Protective ALD Thin Films for Morphologically Diverse Types of Limestone

Abstract

We report on the results of investigations of atomic layer deposited (ALD) amorphous alumina (Al₂O₃) coatings for the protection of limestone with a wide range of porosity against acid-based dissolution. The protective effects of the ALD coatings were investigated by aqueous acid immersion. The solution pH was tracked over time for a constant volume of acetic acid solution with an initial pH of 4 with the stone samples immersed. We find the protective effect of ALD alumina coatings is extremely promising, with 90 nm thick coatings slowing the initial and total rate of substrate mass loss significantly by up to two orders of magnitude. The eventual failure of the ALD coatings during immersion was also investigated. Pitted areas on the substrate were discovered and were found to have an area fraction that correlates to the changing pH of the acid solution during immersion. The variation of the protective action of the films with thickness is consistent with kinetics, which are limited by diffusion within the pits rather than through the films. Our findings point to the dominant role of defects in the coatings in their eventual failure. We also show that the appearance of the stone does not change significantly for the thickest and most protective ALD films, making the treatment promising for cultural heritage applications.

1. Introduction

Limestone, though often considered a durable material, is vulnerable to natural and human-generated pollution [1,2,3,4]. The effects of pollution on limestone were historically evidenced by the formation of gypsum black crusts from SO₂ and acid rain [5,6,7]. With SO₂ emissions now greatly reduced across Europe [8,9], pollutants such as NO₂ and CO₂ have become the primary concerns due to their potential to increase rain acidification and cause stone washout [10,11,12]. To address these concerns, this work examines Atomic Layer Deposition (ALD) as a possible method to protect a variety of morphologically diverse limestone from aqueous acid alteration. ALD metal oxide thin films have previously shown promising results protecting a wide range of materials from varied degradation mechanisms. For example, ALD alumina coatings have been shown to be effective at preventing the tarnishing of silver objects [13] and slowing aqueous alteration of glass [14], and most recently, protecting compact limestone from reaction with aqueous acid solution [15]. This work expands upon these studies by comparing morphologically diverse ALD-coated calcium carbonate substrates, including compact limestone, porous limestone, and single-crystal calcite.

Istria stone is a representative compact limestone. It is a low porosity (<1%) stone found as a building and sculptural material throughout northeastern Italy and Venice in particular [16]. Because of its compactness, the pattern of aqueous deterioration of Istria stone tends to be localized to the surface and by penetration through clay veins, which can cause swelling and localized detachment [17]. Lecce stone is a representative porous stone. It has an open porosity of 30%–45% and is local to southeastern Italy, where it is found commonly in baroque monuments and buildings in the region [18]. The highly porous nature of the stone is instrumental in its deterioration as the pores allow for large amounts of water, acids, and salts to penetrate the bulk [19,20]. Calcite, used in optics, represents the extreme limit of a zero-porosity calcium carbonate mineral. It is the majority component of limestone but with the advantage of nanometer-scale smoothness, which enables optical characterization techniques and the quantification of ALD performance more easily than on rough limestone.

ALD is a vapor-phase technique used to grow thin films on a substrate via exposure to a series of precursor gases that react with a substrate’s surface in a self-limiting manner. In ideal cases, this allows for films to be grown with atomic-level precision. The process of ALD is reviewed elsewhere [21], as is how the idealized model adapts to non-ideal surfaces [22]. In addition, the specific example of ALD alumina on limestone cultural heritage is discussed in detail in our previous work [15]. In brief, when ALD precursor gases impinge on a surface with certain defects and other nonreactive sites, film growth likely follows an island nucleation and coalescence model [21]. The resulting film nucleates only on sites that are available for reaction, creating an initially islanded morphology. The islands may eventually coalesce into a contiguous film as more ALD cycles are carried out. However, incomplete coalescence can result in extended defects analogous to grain boundaries, which can act as paths for relatively fast permeation through the film. ALD growth of alumina at 150 °C produces amorphous films, an advantage, as it eliminates grain boundaries and dislocations that might act as short-circuit permeation paths through the films.

ALD metal oxide films are uniquely applicable for morphologically diverse stone substrates due to the self-limiting nature of the process. In principle, given enough time for the precursor gases to diffuse and chemisorb to every surface of the substrate, even highly porous materials may be coated conformally. The reactive nature of the processes that create the films results in covalent bonding at the interface, which is expected to produce much higher adhesive energies than coatings that rely upon van der Waals interaction, for example. The self-limiting nature of the sub-reactions, in principle, should assure high interface quality, at least in ideal layer-by-layer growth. The ability to deposit conformal ALD films on extremely high-aspect-ratio substrates has been well documented and is a major advantage of ALD for applying coatings to complex morphology [22,23]. In contrast, typical polymer-based protective coatings for stone, such as acrylic, alkyl silicon, and fluorinated polymers, often accumulate on the stone surface in compact areas and fill open pores, limiting the ability to achieve uniform coverage, potentially providing uneven protection and changing appearance [18,24].

In this work, we explore the potential of ALD alumina coatings as protective barriers for morphologically diverse forms of calcium carbonate minerals, including compact limestone, porous limestone, and single-crystal calcite. We consider the ALD coatings in the context of cultural heritage preventative conservation, examining the treatment both for its protective and aesthetic effects. Further, we examine the eventual failure of the coatings, finding evidence for the influence of defects by utilizing single-crystal calcite as a representative and easily characterizable substrate. As pollution-induced stone decay is complex and impossible to replicate exactly in a laboratory setting, we chose to implement a simple acidic aqueous immersion method that is favorable for in situ monitoring. In this way, we examine ALD alumina coatings for protecting diverse morphologies of calcium carbonate broadly from acidic aqueous solutions. Coating quality is a crucial issue but seemingly does not have a unique definition in the literature. For cultural heritage applications, two of the most important contributors to the quality of the coating are its performance as a permeation barrier and its appearance. These are the coating quality-related aspects we have studied for ALD alumina films on limestone. While scaling up atomic layer deposition to treat large objects is an area of intense interest, it has not been completely resolved in the literature. This issue is beyond the scope of our study, which concentrates on two other issues that would be important to the treatment of small or moderately sized cultural heritage objects: efficacy in the retardation of atmospheric acid-induced corrosion and visual impact of the coatings. Additional relevant issues that also fall outside the scope of the present study include the effect of thermal stress on the long-term stability of the coatings, as well as the detailed nature of the buried interface.

Regarding the novelty of the results reported here, while atomic layer deposition has long been successfully employed in encapsulation of semiconductor devices and in the creation of spacer layers in electronic and optical structures, the application of this technique in producing coatings for the protection of cultural heritage objects made from limestone of different degrees of porosity has not been previously reported; part of the novelty of this work comes from its investigation of the efficacity and appearance of ALD alumina films to such objects, for which both are crucial. An additional novel aspect of this work is the method that we have developed in quantifying the performance of these films as corrosion barriers, using the pH of an acid solution in which we immerse coated limestone as a real-time, in situ probe of the erosion of the underlying substrates. Finally, and even more importantly, our results reveal the role of defects in the eventual failure of ALD alumina films during acid immersion.

2. Materials and Methods

2.1. Sample Preparation

Three types of calcium carbonate minerals with differing morphology were examined in this work: Istria stone, Lecce stone, and single-crystal calcite. Istria stone is very compact with an open porosity of less than 1%. Istria stone is typically composed of calcium carbonate in the structure of calcite with MgO, SiO₂, Fe₂O_3, and Al₂O₃ impurities, as well as microfossils [25]. Samples were cut from slabs of Istria stone into 1 cm cubes and polished with 180, then 320 grit silicon carbide paper. They were then rinsed in deionized water and allowed to dry at room temperature. Samples had final masses of 2.50 ± 0.25 g. Lecce stone is a highly porous stone with an open porosity ranging from 30% to 45% [18]. It is primarily composed of calcite with small amounts of fossils, shells, clay, and non-carbonate granules such as quartz, glauconite, and feldspars [26]. Samples were cut from slabs of Lecce stone into 1.5 × 1.5 × 0.2 cm³ wafers and polished with 180, then 320 grit silicon carbide paper. They were then rinsed in deionized water and allowed to dry at room temperature. Samples had final masses of 1 ± 0.05 g. Single-crystal calcite wafers measuring 1 × 1 × 0.05 cm³ with 2 sides polished were purchased from MTI corporation, Richmond, CA, USA.

The amorphous alumina ALD films were grown using a Beneq TFS 500 Atomic Layer Deposition (ALD) system (Beneq, Espoo, Finland) in a class 1000 clean room. TMA and H₂O were used as the precursors with 2 s pulses for each. N₂ was used for 2 s purges. All the films in this work were grown at 150 °C. Uncoated samples are hereafter referred to as “No ALD-samples”, and those coated with 25 cycles, 50 cycles, 250 cycles, and 500 cycles of ALD alumina are hereafter referred to as “ALD samples.” Samples were allowed to equilibrate in temperature within the ALD reaction chamber for at least 30 min prior to deposition. Within the reaction chamber, custom holders were used to support the samples by three points of contact. The samples were flipped upside down halfway through the depositions to mitigate shadowing defects caused by contact with the holders.

The thicknesses of the ALD coatings were estimated based on Variable Angle Spectroscopic Ellipsometry (VASE) measurements taken from silicon wafers that were placed inside the reaction chamber with the calcium carbonate samples. A growth per cycle of 0.18 nm was found for these measurements. Measurements were taken with a J.A. Woollam M-2000DI Ellipsometer, Lincoln, NE, USA.

2.2. Reflectance and Colorimetry

To examine changes in the appearance of the limestone samples from applying the ALD alumina coatings, spectrophotometric and colorimetric measurements were performed. Measurements were taken from 3 spots on each of 7 samples for the Istria stone and 3 spots on each of 10 samples for the Lecce stone. Data was analyzed for both the specular component included (SCI) and the specular component excluded (SCE). The coordinates ΔL, Δa, and Δb correspond to apparent changes in luminosity, red to green appearance, and yellow to blue appearance, respectively. ΔE represents the overall change in appearance. The literature suggests that chromatic variation of ΔE > 5 is considered visually significant, while ΔE < 3 is considered insignificant and ΔE < 5 is generally acceptable for cultural heritage applications [27,28].

The colorimetric coordinates in CIE 1976 L*a*b* were acquired with a Konica Minolta CM-700d spectrophotometer (Konica Minolta, Tokyo, Japan) (illuminant D65, observer 8-degree viewing angle geometry) and analyzed with Spectra Magic NX 6 software. The equations used for calculating the average chromatic coordinates and the associated uncertainty are as follows:

$$L^{\ast }={\displaystyle \frac{\sum _{i=0}^N{L}_i^{\ast }}{N}},$$

(1)

where N is the total number of measurements for each condition (e.g., N = 30 for 3 spots on 10 samples). $a^{\ast }$ and $b^{\ast }$ were calculated similarly.

$${{\sigma }_{L^{\ast }}}^2={\displaystyle \frac{\sum _{i=0}^N{{(L}_i^{\ast }-\overline{L^{\ast }})}^2}{N}},$$

(2)

The change in the chromatic coordinates and associated uncertainties were calculated with the following equations:

$${\Delta L}^{\ast }=L_{ALD}^{\ast }-L_{no ALD}^{\ast },$$

(3)

$\Delta a^{\ast }$ and $\Delta b^{\ast }$ are calculated similarly.

$${{\sigma }_{{\Delta \mathrm{L}}^{\ast }}}^2={{\sigma }_{L_{ALD}^{\ast }}}^2+{{\sigma }_{L_{noALD}^{\ast }}}^2,$$

(4)

${\sigma }_{\Delta \mathrm{a}}$ and ${\sigma }_{\Delta \mathrm{b}}$ are calculated similarly.

$$\Delta E=\sqrt{{\Delta \mathrm{L}}^{\ast 2}+{\Delta \mathrm{a}}^{\ast 2}+{\Delta \mathrm{b}}^{\ast 2}},$$

(5)

$$\begin{gathered} {{\sigma }_{\Delta E}}^2=\left({\displaystyle \frac{{\Delta \mathrm{L}}^{\ast 2}}{{\Delta \mathrm{L}}^{\ast 2}+{\Delta \mathrm{a}}^{\ast 2}+{\Delta \mathrm{b}}^{\ast 2}}}\ast {{\sigma }_{\Delta L}}^2\right)+\left({\displaystyle \frac{{\Delta \mathrm{a}}^{\ast 2}}{{\Delta \mathrm{L}}^{\ast 2}+{\Delta \mathrm{a}}^{\ast 2}+{\Delta \mathrm{b}}^{\ast 2}}}\ast {{\sigma }_{\Delta a}}^2\right) \\ +\left({\displaystyle \frac{{\Delta \mathrm{b}}^{\ast 2}}{{\Delta \mathrm{L}}^{\ast 2}+{\Delta \mathrm{a}}^{\ast 2}+{\Delta \mathrm{b}}^{\ast 2}}}\ast {{\sigma }_{\Delta b}}^2\right). \end{gathered}$$

(6)

2.3. Acqueous Acid Immersion and pH Tracking

To characterize how well the ALD coatings protect the limestone from acid attack, samples were immersed in 100 mL of an aqueous solution of acetic acid with a starting pH of 4 while stirring at 420 rpm. One of the chemical reactions that occurs is CaCO₃ + 2CH₃CO₂H → Ca(C₂H₃O₂)₂ + H₂O + CO₂.

pH 4 was chosen to approximate conditions of severe acid rain. The immersion solution was allowed to evolve until approximately pH 6 while continuously measuring the pH. A Crison GLP 21 pH meter (Crison Instruments, Alella, Spain) and Hanna Edge Multiparameter pH meters (Hanna Instruments, Woonsocket, RI, USA) were used to continuously measure the pH of the acid immersion solutions.

The average pH evolution trends for the Istria stone, Lecce stone, and calcite ALD samples and No-ALD samples were calculated from 5 samples for each condition with uncertainties represented by 1 standard deviation.

2.4. Optical Microscopy

Calcite samples were examined during the acid immersion; these samples were taken out of the acid solution briefly at various times and dried with compressed air before quickly imaging and returning to the acid solution. Optical imaging was performed with a Keyence VHX 7000N digital microscope (Keyence Corporation of America, Itasca, IL).

The optical images were used to estimate the relative surface area where the ALD coating was damaged from immersion and the underlying calcite was exposed. This was performed by transforming the optical images with a global threshold into binary coloring using ImageJ software, version 1.54d. The sum of the number of white pixels (W) represents the exposed calcite areas, while the sum of the number of black pixels (B) represents areas that are still protected by the ALD coating. The “percent area damage” was calculated by

$$\% \mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a} \mathrm{d}\mathrm{a}\mathrm{m}\mathrm{a}\mathrm{g}\mathrm{e}=\left({\displaystyle \frac{W}{W+B}}\right)\times 100$$

(7)

2.5. SEM-EDS

Morphological characteristics and the presence and distribution of aluminum for various samples were measured with a Zeiss Gemini 300 Scanning Electron Microscope (SEM) (Zeiss, Oberkochen, Germany) equipped with an Oxford Ultim max 170 Energy Dispersive Spectroscopy (EDS) detector (Oxford Instruments, Abingdon, England). To mitigate surface charging of the insulating samples without applying a conductive coating, a low working voltage of 3 keV was used to image most samples. Alternatively, some samples were imaged in variable pressure mode at 0.2 Torr with a working voltage of 10 keV. EDS scans were taken in variable pressure mode at 0.2 Torr with a working voltage of 10 keV.

3. Results and Discussion

3.1. Appearance Changes

Color changes from applying the ALD alumina coatings can arise due to scattering and thin film interference effects despite the transparency of ALD alumina films in the visible spectrum. The Fresnel equations describe the constructive or destructive interference that results when light passes through a thin film and reflects from the substrate surface [29]. Depending on the film thickness, the refractive index of both the film and substrate, and the angle of incidence of light, perceivable color changes resulting from the ALD coating may be present. Further, coatings that smooth a rough surface and have a refractive index between that of the substrate and air can reduce light scattering. In contrast, if a coating increases surface roughness, it will enhance light scattering.

The average change in chromatic coordinates ∆L*, ∆a*, ∆b*, and ∆E values with the specular component included are shown in shown in Figure 1. The Istria stone has a large statistical variance in individual stone samples’ appearances, as we show in our previous work [15]. However, despite the large variance, there are systematic trends present in the data. Most notably, ΔE values for Istria stone increase with an increasing number of ALD cycles. The ΔL values for Istria stone decrease with increasing ALD cycles, indicating lower luminosity. The Δb values and Δa values for Istria stone increase with increasing ALD cycles, indicating a shift in the hue from blue toward yellow and a shift from green toward red, respectively. Notably, these shifts in hue correspond to shifts toward longer optical wavelengths. In contrast to the Istria stone, the Lecce stone, which overall has a smaller statistical variance, displays the opposite trends. ΔE and ΔL values for the coated Lecce stone initially increase, corresponding to a lighter appearance. The Lecce stone with the thinnest films studied also shows a relatively large change in the chromatic coordinate Δb, indicating a shift to blue. Though relatively smaller, Δa is also finite and negative, indicating a shift toward green. Both the Δa and Δb shifts are toward shorter wavelengths in the reflected light; this effect, along with the increase in lightness, diminishes with an increased number of ALD cycles. These observations are consistent with the effect of Rayleigh scattering from protrusions or pores whose dimensions are much smaller than the incident optical wavelength and for which the scattered intensity is expected to be proportional to the inverse fourth power of the wavelength. The reflected light intensity is expected to be dominated by the specular reflection, whose value is diminished, and the hue is red-shifted by Rayleigh scattering into other angles, in analogy with the “red sunset” effect, familiar due to atmospheric scattering. Thus, the observations on Istria stone are consistent with an initial slight roughening of the surface due to ALD island nucleation and growth, leading to darkening and a red shift in the perceived hue. In contrast, the results on Lecce stone are consistent with a suppression of roughness due to the filling of pores and crevices with alumina, whose index of refraction is a closer match to that of calcium carbonate than is air, leading to a perceived increase in lightness, and blue shift in the perceived hue. The eventual decrease in these trends with the number of ALD cycles is suggestive that the effective dimensions of the scattering objects grow to values that are less favorable to Rayleigh scattering.

While in principle there might also be some interference contrast based on the thickness of the ALD film, a very rough calculation based upon single scatterings from the surface and buried interface suggests that our films are too thin for interference to give a substantial contribution to the appearance of the samples. The following equation can be used for calculating the film thicknesses “d” for which a condition for constructive interference is met in a single-scattering approximation, assuming normal incidence and taking into account that there will be a phase inversion for reflection from the surface but not for the buried interface:

$$d={\displaystyle \frac{\left(m+\frac{1}{2}\right)\lambda }{2n_{film}}}, m=0, 1, 2\dots$$

(8)

assuming the index of refraction n_film for the ALD alumina is 1.7, larger than both the index of refraction for air n_air = 1 and limestone (majority calcite) n_calcite = 1.4 or 1.6, depending on polarization. The wavelengths in the visible range from 380 to 700 nm, with an average of 540 nm. Based on Equation (8), the first ALD film thickness range for constructive interference is approximately 80 nm, which is close to the estimated thickness only for the 500-cycle coatings corresponding to 90 nm, the thickest of films we have studied. We conclude that interference is likely unimportant for the thinner films, where the trends are most pronounced.

Overall, the calculated average ΔE values for both the Lecce and Istria stone 500-cycle ALD samples were <1.5. This indicates a non-visible color change for the thickest of ALD coatings, which were found to be the most effective at preventing aqueous acid attack. In addition, the colorimetric measurements showed that for all thickness conditions, the total reflectance (specular component included) values and the diffuse reflectance (specular component excluded) values were nearly identical. Overall our results indicate that the slight, transient change in morphology of the stone surface from the island-mode ALD coatings does not produce significant appearance changes [30].

3.2. pH Evolution for Measuring Protection Against Acid Attack

To characterize how well the ALD alumina coatings protect Istria stone, Lecce stone, and single-crystal calcite from acid attack, “No ALD-samples” and “500-cycles ALD-samples” were immersed in aqueous solutions of acetic acid with a starting pH of 4 while stirring. The results of the No-ALD samples are shown in Figure 2a, and the results of 500-cycle ALD samples are shown in Figure 2b. In the absence of the coating, the pH evolution is sublinear with time owing to the decreasing etch rate with pH in the range ~4 to ~5.5 [31]. Notably, the time scale of Figure 2b is much longer than Figure 2a due to the protection provided by the ALD coating. However, the sign of the curvature of the pH vs. time dependence seemingly changes at a certain point for the coated films, indicating a change from sublinear to superlinear evolution of the calcite mass loss with time, perhaps due to the competition between the slowing effect of the changing pH, and the increasing of the exposed effective area, which we discuss in more detail below.

The rate of pH evolution depends on the surface area of the samples because it dictates how much calcium carbonate is available for reaction with the acid at a given time. Rough estimates are possible based upon treating samples as rectangular parallel-pipeds of known dimensions: the Istria stone would have a surface area of 6 cm², the Lecce stone 5.7 cm², and the calcite 2.2 cm². However, the highly porous nature of Lecce stone produces a much larger effective surface area than that associated with the outer dimensions. In contrast, the compact and smooth surface of calcite likely produces an effective surface area close to the simple estimate given above, while the low porosity Istria stone is expected to have an effective surface area somewhat larger than estimated above but likely intermediate between those for the Lecce stone and calcite samples. Although the uncertainties are large, the results shown in Figure 2a suggest systematic trends consistent with the effective areas of the different types of substrates.

An overall slowing of the limestone mass loss to the acid solution with time is expected due to the changing pH [31]. This, in addition to reaction products buffering the solution, results in the slowing trends of the pH for the No-ALD samples seen in Figure 2a. Of more interest than the pH of the solution is the amount of calcium carbonate from the samples that reacted with the acid during the immersion experiments. We can express the calcium carbonate mass loss rate in the diffusion limit as

$${\displaystyle \frac{dm}{dt}}=\eta J{A}_{eff}M$$

(9)

where J is the flux density of acid molecules to the surface of the substrate, η is the probability that an arriving molecule reacts, M is the sample mass loss per successful reaction, and A_eff is the effective area of the substrate available for reaction with the acid.

To obtain the mass losses corresponding to the pH changes in Figure 2a, we carried out measurements of the change in pH of 100 mL of pH 4 acetic acid solution upon dissolving a series of known amounts of CaCO₃ in powder form. Based upon the resulting calibration curve (Figure S1a), we determined the initial and total rates of mass loss for both coated and uncoated Lecce stone, Istria stone, and calcite samples during immersion, as shown in

Table 1. Initial and total rates of mass loss for coated and uncoated Lecce stone, Istria stone, and calcite samples during acid immersion.

Calcium Carbonate Type	Initial Mass Loss Rate (No ALD) (mg/min)	Total Mass Loss Rate (No ALD) (mg/min)	Initial Mass Loss Rate (500 cy ALD) (mg/min)	Total Mass Loss Rate (500 cy ALD) (mg/min)
Lecce Stone	(1.86 ± 0.21) × 10−2	(4.16 ± 0.54) × 10−2	(2.11 ± 0.32) × 10−4	(6.32 ± 0.82) × 10−4
Istria Stone	(1.77 ± 0.20) × 10−2	(3.61± 0.81) × 10−2	(1.43 ± 0.19) × 10−4	(5.73 ± 3.35) × 10−4
Calcite	(4.04 ± 0.45) × 10−3	(1.00 ± 0.49) × 10−2	(3.46 ± 0.45) × 10−5	(2.59 ± 1.24) × 10−4

. Comparing the initial mass loss rates with and without the protective films, it is found that the 500 cycles of ALD alumina slows the initial mass evolution by approximately two orders of magnitude for all calcium carbonate types: a factor of 88 ± 23 for the Lecce stone, of 124 ± 30 for the Istria stone, and of 117 ± 28 for the calcite samples. When averaged over the total range of pH evolution explored, the retardation is somewhat less: a factor of 66 ± 17 for the Lecce stone, 63 ± 51 for the Istria stone, and 39 ± 37 for the calcite samples.

An interesting question regards the probability of failure of the films under the accelerated acid immersion conditions explored here. As a measure of this, if one had an approximate mass loss, which would be judged unacceptable, the results summarized in Table 1 would indeed allow for a determination of the time to failure based upon Equation (9), and the probability would be inversely related to that time.

The initial enhanced efficacy for ALD alumina films on single-crystal calcite is consistent with a model in which calcite is a more ideal surface than limestone for ALD growth. A more chemically homogeneous surface might contain fewer defect sites where ALD precursors do not readily react. Lowering the concentration of nonreactive surface sites would be expected to decrease the likelihood of pinholes or uncoalesced islands in the final film. Pinholes and uncoalesced islands in the ALD film can act as fast paths for acid through the film to the underlying substrate. Further, the increased protective effect for the more ideal calcite surface in comparison with the limestones suggests that defects in the ALD film play a key role in the pH evolution of the ALD samples. As a simple model, we assume that in the presence of a film, the initial effective area available for reaction is that of defects, i.e.,

$$A_{eff0}=N{a}_0$$

(10)

where N is the number of film defects and a₀ is the initial area of each defect. As a function of immersion time, the effective area grows according to

$$A_{eff}\left(t\right)=A_{eff0}+A_{efft}(t)$$

(11)

While we have been unable to determine the initial area of the defects a₀, which we assume to be very small, we have tracked the overall area fraction for the case of ALD alumina on calcite, as summarized below.

The reversal of the mass loss rate trend with sample type, i.e., a smaller retardation of mass loss rate for ALD alumina on calcite as compared to on Lecce and on Istria stone at longer immersion times is at first sight puzzling but can be explained in a model in which the initial number of defects is larger for the latter types of substrates, but that the rate of growth of delaminated regions, corresponding to the second term in Equation (11) is higher in the former case, i.e., calcite. Physically this might occur if the motion of the delamination fronts for each defect is impeded by compositional inhomogeneities in the Lecce and Istria stone samples. Additional evidence for the role of defects in the performance of the ALD alumina films will be discussed in further detail in the following sections.

3.3. pH Evolution to Measure Effect of ALD Thickness

To better understand how the thickness of the ALD alumina coating impacts protective effects, various numbers of ALD cycles were carried out for Lecce stone samples and subjected to acid immersion. Lecce stone was chosen as the substrate to examine this effect as it showed the least statistical variance during the 500-cycle ALD sample immersion experiments (Figure 2b). In addition, Lecce stone is more prone to degradation than Istria stone, representing a crucial objective in conservation science.

The results of acid immersion for various coating thicknesses, as shown in Figure 3, indicate an enhanced protective effect with an increasing number of ALD cycles. We show in the Supplementary Material that the early time mass loss rates dm/dt_initial are not consistent with kinetics limited by diffusion through ideal flat films (Figure S2). Instead, the role of defects resulting in pinholes or uncoalesced islands in the ALD film likely plays a larger role, as discussed in the following sections.

We conclude this section by noting that the sample etch rate can be calculated based upon

$$R_{eff}={\displaystyle \frac{dm}{dt}}{\displaystyle \frac{1}{\rho A_{eff}}}$$

(12)

where ρ is the mass density. For the simplest case, uncoated calcite A_eff is approximately 2.2 cm², while the density of calcite is 2.71 g/cm³ so that the initial etch rate for uncoated calcite is approximately (6.78 ± 0.76) × 10⁻⁷ cm/min or (1.10 ± 0.10) × 10⁻¹ nm/s.

3.4. Morphology of Limestone After Acid Immersion

Examination of the SEM micrographs reveals that the topography produced by acid immersion is far more heterogeneous for the ALD alumina-coated objects due to the local formation of etch pits in each case. For all types of ALD alumina-coated samples, Istria, Lecce, and calcite, surface pitting was observed after immersion in acetic acid. As previously reported for Istria stone [15] and shown in Figure 4c,d, the ALD-coated calcium carbonate grains outside of the pitted regions did not visibly round during acid exposure. This is in contrast to the No-ALD sample calcium carbonate grains, which did visibly round during acid exposure (Figure 4a,b). Similar results are found for the Lecce stone (Figure 5), suggesting that the unpitted regions remained protected by the ALD coating, while the acid was able to penetrate and react with the underlying stone in the pitted regions. Examining the uncoated calcite reveals clearly visible step bunch trains resulting from etching, consistent, for example, with a slight misorientation with respect to a close-packed plane [32,33], and that cover the entire surface after acid immersion (Figure 6a,b). These etching-related artifacts are not found on the surface of the ALD-coated calcite samples away from isolated pits (Figure 6c,d).

Interestingly, in addition to larger etch pits where the ALD coating was entirely removed from the pitted surface some of the smaller pits remain partially covered by the blistered ALD film (Figure 6c,d). This was evidenced by EDS, which shows the uniform aluminum signal partially covering the pit (Figure S3). This is likely from a process of local acid penetration through very small defects and reaction with the underlying calcite, which undercuts the film. The resulting CO₂ formation from the reaction likely leads to the rupture of the ALD blister at some critical pressure. A similar process of blister formation and rupture of aluminum oxide has been studied in other contexts [34] and qualitatively agrees with our morphological findings.

3.5. Optical Imaging, Area Fraction of Damage, and pH Evolution

To quantify better the effects of the defects in the ALD coatings and resulting observed etch pits, the 500-cycle ALD-coated calcite wafers were imaged optically at various times during the acid immersion. The optical images were then transformed using a global threshold into binary coloring, and a “percent area damaged” was calculated by considering the white pixels as areas with damaged ALD coating and the black pixels as undamaged (Figure 7b). Due to the thin and transparent nature of the calcite wafers, the pitting visible in the optical images has contributions from both the top and bottom surfaces, making an image of one side representative of the entire sample.

The pH evolution of the acid immersion solution was measured for each ALD-coated calcite sample, as shown in Figure 7a. Each immersion solution with one sample (labeled C1,2,3…_ALD) evolves to pH 6 with varied reaction rates and overall time. The pH evolution for a given sample is likely strongly influenced by the concentration of defects in the initial ALD film. These defects in the ALD film can act as sites for acid incursion to the underlying calcite. This interpretation is supported by Figure 7a, which shows that the pH evolution trends of the immersion solutions correlate well with the percent area damaged for their respective ALD-coated calcite samples. This correlation suggests that the rate of reactions and resulting pH evolution is dominated by the acid penetration through the defects in the ALD film. The penetration through defects results in a local reaction with the underlying calcite, which undercuts the film, leading to the blistering of the ALD film as CO₂ evolves. As the etch pits grow larger with time, the blistered regions likely burst. In this process the defects in the film and resulting etch pits allow for a fast path to the underlying substrate and, as a result, control the pH evolution process. This model provides insight into the reversal of the relative protective efficacy of the ALD alumina films on limestone vs. calcite discussed above. In Equation (11) the second term corresponds to the time evolution of the existing defects in the films, which is seemingly slower for Lecce and Istria stone than for calcite. We suggested above that this might be an impurity effect. Indeed, it has been found that certain impurities partially suppress the dissolution of calcium carbonate, seemingly by impeding the motion of etch pit walls [35,36]. We believe this is the dominant mechanism for the delamination, as evidenced in Figure 7a. Such an impurity effect may indeed explain the slower eventual time evolution we discussed above (see Table 1). We note that the form of the time evolution given by the second term in Equation (11) is likely to be complicated as it should be sensitive to the pH [31], which evolves with time.

3.6. Reaction Products

While the acid–calcite reactions almost certainly dominate the pH evolution, it is also important to consider the interaction between the acid and the ALD alumina film. The aluminum EDS maps shown in Figure 8b,d indicate that away from the defects, an aluminum-containing film remains intact subsequent to prolonged acid immersion. As we previously reported for ALD-coated Istria stone, it is likely that the ALD alumina film undergoes a series of hydration reactions that dissolve the alumina uniformly across the sample surface [15]. It is important to note that the solution–alumina reactions likely proceed at a much slower rate than the solution–calcite reactions and are in fact only evidenced by the selective re-precipitation of fully hydrated Al₂(OH)₃, probably in the form of Gibbsite in the etch pits (Figure 8). The rounded morphology of the precipitates observed on calcite differs from the platelets previously observed on ALD-coated Istria stone but can still be characteristic of Gibbsite [37,38]. The dissolution of ALD alumina and re-precipitation of aluminum hydroxide was proposed by Willis et al. [39] and is supported by the Pourbaix diagram for bulk crystalline alumina, which predicts instability below a pH of 5.8 [40]. In control experiments, we find that the initial rate of change of the pH for a 500-cycle ALD alumina film on an inert SiO₂ substrate is more than a factor of 5 slower than what we observe for a 500-cycle ALD alumina film on limestone. The finding again supports the conclusion that defects in the ALD film, which help selectively etch the calcite, play a dominant role in the process of acid incursion and the overall efficacy of the treatment.

4. Conclusions

Our results show that ALD Al₂O₃ films can slow the acid attack of limestone drastically, with the rate of attack varying systematically both with the thickness of the films and with the porosity of the substrate. Sub-100 nm films delay the initial and total rate of acid attack up to two orders of magnitude. The films produce only minor changes in the perceived appearance of the substrates, at levels generally considered insignificant, and whose variation with substrate morphology and film thickness is consistent with the effect of scattering from surface roughness. Observations on flat calcite substrates reveal that the rate of reaction is well correlated with the localized appearance and growth of pits on the substrate surface, with rupture of the overlying film, seemingly due to CO₂ generation. The initial reaction rate is inconsistent with kinetics, which are limited by diffusion through the film but are consistent with diffusion of acid within the pits. These observations support the idea that defects in the film allow local permeation by the acid and ultimately dominate the system evolution.

Based upon our observations, our model for the etching of the coated limestone surfaces is that local defects in the ALD layers, possibly originating from incomplete coalescence of 3D islands of alumina, act as paths for fast permeation of acid through the films. The result is a local etching of the underlying calcite, with etch fronts that propagate inward, undercutting the film. As the reaction of acid with calcite results in the production of CO₂ gas, we expect that there will be the generation of increasing pressure within the region between the film and the growing etch pits, along with local heating, due to the exothermic nature of the reaction. The combination of these two types of stress seemingly results in the local rupturing of the films, as evidenced in the SEM images shown in Figure 6c,d and Figure 8. This film rupture increases the effective exposed area, in principle accelerating the etch rate. In our case, however, the finite volume of acid solution results in a decrease in its concentration with time, opposing this effect and resulting in an eventual decrease in the etch rate.

Finally, we have not attempted to optimize the film thickness in our work. In this application of ALD alumina, two metrics are important. The first is the retardation of acid-induced corrosion of coated limestone, which does not obviously have an optimum. As we show in the Supplementary Materials, the initial rate of mass loss varies approximately proportional to the inverse of the coating thickness and is not expected to show an optimum in this regard. The second is the change in appearance, which might be expected to degrade as the coating thickness results in interference color. Our results indicate, however, that for our coatings, the appearance change is dominated by changes in light scattering and continues to improve with thickness for the thickest films investigated here. We anticipate that a metric consisting, e.g., of the product of these two might show an optimum, but it would be at a thickness larger than those studied here.