**1. Introduction**

Cultural heritage materials including wall paintings and other forms of polychromy and painted architectural surfaces were central to the culture of ancient people. These complex, heterogeneous, and multilayer systems are usually composed of the paint layer (a binary system of pigment(s) and a binding medium) and the substrate (a rock surface or plaster(s) layers) [1,2]. In ancient and historical times, two different techniques were predominantly employed for painting on walls: the fresco (from the Italian, meaning 'fresh') and the secco (from the Italian, meaning 'dry') techniques. In the fresco technique, a small number of pigment powders—compatible with fresco application—are mixed with water and applied on a freshly laid or moist calcium hydroxide/lime (Ca(OH)2)-rich plaster layer. Setting (hardening) of the lime plaster involves a chemical reaction between Ca(OH)2 and carbon dioxide (CO2) present in the atmosphere to form a calcium carbonate lattice within which the pigments are 'fixed' and become an integral part of the wall. These chemical reactions help produce durable wall paintings. Owing to the high alkalinity of the lime and the exothermic reaction associated with the setting of the lime, only a small number of pigments are compatible with the fresco technique, and therefore ancient fresco paintings contain a limited palette of colors. The secco technique, on the other hand, involves no chemical reaction for the fixation of the pigments. In a secco application, the pigments are mixed with any film-forming binding medium such as egg, siccative oil, gum, and others [1] and applied on any type of finished plaster layer including gypsum, earth-based plasters, and lime plaster layers (fully carbonated).

As wall paintings constitute an integral part of the architectural ensemble where they are found, they are inevitably exposed to an open system of environmentally-linked events. As a result, the physical and chemical attributes of the system and individual constituent materials (i.e., plaster(s), pigment(s), binding media) can be impacted by fluctuations in the temperature, relative humidity, and presence of salts, microorganisms, and pollution in the surrounding environment. These conditions can compromise the stability of the system, resulting in the delamination of the plaster layers, staining, flaking, and losses of the paint and plaster layers, and powdering [1,3]. For archaeological wall paintings in particular, the risks for their preservation are even greater as the sudden change in the environmental conditions at the time of the excavation—mainly of the temperature, relative humidity, and light—can cause irreversible damage and degradation [1].

Over the course of the past decades, extensive studies have been carried out using a variety of consolidation treatments to improve the condition and re-establish the lost cohesion of decorated architectural surfaces and wall paintings [4–12]. These studies critically indicate that choosing a proper consolidating agent for these porous materials, especially those found in situ, is challenging. An appropriate consolidant for wall paintings needs to re-establish cohesion of the powdery layers at the surface and subsurface levels and provide mechanical strength and abrasion resistance, without causing any discernible color alteration [13].

Recent studies [14–25] have demonstrated a considerable potential for improving consolidation methods of degraded calcium-carbonate matrices of a technique consisting in bio-mimicking the growth of hydroxyapatite (HAP, with the formula Ca5(PO4)3(OH) but usually written as Ca10(PO4)6(OH)2 to denote that the crystal unit cell comprises two formula units), the main mineralogical component of teeth and bones [15,26,27]. HAP was proved to be effective in binding grain boundaries and improving the mechanical properties of limestone, such as tensile strength, ultrasonic pulse velocity, resistance to abrasion [16,19,20].

HAP is formed in situ by activating reactions between Ca in calcium carbonate (CaCO3)-rich layers and ammonium phosphate precursors. The theoretical chemical pathway of HAP formation using diammonium hydrogen phosphate (DAP) as the precursor is presented below (Reaction 1) [28]. The resulting hydroxyapatite network is expected to improve the cohesion between loose particles at the surface and subsurface of a wall painting [21,29].

$$10\text{ CaCO}\_3 + 6\text{ (NH4})\_2\text{HPO}\_4 \rightarrow \text{Ca}\_{10}\text{(PO4})\_6\text{(OH)}\_2 + 10\text{ CO}\_2\uparrow + 12\text{ NH3}\uparrow + 8\text{ H}\_2\text{O}$$

**Reaction 1.** Theoretical pathway of the formation of hydroxyapatite (HAP) using diammonium hydrogen phosphate as a precursor.

The superior qualities of HAP as a consolidating agent for calcium carbonate matrices lie in the fact that it has a much lower solubility (Ksp <sup>=</sup> 1.6 <sup>×</sup> <sup>10</sup>−<sup>117</sup> at 25 ◦C [30]) than calcite (Ksp <sup>=</sup>3.4 <sup>×</sup> <sup>10</sup>−<sup>9</sup> at 25 ◦C [31]). The lattice parameters of hydroxyapatite and calcite are relatively close, respectively, a = b = 9.43 Å and c = 6.88 Å for HAP [32], and a = b = 9.96 Å and c = 17.07 Å for calcite, considering two molecules per unit cell [33]. This indicates compatibility in the nucleation of the phosphate layer onto the surface of carbonate stones and strong bonding of the newly formed layer onto the substrate [21]. The other advantage is that hydroxyapatite is the least soluble and the most stable calcium phosphate phase in aqueous solutions at pH values higher than 4.2 [34,35]. Also, it has a dissolution rate about 4–5 orders of magnitude lower than that of calcite: Rdiss, HAP = 1 x 10−<sup>14</sup> moles·cm−2·s−1, and Rdiss, calcite = 2 <sup>×</sup> 10−<sup>10</sup> moles·cm−2·s−<sup>1</sup> at pH = 5.6; Rdiss, HAP = 3.7 <sup>×</sup> 10−<sup>14</sup> moles·cm−2·s−1, and Rdiss, calcite = 5.4 <sup>×</sup> 10−<sup>9</sup> moles·cm−2·s−<sup>1</sup> at pH = 4 [36,37]. It is therefore more stable in a range of pH and it is expected to provide additional protection against acid dissolution. In addition, the precursor ammonium phosphate is non-toxic, and a good penetration depth could be obtained in the consolidation treatment [21].

However, despite successful results for the consolidation of decohesive plaster layers as substrates/surface layers of fresco wall paintings [21] and regardless of the fact that some other consolidants, such as a nano calcium hydroxide suspension, have been tested on fresco wall painting mock-ups [38], this DAP-based method has not yet been tested on archaeological wall paintings nor has any thorough assessment been performed on pigments. This research aims to fill this gap of knowledge. Following from our previous research on the application of DAP for the consolidation of fresco plaster layers, here, as a first step, we systematically investigate and evaluate in laboratory-controlled conditions the optical, physical, and chemical effects of the ammonium phosphate precursor of HAP on selected pigments (mainly those compatible with fresco application). The aim is to have a fundamental understanding of the effects (mainly on color change and phase transformations) of this inorganic 'consolidant' precursor on pigments, prior to any testing of the consolidating effect on the paint layer (both fresco and secco) in wall painting mockups and archaeological/historic wall paintings and other polychrome monuments. More specifically, this research investigates the interactions between DAP solutions and seven pigments commonly found in wall paintings and other polychrome surfaces and focuses on answering the following questions:

