Determining Gold Thickness in Multilayer Samples by Measuring the Intensity Ratio of the Au-Lα/Fe-Kα X-Ray

Abstract

Multilayer samples are used in a wide range of sectors for their functionality. In the field of cultural heritage, multilayer samples are also common, as in the case of gilded or silvered alloys in the pigment layers in paintings. The X-ray ratios Lα/Lβ, Kα/Kβ, or K/L for an element or for different elements in a multilayer sample depend on the chemical composition and thickness of the superimposed layers and on the chemical composition and thickness of the layer in which the element is situated. Gold decorations of paintings on wood represent examples of multilayered structures and, for this reason, it is important to be able to determine the thickness of the gold layer. In the present paper, gold coatings of several paintings on gilded wood, by Italian artist Taddeo Gaddi (1300–1366 AD), were examined using portable energy-dispersive X-ray fluorescence (ED-XRF) in order to calculate the thickness of the gold layer on ochre by measuring the intensity ratio of the Au-L_α/Fe-K_α X-ray. The experimental results obtained showed that the gold leaves used by the artist have a thickness of approximately 0.3 to 0.4 µm; this also demonstrates the artist’s remarkable ability in creating the gilding.

1. Introduction

Many objects in common use have a multilayered structure composed by a substrate and one or more superficial coatings [1,2]. In the industrial sector, multilayer samples are widely used, not only to improve or modify their aesthetic appearance, but, more commonly, to improve their chemical–physical and mechanical–structural properties; examples of these include corrosion resistance, minimizing stresses, improving substrate adhesion, modifying resistance, and improving hardness.

When two or more materials are combined, each layer, with its own chemical composition, thickness, and properties, performs separate tasks and contributes to modifying the properties of the resulting object.

Adjusting the chemical composition, sequence, and thickness of each layer contributes to determining the final properties of the artifact and, consequently, the specific applications that the multilayer sample will have on the market.

For example, a very common practice in different fields is the use of metal coatings on the surfaces of objects with the aim of giving more value to the manufact, protecting the surface, or obtaining specific properties [3].

Ancient populations used several metals in order to embellish and decorate objects of historical art, such as paintings, frescoes, doors, ceramics, jewellery, and statues. The metals most commonly used were gold, silver, copper, mercury, lead, tin, and iron [4].

Thus, in the field of cultural heritage, multilayer materials are very common [5,6,7]. In the case of paintings, many layers are generally present (substrate, preparation, several pigment layers) [8]. Also, the use of gold leaf is important; it was used in antiquity to cover objects made of various materials such as wood, glass, metal, ceramic, and stone [9,10,11].

Examples of multilayer samples are the gilding of paintings on wood which were very popular in the Italian Renaissance. For example, gold leaf is very common in many works of art of the Italian Renaissance in the 13th and 14th centuries, where it was used as a background, for decoration, and for the halos of the saints.

In “Libro dell’arte” by Cennino Cennini [12,13], the procedure to be used for the creation of gilding on wood is described in detail: The well-polished table (“ancona”) was primed with chalk or calcium carbonate and animal glue. Then, the smoothing was carried out using animal skin until the surface was “ivory-like”. Subsequently, the drawing was carried out with charcoal. A layer of Armenian bole (iron oxide, Fe₂O₃) mixed with egg white and water was then spread. When the layer of bole was well dried and smoothed, the gold leaf was spread using fish glue or rabbit glue and then it was smoothed (burnishing).

Energy-dispersive X-ray fluorescence (ED-XRF) is a very convenient technique for the analysis of multilayered samples because it is non-destructive, portable, and does not require sample pretreatment procedures [14,15].

ED-XRF analyses are frequently combined with the partial least squares (PLS) regression method, Monte Carlo simulations, and FLUKA simulations to improve the accuracy of the experimental results [16,17,18,19].

For this type of research, confocal XRF can also be employed, which can also be used to perform 3D scanning [20,21]. Other methods for determining the chemical composition and thickness of surface layers are grazing emission XRF (GE-XRF), grazing incident XRF (GI-XRF), X-ray reflectivity (XRR), and angle-resolved XRF (AR-XRF) [22,23].

When a multilayered sample is analysed using energy-dispersive X-ray fluorescence (ED-XRF), it is of fundamental importance to determine the correct position of the various layers, the chemical composition of each layer, and the thickness of the various layers [24]. In fact, by varying these parameters, the intensity of the various fluorescence radiations changes.

Therefore, the determination of gold leaf thickness is very useful in deducing the characteristics of the manufact [25].

In this work, several paintings on wood with gilding by the artist Taddeo Gaddi, from the period between 1335 and 1340 AD, known as “Formelle dell’armadio della sacrestia di Santa Croce” (Florence, Italy), were examined using portable ED-XRF in order to calculate the thickness of the gold layer.

2. Materials and Methods

2.1. The “Formelle Dell’armadio Della Sacrestia di Santa Croce”

The “Formelle dell’armadio della sacrestia di Santa Croce” are so called because they were the painted panels of a cabinet for the sacristy of the Franciscan Basilica of Santa Croce in Florence, Italy.

Without a shadow of a doubt, they represent one of the most fascinating pictorial cycles of the 14th century. They consist of twenty-eight paintings on wood with gilding by Taddeo Gaddi (1300–1366), painted between 1335 and 1340 [26,27]. Taddeo Gaddi was Giotto’s favourite pupil.

In particular, the “Formelle dell’armadio della sacrestia di Santa Croce” are twenty-six barbed quatrefoils (35 × 30 cm² o 35 × 25 cm²) and two semi-lunettes (67 × 76 cm²), which decorated a wooden reliquary cabinet.

The quatrefoils depict stories from the Life of Christ (thirteen quatrefoil panels) and stories from the Life of Saint Francis (thirteen quatrefoils) and the semi-lunette is divided in two: one part represents the Ascension, and the second part represents the Annunciation.

In 1945, twenty-two of the panels and the two semi-lunettes were reunited to recreate the piece at the Galleria dell’Accademia in Florence, Italy, where they have remained ever since.

Four of the paintings, which were originally part of the work, had been placed on the antiques market and today reside in Germany: two at the Gemäldegalerie in Berlin (Pentecost and Resurrection of the Child) and two at the Alte Pinakothek in Munich (Trial by Fire, the Death of the Knight of Celano).

This paper reports the experimental results obtained using portable ED-XRF to evaluate the thickness of the gilding of the precious artefacts, which were created by the artist Taddeo Gaddi and are now preserved in the Galleria dell’Accademia in Florence.

Figure 1 and Figure 2 show two of the paintings analysed with the measurement points used.

Figure 1. Photo of the Incredulity of St. Thomas (inventory number 8593). The measuring points IT01, IT04, IT05, and IT06 are with single gold leaf, point n. IT02 is double leaf, and point IT03 is triple leaf. Height: 40.5 cm; width: 36.5 cm.

Figure 2. Photo of The Visitation (inventory number 8582). Height: 35.5 cm; Width: 25.5 cm.

2.2. Instrument

Energy-dispersive X-ray fluorescence (ED-XRF) analysis was performed using a portable instrument designed at the University of Salento [28]. It is composed of an X-ray tube produced by MOXTEK^® (Orem, UT, USA) with a palladium anode operating at 4–40 kV voltage and 0–100 µA current, and a Si-PIN detector produced by AMPTEK^®, model XR_100CR, thermoelectrically cooled, with a beryllium window of 25 µm.

It has a resolution of 150 eV at 5.9 keV, a resolution of about 250 eV in the range 10–15 keV, and a pocket multi-channel analyser produced by AMPTEK^® (Bedford, MA, USA), model MCA8000A, interfaced with a laptop.

An aluminium filter, with a thickness of 20 μm, was placed in front of the X-ray tube.

The working distance between instrument and paintings is equal to 5 mm.

The diameter of the X-ray beam is an ellipse, whose axes are equal to 2 mm and 3 mm.

Experimental measurements were carried out by using commercial gold leaf purchased from Sigma-Aldrich^® (St. Louis, MO, USA) (thickness of 0.20 ± 0.02 μm; 99.9% wt). In particular, the different thicknesses of the gold were obtained by superimposing two, three, and four layers of gold leaf. This allowed us to obtain the standards used for calibration.

All samples were analysed at 15 kV voltage and 5 µA current, with an acquisition time of 60 s.

For each sample, three acquisitions were performed, and it was observed that the variations in the signal intensity values were less than 5%. In particular, for each acquisition, the intensities of the Au-L_α and Fe-K_α signals were determined by calculating their ratio with the respective uncertainties. The reported data were obtained by determining the weighted average of the three values.

The intensities of the ED-XRF peaks were determined using the Microcalc-Origin^® 2020 software.

2.3. Determining the Thickness of the Gold

The peak intensity ratios of K or L line for selected elements are measured in order to determine the thickness. In particular, for infinitely thin samples, values for K_α/K_β and L_α/L_β peak intensity ratios (here, on K_α/K_β or L_α/L_β ratios) are generally tabulated [29,30].

The gold layer on the surface of a sample of thickness l (µm), with the appropriate energy excitement, produces a fluorescence X line L_α of intensity I_Au; self-attenuation effects must be considered, as given by Equation (1).

$${\mathbf{I}}_{\mathbf{A}\mathbf{u}}=\mathbf{A}·{\displaystyle \frac{1-{\mathbf{e}}^{-\left({\mathsf{\mu }}_{\mathbf{0}} +{\mathsf{\mu }}_{\mathbf{1}}\right)\mathit{l}}}{{\mathsf{\mu }}_0+{\mathsf{\mu }}_{\mathbf{1}}}},$$

(1)

where A represents a constant that takes into account the intensity of the radiation incident on the sample, the fluorescence yield for the radiation considered, the efficiency of the detector, and the relative distances among the sample, source, and detector; µ₀ is the linear attenuation coefficient (µm⁻¹) of element Au at incident energy E₀; µ₁ is the linear attenuation coefficient (µm⁻¹) of element Au at energy of fluorescence E₁ (9.7 keV).

The intensity I_Fe of the K_α fluorescence radiation produced by the iron at energy E₂ = 6.4 keV, assumed to be of infinitesimal thickness, underlying the gold foil, can be determined from Equation (2) [31]:

$${\mathbf{I}}_{\mathbf{Fe}} = \mathbf{B}·{\mathbf{e}}^{-{\mathsf{\mu }}_{\mathbf{0}}\mathit{l}}·{\mathbf{e}}^{-{\mathsf{\mu }}_{\mathbf{2}}\mathit{l}}=\mathbf{B}{·\mathbf{e}}^{-\left({\mathsf{\mu }}_{\mathbf{0}}+{\mathsf{\mu }}_{\mathbf{2}}\right)\mathit{l}},$$

(2)

where B represents a constant that takes into account the intensity of the radiation incident on the sample, the fluorescence yield for the radiation considered, the efficiency of the detector, and the relative distances between the sample, source, and detector; µ₂ is the linear attenuation coefficient (µm⁻¹) of element Au at fluorescence energy E₂ (6.4 keV).

By considering the ratio between the two intensities (I_Au/I_Fe) and indicating the overall constant with C, Equation (3) is obtained:

$${\displaystyle \frac{{\mathbf{I}}_{\mathbf{Au}}}{{\mathbf{I}}_{\mathbf{Fe}}}}=\mathbf{C}·{\displaystyle \frac{\mathbf{1}-{\mathbf{e}}^{-\left({\mathsf{\mu }}_{\mathbf{0}}+{\mathsf{\mu }}_{\mathbf{1}}\right)\mathit{l}}}{{\mathbf{e}}^{-\left({\mathsf{\mu }}_{\mathbf{0}}+{\mathsf{\mu }}_{\mathbf{2}}\right)\mathit{l}}}}=\mathbf{C}·\left[{\mathrm{e}}^{\left({\mathsf{\mu }}_{\mathbf{0}}+{\mathsf{\mu }}_{\mathbf{2}}\right)\mathit{l}}-{\mathrm{e}}^{\left({\mathsf{\mu }}_{\mathbf{2}}-{\mathsf{\mu }}_{\mathbf{1}}\right)\mathit{l}}\right],$$

(3)

where the constants µ₀, µ₁, and µ₂ are tabulated values, and so C is the only unknown parameter. Therefore, Equation (3) can be written in the form of Equation (4):

$${\displaystyle \frac{{\mathbf{I}}_{\mathbf{Au}}}{{\mathbf{I}}_{\mathbf{Fe}}}}={\mathbf{P}}_{\mathbf{1}}·\left({\mathbf{e}}^{{\mathbf{P}}_{\mathbf{2}}\mathit{l}}-{\mathbf{e}}^{{\mathbf{P}}_{\mathbf{3}}\mathit{l}}\right),$$

(4)

where the P₂ and P₃ parameters are tabulated, while the P₁ parameter was determined by interpolation.

Therefore, for each measurement point, by measuring the ratio I_Au/I_Fe with the relative uncertainty and knowing the values P₂ and P₃, it was possible to determine the gold thickness (l), with the relative uncertainty, by graphic extrapolation also taking into account the error on the parameter P₁.

In order to determine the parameter P₁, a multilayer sample was prepared as follows: a layer of calcium carbonate (CaCO₃) was spread on a wooden board as a primer. This layer was then covered with bole (red ochre, Fe₂O₃) and finally the commercial gold leaf.

The different thicknesses of the gold were obtained by superimposing two, three, and four layers of gold leaf.

Figure 3 shows a simplified schematic of the sequence of layers of the multilayer sample prepared in laboratory.

Figure 3. Simplified diagram of the sequence of the layers of the multilayer sample prepared in the laboratory.

Figure 4 shows the ED-XRF spectrum of standard 4, which highlights the signals of the Ca-K (primer), Fe-K_α, and K_β lines relating to the Armenian bolus and the Au-L_α, Au-L_β, and Au-M lines, relating to gold coating.

Figure 4. ED-XRF spectrum of a standard.

Figure 5 shows a typical ED-XRF spectrum of an analysed sample, which highlights the same signals. The intensities of the Fe-K_α and K_β signals (given the partial overlap of the two signals) and Au-L_α were determined using the Microcalc-Origin^® software using the Gaussian function:

$$\mathbf{y}={\mathbf{y}}_{\mathbf{0}}+{\displaystyle \frac{\mathbf{A}}{\mathbf{w}\sqrt{\frac{\mathsf{\pi }}{\mathbf{2}}}}}{\mathbf{e}}^{-{\displaystyle \frac{\mathbf{2}{\left(\mathbf{x}-{\mathbf{x}}_{\mathbf{c}}\right)}^{\mathbf{2}}}{{\mathbf{w}}^{\mathbf{2}}}}}$$

(5)

where A is the signal intensity, x_c represents the signal energy to be integrated, y₀ represents the background, and w represents the peak width at half height (FWHM).

Figure 5. Typical ED-XRF spectrum of the analysed samples.

Figure 6 shows the intensity ratios as a function of gold thickness. The experimental data were interpolated with the function reported in Equation (4) in order to determine the parameter P₁. The results obtained established that the parameter P₁ is equal to (1.87 ± 0.09).

Figure 6. Intensity ratios I_Au/I_Fe as a function of gold thickness. The experimental data were interpolated with the function reported in Equation (4).

In particular, with an anode voltage of 15 kV, a maximum excitation energy of 10 keV can be assumed and the absorption coefficient of gold at this energy is equal to µ₀ = 0.2125 µm⁻¹ (tabulated value), the mass absorption coefficient of gold at 6.4 keV (energy of Fe-K_α radiation) is equal to µ₂ = 0.7206 µm⁻¹ (tabulated value), and the mass absorption coefficient of gold at 9.7 keV (energy of Au-L_α radiation) is equal to µ₁ = 0.2512 µm⁻¹ (tabulated value) [32].

In Equation (4), P₂ = µ₀ + µ₂ and P₃ = µ₂ − µ₁, which are without uncertainty since they are the sum and difference of the tabulated values.

We assumed that the calibration curve maintains the same trend even in the uncalibrated range (up to 1.22 µm).

Moreover, the effect of calcium (in the imprinting) was not considered since the calcium carbonate layer is underneath. Therefore, the calcium signal is attenuated by both the iron (ochre layer) and the gold layer.

3. Results and Discussion

Overall, 106 regions were analysed in situ and the determined gold thicknesses ranged from approximately 0.30 µm to 1.20 µm.

Table 1 provides a brief description of the measurement points analysed and their gold thicknesses.

Table 1. Brief description of the measurement points analysed and their gold thickness.

Sample	Description	Gold Thickness (µm)
LNS_01	Gold background. Upper part (original)	0.47 ± 0.04
LNS_02	Gold background. Upper part (rectangular integration region)	0.65 ± 0.06
LNS_03	Frame. Vertical side	0.43 ± 0.04
LNS_04	Gold background. Under Christ’s feet. Probable overlay of gold	1.00 ± 0.10
LNS_04bis	Repeated measurement of the previous point	1.00 ± 0.10
LNS_05	Gold background. To the right of LNS_04 (single leaf)	0.56 ± 0.05
LNS_06	Gold background. To the left of LNS_04 (single leaf)	0.69 ± 0.07
LNS_07	Gold background. In the upper right corner	0.29 ± 0.03
LND_01	Gold background. Top area (overlapping of two leaves)	0.75 ± 0.07
LND_01bis	Repeated measurement of the previous point	0.72 ± 0.07
LND_02	Gold background. Top part, left of the point LND_01	0.59 ± 0.06
LND_03	Gold background. Top part, right of the point LND_01	0.46 ± 0.04
LND_04	Gold background. Under the hand of the angel on the left	0.46 ± 0.04
LND_05	Gold background. Above wings of the Archangel Gabriel (overlapping)	0.84 ± 0.08
LND_06	Frame. Vertical side	0.56 ± 0.05
AM_01	Gold background. Top left area. Height of the mountain (original)	0.50 ± 0.05
AM_02	Gold background. On integration over the rift (restoration)	0.75 ± 0.07
AM_03	Gold on frame. Top left area. Outermost edge	0.38 ± 0.04
AM_04	Gold on frame. Top right area. Outermost edge	0.33 ± 0.03
AM_05	Gold background. Child and Madonna’s hand (original)	0.41 ± 0.04
AD_01	Gold background. Next to the Madonna (original)	0.37 ± 0.04
AD_02	Gold background. On grouting under the roof of the hut	0.39 ± 0.04
AD_03	Gold background. Top left area	0.40 ± 0.04
AD_04	Frame. On left side cusp	0.39 ± 0.04
AA_01	Gold background. Above the cusp (original)	0.49 ± 0.05
AA_02	Gold background. Upper right area (original)	0.45 ± 0.04
AA_03	Frame. Left area, bottom part	0.46 ± 0.04
AP_01	Gold background. Right area (original)	0.68 ± 0.06
AP_02	Gold background. Kneeling characters (restoration)	0.72 ± 0.07
AP_03	Frame. Top left area. Lower area	0.49 ± 0.05
AP_04	Gold background. Left area (original)	0.59 ± 0.06
AR_01	Gold background. Left side area (original)	0.60 ± 0.06
AR_02	Gold leaf. Square on the upper left side of the roof (restoration)	0.73 ± 0.07
AR_03	Gold background. Right area (original)	0.41 ± 0.04
AR_04	Frame. Upper right area	0.45 ± 0.04
AR_05	Gold Leaf. Bottom square, left roof area (two leaves)	0.94 ± 0.09
BG_01	Gold background. Right area (original)	0.46 ± 0.04
BG_02	Gold background. Sideways to the dove (restoration)	0.54 ± 0.05
BG_03	Gold background. Above ground (restoration)	0.64 ± 0.06
BG_04	Gold background. Between Jesus and Saint John (original)	0.47 ± 0.04
BG_05	Frame. Top left area	0.38 ± 0.04
CR_01	Gold background. Top left area, next to the arm of the cross (original)	0.50 ± 0.05
CR_02	Gold background. To the right of the cartouche (restoration)	0.83 ± 0.08
CR_03	Frame. Top left area	0.56 ± 0.05
DD_01	Gold background. Right side, right area (original)	0.42 ± 0.04
DD_02	Gold background. Right side, left area (restoration)	0.65 ± 0.06
DD_03	Gold halo. Madonna/Saint Joseph	0.39 ± 0.04
DD_04	Frame. Top left area	0.31 ± 0.03
FG_01	Gold background. Left area (original)	0.43 ± 0.04
FG_02	Gold background. On the right near a woodworm hole (restoration)	0.50 ± 0.05
FG_03	Gold background. Below angel at left near a woodworm (restoration)	0.55 ± 0.05
FG_03_bis	Repeated measurement of the previous point	0.60 ± 0.06
FG_04	Frame. Cusp at the top	0.71 ± 0.07
FG_05	Halo of Saint Francis among the angels near woodworm (restoration)	0.72 ± 0.07
MF_01	Gold background. Central area under the hand (perhaps original)	0.44 ± 0.04
MF_02	Frame. Top left area	0.48 ± 0.05
MF_03	Gold background. Left area above the tower	0.34 ± 0.03
MF_04	Gold background. At the top near an integrated square (restoration)	0.66 ± 0.06
MF_05	Gold background. Very shiny lower central area	0.44 ± 0.04
PR_01	Halo of the priest. Near the forehead (original)	0.56 ± 0.05
PR_02	Halo of the priest. Woodworm hole integration sheet (restoration)	0.61 ± 0.06
PR_03	Gold background. Top left area (original)	0.46 ± 0.04
PR_04	Frame. On left side cusp	0.54 ± 0.05
IT_01	Gold background. Right area (original)	0.46 ± 0.04
IT_02	Halo. Figure behind Jesus. Woodworm hole (two leaves)	0.87 ± 0.08
IT_03	Gold background. Top left area, shinier area (more leaves)	1.22 ± 0.12
IT_03bis	Repeated measurement of the previous point	1.13 ± 0.11
IT_04	Gold background. Top left area, less shiny area (original)	0.50 ± 0.05
IT_05	Frame. Top right area	0.44 ± 0.04
IT_06	Gold background. Below the measuring area IT_03. Similar to IT_04	0.50 ± 0.05
PO_01	Gold background. Right area. Next to the woodworm hole	0.50 ± 0.05
PO_02	Halo of Saint Francis	0.55 ± 0.05
PO_03	Frame. Towards the centre, top right area	0.48 ± 0.05
PG_01	Gold background. Left side (original)	0.31 ± 0.03
PG_02	Gold background. Base of the plate on the left	0.44 ± 0.04
PG_03	Gold background. Central cusp, perhaps area of the frame (two leaves)	0.95 ± 0.09
PG_04	Frame. Top left area	0.45 ± 0.04
PG_05	Gold background. On the right area, near a drip	0.53 ± 0.05
PG_06	Gold background. Between the two spires at the top right (original)	0.37 ± 0.04
RC_01	Gold background. To the right of the tree trunk	0.55 ± 0.05
RC_02	Gold background. To the left of the lateral cusp	0.57 ± 0.05
RC_03	Gold background. Left area near the mountain (two leaves)	0.95 ± 0.09
RC_04	Frame. Right area	0.46 ± 0.04
FS_01	Gold background. Central part above the trees (restoration)	0.40 ± 0.04
FS_02	Gold background. Behind the Angel (original)	0.45 ± 0.04
FS_03	Gold background. Right area (restoration)	0.54 ± 0.05
FS_04	Frame	0.48 ± 0.05
FT_01	Gold background. Central area under arm of Saint Francis (restoration)	0.74 ± 0.07
FT_02	Gold background. Upper part (restoration)	0.75 ± 0.07
FT_03	Frame. Top left area	0.47 ± 0.04
FF_01	Gold background. High area, right side (original)	0.33 ± 0.03
FF_02	Halo of Saint Francis. Restoration area (two leaves)	0.86 ± 0.08
FF_03	Halo of Saint Francis. Original side	0.41 ± 0.04
FF_04	Frame. Top left area	0.39 ± 0.04
TR_01	Gold background. Top right area (original)	0.45 ± 0.04
TR_02	Gold background. Top left area (perhaps restoration)	0.52 ± 0.05
TR_03	Gold background. Upper left area, near the cusp (original)	0.46 ± 0.04
TR_04	Halo of the character at the feet of Christ (original)	0.51 ± 0.05
TR_05	Frame. Left side of the cusp	0.44 ± 0.04
UC_01	Gold background. Top left area. Left area abraded (original)	0.53 ± 0.05
UC_02	Gold background. Top left area. Right area less abraded (original)	0.65 ± 0.06
UC_03	Gold background. Top right area (two leaves)	0.96 ± 0.09
UC_04	Frame. Top right area	0.36 ± 0.03
VI_01	Gold background. Above central character (two leaves)	1.00 ± 0.10
VI_02	Gold background. Near the little temple (two leaves)	0.89 ± 0.08
VI_03	Frame. Lower left area	0.36 ± 0.03

LNS: The upper bezel Ascension of Christ (inventory number 8581), left side. LND: The upper bezel Annunciation of Christ (inventory number 8581), right side. AM: Adoration of the Magi (inventory number 8584). AD: Adoration of the Shepherds (inventory number 8583). AA: The Apparition at the Chapter House at Arles (inventory number 8601). AP: Appearance of the Risen Christ to the Pious Women (inventory number 8592). AR: St Francis Presenting his Rule to the Pope (inventory number 8599). BG: Baptism of Christ (inventory number 8587). CR: Crucifixion of Christ (inventory number 8590). DD: Dispute of Jesus with the Doctors of the Temple (inventory number 8586). FG: Death of Francis (inventory number 8603). MF: Martyrdom of the Franciscans in Ceuta (inventory number 8598). PR: Crib of Greccio (inventory number 8600). IT: Incredulity of St. Thomas (inventory number 8593). PO: The Sermon in Front of Onorio III (inventory number 8596). PG: Presentation of Jesus in the Temple (inventory number 8585). RC: Resurrection of Christ (inventory number 8591). FS: Saint Francis Receiving the Stigmata (inventory number 8602). FT: St. Francis Renounces his Father’s Earthly Wealth (inventory number 8594). FF: The Apparition of St. Francis in the Chariot of Fire (inventory number 8597). TR: Transfiguration (inventory number 8588). UC: Last Supper (inventory number 8589). VI: Visitation (inventory number 8582).

The errors were determined by propagating the uncertainties on the calibration parameter P₁ and on the intensities of the analytical signals of gold and iron. In particular, taking into account the calibration curves obtained for P₁ ± ∆P₁ and taking into account the range of the I_Au/I_Fe ratio from Figure 6, by graphical extrapolation, a range of the gold thickness was obtained. Therefore, the mean value of this range provides the best estimate of the gold thickness, and the half-width of the range provides the uncertainty of the thickness.

The 106 analysed regions can be differentiated into three large clusters.

The first cluster includes approximately 75 regions with thicknesses between 0.30 µm and 0.60 µm. This group includes all the frames and unrestored backgrounds where there is no obvious overlapping of gold leaf. This allows us to evaluate the average thickness of the gold leaf used by Taddeo Gaddi in the creation of the precious artifacts. Performing the weighted average of the values relating to these regions, we find an average value of (0.34 ± 0.03) µm.

The second cluster includes 15 regions with gold thicknesses between 0.60 µm and 0.74 µm. This group contains most of the regions showing restorations: prevalent holes in which restoration interventions with additions of gold leaves are evident and rare degraded regions. These regions, identified visually, did not show the presence of other chemical elements by ED-XRF.

The third group includes 15 regions with gold thicknesses between 0.75 µm and 1.00 µm. These areas are all regions that visually show the overlapping of two layers of gold leaf. The weighted average of the thicknesses of these regions is equal to (0.75 ± 0.05) µm.

Within experimental errors, this thickness is comparable to double the value determined for a single layer of gold leaf.

Finally, there is the region indicated IT_03, where the overlapping of three layers of gold leaf is evident. The average thickness over multiple measurements performed in the same region is equal to (1.17 ± 0.08) µm. Within experimental errors, this value is comparable to three times the value determined for the individual layers.

Table 2 shows the average values of the gold thicknesses analysed and the gold thickness referred to a single gold leaf.

Table 2. Average thickness values of the gold coating analysed, and gold thickness referring to a single gold leaf.

	Determined Average Gold Thickness (µm)	Gold Thickness Referred to the Single Leaf (µm)
Single leaf	0.34 ± 0.03	0.34 ± 0.03
Double leaf	0.75 ± 0.05	0.38 ± 0.03
Triple leaf	1.17 ± 0.08	0.39 ± 0.03

The experimental results obtained show that the thickness of the gold referred to a single gold leaf is very similar for the various areas analysed. This result demonstrates the skill and the remarkable technological capacity of the artists of the time in beating the gold and obtaining the desired decorations.

4. Conclusions

The analytical procedure used in this work allowed us to quantitatively determine, in a non-invasive and in situ way, the thickness of the gold leaf.

In particular, we investigated by ED-XRF the gold decorations used by Italian artist Taddeo Gaddi in the creation of the valuable artifacts known as “Formelle dell’armadio della sacrestia di Santa Croce” in Florence, Italy.

The experimental results obtained showed that the gold leaves used by the artist have thicknesses of approximately 0.3 and 0.4 µm. The regions showing restorations, holes, areas with added gold leaf, and degraded regions, did not show any different chemical compositions.

This methodology can certainly be used for other precious manufacts with gold coatings on ochre. In particular, the future hope is certainly to apply the same analytical methodology to the four paintings by Taddeo Gaddi preserved in the museums of Berlin and Munich in order to confirm the results obtained.