1 Introduction

Miniature portraits represent a highly specific type of painted artworks popular in Europe between the 16th and the early 20th century. The portrait miniature has developed as an independent art form at the beginning of the 16th century from medieval book illumination. The origin of the term “miniatureˮ is not related to size, as it cannot be primarily derived from the Latin "minimum"—the smallest, but rather from the word “miniumˮ, the Latin term for an orange-red pigment, also called red lead (Pb3O4), which was often used to decorate the initials of manuscripts in the Middle Ages [1, 2]. During centuries, both the materials and the painting techniques used for the creation of miniatures had been subject of significant changes. The first miniatures were executed on stretched vellum [3], however, the number of employed supports increased with time [4] including, e.g., paper, parchment, metal or ivory. The ivory plate rose to prominence and became the most frequent support starting from the 18th century and remained highly popular till the late 19th century [5]. The selection and popularity of ivory support originated from its advantageous properties. It allowed the artists to exalt the light tone of the painting, resembling human skin, and provided a unique luminosity and more realistic appearance [5], thus resulting in the application of a very thin paint layer. Watercolour and gouache were the most common painting techniques used on ivory plates, however, the use of oil as a solo binder [5, 6] or in combination with gum have been also recently reported [7].

Among the white pigments, lead carbonate (Pb3(CO3)2(OH)2) was the most recurrent one [3, 8]. However, other white pigments such as barium sulfate (BaSO4) or zinc oxide (ZnO) were also introduced during the late 18th and the early 19th centuries [6]. Miniaturists’ palette also encompassed other common pigments like Prussian blue (Fe4[Fe(CN)6]3), ultramarine (Al6Na8O24S3Si6), azurite ((Cu3(CO3)2(OH)2), cobalt blue (CoAl2O4), emerald green (Cu(C2H3O2)2·3Cu(AsO2)2), orpiment (As2S3), minium (Pb3O4) and cinnabar (HgS) [2, 9]. Concerning the choice of red pigments, cinnabar was one of the most popular. Until the industrial production of cadmium red (CdS·xCdSe) in the early 20th century, cinnabar had been the most widely used red pigment with the most vibrant colour shade. While the term “cinnabarˮ refers to the pigment made from the ground natural mineral, the term “vermilionˮ has been reserved for the artificial product used by artists [10]. Historically, cinnabar was frequently mixed with red/orange pigments such as minium (Pb3O4) or organic dyes [11]. In oil-medium, cinnabar was often used with lead white to produce flesh tones in paintings without any sign of degradation to black lead sulphide [12]. As already shown by Burgio et al. [3], the mixture of lead white and cinnabar was also commonly used for the realization of miniatures on vellum.

Cinnabar has been frequently used in oil-based artworks, especially when mixed with lead-based pigments (e.g., minium, lead white) [13]. Nevertheless, Rasti and Scott [14] have shown that cinnabar appears to accelerate the photo-oxidation of linseed oil films. During the last two decades, a great effort is put to unravel degradation of paintings resulting from pigment-binder interactions. High attention is paid especially to the formation of metal soaps (i.e., metal long-chain carboxylates) which, being manifested as protrusions, efflorescence, hazes, increased transparency, etc., affect the stability and appearance of paintings. While zinc and lead-based pigments have been predominantly studied [7, 15,16,17,18], the role played by cinnabar in the formation of metal carboxylates remains unexplored. Mercury carboxylates have been studied in the past for their thermal behaviour [19], while their crystal structure has been recently described by Barannikov et al. [20]. Nevertheless, they have never been identified in real paintings, therefore, the risk that the formation and consequent crystallization of mercury carboxylates may entail into the paint layer is still unknown.

While the previous studies on saponification processes [21,22,23] employed mainly invasive analytical approach, this work focuses on a fully non-invasive procedure of distinguishing mercury soaps from the frequently found lead soaps in miniature paintings on ivory plates, containing both Hg-based and Pb-based pigments. Such analytical approach involves large-area X-ray fluorescence scanning (MA-XRF), spectroscopic methods (portable FTIR and Raman) and powder X-ray diffraction (XRPD), already reported in our previous papers [2, 7]. XRPD data processing, such as Rietveld refinement or LeBail fit, was also used for the detection of mercury soaps and deduction of their approximate compositions. The calculations of the approximate amounts of original pigments consumed during the saponification process enabled a better understanding of the role of cinnabar, which was further investigated on model experiments as part of a long-term experiment.

2 Experimental

2.1 Large-area X-ray fluorescence scanning (MA-XRF)

Measurements were performed on M6 Jetstream instrument (Bruker Nano GmbH, Germany). The instrument is equipped with rhodium anode, beryllium window, 60 mm2 silicon drift detector (SDD) and polycapillary optics allowing the use of 100–350 μm spot size. X-ray source has a maximum power of 30 W (50 kV, 600 μA). Scanning mechanism has a range of 60 × 80 cm. Element mapping was performed with a resolution of 847 × 1174 pixels (1 MPix), spot size of 100 µm, pixel (step) size of 70 µm and pixel time of 20 ms at 50 kV, 0.6 µA. The total mapping time was 5.5 h. Data were collected using Bruker M6 Jetstream software ver. 1.6.0.286.0 and element maps were exported using a fast deconvolution algorithm. Incomplete deconvolution of As elemental map exported from the Jetstream software was improved by subtracting Pb-Kα from the As-Kα map using a custom script written in Python 3.8 and Numpy 1.21.

2.2 X-ray powder diffraction (XRPD)

Diffraction patterns were collected with PANalytical X’PertPRO diffractometer in Bragg–Brentano setup with 0.04 rad Soller slit, 0.125° divergence slit, 0.25° anti-scatter slit and 5 mm mask in the incident beam, 5.0 mm anti-scatter slit, 0.04 rad Soller slit and Fe beta-filter in the diffracted beam. Diffractometer was equipped with a conventional X-ray tube (Co Kα radiation, 40 kV, 30 mA, line focus) and a multichannel detector X’Celerator. A multi-purpose sample stage was adapted by adding a homemade supporting table to analyse the studied objects. X-ray patterns were usually measured in the range of 1.5° to 80°/2θ with a step of 0.0334°. In one case (J2018), low angle measurements were not possible, since the miniature painting was curved, and its edge shielded the X-ray beam. Qualitative-phase analysis was performed using HighScorePlus software package (Malvern PANalytical, the Netherlands, version 5.1.0) and the current JCPDS PDF-4 + database [24].

All the diffraction data were corrected for minor misalignment (sample displacement) of the miniature painting. Hydrocerussite (PDF-4+# 04-016-7055) and/or cinnabar (PDF-4+# 04-007-0835) [24, 25] present in the paint layers were used as internal standard to track and correct for small displacement [26], allowing to assess positions of diffraction lines of lead long-chain carboxylates (soaps). Profile fitting of diffraction lines of lead carboxylates was performed using procedures implemented in the HighScorePlus package (Malvern PANalytical, the Netherlands, version 4.9.0). A Pseudo-Voigt profile function with split shape and width was used. Correction for instrumental broadening was also performed (SRM660a, LaB6, was used as a standard). Rietveld method [27] was used for the estimation of weight fractions of crystalline phases. Profex 4.3.6 / BGMN 4.2.23 code was used for all the calculations [28,29,30].

XRPD measurements on model experiments were performed in reflection mode (on glass slides) using conventional Brag-Brentano geometry with a 0.02 rad Soller slit, 0.0625° divergence slit, 0.125° anti-scatter slit, and 15 mm mask in the incident beam, 5.0 mm anti-scatter slit, 0.02 rad Soller slit and Fe beta-filter in the diffracted beam. X-ray patterns were measured in the range of 1– 40° 2θ with a step of 0.0167° and 200 s counting per step. It represents a scan of approx. 1 h.

2.3 Fourier transform infrared spectroscopy (FTIR)

Measurements on miniature portraits were carried out with Alpha II spectrometer (Bruker Optics, Germany) equipped with an external reflection module which allows fast, contactless, and non-destructive FTIR analysis of samples. Spectra were acquired in the mid-infrared region (from 400 to 4000 cm−1) at a resolution of 4 cm−1 by summing 32 scans. Qualitative evaluation as well as Kramers–Kronig (KK) transformation [31] of the acquired data (if needed) was performed in OPUS Spectroscopy Software.

For measurements of model systems in transmission mode, samples were collected from model experiments and pressed into KBr pellets. The transmission measurements were performed using Vertex V70 (Bruker Optics, Germany) spectrometer with resolution of 4 cm−1 and accumulation of 64 scans. Acquisition and qualitative evaluation of the data were performed in OPUS 8.5 spectroscopy software (Bruker Optics, Germany). Spectra were exported in OriginPro 2020 software (OriginLab, Northampton, MA, USA).

2.4 Raman spectroscopy

Raman spectra were recorded with a portable i-Raman Pro (B&WTEK) spectrometer equipped with 785 nm laser source excitation wavelength, and an optical microscope (BAC151) with two objectives (×20, and ×50), high quantum efficiency CCD array detector with deep cooling (− 25 °C) and high dynamic range. Sample irradiation was performed using the × 50 microscope objective of the microscope. The exposure time, beam power, and accumulations were selected for each measurement to get sufficiently informative spectra while avoiding sample damage. In particular, laser power was kept between 10 and 70% to avoid changes in the sample’s structure. Miniatures were directly analysed on a microscope stage in the spectral range of 100–1800 cm−1. Spectra were acquired with BWSpec® software and qualitative evaluation of the acquired data was performed in OPUS Spectroscopy Software. For the pigments’ identification, IRUG [32] database and RRUFF [33] database as well as existing literature were used.

2.5 Selected portrait miniatures

Within a comparative study of miniatures which took place in our laboratory, tens of works were screened using a portable FTIR spectrometer. The identification of binders and degradation products was excluded in case of pure oil paintings, where top varnish is present. However, it was found that even watercolours (not covered with varnish) may contain oil as an admixture, resulting in the formation of metal carboxylates. In some of the miniatures, the soap formation was particularly noticeable, and all these soaps were considered to be lead-based [7]. To study the effect of mercury on the formation and structure of carboxylates, two degraded paintings on ivory where Pb and Hg occur together were selected (Table 1). They were part of one family tableau—therefore, the same storage conditions and atmospheric influences can be assumed. In one of these artworks (J2018), metal soaps have already been detected in the past, but thought to be exclusively lead-based [7], while the second portrait (with more noticeable degradation and greater extent of cinnabar) was studied for the first time. The reconsideration of previous measurements and interpretation of new analyses were also enabled by the recently reported crystal structure of mercury carboxylates [20].

Table 1 Description of studied miniature portraits on ivory
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2.6 Model experiments

Experimental model paints resembling the composition of the studied miniature portraits were prepared to investigate the pigment-binder interactions. Lead white (hydrocerussite, 2PbCO3·Pb(OH)2, Sigma-Aldrich) and/or cinnabar (HgS, very fine, 10,624, Kremer Pigmente, declared as natural cinnabar form Hunan district, China) were mixed in concentration series with cold pressed linseed oil (73,020, Kremer Pigmente, Germany) (Table 2) with constant weight ratio of pigment to oil set to 3:1 and immediately applied by a double-ended micro spatula on 50 × 75 mm glass slides (for monitoring by both FTIR and XRPD) as a thin film (~ 0.3 mm in average). The use of pure oil instead of mixed binders (oil and gum) was selected in order to enable careful monitoring of the saponification reaction in ca. 1600–1500 cm−1 FTIR spectral region that would be otherwise partially hidden by the broad gum-related band at ca. 1660 cm−1. Model experiments were exposed to fixed external conditions using a climatic chamber (Climacell®, 111—EVO line, BMT, Czech Republic) to reproduce the environmental conditions more suitable for the conservation of these specific category of artworks (RH = 40%, T = 25˚C). Fluctuation of ca. 2–3% of relative humidity and ca. 1˚C have been sporadically recorded. The lighting in the climatic chamber was set to reproduce the day/night conditions by using a light source with a maximum peak wavelength between 550 and 650 nm—with light in turns on and off for 12 h. Samples were kept under the same controlled conditions during the entire experiment (one year).

Table 2 Composition of model experiments (C cinnabar, H hydrocerussite)
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The FTIR and XRPD monitoring was performed regularly, involving (i) day by day measurements for the description of immediate processes during the early stages of drying and (ii) long-term monitoring for the evaluation of secondary changes during the hardening of paints up to one year.

3 Results and discussion

3.1 Identification of pigments and binders

Elemental maps obtained by MA-XRF showed that the main elements present in both studied portraits were similar (Table 3). Calcium, which is spread over the whole area of the painting, corresponds to both the ivory support (hydroxyapatite, Ca5(OH)(PO4)3) and the calcite (CaCO3) admixed in the paint layer (Fig. 1). MA-XRF maps also indicated the extensive use of lead white in both miniatures in whitish areas, as well as in differently coloured areas combined with various other (e.g., Hg-, Cu-, Fe- or As-based) pigments. The presence of lead white was then confirmed by XRPD, FTIR and Raman measurements (Table 3). In the FTIR spectra, lead white showed its characteristic absorption bands at ca. 1405 and 680 cm−1 [32, 33], while in the Raman spectra (Fig. S2) its most intense band appeared at ca. 1050 cm−1 [8]. In the XRPD patterns, hydrocerussite (2PbCO3·Pb(OH)2) was identified as the predominant component of lead white (accompanied by lower amount of cerussite (PbCO3) in the J2015 miniature). In the flesh tones (incarnate), the use of lead white was remarkably reduced (as visible from the distribution of Pb in Fig. 1), as the natural hue and transparency of the thin ivory support was used to achieve the unique luminosity and more realistic appearance of human skin. In pink tones of the skin, in lips, and also in intensely red areas, the presence of cinnabar (HgS) was clearly identified by XRPD and Raman spectroscopy. XRPD measurements enabled also the detection of azurite (2CuCO3·Cu(OH)2) and hematite (Fe2O3) together with kaolinite (Al2Si2O5(OH)4) and illite (K0.65Al2.0[Al0.65Si3.35O10](OH)2), which may indicate the use of earth pigments (Figs. S5–S8). Furthermore, the use of orpiment (As2S3) in orange shades was also detected (Table 3), as well as realgar and pararealgar, as already reported by Garrappa et al. [7].

Table 3 Major elements indicated in the studied miniature portraits by MA-XRF and binders, pigments and metal carboxylates identified by FTIR, XRPD and Raman spectroscopy
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Fig. 1
figure 1

Selected elemental maps obtained by MA-XRF

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FTIR in diffuse reflection mode is the only non-invasive technique suitable for the identification of organic materials in miniature paintings. However, in diffuse IR reflection mode, the presence of carbonates (lead white, calcite, etc.) may significantly affect the 1900–1500 cm−1 spectral region due to the main carbonate absorption band, thus making challenging the detection of other compounds. The strong absorption coefficient of the v3(CO32−) usually results in an intense and broad reststrahlen band [34] giving rise to a very complex spectra.

In both studied miniatures, characteristic absorption band of polysaccharides (at ca. 1660 cm−1) was detected in their FTIR spectra (Figs. 2 and 3), indicating the use of gum Arabic as binder in watercolour and/or gouache technique, which was the most commonly used technique in miniature paintings. However, in areas containing lead white, the presence of oil binder was detected by its characteristic absorption band at ca. 1745 cm−1 either as a solo binder or together with gum, as already reported in our previous work [7]. Its presence can be clearly observed from the FTIR spectrum acquired on the white coat of the J2018 miniature depicted in Fig. 3. From the technological point of view, the addition of oil may be explained as prevention of undesirable blackening of lead white in watercolour technique [13, 35]. Blackening is the most reported degradation of lead white – caused by its transformation to galena (PbS) or plattnerite (β-PbO2), depending on the composition of paint layers as well as the surrounding environment or microbiological activity [8, 13, 35]. In areas where lead white was mixed with other pigments (e.g., cinnabar), the presence of both gum and oil was clearly detected in all cases (Figs. 2 and 3). Nevertheless, the employed paint technology is still not fully elucidated. It remains unclear whether both binders and pigments were mixed together, or the oil was mixed with lead white and applied separately to the paint layer.

Fig. 2
figure 2

FTIR spectra of the J2015 miniature acquired in reflection mode (region 4000–400 cm−1) showing the presence of gum, oil and lead carboxylates in white (a), and gum, oil, lead and mercury carboxylates in red–orange (b) parts of the uniform. 1745 cm−1 (oil); 1660 cm−1 (gum); 1574 cm−1 (mercury carboxylates); 1540, 1520, 1510 cm−1 (lead carboxylates)

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Fig. 3
figure 3

FTIR spectra of the J2018 miniature acquired in reflection mode (region 4000–400 cm−1) showing the presence of gum, oil and lead carboxylates in the white uniform (a), and gum, oil, lead and mercury carboxylates in the pink paint of lips (b). 1745 cm−1 (oil); 1660 cm−1 (gum); 1574 cm−1 (mercury carboxylates); 1557, 1540, 1510 cm−1 (lead carboxylates)

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3.2 Evidence of lead and mercury soaps

In addition to the detection of pigments and the employed ivory support, XRPD measurements also revealed the presence of crystalline metal long-chain carboxylates (soaps) indicated by a characteristic set of basal diffraction lines (indexed as h00) in the low angular 2θ region [36, 37]. The metal soaps were found usually together with lead white, however, they were also abundant in the areas where cinnabar was the predominant pigment or where cinnabar was mixed with lead white in a comparable amount (Figs. 4 and 5). The presence of crystalline metal soaps was also reflected in infrared spectra (Figs. 2 and 3), where inverted bands ascribed to the COO− stretching in lead carboxylates were detected at 1557, 1540 and 1510 cm−1 in combination with absorption bands ascribed to the presence of both oil (1745 cm−1) and gum (1660 cm−1) [38]. However, in areas with increased content of cinnabar, an additional inverted band at ca. 1575–1568 cm−1 was also detected (Figs. 2 and 3), indicating the presence of carboxylates with a different metal. According to Barannikov et al. [20], in tempera-based model experiments, mercury form metal soaps with a COO− band at ca. 1562 cm−1 in FTIR spectra, thus being clearly distinguishable from lead carboxylates, whose absorption bands are at lower wavenumbers (1550, 1440, 1527, 1510 cm−1) [15, 39]. In order to assign the weak and broad band at 1575–1568 to Hg-containing carboxylates, it must be considered that (i) no other explanation for this vibration recently exists, (ii) the position may be slightly shifted with respect to the FTIR measurement mode used and/or the degree of crystallinity, (iii) the intensity of this weak vibration increases with higher Hg contents. Even though the obtained FTIR data suggest the presence of Hg soaps, an additional method was needed to confirm this interpretation. Unfortunately, similar structures of Pb and Hg carboxylates cannot be visually distinguished in the diffraction pattern. To overcome this difficulty, Rietveld refinement was used.

Fig. 4
figure 4

Diffraction patterns of various areas in the J2015 miniature showing the evidence of metal soaps (S), lead white (H), aluminium silicates (A), orpiment (O) and cinnabar (C))

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Fig. 5
figure 5

Diffraction patterns of various areas on the J2015 miniature showing the evidence of metal soaps (S), lead white (H), gypsum (G), azurite (A), cinnabar (C), and calcite (Ca)

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The Rietveld method [27] has been successfully used for quantitative phase analysis of crystalline phases in the last decades [40]. The principal conditions to obtain correct results are following (i) the analysed sample contains many small isotropic particles randomly distributed in an area larger than the trace of the primary beam to prevent beam overflow and (ii) the thickness of a sample is sufficient to exceed the penetration depth of X-rays. Any deviation from these conditions may reduce the precision of the analysis. In case of fully non-invasive XRPD measurements of miniature paintings, these conditions cannot be fulfilled entirely due to the thin paint layers containing inhomogeneously distributed phases.

Therefore, before the application of Rietveld refinement on data acquired, it was necessary to consider all the limitations of such type of analysis arising from the character of the painting and take into account the following complicating factors: low thickness of the analysed paint layer, preferential orientation of some pigments, irregular surface, and shape of the painting.

In the first step, an initial calculation of all phases (i.e., including hydroxyapatite as the main constituent of ivory) was performed for both miniatures. The Profex/BGMN software allows to separate XRPD patterns of individual phases in the overall pattern and the BGMN code also permits to use an XRPD pattern as a part of background [41] if the pure support cannot be analysed separately, and its signal is clearly visible and describable. Thus, hydroxyapatite corresponding to the ivory support was added to the background of the XRPD pattern.

The pitfalls arising from the non-invasive analysis of a painting can be demonstrated by the measurements acquired on the points #f and #e (Fig. 4) where preferred orientation of grains of orpiment and cinnabar is clearly visible in the X-ray patterns (Figs. S6 and S7). The increased intensity of the diffraction line 020 of orpiment is in agreement with the cleavage of orpiment along {010} crystal faces [42]. Similarly, the intensity of the diffraction line of cinnabar 100 (1010 in hexagonal hkil notation) is also rather higher than expected from the structural model, however, in agreement with the perfect cleavage of cinnabar along {1010} crystal faces [43]. In both cases, these micro-structural features pointed out the natural (mineral) origin of orpiment and cinnabar.

In addition, the observed intensities of cinnabar diffraction lines at 2θ angles above 60˚ are lower than the calculated ones (point #f, Fig. S8), reflecting the fact that the thickness of paint layers is lower than the penetration depth of X-rays.

The results of calculations are plotted in Figs. S3–S12, and the estimated weight fractions of crystalline phases are summarised in Tables 4 and 5. While the amount of lead soaps ranges between ca. 20 and 50 wt. %, mercury soaps are less abundant (ca 1–5 wt. %), except the point #c on the J2015 miniature (incarnate of forehead), where ca. 16 wt. % of mercury soaps was detected. Mercury soaps are clearly distinguishable and roughly correlate with the contents of cinnabar (except for points #c and #f on the J2015 miniature). The results confirmed the assumptions based on the FTIR data.

Table 4 Estimated weight fractions of crystalline phases found in J2015 (wt. %)
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Table 5 Estimated weight fractions of crystalline phases found in J2018 (wt. %)
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3.3 Structures of Pb and Hg soaps

In order to estimate the unit cell parameters, LeBail fit was performed. Comparison of the calculated values of the parameter a with the data reference published by Kočí et al. [37] and Barannikov et al. [20] enabled to deduce the approximate composition of the detected soaps (Tables 6 and 7). Obviously, all detected metal soaps are mixed carboxylates, consisting of both palmitate (C16) and stearate (C18) anions. However, palmitate (C16) fraction is more abundant in the lead soaps while palmitate and stearate fractions in mercury soaps are more equipollent, oscillating around fifty-fifty ratio. The formation of mixed lead and/or mercury carboxylates in emulsion systems based on egg yolk was reported by Kočí et al. [37] and Barannikov et al. [20]. Hermans et al. [44], reporting the synthesis and characterisation of mixed lead and zinc carboxylates, pointed out that lead soap inclusion from the painting Avenue at Middelharnis by Hobbema [23] consisted of 25–40% of stearate.

Table 6 Calculated values of unit cell parameter a of Pb and Hg soaps found in J2015, and their estimated chemical composition
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Table 7 Calculated values of unit cell parameter a of Pb and Hg soaps found in J2018, and their estimated chemical composition
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Knowing the possible composition of the neo-formed soaps, the amounts of reacted pigments were estimated based on the mass balance, and the following conditions were considered. (i) All soaps in the systems are crystalline (thus detectable and computable by means of XRPD). (ii) The mercury soaps of a general formula Hg(C16)2−x(C18)x, where C16 stands for palmitate and C18 for stearate, result from the stoichiometric reaction between cinnabar (HgS), palmitic acid (C15H31COOH) and stearic acid (C17H35COOH) as given in Eq. 1. (iii) The lead soaps of a general formula Pb(C16)2−x(C18)x, where C16 stands for palmitate and C18 for stearate, result from the stoichiometric reaction between hydrocerussite (2PbCO3·Pb(OH)2), palmitic acid (C15H31COOH) and stearic acid (C17H35COOH) as given in Eq. 2. (iv) The possible reaction of minor cerussite (PbCO3) is omitted for simplicity.

$${\text{HgS}} + \left( {{2} - x} \right){\text{ C}}_{{{15}}} {\text{H}}_{{{31}}} {\text{COOH}} + x{\text{ C}}_{{{17}}} {\text{H}}_{{{35}}} {\text{COOH}} \to {\text{Hg}}\left( {{\text{C}}_{{{15}}} {\text{H}}_{{{31}}} {\text{COO}}} \right)_{{{2} - x}} \left( {{\text{C}}_{{{17}}} {\text{H}}_{{{35}}} {\text{COO}}} \right)_{x} + {\text{H}}_{{2}} {\text{S}} = {\text{Hg}}\left( {{\text{C16}}} \right)_{{{2} - x}} \left( {{\text{C18}}} \right)_{x} + {\text{ H}}_{{2}} {\text{S}}$$
(1)
$${\text{2PbCO}}_{{3}} \cdot{\text{Pb}}\left( {{\text{OH}}} \right)_{{2}} + { 3}\left( {{2} - x} \right){\text{ C}}_{{{15}}} {\text{H}}_{{{31}}} {\text{COOH }} + { 3}x{\text{ C}}_{{{17}}} {\text{H}}_{{{35}}} {\text{COOH }} \to {\text{ 3 Pb}}\left( {{\text{C}}_{{{15}}} {\text{H}}_{{{31}}} {\text{COO}}} \right)_{{{2} - x}} \left( {{\text{C}}_{{{17}}} {\text{H}}_{{{35}}} {\text{COO}}} \right)_{x} + {\text{ 2 CO}}_{{2}} + {\text{ 4 H}}_{{2}} {\text{O}} = {\text{ 3 Pb}}\left( {{\text{C16}}} \right)_{{{2} - x}} \left( {{\text{C18}}} \right)_{x} + {\text{2CO}}_{{2}} + {\text{ 4H}}_{{2}} {\text{O}}$$
(2)

The mass fraction of the pigment consumed by the saponification reaction (wP2) according to Eq. 1 and 2 follows from the mass balance relations and is given by Eq. 3:

$$w_{P2} = w_{S} \cdot \frac{{\nu_{P} }}{{\nu_{S} }} \cdot \frac{{M_{P} }}{{M_{S} }},$$
(3)

where wS is mass fraction of the formed soap (the value is calculated by the Rietveld refinement), νP and νS is the stochiometric coefficient of pigment and soap, respectively, according to the given reaction, MP and MS is molar mass (g/mol) of pigment and soap, respectively.

The original mass fraction of pigment used for painting (wP0) can be then calculated as a sum of the mass fractions of the remaining pigment (i.e., detected by XRPD and calculated by the Rietveld refinement) and the consumed pigment (wP2) as given by Eq. 4:

$$w_{P0} = w_{P1} + w_{P2}$$
(4)

The portion of the pigment consumed by the saponification reaction (φ) can be then derived (Eq. 5):

$$\varphi \left( \% \right) = \frac{{w_{P2} }}{{w_{P0} }} \cdot 100\% = \frac{{w_{P2} }}{{w_{P1} + w_{P2} }} \cdot 100\%$$
(5)

The results obtained from the mass balance calculations are summarised in Tables 8 and 9. It is important to realise that the estimated portions of pigments consumed by the saponification reaction in the analysed areas are approximate since the values of mass fractions of soaps and pigments calculated by the Rietveld refinement are also approximate, being affected by the deviation from the standard procedure for quantitative XRPD analysis as above discussed. However, like in the here reported case, where comparable errors of measurements can be considered, it can provide interesting insight into the reactions occurred. In case of the J2015 miniature, approximately half of cinnabar content was transformed into mercury soaps in point #c (incarnate of forehead). In points #a, #d and #e, the pigment consumption ranges between ca. 15 and 25%, while the lowest conversion (around 3%) occurred in the point #f corresponding to the orange-red area with predominant presence of cinnabar. On the contrary, in this area, where lead white was admixed in the lowest quantity (among the analysed areas), the highest conversion of hydrocerussite (ca. 57%) was found. In other cases, the consumption of hydrocerussite ranged ca. between 20 and 50%. In comparison, in the J2018 miniature, lower conversion of hydrocerussite (ca. 12–32%) and comparable conversion of cinnabar (ca. 14–24%) to corresponding soaps (Tables 7 and 9) was calculated from the mass balance.

Table 8 Mass fractions of metal soaps and corresponding pigments in J2015*
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Table 9 Mass fractions of metal soaps and corresponding pigments in J2018*
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3.4 Results of model experiments

To better understand the effect of cinnabar on the formation of lead and/or mercury carboxylates in paint layers observed in the studied miniatures, model experiments were prepared involving pure oil, lead white and cinnabar in different concentrations (Table 2). The preliminary data are presented in Figs. 6 and 7. Figure 6a, depicting FTIR spectra related to model experiments with pure cinnabar and lead white, show that after one year, no mercury carboxylates were formed. A band ascribed to the asymmetric COO− stretching mode typical for amorphous lead carboxylates was detected at 1550 cm−1 only in the experiment with pure lead white.

Fig. 6
figure 6

FTIR spectra of model experiments after one year of drying containing pure cinnabar (C) or lead white (H) in linseed oil (a) and with mixtures of cinnabar and lead white in linseed oil in various ratios (b, c); FTIR spectral region where the carboxylates absorption bands are detected and/or expected is highlighted (1610–1500 cm.−1) (c). (red line: C10%-H90%; pink line:C25%-H75%; green line: C50%-H50%; grey line: C75%-H25%; blue line: C90%-H10%)

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Fig. 7
figure 7

Diffraction patterns after one year of model experiments with cinnabar and lead white in various proportions in oil. (C, cinnabar; H, lead white)

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However, the here-reported FTIR spectra of model experiments made from mixed cinnabar and lead white in different concentrations and oil show interesting data related to the formation of both lead and mercury carboxylates after one year of drying (Fig. 6b,c). In all model experiments containing both cinnabar and lead white, a broad band at ca. 1550 cm−1 ascribed to asymmetric COO− stretching mode typical for amorphous lead carboxylates was clearly detected (Fig. 6b,c). This feature is in accordance with our previous study based on the initial stage of lead carboxylates formation [45]. In relation to the amount of lead white present in the mixture evidenced by the characteristic high intensity carbonate band at ca. 1400 cm−1, the lead carboxylate band appears as a shoulder (in case of high concentration of lead white) or as a well separated band (in case of low concentration of lead white) (Fig. 6c). Additionally, the formation of another absorption band at ca. 1608 cm−1 was detected in all model experiments after one year of drying. This band appeared more intense in model experiments containing higher concentration of cinnabar. According to these data, the newly detected band at ca. 1608 cm−1 might be ascribed to the formation of amorphous mercury carboxylates. As mentioned above, the characteristic asymmetric COO− stretching mode of well-crystalline mercury carboxylates appears at ca. 1562 cm−1 [20]. Nevertheless, information about amorphous mercury carboxylates have not yet been reported and/or investigated. Furthermore, as already discussed, the shift of the mercury carboxylates band can be affected by crystallinity, as also known for lead or zinc carboxylates [45, 46]. As already reported in the literature [46, 47], significant changes in the shape and position of the asymmetric COO− stretching band are attributed (among others) to nature of the metallic cations and the geometrical distortion of the carboxylate groups around them. For example, the position of the carboxylate band in the spectra of lead and zinc soaps clearly differs. In case of lead carboxylates, the band shape and frequency vary from ca. 1510 cm−1 (when crystalline) to ca. 1550–1540 cm−1 band (when amorphous/poorly crystalline) [45, 46]. Slightly different is the case of zinc carboxylates, where an amorphous phase is represented by a broad band around 1580 cm−1 as opposed to a sharp band at around 1538 cm−1 typical for the crystalline phase [46]. Thus, it can be assumed that also poorly crystalline mercury carboxylates may show the FTIR absorption band relative to the characteristic asymmetric COO− stretching mode shifted to higher wavenumbers. It is also reflected in the XRPD measurements (Fig. 7), where growing humps around 45 Å are visible in the low angle region of diffraction patterns. The formation of this hump appears to be proportional to the concentration of lead white in the model experiments (Fig. 7) and it may be assigned to the formation of non-crystalline lead carboxylates. However, it cannot be excluded that the hump is related to the formation of not only the lead carboxylates, but also the mercury ones, both present in the form of ionomers.

Further detailed long-term experiments are still necessary to clarify the effect of mercury compounds on the saponification-related degradation of painted works of art. In addition to the analytical approach here-described, additional use of ssNMR, providing important insight into the molecular structure of mercury carboxylates determining the different possible coordination environment of the mercury atom in long-chain carboxylates, might be beneficial in the investigation of this process. Furthermore, considering that the conservation and storage of painted miniatures on ivory require higher humidity levels (around 50% RH is recommended) to avoid warping, cockling or splitting of the ivory, it would be highly desirable to study the saponification processes in model experiments containing oil, cinnabar and lead white under different humidity levels.

4 Conclusions

For the first time, the presence of mercury soaps as a result of degradation processes was detected and reported in paintings. In the case of the miniatures on ivory presented here, a fully non-invasive approach was used. FTIR and XRPD proved to be synergic in the identification of both mercury and the more frequently found lead soaps. Despite the limitations related to the analyzed painted miniatures, Rietveld method proved to be an efficient way to estimate the weight fractions of crystalline phases allowing to distinguish both lead and mercury carboxylates.

Furthermore, the detection of saponified area characterised by the presence of both lead white and cinnabar brought some questions related to the effect of cinnabar in saponification reactions. Preliminary data obtained by the study of model experiments revealed that the formation of mercury carboxylates was detected just in mixtures containing both cinnabar and lead white. While the presence of lead white in model samples seems to facilitate the saponification reaction involving both mercury and lead cations, the presence of mercury accelerates the formation of lead carboxylates in comparison to pure lead white-based model samples. However, further experiments will be necessary to elucidate the nature of saponification processes in more complex paint mixtures.