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Vol. 9. Issue 1.
Pages 687-699 (January - February 2020)
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Vol. 9. Issue 1.
Pages 687-699 (January - February 2020)
Original Article
DOI: 10.1016/j.jmrt.2019.11.010
Open Access
Non-destructive thickness measurement as a tool to evaluate the evolution of patina layer formed on weathering steel exposed to the atmosphere
S.J. Travassosa,
Corresponding author

Corresponding author.
, M.B. Almeidab, C.R. Tomachukc, H.G. de Meloa
a Departamento de Engenharia Metalúrgica e de Materiais, Universidade de São Paulo, São Paulo, SP, Brazil
b Laboratório de Corrosão e Tratamento de Superfície, Instituto de Pesquisas Tecnológicas, São Paulo, SP, Brazil
c Departamento de Ciências Básicas e Ambientais, Universidade de São Paulo, Lorena, SP, Brazil
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Tables (4)
Table 1. Thickness of the patina developed on the WS surface exposed at ACS-IPT after different exposure times in the urban atmosphere of São Paulo City. Thicknesses values were measured by magnetic induction thickness gauge. Thicknesses determined at two WS sculptures exposed at the Campus of the University of São Paulo during 16 and 24 years are also provided.
Table 2. PAI index determined from the XRD spectra of patina formed after different exposure periods.
Table 3. Thickness of the patina layer developed on WS bridges surfaces in Czech Republic (μm).
Table 4. WS patina thickening rate in São Paulo atmosphere.
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This work considers the magnetic induction method on rough surfaces (ABNT NBR 10443) to determine the thickness of the patina layer formed on weathering steel (WS) sheets exposed for up to two years at São Paulo atmosphere and on WS sculptures exposed for sixteen and twenty-four years at the same site. A good agreement was found with SEM measurements. It was also found that patina thickening followed a two slopes bilogarithmic law, with a steeper slope for short exposure periods, in agreement with increased corrosion rate. For long-term exposure, it was found a low thickening rate (<2μmyear−1), suggesting stabilization of the patina layer. The increase in goethite (α-FeOOH) content over time reinforces the hypothesis of a more protective layer as indicated by Protective Ability Index (PAI) for 24 years old sculpture.

Weathering steel
Thickness measurements
Magnetic induction
Patina layer
PAI index
Atmospheric corrosion tests
Full Text

Weathering steel (WS), also known as COR-TEN®, is a low-alloy steel containing small amounts of copper, chromium, nickel, phosphorus, silicon and manganese. According to the American Society for Testing and Materials – ASTM G101 [1], the total alloying elements in this steel can range from 1% to 5%. WS has been employed worldwide due to its peculiar ability to form a protective rust layer with attractive appearance, denominated patina. Therefore, in this work, patina does not correspond to the green film formed on copper and bronze after long-term exposure [2–4]. ArcelorMittal defines the WS patina as a fine wine; it is enriched by air and enhanced with age[5]. In Brazil, WS is widely produced by the steelmaking companies under various commercial names and has a history of more than 50 years [6]. In Brazil WS has been used with structural purpose, for instance: Nossa Senhora das Graças viaduct (COR-TEN) and Presidente Dutra highway viaduct (NIOCOR), both in Volta Redonda-RJ, and Santo Amaro Station (COS-AR-COR), Headquarters of the Brazilian Association of Metallurgy, Materials and Mining – ABM (USI-SAC) and Cidade Jardim footbridge (CSN COR) in the city of São Paulo, as well as in architectural sculptures like Palas Atena Monument (COS-AR-COR) and Ayrton Senna Sculpture (GERDAU COR), both in the city of São Paulo (the designations in parentheses correspond to different WS trademarks). For its aesthetic value, WS patina has been much appreciated by artists and architects from all over the world. Some examples of works of art in WS are: “the Angel of the North” designed by Antony Gormley (England) [7], “Te Tuhirangi Contour” by Richard Serra (USA) [8], “Buscando La Luz IV” by Eduardo Chillida (Spain) [9,10] and the Luxembourg World Expo Pavilion by architect Valentiny (Luxembourg) [5].

Two recent studies demonstrate interesting approaches to the study of patina on WS sheets and sculptures. Raffo and co-workers [11], studying different surface finishing, showed that artificial ageing through chemicals, i.e., the pre-patination treatment usually used by sculptors to accelerate patina growth, has no beneficial effects on corrosion, affecting the stability of the patina and Aramendia and co-workers [12–14] described the influence of urban pollution on patina development, taking into account the orientation and geometry of three WS sculptures in Spain. Studies on the patina protectiveness are of great importance in the scientific community. This property has been usually evaluated by the corrosion rate (CR), structure and composition of the layer [9,15–20]. However, to determine the CR, the patina layer must be removed from the substrate by chemical, mechanical or electrochemical procedure, and the weight loss is converted to a suitable CR expression, representing the average mass loss at the surfaces facing upward and downward [21]. However, it has been observed that both sides of the samples often corrode at different rates [22]. The mass loss test is also not indicated for evaluating corrosion rates during early stages of exposure and when the corrosion process is highly localized (pitting corrosion) (ASTM Standard Practice G50 [22]). Other main drawback of the weight loss methodology is that these tests are destructive. Therefore, considering that WS is frequently used for producing sculptures (as those previously mentioned and those that will be showed in this work), it is of interest to correlate the patina growth rate with its stabilization by non-destructive in situ measurements, as from these artefacts physical sampling is quite limited. Therefore, it is important to use non-destructive techniques to evaluate the patina growth rate.

Different methodologies may be used for non-destructive evaluation of the corrosion process. He et al. [23] used pulsed eddy current (PEC) to characterize atmospheric corrosion of uncoated and coated mild steel samples exposed to marine atmosphere between 1 and 10 months. By means of conductivity, permeability and material thickness variation they verified decreasing CR for increased exposure time. However, as stated by the authors in the summary of the paper “the PEC response due to corrosion is a complex mix of many factors, including conductivity, permeability and material thickness variation” [23]. Sunny et al. [24] used low frequency (LF) radio frequency identification (RFID) sensors for corrosion characterization, using a WPT (wireless power transfer) concept, while Zhang and Tian [25], used a UHF (ultra-high frequency) RFID tag antenna. Although both methodologies [24,25] were successfully used for corrosion evaluation of uncoated and coated samples, the experimental procedures seem to be laborious and data treatment complex, which could be a drawback for a wide range of users, like architects, curators and restorers.

More recently, patina development on different WS bridges in Czech Republic has been studied by thicknesses measurements by magnetic induction (measurement of non-magnetic coatings on magnetic substrates), which is a standard practice for monitoring of atmospheric corrosion on WS [7]. Krivy et al. [26,27] and Urban et al. [28] examined the protective ability of these patinas and found a close correlation between the corrosion (mass) loss and the thickness of the patina. Based on this approach, in the present study, the thicknesses of patina layers formed on WS sheets exposed in an atmospheric corrosion station (ACS) and on two WS sculptures exposed at the campus of the University of São Paulo, in the city of São Paulo, Brazil, for a long period were determined using a commercial portable thickness gauge based on magnetic induction. The measurements were performed according to the recommendations of standard reference ABNT NBR 10443 [29], equivalent to ISO 19840 [30]. This technique is non-destructive and allows, thus, obtaining information of patina layer thickness in situ, without the need of sampling. The thickening of the rust layer/patina with exposure time is then discussed and correlated to its protectiveness by means of microstructural characterization and Open Circuit Potential (OCP) measurements.


The research has been carried out with a commercial WS, corresponding to ASTM A242, with the following chemical composition: 0.10%C, 0.65%Mn, 0.020%P, 0.003%S, 0.217%Si, 0.246%Cu, 0.63%Cr, 0.01%Ni and 0.039%Al, which was provided by a steelmaking company. The coupons measuring (150mm×100mm×4.75mm) were previously submitted to abrasive blasting for removing the mill scale (iron oxides) formed during the hot rolling manufacturing process. The tests were conducted at the atmospheric corrosion station (ACS) of the Institute of Technological Researches of São Paulo State (Instituto de Pesquisa Tecnológica – IPT) in the urban environment of the city of Sao Paulo, Brazil (Fig. 1). The tests started in December 2016, corresponding to the beginning of the summer in the South Hemisphere, and finished in December 2018, totalizing 2 years of exposure. Intermediate removals of coupons were scheduled for three months (end of Summer time), one year, one year and three months, one year and six months and one year and nine months. The weathering characteristics of the site are given in Fig. 2. The monitored atmospheric parameters were temperature, relative humidity and concentration of contaminants such as sulphur dioxide. Meteorological and pollutants information from the site were supplied by the São Paulo State Environment Agency (Companhia Ambiental do Estado de São Paulo – CETESB) [31] from the station located at Pinheiros, SP, and Osasco, SP, very close to ACS/IPT.

Fig. 1.

View of the atmospheric corrosion station (ACS-IPT) on 12/19/2018. Test coupons installed at 12/21/2016.

Fig. 2.

Climatic parameters and pollutants of the Sao Paulo City during the exposure period – monthly average: (a) relative humidity (RH%) and temperature (T°C), (b) concentration of sulphur dioxide (SO2)

Source: CETESB.

Patina samples produced after different exposure periods were characterized by visual evaluation, Scanning Electron Microscopy (SEM), X-ray diffraction (XRD) and Open Circuit Potential (OCP) measurements.

Periodic observations with photographic documentation were made in the early stages of corrosion for evaluating colour evolution, whether specimens were removed or not. After removal from the rack (3 months to 2 years), colour registration was performed by scanning the surface.

SEM characterization of the exposed surface and of the cross-sections of the patinas was carried out using a FEI Inspect F50 FE-SEM equipped with secondary and backscattered electron detectors.

X-ray diffraction (XRD) analysis was performed either with a Bruker D8 Advance 3kW diffractometer, equipped with copper radiation tube, 250mm goniometer, graphite monochromator and scintillation detector, at which data were collected over a 12h range from 10° to 90° using a 0.02° step and a counting time of 10s per step, or with a PANalytical X’Pert – MPD diffractometer using Cu Kα radiation in conventional Bragg–Brentano geometry, with a step width of 0.02° and a counting time of 200s per step (2 years and 24 years samples). XRD patterns were obtained directly on the specimen surface and identified by the search-match technique using the HighScore Plus software and the ICDD database [32]. The peak area measurement method [33] was employed in order to determine the ratio between relevant phases identified in the XRD spectra. In order to validate this method, quantitative phase analysis was determined by the Rietveld refinement method using the High Score programme for the sample correspondent to one year of exposure.

Patina layer thicknesses were determined in WS coupons with 150mm×100mm by means of a commercial coating thickness gauge based on magnetic induction, FISCHER, DUALSCOPE MP0, with statistics function and probe integrated in the measuring instrument. The magnetic induction method is based on the energization of a low frequency alternating current or direct current coil that acts as an electromagnet. The magnetic flux varies inversely with the distance between the magnetizable substrate and the coil. If this distance corresponds to a non-magnetizable layer, the result must be a function of this layer thickness [29]. The thicknesses measurements were performed after gauge adjustment (optimization) using the rough substrate method, aiming to correct the surface conditions effect of the base metal. Thicknesses standards were employed for verification of accuracy and adjustments in the intended range of use. The measurement statistics was obtained based on 32 minimum readings for each coupon. These reading numbers are acceptable for the size of the analyzed area and are well above the 12 measurements suggested by the ABNT NBR 10443 [29], equivalent to ISO 19840 [30]. The arithmetic mean was read directly from the gauge and calculated without discarding the minimum and maximum values, as advised in the standard.

Patina layer thicknesses (minimum of 77 readings) were also determined in two WS sculptures: O Quadrado, o Círculo e o Disco fragmentado (2003) e o Monumento ao Politécnico-Palas Atena or Ágora (1994) (Fig. 3). They have been exposed, respectively, during 16 and 24 years at the Campus of the University of São Paulo (USP), very close to the exposure site of the investigated coupons. Patina sample collected in 2019 from the Palas Atenas surface was characterized by SEM and XRD in PANalytical equipment, X’Pert PRO model. The collected sample was brought rapidly to the laboratory and kept sheltered from air until analysis in order to limit possible transformations. In this case, SEM and XRD analysis were carried out in powder samples.

Fig. 3.

WS sculptures exposed at the Campus of the University of São Paulo (USP)/Brazil. (a) O Quadrado, o Círculo e o Disco fragmentado (2003) and (b) Monumento ao Politécnico-Palas Atena or Ágora (1994).


Open Circuit Potential (OCP) measurements were carried out in 3 months and 1 year patina samples using a potentiostat/galvanostat (AUTOLAB PGSTAT30) in a classical three electrode cell arrangement, with an Ag/AgCl reference electrode, a Pt foil as counter electrode and the exposed specimens as working electrode. The electrolyte was 0.01molL−1 Na2SO4 solution.

3Results3.1Visual evaluation of colour evolution

Fig. 4 shows images of the test coupons surfaces after 7, 14 and 50 days, 3 months and 1 and 2 years of exposure. The samples develop a yellow (orange) patina after only one-week exposure, evolving to an orange colour with 14 days, and then, after 50 days, they acquire a brownish hue that darkens for increasing exposure time. The early sequence of colour variation, up to three months, was also observed in coupons exposed to each season of the year (presented in another paper [34]), indicating a common pattern of patina colour evolution.

Fig. 4.

WS patina colour evolution with exposure time in test coupons exposed at São Paulo City. The colour varies from (yellow) orange to dark brown. Photographs (7, 14 and 50 days) and scanned images (3 months, 1 and 2 years) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


Antunes et al. [35] showed that it is possible to associate the colour of the iron oxides to a particular phase of the patina. According to Cornell and Schwertmann [36], natural iron oxides and oxide–hydroxides present the following colours: Lepidocrocite, γ-FeOOH, has an orange colour (krokus=saffron); Goethite, α-FeOOH, is yellow-brown, if in massive crystals aggregates it is dark brown or black, whereas the powder is yellow ochre; Feroxyhyte, δ′-FeOOH, Ferrihydrite, Fe5HO8·4H2O, and Maghemite, α-Fe2O3, are dark reddish brown, with the latter displaying more intense red patterns; Magnetite, Fe3O4 and Wüstite, FeO, are both black, and Hematite, Fe2O3, has a blood-red colour (Greek haima=blood).

In addition to the colour variation, the literature provides a lot of data showing that the time for stable patina formation varies with local atmosphere or geographic location, and there are some suggestions that it takes about 2–3 years [5,37] to acquire a final dark brown colour. In this work, 1 and 2 years old patina already got a dark brown colour, which are similar, respectively, to those exhibited by the sculptures “O Quadrado, o Círculo e o Disco fragmentado” (Fig. 3(a)) and “Palas Atena” (Fig. 3(b)), both exposed at the Campus of the University of São Paulo (the same site of the exposed coupons) since 2003 and 1994, respectively.

3.2X-ray diffraction (XRD)

The patina layer has a very complex chemical composition, including many iron oxides, oxy-hydroxides, miscellaneous crystalline and amorphous phases. Fig. 5 shows typical XRD patterns of the patina formed on the coupons after three months and two years of atmospheric exposure. Lepidocrocite (γ-FeOOH) and goethite (α-FeOOH) were found as the main crystalline phases, as identified by the (020) and (110) diffraction lines at 14.3° and 21.3° [9]. Magnetite (Fe3O4) and/or maghemite (α-Fe2O3) can also be present at small proportions, as indicated by the diffraction angle at 30° [16]. As these constituents have crystal structures with practically identical lattice parameters, they are very difficult to differentiate using only XRD. In general, these results are in agreement with those found by Kenny et al. [15] and by Antunes et al. [38] for atmospheric corrosion tests carried out with WS in the city of São Paulo, Brazil.

Fig. 5.

XRD patterns on test coupons after 3 months and 2 years of atmospheric exposure. Only some relevant peaks are indicated in the figure. L, G, M and Mh correspond to lepidocrocite, goethite, magnetite and maghemite, respectively.


The diffractograms presented in Fig. 5 show that the intensity of the peak ascribed to goethite (α-FeOOH) increases with exposure time. This phase is formed from lepidocrocite (γ-FeOOH), and is considered to be the most stable iron oxy-hydroxide, thus indicating increased protective properties of the patina layer.

3.3SEM observation

Secondary (SE) and backscattered (BSE) electron images were acquired from the exposed surface (top view) and the cross-section of the patina.

3.3.1Top view

Fig. 6 shows a SEM image of the patina layer after 3 months of exposure. It displays laminar structure characteristic of lepidocrocite (γ-FeOOH), which has been termed as bird's nest and reported by several researchers [38–41]. The goethite (α-FeOOH) is located at the inner layer and, due to its small amount, it could not be easily identified in short term exposed samples. Other features associated with these iron oxyhydroxides can be found elsewhere [34].

Fig. 6.

Representative SEM micrograph of lepidocrocite (γ-FeOOH) in the WS patina (top view) after 3 months of exposure to the urban atmosphere of São Paulo City.


Fig. 7 shows SEM micrographs of the patina formed on samples exposed during 1 (Fig. 7(a)) and 2 years (Fig. 7(b)) to the atmosphere of São Paulo. They show goethite basic morphology – acicular [34,36,39–44], as whiskers and tiny rods [39,42,45] (Fig. 7(a)) and sharp laminas, which, according to some authors, resemble to a stellar [36,39] or flowery pattern [34,45,46] (Fig. 7(b)).

Fig. 7.

Representative SEM micrographs of goethite (α-FeOOH) in the WS patina after (a) 1 year and (b) 2 years of exposure to the São Paulo Metropolitan Area.

3.3.2Cross-section analysis

Fig. 8 presents cross-sectional views of the patina after different exposure periods. All micrographs display a corrugated and non-uniform profile, consisting of thinner and thicker regions. The undulations at the sample surface and at the patina/substrate interface, can be ascribed both to the surface roughness profile of the as-prepared coupons, and to the non-uniformity of the corrosion process occurring under uncontrolled conditions. As evidenced in the images, usually, more porous structures were found at regions covered with thicker patina. Cracks normal to the surface were observed in all the examined specimens, which may lead to lower protective characteristics due to easier electrolyte penetration. However, some of these cracks may be ascribed to the specimen preparation procedure. The images also indicate that the patinas become more compact with increasing exposure time, therefore, the 2 years patina (Fig. 8(c)) presents less defects, pores and cracks.

Fig. 8.

Backscattered electron images obtained from the cross-section of the WS patina after (a) 3 months, (b) 1 year, and (c) 2 years of atmospheric exposure in São Paulo City.

3.4Thickness measurement

Table 1 summarizes the thicknesses of the patina layer determined by the magnetic induction method on WS exposed during three months, one year, one year and three months, one year and six months, one year and nine months, and two years to the urban atmosphere of São Paulo City, Brazil. In accordance with the SEM images (Fig. 8), the patina layer thickness is not uniform, consisting of thin and thick regions. According to these results, the mean thickness varied from 16.4μm (3 months) to 48.5μm (2 years), indicating thickening with ageing. However, most of the thickening takes place during the first year of exposure. As shown in the table, the minimum thickness increases up to 1.6 years of exposure, when it becomes apparently stable, and the maximum thickness increases up to 1.9 years. Conversely, after one year exposure, the standard deviations stabilize; however, it is still high, in accordance with the cross-section images (Fig. 8).

Table 1.

Thickness of the patina developed on the WS surface exposed at ACS-IPT after different exposure times in the urban atmosphere of São Paulo City. Thicknesses values were measured by magnetic induction thickness gauge. Thicknesses determined at two WS sculptures exposed at the Campus of the University of São Paulo during 16 and 24 years are also provided.

2017 ACS3 months  2017 ACS1 year  2018 ACS1.3 years  2018 ACS1.6 years  2018 ACS1.9 years  2018 ACS2 years 
16 years 
24 years 
Mean thickness (μm)  16.4  34.3  39.5  44.7  44.4  48.5  69.2  76.8 
Minimum thickness (μm)  1.6  9.0  18.2  23.2  22.8  23.4  36.6  45.8 
Maximum thickness (μm)  39.6  70.8  78.2  96.7  108.0  107.4  130.8  121.3 
Standard deviation  9.1  13.8  15.8  15.0  13.5  16.6  25.1  19.1 
Number of determinations  35  53  32  48  50  44  91  77 

Table 1 also presents thicknesses determined in the two WS sculptures presented in Fig. 3. As already stated, they have been exposed during 16 and 24 years to the atmosphere of the campus of the University of São Paulo (USP), very close to the site at which the tests were performed, being, therefore, a good reference for the long-term behaviour of our samples. In the evaluated sculptures, O Quadrado, o Círculo e o Disco fragmentado and Palas Atena, the minimum thicknesses of the patina layers were 36.6μm and 45.8μm, respectively, which are lower than 50μm, which, according to Asami and Kikuchi [47], is the maximum thickness that a protective patina must display at its thinnest region. Thus, our findings corroborate with the investigation of these authors [47] performed on a WS bridge exposed to coastal–industrial atmosphere for 17 years in Japan. As for the samples exposed at ACS of IPT, the thicknesses measurements of the sculptures showed high dispersion, confirming that patina growth exposed to the atmosphere is an uneven process [47]. According to Asami and Kikuchi [47], there will be no argument about the fact that origin of unevenness in patina layers thicknesses arises from non-uniform distribution of physical and chemical factors such as deposits from environment and the crystallographic orientation distribution of the steel. Nevertheless, the maximum and minimum thicknesses were higher than those determined for the samples exposed during two years, indicating that, even though not uniformly, the thickness of the whole patina layer steadily increases. Therefore, the apparent steady values for the minimum and maximum thicknesses verified at the end of the two years exposure period and mentioned in the previous paragraph must represent a slow thickening rate of the patina.

4Discussion4.1Protective ability of the patina layer

The nature of the patina layer is strongly dependent on the environmental conditions and exposure time. In fact, some constituents or phases are always detected in a certain type of atmosphere; however, their proportions depend on exposure time. de la Fuente et al. [48] report that the time factor only changes the proportions of the main constituents, or, at most, promotes the appearance or disappearance of minor constituents. In the present study, lepidocrocite (γ-FeOOH) and goethite (α-FeOOH) were the main crystalline phases detected in the patinas formed at São Paulo atmosphere (Fig. 5).

The literature reports that crystalline lepidocrocite is the first phase to form on steel surface [18,48–50]. As exposure time increases and the patina becomes thicker, it is partially transformed into stable goethite, producing a more consolidated layer, which presence is associated to the protective ability of the patina [18,48–50]. Yamashita et al. [18–20] studied and defined the so-called Protective Ability Index (PAIα), calculated as the ratio between goethite to lepidocrocite (α/γ) content in the patina layer. This ratio is about 1 for WS exposed during the first 5–10 years and higher than 2 for WS exposed for longer than 10 years [9,18,26,44].

Table 2 displays the (α/γ) ratios determined from the XRD data for patinas formed on samples exposed for different periods to the atmosphere of the city of São Paulo. They were calculated from the areas of the α-FeOOH (110) and γ-FeOOH (020) peaks, as it is well recognized that this relationship is more reliable than peak heights for quantitative evaluation [33]. The results, corroborated by additional SEM and colour analysis, show an increase in the amount of goethite with exposure time and, thus, a positive correlation between composition and protectiveness of the patina can be predicted. Comparing these results with the literature, Krivý et al. [26] found PAIα value of 1.09 on the bottom flange of the main girder (external upper surface) of 16 years old bridge exposed to the urban atmosphere influenced by chloride deposition. In the present work, we found PAIα of 1.03 for a 2 years old patina exposed at São Paulo urban atmosphere and for a test coupon facing north (Equator).

Table 2.

PAI index determined from the XRD spectra of patina formed after different exposure periods.

Exposure time  Thickness (μm)  Layer composition (XRD)  α110/γ020a  α/γb 
3 months  16.4  Very strong lepidocrocite and very weak goethite  0.02  – 
1 year  36.4  Strong lepidocrocite and weak goethite  0.33  0.34 
2 years  48.5  Similar lepidocrocite and goethite  1.03  – 
24 years  76.8  Strong goethite and weak lepidocrocite  2.15  – 

Peak area measurement of the (110) reflection of α-FeOOH and (020) reflection of γ-FeOOH.


Rietveld refinement method.

Table 2 also presents the (α/γ) ratio for the patina layer formed on the surface of Palas Atena monument. In this case the XRD pattern (Fig. 9) and the SEM image (Fig. 10) were acquired from powder collected from the outmost layer. Goethite is the dominant phase and the PAIα is 2.15 indicating a stabilized patina according to Yamashita et al. [18] criteria (Fig. 11).

Fig. 9.

XRD pattern of 24 years old patina (outmost layer) of Palas Atena monument, showing a marked presence of goethite. L, G, M and Mh correspond to lepidocrocite, goethite, magnetite and maghemite, respectively.

Fig. 10.

SEM micrograph of 24 years old patina (outmost layer) of Palas Atena monument. It shows goethite (α-FeOOH) as crystalline aggregates growing parallel with appearance similar to clumps of grass or a filiform morphology [27].

Fig. 11.

Open-circuit potential for WS specimens as a function of immersion time in 0.01molL−1 Na2SO4 solution. *Initial exposure in the beginning of summer 16/17 in the South hemisphere (December).


In order to validate our PAI values, for the one year old patina, additional XRD measurement was performed by the Rietveld refinement method. It revealed 74.2% of lepidocrocite and 25.4% goethite providing and α/γ ratio (PAIα) of 0.34, which is practically the same value (0.33) obtained by the peak area measurement method (Table 2), validating our results.

According to the literature as the patina becomes more protective the OCP tends to become nobler [34,51,52]. Kashima et al. [51] attribute this behaviour to the increase of the amount of goethite in the layer. Therefore, OCP measurements were performed on WS samples exposed for different periods to the atmosphere of São Paulo. The results are presented in Fig. 12 as a 300s period after the samples have been in contact with the test solution (0.01molL−1 Na2SO4 solution) during 1h. As a reference the OCP of an unexposed sample (just submitted to the abrasive blasting) is also presented. The plots show OCP values in the following order: 1 year old WS patina (−0.04V vs. Ag/AgCl)>3 months old WS patina (−0.49V vs. Ag/AgCl)>unexposed WS (−0.67V vs. Ag/AgCl). Adopting the criteria of Kashima et al. [40], the results indicate that the 1 year old patina is already protective, as the OCP is about −0.04V (vs. Ag/AgCl), which is similar to the threshold value for satisfactory protectiveness of the patina layer on steel substrates in this same electrolyte defined by these authors [51].

Fig. 12.

(a) Mean thickness evolution and (b) relative thickening rate (RTR) as a function of the exposure time for WS exposed at São Paulo atmosphere. The plots were built considering the patina thickness determined for the two sculptures.

4.2Correlation between patina thickness and protective ability

Thicknesses determination by magnetic induction provides valuable information about the patina thickness profile by the maximum and minimum values. They contribute to clarify the non-uniform corrosion process taking place on samples exposed to the atmosphere, even if the substrate is rough. This information cannot be obtained by the gravimetric technique commonly used to evaluate the atmospheric corrosion resistance of metals (ASTM G1) [21], once, as previously mentioned, with this methodology a uniform corrosion rate is considered. Besides being highly coherent with thicknesses determination of sculptures exposed for a long period at a similar site, the patinas thicknesses determined in the present work are in good agreement with literature findings. Table 3 summarizes data published by Krivý et al. [27] of patina thicknesses on eight WS bridges exposed for various periods to different urban environments in Czech Republic. The table includes measurements performed on the vertical surfaces of the main supporting structure (long-term exposure) and of coupons installed on the bridges (one year exposure). The values displayed in Tables 2 and 3 are in good agreement both for specimens exposed during 1 year and after long-term exposure. In the first case the average thickness obtained in the present work was 36.4μm compared to 38.2μm in Krivý‘s work [27]. On the other hand, for similar periods, 29 years in Krivý ‘s work [27] and 24 years in the present investigation, the patinas’ thicknesses were 88.8μm and 76.8μm, respectively. This latter corresponds to the mean thickness determined on the Palas Atena sculpture and presented in Table 1.

Table 3.

Thickness of the patina layer developed on WS bridges surfaces in Czech Republic (μm).

Surface  1 year specimens  7 years Bridge A  7 years Bridge B  7 years Bridge C  7 years Bridge D  14 years Bridge E  29 years Bridge F  32 years Bridge G  34 years Bridge H 
Outer web of the main girder  32.9  60.9  59.4  63.7  67.4  127.1  76.3  90.9  81.8 
Outer web of the main girder 50mm above the bottom flange  43.4  72.7  79.8  61.4  68.5  183.7  101.4  146.0 
Average  38.2  66.8  69.6  62.55  67.95  155.4  88.85  90.9  113.9 

Note: The bridges ages were calculated based on thickness measurements taken in 2015. A, road bridge over the railway line on the road II/456 in Ostrava (2008); B, road bridge over the river Odra on the road II/456 in Ostrava (2008); C, road bridge over the railway line on the road I/56 in Ostrava (2008); D, road bridge over the river Opavice in Opava (2008); E, road bridge on Opavska street over the highway D1 in Ostrava (2001); F, road bridge over the river Ostravice in Frydek-Mistek (1986); G, road bridge on Opavska street over the railway line in Ostrava (1983); H, railway bridge in Prague (1981).

Data extracted from Krivy et al. [27].

Table 4 presents the patina thickening rate at São Paulo atmosphere for each analyzed period. They were calculated based on the mean thicknesses determined with the portable thickness gauge. Two methodologies were adopted: the first one, denominated absolute thickening rate (ATR), was determined simply dividing the mean thickness by the exposure period. The other, denominated relative thickening rate (RTR) was calculated by subtracting from each layer thickness the mean thickness determined in the preceding sampling period and then calculating the thickening rate relative to the new period. These methodologies were also applied for the two sculptures. In this case, for RTR, note a gap of 14 and 22 years.

Table 4.

WS patina thickening rate in São Paulo atmosphere.

Exposure period  Thickness (μm)  Absolute thickening rate (ATR) (μm/year)  Relative thickening rate (RTR) (μm/year) 
3 months  16.4  65.6  65.6 (5.5mm/month) 
1 year  36.4  36.4  26.7 (2.2μm/month after 3 months of exposure) 
2 years  48.5  24.2  12.1 (1μm/month) 
16 yearsa  69.2  4.3  1.5μm per year (after 2 years of exposure) 
24 yearsb  76.8  3.2  1.3μm per year (after 2 years of exposure) 

O Quadrado, o Círculo e o Disco fragmentado.


Palas Atena.

The results displayed in Table 4 show that the thickening rate of the WS patina decreases with exposure time. For the exposed coupons, ATR decreases from 66μm/year for the samples exposed for only 3 months, to about 24.2μm/year after two years exposure, and RTR decreases to about 12μm/year after two years exposure. Considering the two sculptures which patina thicknesses were determined in the present study, ATR and RTR were, respectively, 4.3 and 1.5μm/year and 3.2 and 1.3μm/year, for the “O Quadrado, o Círculo e o Disco fragmentado” and the “Palas Atena”. The decrease in the growth rate with exposure time can be correlated with the increased amount of goethite (α-FeOOH) in the patina composition, as verified by means of XRD (Figs. 5 and 9) and SEM (Fig. 10) measurements and also by the determination of the Protective Ability Index (PAI) increasing from 0.02 to 2.15 (Table 2). The increase in goethite (α-FeOOH) content over time reinforces the hypothesis of a more protective layer and increased corrosion resistance. For long-term exposure, it was found a low thickening rate (<2μmyear−1), suggesting stabilization of the patina layer.

Hao et al. [53–55] studied the evolution of atmospheric corrosion of MnCuP weathering steel submitted to wet/dry cyclic accelerated corrosion tests (CCT) in various simulated environments. They verified that weight gain, as a consequence of the thickening of the patina layer, followed an ascending bilogarithmic law as a function of the number of CCT cycles [55], which, indirectly, represents increasing exposure time. They reported two different slopes: the steeper one is representative of the initial CCT cycles, indicating a higher patina growth rate at the early stages [53–55]. Fig. 12(a) presents the plot of the average patina thicknesses (including the average value for the two sculptures to forecast the long-term behaviour) as a function of exposure time, it follows a bilogarithmic law with steeper slope for the first years, in fully agreement with Hao's et al. work [55]. By means of polarization curves and EIS measurements, these authors showed that, generally, the corrosion resistance increases with immersion time [55].

Fig. 12(b) displays the plot of RTR as a function of exposure time, employing a bilogarithmic scale. The long-term behaviour is forecasted by the average value for the two sculptures. It shows a decreasing linear behaviour represented by Eq. (1). This must be a consequence of the increasing protectiveness of the patina layer, due the increasing of goethite (α-FeOOH) content over time, leading to smaller corrosion rates and, therefore, decreasing the thickening rate. This is in accordance with several works reporting decreasing corrosion rates for WS as a function of exposure time in urban atmosphere with SO2 level not exceeding about 115μg/m3[15,16,37,56,57].


Thicknesses measurements of patina layers using the magnetic induction method were carried out on rough surfaces of WS after different exposure periods to the atmosphere of São Paulo, Brazil. As expected for the atmospheric corrosion process taking place on rough surface, for each sample, the thicknesses values were very scattered. However, the mean thicknesses were in good agreement with the data presented in the literature and the layer thickening followed a bilogarithmic law with a steeper slope for the initial stage of atmospheric corrosion, as proposed by Hao et al. [55]. The results showed that the patina growth rate decreases with exposure time, which can be correlated with the increased amount of goethite (α-FeOOH) as verified by means of SEM and XRD measurements and also by the determination of the Protective Ability Index (PAI) proposed by Yamashita et al. [18].

Using the mean thicknesses values determined from two WS sculptures exposed during 16 and 24 years at a similar site to those of WS sheet samples to predict the long-term behaviour a decreasing monologarithmic law could be determined representing a relative thickening rate.

The magnetic induction technique is non-destructive and allowed to obtain information about the patina layer formed in works of art, in situ, without the need of sampling. Therefore, it can be a valuable tool to monitor the development and stabilization of patina formed in historical monuments.

Conflicts of interest

The authors declare no conflicts of interest.


This research was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) of Brazil (Finance Code 001). The authors would like to thank IPT for the use of corrosion station and others laboratory facilities, IPEN by performing XRD tests, Maitê Moura by helping in the thickness measurements and Cátia Fredericci (IPT) for her helpful contribution in the Rietveld refinement (XRD). The authors also thank IPT technicians and officials for their kind assistance. We are grateful to the board of polytechnic school (POLI-USP) for the kindly permission for the sample collection of Palas Atena sculpture.

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