, 35–47.

133.

Khaled

K. F.

and Abdel-Shafi

N. S.

: ‘Quantitative structure and activity relationship modeling study of corrosion inhibitors: genetic function approximation and molecular dynamics simulation methods’, Int.J. Electrochem. Sci., 2011, 6, (9), 4077–4094.

134.

Musa

A. Y.

Mohamad

A. B.

Kadhum

A. A. H.

Takriff

M. S.

and Ahmoda

: ‘Quantum chemical studies on corrosion inhibition for series of thio compounds on mild steel in hydrochloric acid’, J. Ind. Eng. Chem., 2012, 18, 551–555.

135.

Adnani

Z. E.

Mcharfi

Sfaira

Benzakour

Benjelloun

A. T.

and Touhami

M. E.

: ‘DFT theoretical study of 7-R-3methylquinoxalin-2(1H)-thiones (R = H; CH3; Cl) as corrosion inhibitors in hydrochloric acid’, Corros. Sci., 2013, 68, 223–230.

136.

Kokalj

: ‘Formation and structure of inhibitive molecular film of imidazole on iron surface’, Corros. Sci., 2013, 68, 195–203.

137.

Dion

: ‘Van der Waals density functional for general geometries’, Phys. Rev. Lett., 2004, 92, (24). 246401-1–246401-4.

138.

von Lilienfeld

O. A.

: ‘Optimization of effective atom centered potentials for London dispersion forces in density functional theory’, Phys. Rev. Lett., 2004, 93, 153004-1–153004-4.

139.

Zhao

and Truhlar

D. G.

: ‘The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals’, Theor. Chem. Acc., 2008, 120, (1–3), 215–241.

140.

Grimme

: ‘Semiempirical GGA-type density functional constructed with a long-range dispersion correction’, J. Comput. Chem., 2006, 27, (15), 1787–1799.

141.

Spohr

: ‘Some recent tends in the computer simulations of acqueous double layers’, Electrochim. Acta, 2003, 49, 23–27.

142.

Taylor

D. T.

Kelly

R. G.

and Neurock

: ‘First-principles prediction of equilibrium potentials for water activation by a series of metals’, J. Electrochem. Soc., 2007, 154, (12), F217–F221.

143.

Yeh

K. Y.

and Janik

M. J.

144.

Taylor

C. D.

Wasileski

S. A.

Filhol

J. S.

and Neurock

: ‘First principles reaction modeling of the electrochemical interface: consideration and calculation of a tunable surface potential from atomic and electronic structure’, Phys. Rev. B, 2006, 73, (16). 165402-1–165402-16.

145.

Fletcher

: ‘The theory of electron transfer’, J. Solid State Electrochem., 2010, 14, 705–739.

146.

Sangaranarayanan

M. V.

and Sebastian

K. L.

: ‘Theoretical chemistry and electrochemistry’, J. Chem. Sci., 2009, 121, (5), 559–560.

147.

Winkler

Horbach

Kob

and Binder

: ‘Structure and diffusion in amorphous aluminum silicate: A molecular dynamics computer simulation’, J. Chem. Phys., 2004, 120, (1), 384–393.

148.

Islam

M. M.

Diawara

Maurice

and Marcus

: ‘Atomistic modeling of voiding mechanisms at oxide/alloy interfaces’, J. Phys. Chem., 2009, 113, 9978–9981.

149.

Khaled

K. F.

: ‘Studies of iron corrosion inhibition using chemical, electrochemical and computer simulation techniques’, Electrochim. Acta, 2010, 55, (22), 6523–6532.

150.

Baboian

: ‘Corrosion tests and standards: application and interpretation’; 2005, Philadelphia, PA, ASTM International.

151.

Kennedy

J. L.

: ‘Oil and gas pipeline fundamentals’; 1993, Tulsa, OK, PennWell Publishing Company.

152.

Arya

and Vassie

P. R. W.

: ‘Influence of cathode-to-anode area ratio and separation distance on galvanic corrosion currents of steel in concrete containing chlorides’, Cem. Concr. Res., 1995, 25, (5), 989–998.

153.

Birbilis

and Buchheit

R. G.

: ‘Electrochemical characteristics of intermetallic phases in aluminum alloys – an experimental survey and discussion’, J. Electrochem. Soc., 2005, 152, (4), B140–B151.

154.

Fontana

M. G.

: ‘Corrosion engineering’; 1986, New York, Mc-Graw Hill Book Company.

155.

Garfias-Mesias

L. F.

and Sykes

J. M.

: ‘The influence of Cu on the pitting corrosion of duplex stainless steel UNS S32550’, Corrosion 96, Denver, CO, March 24–29, 1996.

156.

Jones

D. A.

: ‘Principles and prevention of corrosion’; 1996, Upper Saddle River, NJ, Prentice-Hall.

157.

Kirk

W. W.

: ‘Atmospheric corrosion’; 1995, Materials Park, OH, American Society for Testing Materials.

158.

Lacroix

Ressier

Blanc

and Mankowskia

: ‘Combination of AFM, SKPFM, and SIMS to study the corrosion behavior of S-phase particles in AA2024-T351’, J. Electrochem. Soc., 2008, 155, (4), C131–C137.

159.

Koleske

J. V.

: ‘Paint and coating testing manual: fourteenth edition of the Gardner-Sward handbook’; 1995, Philadelphia, PA, ASTM.

160.

Alkire

and Siitari

: ‘The location of cathodic reaction during localized corrosion’, J. Electrochem. Soc., 1979, 126, (1), 15–22.

161.

Alodan

M. A.

: ‘Modeling of pH distribution over corrosion sites’, J. King Saud Univ., 2002, 15, (1), 1–12.

162.

Vautrin-Ul

Mendy

Taleb

Chausse

Stafiej

and Badiali

J. P.

: ‘Numerical simulations of heterogeneity formation in metal corrosion’, Corros. Sci., 2008, 50, 2149–2158.

163.

Magnussen

O. M.

Zitzler

Gleich

Vogt

M. R.

and Behm

R. J.

: ‘In-situ atomic-scale studies of the mechanisms and dynamics of metal dissolution by high-speed STM’, Electrochim. Acta, 2001, 46, (24–25), 3725–3733.

164.

Williams

D. E.

Mohiuddin

T. F.

and Zhu

Y. Y.

: ‘Elucidation of a trigger mechanism for pitting corrosion of stainless steels using submicron resolution scanning electrochemical and photoelectrochemical microscopy’, J. Electrochem. Soc., 1998, 145, (8), 2664–2672.

165.

Sevick

E. M.

Prabhakar

Williams

S. R.

and Searles

D. J.

: ‘Fluctuation theorems’, Annu. Rev. Phys. Chem., 2008, 59, 603–633.

166.

Legrand

Diawara

Legendre

J.-J.

and Marcus

: ‘Three-dimensional modelling of selective dissolution and passivation of iron-chromium alloys’, Corros. Sci., 2002, 44, 773–790.

167.

Williams

D. E.

Stewart

and Balkwill

P. H.

: ‘The nucleation, growth and stability of micropits in stainless steel’, Corros. Sci., 1994, 36, (7), 1213–1235.

168.

Wang

Xie

Yan

K. P.

Duan

and Zuo

: ‘The nucleation and growth of metastable pitting on pure iron’, Corros. Sci., 2009, 51, 181–185.

169.

Budiansky

Organ

Mikhailov

A. S.

Hudson

J. L.

and Scully

J. R.

: ‘Co-operative spreading of pit sites as a new explanation for critical threshold potentials’, Pits and Pores III: Formation, Properties, and Significance for Advanced Materials, 313–324; 2004, Pennington, NJ, The Electrochemical Society.

170.

Mikhailov

A. S.

Scully

J. R.

and Hudson

J. L.

: ‘Nonequilibrium collective phenomena in the onset of pitting corrosion’, Surf. Sci., 2009, 603, (10–12), 1912–1921.

171.

Scully

J. R.

Budiansky

N. D.

Tiwary

Mikhailov

A. S.

and Hudson

J. L.

: ‘An alternate explanation for the abrupt current increase at the pitting potential’, Corros. Sci., 2008, 50, 316–324.

172.

Frankel

G. S.

: ‘Pitting corrosion of metals: a review of the critical factors’, J. Electrochem. Soc., 1998, 145, (6), 2186–2198.

173.

Burstein

G. T.

Pistorius

P. C.

and Mattin

S. P.

: ‘The nucleation and growth of corrosion pits on stainless steel’, Corros. Sci., 1993, 35, (1–4), 57–62.

174.

Ezuber

and Newman

R. C.

: ‘Growth-rate distribution of metastable pits’, Critical Factors in Localized Corrosion, Pennington, NJ; 120,1992, Pennington, NJ, The Electrochemical Society.

175.

Baker

M. A.

and Castle

J. E.

: ‘The initiation of pitting corrosion at MnS inclusions’, Corros. Sci., 1993, 34, (4), 667–682.

176.

and Alkire

: ‘Surface analysis of corrosion pits initiated at MnS inclusions in 304 stainless steel’, J. Electrochem. Soc., 1993, 139, (6), 1573–1580.

177.

Ryan

M. P.

Williams

D. E.

Chater

R. J.

Hutton

B. M.

and McPhall

D. S.

: ‘Why stainless steel corrodes’, Nature, 2002, 415, 770–774.

178.

Rynders

R. M.

Paik

C.-H.

and Alkire

R. C.

: ‘Use of in situ atomic force microscopy to image corrosion at inclusions’, J. Electrochem. Soc., 1994, 141, (6), 1439–1445.

179.

Wranglen

: ‘Pitting and sulphide inclusions in steel’, Corros. Sci., 1974, 14, (5), 331–349.

180.

Shibata

and Takeyama

: ‘Stochastic theory of pitting corrosion’, Corrosion, 1977, 33, 243–251.

181.

Punckt

Bolscher

Rotermund

H. H.

Mikhailov

A. S.

Organ

Budiansky

Scully

J. R.

and Hudson

J. L.

: ‘Sudden onset of pitting corrosion on stainless steel as a critical phenomenon’, Science, 2004, 305, 1133–1136.

182.

Organ

Scully

J. R.

Mikhailov

A. S.

and Hudson

J. L.

: ‘A spatiotemporal model of interactions among metastable pits and the transition to pitting corrosion’, Electrochim. Acta, 2005, 51, 225–241.

183.

Walton

J. C.

Cragnolino

and Kalandros

S. K.

: ‘A numerical model of crevice corrosion for passive and active metals’, Corros. Sci., 1996, 38, (1), 1–18.

184.

Lei

Xiaogang

Chaofang

Kui

and Lin

: ‘Cellular automata modeling on pitting current transients’, Electrochem. Commun., 2009, 11, (9), 1826–1829.

185.

Malki

and Baroux

: ‘Computer simulation of the corrosion pit growth’, Corros. Sci., 2005, 47, (1), 171–182.

186.

Malki

and Baroux

: ‘Study of metastable pitting of stainless steels by computer simulations’, Proc. COMSOL Unsers’ Conf., Paris, 2005, COMSOL Inc., Burlington, MA.

187.

Malki

and Baroux

: ‘Modeling of metastable pitting: towards a better understanding of the effect of alloying elements ‘, ECS transactions, Washington, DC,273–284; 2007, Pennington, NJ, The Electrochemical Society.

188.

Hoerle

Malki

and Baroux

: ‘Corrosion current fluctuations at metastable to stable pitting transition of aluminum’, J. Electrochem. Soc., 2006, 153, (12), B527–B532.

189.

Cobb

J. W.

: ‘The influence of impurities on the corrosion of iron’ J. Iron Steel Inst., 1911, 83, 170.

190.

Sasaki

and Isaacs

H. S.

: ‘Origins of electrochemical noise during pitting corrosion of aluminum’, J. Electrochem. Soc., 2004, 151, (3), B124–B133.

191.

Strehblow

H.-H.

: ‘Mechanisms of pitting corrosion’, in ‘Corrosion mechanisms in theory and practice’, (eds. P. Marcus, et al.), 1995, New York, Marcel Dekker, 201–238.

192.

Webb

E. G.

Suter

and Alkire

R. C.

: ‘Microelectrochemical measurements of the dissolution of single MnS inclusions, and the prediction of the critical conditions for pit initiation on stainless steel’, J. Electrochem. Soc., 2001, 148, (5), B186–B195.

193.

Janik-Czachor

Wood

G. C.

and Thompson

G. E.

: ‘Assessment of the processes leading to pit nucleation’, Br. Corros. J., 1980, 15, (4), 153–161.

194.

Galvele

J. R.

: ‘Transport processes and the mechanism of pitting in metals’, J. Electrochem. Soc., 1976, 123, (4), 464–474.

195.

Galvele

J. R.

: ‘Transport processes in passivity breakdown – II: full hydrolysis of the metal ions’, Corros. Sci., 1981, 21, (8), 551–579.

196.

Gravano

S. M.

and Galvele

J. R.

: ‘Transport processes in passivity breakdown – III. Full hydrolysis plus ion migration plus buffers’, Corros. Sci., 1984, 24, (6), 517–534.

197.

Sawford

M. K.

Ateya

B. G.

Abdullah

A. M.

and Pickering

H. W.

: ‘The role of oxygen on the stability of crevice corrosion’, J. Electrochem. Soc., 2002, 149, (6), B198–B205.

198.

Laycock

N. J.

and White

S. P.

: ‘Computer simulation of single pit propagation in stainless steel under potentiostatic control’, J. Electrochem. Soc., 2001, 148, (7), B264–B275.

199.

Scheiner

and Hellmich

: ‘Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary’, Corros. Sci., 2007, 49, 319–346.

200.

Papavinasam

Revie

R. W.

Friesen

W. I.

Doiron

and Panneerselvam

: ‘Review of models to predict internal pitting corrosion of oil and gas pipelines’, Corros. Rev., 2006, 24, 173–230.

201.

Newman

: ‘Pitting corrosion of metals’, in ‘The electrochemical society interface’, Editor: K. Rajeshwar, Pennington, NJ, The Electrochemical Society, 33–37; 2010.

202.

Alkire

and Siitari

: ‘Initiation of crevice corrosion II. Mathematical model for aluminum in sodium chloride solutions’, J. Electrochem. Soc., 1982, 129, (3), 488–496.

203.

Sharland

S. M.

: ‘A mathematical model of the initiation of crevice corrosion in metals’, Corros. Sci., 1992, 33, (2), 183–201.

204.

Laycock

N. J.

and Newman

R. C.

: ‘Localised dissolution kinetics, salt films and pitting potentials’, Corros. Sci., 1997, 39, (10–11), 1771–1790.

205.

Cong

Michels

H. T.

and Scully

J. R.

: ‘Passivity and pit stability behavior of copper as a function of selected water chemistry variables’, J. Electrochem. Soc., 2009, 156, (1), C16–C27.

206.

Williams

D. E.

Newman

R. C.

Song

and Kelly

R. G.

: ‘Passivity breakdown and pitting corrosion of binary alloys’, Nature, 1991, 350, 216–219.

207.

Qian

Newman

R. C.

Cottis

R. A.

and Sieradzki

: ‘Computer simulation of alloy passivation and activation’, Corros. Sci., 1990, 31, 621–626.

208.

Sieradzki

and Newman

R. C.

: ‘A percolation model for passivation in stainless steels’, J. Electrochem. Soc., 1986, (133), 1979–1980.

209.

Rashkeev

S. N.

Sohlberg

K. W.

Zhuo

and Pantelides

S. T.

: ‘Hydrogen-induced initiation of corrosion in aluminum’, J. Phys. Chem. C, 2007, 111, (19), 7175–7178.

210.

Chang

C.-L.

Sankaranarayanan

S. K. R. S.

Engelhard

M. H.

Shutthanandan

and Ramanathan

: ‘On the relationship between nonstoichiometry and passivity breakdown in ultrathin oxides: combined depth-dependent spectroscopy, Mott-Schottky analysis, and molecular dynamics simulation studies’, J. Phys. Chem. C, 2009, 113, (9), 3502–3511.

211.

Seyeux

Maurice

and Marcus

: ‘Breakdown kinetics at nanostructure defects of passive films’, Electrochem. Solid State Lett., 2009, 12, (10), C25–C27.

212.

Hong

and Nagumo

: ‘Effect of surface roughness on early stages of pitting corrosion of type 301 stainless steel’, Corros. Sci., 1997, 39, (9), 1665–1672.

213.

Olson

D. L.

Lasseigne

Marya

N. M.

and Mishra

: ‘Weld features that differentiate weld and plate corrosion’, Pract. Failure Anal., 2003, 3, (5), 43–57.

214.

Turnbull

: ‘Review of modelling of pit propagation kinetics’, Br. Corros. J., 1993, 28, 297–308.

215.

Macdonald

D. D.

and Engelhardt

G. R.

: ‘Predictive modeling of corrosion’, in ‘Shreir’s corrosion’, (eds. T. Richardson, et al.), 4th edn, 1630–1679; 2010, Toronto, ChemTec Publishing Inc.

216.

Pickering

H. W.

: ‘On the roles of corrosion products in local cell processes’, Corrosion, 1986, 42, 125–140.

217.

Pickering

H. W.

and Frankenthal

R. P.

: ‘On the mechanism of localized corrosion of iron and stainless steel; I. Electrochemical studies’, J. Electrochem. Soc., 1972, 119, (10), 1297–1304.

218.

Sharland

S. M.

and Tasker

P. W.

: ‘A mathematical model of crevice and pitting corrosion – I. The physical model’, Corros. Sci., 1988, 28, (6), 603–620.

219.

Engelhardt

Urquidi-Macdonald

and Macdonald

D. D.

: ‘A simplified method for estimating corrosion cavity growth rates’, Corros. Sci., 1997, 39, (3), 419–441.

220.

Hartnig

and Koper

M. T. M.

: ‘Molecular dynamics simulation of the first electron transfer step in the oxygen reduction reaction’, J. Eloectroanal. Chem., 2002, 532, 165–170.

221.

Koper

M. T. M.

and Voth

G. A.

: ‘A theory for adiabatic bond breaking electron transfer reactions at metal electrodes’, Chem. Phys. Lett., 1998, 282, 100–106.

222.

Macdonald

D. D.

: Email dated 24 August, personal communication, 2013.

223.

Chen

Z. Y.

and Kelly

R. G.

: ‘Computational modeling of bounding conditions for pit size on stainless steel in atmospheric environments’, J. Electrochem. Soc., 2010, 157, (2), C69–C78.

224.

Pickering

H. W.

: ‘The significance of the local electrode potential within pits, crevices and cracks’, Corros. Sci., 1989, 29, (2–3), 325–341.

225.

Refaey

S. A. M.

: ‘Inhibition of steel pitting corrosion in HCl by some inorganic anions ‘, Appl. Surf. Sci., 2005, 240, 396–404.

226.

Turnbull

: ‘The solution composition and electrode potential in pits, crevices and cracks’, Corros. Sci., 1983, 23, (8), 833–870.

227.

Evitts

R. W.

: ‘Modelling of crevice corrosion’; 1997, University of Saskatchewan, Saskatchewan.

228.

White

S. P.

Weir

G. J.

and Laycock

N. J.

: ‘Calculating chemical concentrations during the initiation of crevice corrosion’, Corros. Sci., 2000, 42, (4), 605–629.

229.

Alavi

and Cottis

R. A.

: ‘The determination of pH, potential and chloride concentration in corroding crevices on 304 stainless steel and 7475 aluminium alloy’, Corros. Sci., 1987, 27, (5), 443–451.

230.

Taxen

and Persson

: ‘Zinc corrosion in a crevice’, Proc. COMSOL Conf.; 2008, Hannover.

231.

Heppner

K. L.

Evitts

R. W.

and Postlethwaite

: ‘Effect of ionic interactions on the initiation of crevice corrosion in passive metals’, J. Electrochem. Soc., 2005, 152, (3), B89–B98.

232.

Pitzer

K. S.

: ‘Thermodynamics of electrolytes, I. Theoretical basis and general equations’, J. Phys. Chem., 1973, 77, 268–277.

233.

Anderko

McKenzie

and Young

R. D.

: ‘Computation rates of general corrosion using electrochemical and thermodynamic models’, Corrosion, 2001, 57, (3), 202–213.

234.

Pitzer

K. S.

(ed.): ‘Activity coefficients in electrolyte solutions’, 2nd edn, 1991, Boca Raton, FL, USA, CRC Press.

235.

Chowdhuri

and Chandra

: ‘Dynamics of ionic and hydrophobic solutes in water-methanol mixtures of varying composition’, J. Chem. Phys., 2005, 123, (23), 234501–234509.

236.

Lyubartsev

A. P.

and Laaksonen

: ‘Concentration effects in aqueous NaCl solutions. A molecular dynamics simulation’, J. Chem. Phys., 1996, 100, (40), 16410–16418.

237.

Caldin

: ‘The mechanisms of fast reactions in solution’; 2003, Amsterdam, The Netherlands, IOS Press.

238.

Chorkendorff

and Niemantsverdriet

J. W.

: ‘Concepts of modern catalysis and kinetics’; 2007, Weinheim, Wiley-VCH.

239.

Phillips

L. F.

: ‘Collision-theory calculations of rate constants for some atmospheric radical reactions over the temperature range 10–600 K’, J. Phys. Chem., 1990, 94, 7482–7487.

240.

Lee

K. L. J.

: ‘A mechanistic modeling of CO2 corrosion of mild steel in the presence of H2S’; 2004, Athens, OH, Ohio University.

241.

Graedel

T. E.

: ‘Gildes model studies of aqueous chemistry. I. Formulation and potential applications of the multi-regime model’, Corros. Sci., 1996, 38, (12), 2153–2180.

242.

Nesic

and Lee

K. L. J.

: ‘A mechanistic model for carbon dioxide corrosion of mild steel in the presence of protective iron carbonate films – part 3: film growth model’, Corros.: J. Sci. Eng., 2003, 59, (7), 616–628.

243.

Sun

and Nesic

: ‘A mechanistic model of H2S corrosion of mild steel’, Corrosion 2007 Conf. Expo, Nashville TN, 2007, NACE International, Paper No. 07655.

244.

Tidblad

Aastrup

and Leygraf

: ‘Gildes model studies of aqueuos chemistry’, J. Electrochem. Soc., 2005, 152, (5), B178–B185.

245.

Castin

Pascuet

M. I.

and Malebra

: ‘Modeling the first stages of Cu precipitation in α-Fe using a hybrid atomistic kinetic Monte Carlo approach’, J. Chem. Phys., 2011, 135, 064502.

246.

Yang

Meng

L. F.

Wang

E. G.

and Gao

: ‘Dissolution dynamics of NaCl nanocrystal in liquid water’, Phys. Rev. E, 2005, 72, 012602.

247.

McCafferty

: ‘Introduction to corrosion science’; 2010, New York, Springer.

248.

Chidambaram

Vasquez

M. J.

Halada

G. P.

and Clayton

C. R.

: ‘Studies on the repassivation behavior of aluminum and aluminum alloy exposed to chromate solutions’, Surf. Interface Anal., 2003, 35, 226–230.

249.

Cho

E.-A.

Kim

C.-K.

Kim

J.-S.

and Kwon

H.-S.

: ‘Quantitative analysis of repassivation kinetics of ferritic stainless steels based on the high field ion conduction model’, Electrochim. Acta, 2000, 45, (12), 1933–1942.

250.

Scully

J. C.

: ‘The Role of Surface Films in Stress Corrosion Cracking and Corrosion Fatigu’ in ‘Environment sensitive fracture of engineering materials’, (ed. Foroulis

Z. A.

), 1979, NY, USA, AIME.

251.

Song

F. M.

Raja

K. S.

and Jones

D. A.

: ‘A film repassivation kinetic model for potential-controlled slower electrode straining’, Corros. Sci., 2006, 48, (2), 285–307.

252.

Anderko

Sridhar

and Dunn

D. S.

: ‘A general model for the repassivation potential as a function of multiple aqueous solution species’, Corros. Sci., 2004, 46, 1583–1612.

253.

Anderko

Sridhar

Jakab

M. A.

and Tormoen

: ‘A general model for the repassivation potential as a function of multiple aqueous species. 2. Effect of oxyanions on localized corrosion of Fe-Ni-Cr-Mo-W-N alloys’, Corros. Sci., 2008, 50, (12), 3629–3647.

254.

Ahn

S.-J.

Kim

D.-Y.

and Kwon

H.-S.

: ‘Analysis of repassivation kinetics of Ti based on the point defect model’, J. Electrochem. Soc., 2006, 153, (9), B370–B374.

255.

P.-Q.

and Celis

J.-P.

: ‘Ion conduction model applied to repassivation kinetics of tribo-activated surfaces’, J. Electrochem. Soc., 2004, 151, (10), B551–B557.

256.

Marshall

P. I.

and Burstein

G. T.

: ‘The effects of pH on the repassivation of 304L stainless steel’, Corros. Sci., 1983, 23, (11), 1219–1228.

257.

Park

C.-J.

and Kwon

H.-S.

: ‘Comparison of repassivation kinetics of stainless steels in chloride solutions’, Met. Mater. Int., 2005, 11, (4), 309–312.

258.

Schroder

Fasel

and Kiejna

: ‘Mg(0001) surface oxidation: a two-dimensional oxide phase’, Phys. Rev. B, 2004, 69, 193405.

259.

Popov

Y. A.

: ‘Theory of pit nucleation. II- interaction between pits at the early stage of development. The role of solvent.’, Prot. Met., 2008, 44, (2), 126–133.

260.

Lunt

T. T.

Scully

J. R.

Brusamarello

Mikhailov

A. S.

and Hudson

J. L.

: ‘Spatial interactions among localized corrosion sites. Experiments and modeling’, J. Electrochem. Soc., 2002, 149, (5), B163–B173.

261.

White

S. P.

Krouse

D. P.

and Laycock

N. J.

: ‘Numerical simulation of pitting corrosion: intercations between pits in potentiostatic conditions’, ECS Trans., 2006, 16, 37–45.

262.

Harlow

D. G.

and Wei

R. P.

: ‘A probability model for the growth of corrosion pits in aluminum alloys induced by constituent particles’, Eng. Fract. Mech., 1998, 59, (3), 305–325.

263.

Curtin

W. A.

and Miller

R. E.

: ‘Atomistic/continuum coupling in computational materials science’, Model Simul. Mater. Sci., 2003, 11, R33–R68.

264.

Makov

Gattinoni

C. C.

and De Vita

: ‘Ab initio based multiscale modelling for materials science’, Model. Simul. Mater. Sci., 2009, 17, (8), 084008.

265.

Ganzenmüller

G. C.

Hiermaier

and Steinhauser

M. O.

: ‘Energy-based coupling of smooth particle hydrodynamics and molecular dynamics with thermal fluctuations’, Eur. Phys. J. Spec. Top. 2012, 206, (1), 51–60.

266.

LeVeque

R. J.

: ‘Finite difference methods for ordinary and partial differential equations – steady state and time dependent problems; 2007, Philadelphia, Society for Industrial and Applied Mathematics.

267.

Zienkiewicz

O. C.

and Taylor

R. L.

: ‘The finite element method’; 1977, London, McGraw-Hill.

268.

Patankar

S. V.

: ‘Numerical heat transfer and fluid flow’; 1980, Washington DC, Hemisphere Publishing Company.

269.

Voller

V. R.

: ‘Basic control volume finite element methods for fluids and solids; 2009, Singapore, World scientific Publishing Co. Pte. Ltd.

270.

Bartosik

di Caprio

and Stafiej

: ‘Cellular automata approach to corrosion and passivity phenomena’, Pure Appl. Chem., 2012, 85, (1), 247–256.

271.

Stratmann

and Streckel

: ‘On the atmospheric corrosion of metals which are covered with thin electrolyte layers-I. Verification of the experimental technique’, Corros. Sci., 1990, 30, (6), 681–696.

272.

Venkatraman

M. S.

Cole

I. S.

and Emmanuel

: ‘Corrosion under a porous layer: a porous electrode model and its implications for self-repair’, Electrochim. Acta 2011, 56, (24), 8192–8203.

273.

Tartakovsky

A. M.

Meakin

Scheibe

T. D.

and West

R. M. E.

: ‘Simulations of reactive transport and precipitation with smoothed particle hydrodynamics’, J. Comput. Phys., 2007, 222, (2), 654–672.

274.

Grubmüller

Heller

Windemuth

and Schulten

: ‘Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions’, Mol. Simul., 1991, 6, 121–142.

275.

Hoover

W. G.

: ‘Isomorphism linking smooth particles and embedded atoms’, Phys. A, 1998, 260, (3), 244–254.

276.

Bataillon

Bouchon

Chainais-Hillairet

Fuhrmann

Hoarau

and Touzani

: ‘Numerical methods for simulation of a corrosion model with moving oxide layer.’, J. Comput. Phys., 2012, 231, (18), 6213–6231.

277.

Newman

J. S.

and Thomas-Alyea

K. E.

: ‘Electrochemical systems’; 2004, Hoboken, NJ, John Wiley & Sons Inc.

278.

Cole

I. S.

Chan

W. Y.

Trinidad

G. S.

and Paterson

D. A.

: ‘An holistic model for atmospheric corrosion: Part 4 – a geographic information system for predicting airborne salinity’, Corros. Eng. Sci. Tech., 2004, 39, (1), 89–96.

279.

Cole

I. S.

Muster

T. H.

Azmat

N. S.

Venkatraman

M. S.

and Cook

: ‘Multiscale modelling of the corrosion of metals under atmospheric corrosion’, Electrochim. Acta, 2011, 56, 1856–1865.

280.

Cole

I. S.

and Paterson

D. A.

: ‘Mathematical models of dependence of surface temperatures of exposed metal plates on environmental parameters’, Corros. Eng., Sci. Technol., 2006, 41, (1), 67–76.

281.

Cole

I. S.

Paterson

D. A.

and Ganther

W. D.

: ‘Holistic model for atmospheric corrosion part 1 – theoretical framework for production, transportation and deposition of marine salts’, Corros. Eng., Sci. Tech., 2003, 38, (2), 129–134.