The Egyptian blue pigment was synthesized by solid-state reaction from calcium carbonate CaCO3, amorphous silica SiO2, copper oxide CuO and 3 wt % of sodium carbonate Na2CO3. The powders were mixed, ground together and then pressed into pellets under a uniaxial pressure of 4 t cm-2. The pellets were first sintered in air at 1000 ∘C for 5 h. The resulting samples were then ground, pressed into new pellets, and sintered again for 17 h in air at 1000 ∘C. After this final sintering, the samples were ground again in powder. The purity of the material was tested by X-ray diffraction (XRD) using an X Panalytical X'Pert Pro diffractometer with the Kα1 ray of a copper anticathode (λ=0.15406 nm). XRD patterns show that the synthesized powder consists of cuprorivaite CaCuSi4O10 with traces of wollastonite CaSiO3 and SiO2 (Binet et al., 2021). Cuprorivaite is a member of the phyllosilicate group, all minerals of which have the form of platelets. Its structure is made up of double layers of corner-sharing [SiO4] tetrahedra separated by a layer of Ca2+ ions. It is tetragonal, with space group P4/nnc (Pabst, 1959), which means that the crystallographic c axis (C4 axis) is normal to the silicate layers and thus to the platelets. Cu2+ ions occupy plane-square sites with D4h point symmetry (Pabst, 1959), with the C4 axis (which is also the g|| axis) parallel to the crystallographic c axis.

The as-obtained Egyptian blue pigment was then mixed with boiled linseed oil as a binder in a proportion of 10 wt % of pigment. The liquid pigment–oil mixture was deposited on horizontal supports to allow drying. Either a glass plate or a semi-rigid transparent polymer substrate (transparency for an overhead projector) were used. Four different deposition methods were tested (Fig. 1): (i) a one-way spreading with a film applicator to produce a 250 µm-thick (before drying) film, (ii) a one-way spreading with a paint brush, (iii) a dabbing with a paint brush, and (iv) a droplet deposition with a pipette. The samples were then left to dry for several days until the linseed oil became rigid. Of relevance for further discussion is the fact that, during the drying, the vertical direction, and hence gravity, was perpendicular to the sample plane. For EPR analysis and for samples which had to be rotated about an in-plane direction, small pieces with dimensions 25 mm × 2–3 mm were cut perpendicularly to the spreading direction (when relevant), as shown in Fig. 1. For samples which had to be rotated about the normal to the plane, pieces of approximate size 2 mm ×2 mm were cut to fit into standard EPR tubes.

EPR spectra were recorded at room temperature with a Bruker Elexsys E500 spectrometer equipped with a Bruker SHQE resonator operating at X-band (microwave frequency ≈ 9.25–9.39 GHz, depending on the sample). The applied magnetic field was modulated at 100 kHz with a 1 mT amplitude for lock-in detection. The microwave power was 2 mW. To analyze theoretically the orientation distribution of pigment grains in a fluid medium, a sample made of pigment powder in fluid linseed oil was submitted to a 20 mT magnetic field in the EPR spectrometer at room temperature. Then the sample was cooled down to 200 K with gaseous nitrogen to freeze the oil and to keep the grain orientations fixed in the sample. EPR spectra at different orientations of the sample in the external field were then recorded at this temperature. Datasets are available in Binet et al. (2022a).

All calculations for EPR spectral analysis were performed with Matlab (script available in Binet et al., 2022b). The Easyspin package (Stoll and Schweiger, 2006) was used for EPR spectrum simulation by taking an axial g matrix with principal values gx=gy=2.055=g⊥ and gz=2.350=g∥ for Cu2+ in the Egyptian blue pigment. Here the (x, y, z) molecular frame is such that the z axis is the C4 symmetry axis of the Cu2+ coordination site with D4h symmetry (Ford and Hitchman, 1979). This axis is also the crystal c axis of the structure (Pabst, 1959). A Voigt line shape was considered for the EPR transitions, with an empirical dependence of the peak-to-peak width ΔB on the angle θ between the applied field and the z axis as ΔB=0.86+0.37cos⁡2θ+0.12sin⁡2θ (mT) for both Lorentzian and Gaussian components.

The EPR of the Cu2+ ion in cuprorivaite can be described by a spin Hamiltonian including only the Zeeman interaction with the external applied magnetic field B: 1H^=μBB⋅gS, where μB is the electron Bohr magneton, g the electron g factor matrix and S the electron spin. The hyperfine interaction with the central nucleus 63Cu or 65Cu is not to be considered in the Hamiltonian as it is averaged out by exchanged interaction between Cu2+ ions (Binet et al., 2021). The resonance field is then determined by the g factor only and its anisotropy. An EPR spectrum is recorded by scanning the applied field at fixed frequency ν of the electromagnetic wave. For the magnetic field making an angle θ with the molecular z axis, an EPR transition occurs at a resonance magnetic field 2Br(θ)=hνμBg∥2cos⁡2(θ)+g⊥2sin⁡2(θ), with h the Planck constant. The resonance field thus varies in a range defined by the boundary values Br∥=Brθ=0=hν/g∥μB and Br⊥=Brθ=π2=hν/g⊥μB, with Br∥<Br⊥ in the present case. The EPR transition of a Cu2+ ion thus depends on the orientation of the molecular frame x,y,z within the laboratory frame X0,Y0,Z0 defined such as B∥Z0 through the angle θ. In the case of a powder sample where crystallites exhibit a perfectly isotropic distribution of orientations, the EPR spectrum is given by summing over all possible orientations θ: 3S(B)=∫θ=0π∫φ=02π∫ψ=02πωφ,θ,ψfB-Br(θ)sin⁡θdθdφdψ, where fB-Br(θ) is a normalized lineshape function, and ωφ,θ,ψ is the transition probability, which depends on the orientation, given by the set of Euler angles φ,θ,ψ of the molecular frame within the laboratory frame. A typical EPR spectrum in the case of an isotropic distribution of crystallite orientations and for an axial g matrix is shown in Fig. 2. It exhibits a low-field maximum at Br∥ and a baseline crossing close to (but not exactly at) Br⊥.

To describe the EPR spectrum of a sample with a non-uniform distribution of crystallite orientations, three different frames need to be considered, namely, the molecular frame (x,y,z), the sample frame X,Y,Z with the X, Y and Z axes having a defined position with respect to the sample, and the laboratory frame X0,Y0,Z0, as shown in Fig. 3a. The orientation of the molecular frame within the sample frame is specified by a set of three Euler angles Ω=α,β,γ, its orientation within the laboratory frame by the set Ω′=φ,θ,ψ and the orientation of the sample frame within the laboratory frame by the set Ω0=α0,β0,γ0 (Fig. 3b).

The relevant quantity to characterize the non-random orientations is the orientation probability density PΩ of the crystallites in the sample frame X,Y,Z such that P(Ω)dαsin⁡βdβdγ is the probability of the molecular frame orientation in the sample frame being found in the range [α,α+dα[×[β,β+dβ[×[γ,γ+dγ[. This density P(Ω) is directly related to the way the pigment was applied on the sample. It is normalized so that ∫α=02π∫β=0π∫γ=02πP(Ω)dαsin⁡βdβdγ=1. For a specific orientation Ω0=α0,β0,γ0 of the sample in the laboratory frame, the EPR spectrum is then given by 4SB,Ω0=∫ΩP(Ω)ωΩ,Ω0fB-BrΩ,Ω0dΩ. In the case of an isotropic orientation distribution, P(Ω) is constant with P(Ω)=1/8π2 and can be omitted in Eq. (4), which then reduces to Eq. (3). The transition probability ωΩ,Ω0 scales as the g value in the case of a field-swept EPR spectrum (Aasa and Vänngård, 1975). When the anisotropy of the g factor is small, as is the case here, the transition probability is almost independent of the orientation Ω,Ω0. It then appears as an irrelevant scaling factor and will be dropped hereafter for the sake of simplification. The determination of P(Ω) from experimental EPR spectra is essentially adapted from Hentschel et al. (1978). The unknown probability density P(Ω) is first expanded as a combination of Wigner matrix elements Dmn(l)(Ω): 5P(Ω)=∑l=0∞∑m=-ll∑n=-llplmnDmn(l)(Ω), where Dmn(l)α,β,γ=e-imαe-inγ〈Yl,m|exp-iβL^y/|Yl,n〉, with Yl,m and Yl,n being spherical harmonics and L^y the y component of the orbital angular momentum operator. An essential simplification can be introduced here because all samples happened to have a revolution symmetry about the Z axis of the sample frame (see below) and because the g factor is axially symmetric about the molecular z axis (C4 axis), meaning that the spectrum is unchanged by any rotation of the crystallites about the molecular z axis. The probability density P(Ω) then no longer depends on α and γ, but only on β. The dependence on α and γ arises from terms plmnDmn(l)(Ω) in Eq. 5 with non-zero values of n or m. The general way to get rid of this dependence is to set plmn=pl×δn,0×δm,0. This selects terms in Eq. (5) with m=n=0 so that 6P(Ω)=P(β)=∑l=0∞plD00(l)(Ω), where D00(l)(Ω)=Plcos⁡β, with Pl(x) being the lth-order Legendre polynomial. The orientation probability density P(Ω) is then fully determined by the set of coefficients pl with l∈N, which must be obtained from experimental EPR spectra. Detailed calculations given in the Supplement show that the EPR spectrum for a specific orientation Ω0=α0,β0,γ0 of the sample in the laboratory frame is given by 7SB,Ω0=SB,β0=∑l=0∞plPl(cos⁡β0)×∫θ=0πfB-Br(θ)Plcos⁡θsin⁡θdθ. From the above equation, the EPR spectrum only depends on the angle β0 between the sample Z axis and the applied magnetic field. Therefore, only a set of spectra at different β0 angles is needed to determine the pl coefficients. The numerical implementation of the determination of the pl coefficients from a set of experimental spectra at different orientations β0 of the sample in the laboratory frame is given in the Supplement. It should however be noted that since the EPR phenomenon is unchanged by reverting the orientation of the applied field, only pl coefficients with l even can be determined so that the actual probability density P(Ω) cannot be fully obtained from EPR.

Films were deposited on a flat substrate with an applicator by a one-way spreading along the X direction in the substrate plane (Fig. 3a) of a mixture of fluid linseed oil and pigment grains. This application process is expected to be the most reproducible one among those used in this work. Since an anisotropy along the X direction is induced by the process, it is meaningful to determine whether a preferred orientation of the grains is induced and how the distribution is oriented with respect to the spreading X direction. EPR spectra corresponding to the rotation of the sample about the sample Z axis and about the sample Y axis are shown in Fig. 6a and b, respectively. It turns out that there is no significant change in the spectrum shape upon rotation about the Z axis (Fig. 6a). This means that the orientation distribution has a revolution symmetry about the Z axis.

This is confirmed by the polar plot of the corresponding density P(β) (here β is the angle from the X axis in the X–Y plane), which is very close to a circle (Fig. 7a), and by the pl coefficients close to zero except for l=0 (Fig. 8).

Significant changes in the EPR spectrum shape are observed upon rotation about the Y axis, the magnetic field direction moving from the Z direction (β0=0) perpendicular to the sample plane to the X direction (β0=π/2) in the sample plane (Fig. 6b). The low-field part of the spectrum, corresponding to crystallites with the c axis parallel to the field, is enhanced at β0≈0, while the high field part (crystallites with the c axis perpendicular to the field) is enhanced at β0≈π/2. This means that crystallites are mostly oriented with their c axis perpendicular to the sample plane. This is confirmed by the probability density P(β) being maximum at β=0 (Fig. 7b). Calculated EPR spectra are given in Figs. S2 and S3. The variability in the preferred orientation of the crystallites has been analyzed in a set of six samples prepared under the same conditions and the corresponding P(β) densities shown in Fig. 7b with different colors. The average values of the pl coefficients over those six samples are plotted in Fig. 8, with the error bars given by their standard deviation. The maximum value Pβ=0= 0.04–0.06 of the probability density for the films is lower than in the case of magnetically oriented grains in fluid oil where the maximum value was Pβ=0≈0.15. For films, the highest value of pl is at l=0, corresponding to the isotropic contribution to P(β), while for magnetically oriented grains in fluid oil the anisotropic contributions at non-zero orders l=2-10 dominate the isotropic one (Fig. 5b). All these results indicate that the preferred grain orientation in dried films after mechanical application is less pronounced than under an external magnetic field in fluid oil.

The preferred orientation with more operator-dependent modes of deposition was also investigated, namely, spreading along the X direction in the sample plane with a paint brush, dabbing onto the substrate with a paint brush and droplet deposition with a pipette. In each case two or three samples were prepared and analyzed. All samples exhibited a revolution symmetry about the Z axis, as in the case of films deposited with the applicator. The EPR spectra under rotation about the Y axis are given in Figs. S4 to S6. The orientation probability densities are shown in Fig. 9a and b and the corresponding pl coefficients (average values over two to three samples and standard deviations as error bars) in Fig. 10.

In all cases, the probability densities P(β) exhibit a maximum value for β in the range 0–17∘. This again shows a preferred orientation with the crystal c axis close to the sample Z axis. However, the maximum values of P(β), about 0.02–0.03, are significantly lower than for films deposited with the applicator. This is in line with the pl coefficients for l≠0 in Fig. 10, which are lower than for films deposited with the applicator showing that the orientation distribution with paint brushing, dabbing or droplet deposition is less anisotropic than when the film is deposited with an applicator. When using a paint brush, increasing the strength of the gesture (“strong brush painting” data as compared to “brush painting” data in Figs. 9a and 10) does not seem to induce a significant difference in the orientation distribution, as shown by close P(β) curves in Fig. 9a and almost equal leading pl coefficients for l=2,4,6 in Fig. 10. The orientation distributions in the cases of dabbing and droplet deposition appear to be slightly less anisotropic than for brush painting because their maximal values of P(β) are closer to the lower bound 0.02 and because they have lower values of the leading pl coefficients for l=2,4,6.

Whatever the application mode of the oil–pigment mixture, two common features were revealed by the above analyses: (i) the pigment crystallites exhibit a preferred orientation with their crystal c axes oriented almost perpendicularly to the sample plane, and (ii) the orientation distribution has a revolution symmetry about the normal to the sample plane. More surprising is that these features are observed even when a mechanical stress is applied along the sample plane (X axis) during the deposition (whether with the applicator or with a paint brush) and that this mechanical stress seems to induce the most pronounced preferred orientations. It must also be mentioned that, during the film deposition and drying, the gravitational force was perpendicular to the sample plane. A possible explanation for this preferred orientation is based on the sedimentation of the pigment crystallites within the oil while the latter is still viscous. Indeed, microcrystals of cuprorivaite exhibit a tabular morphology (Bloise et al., 2016). Then, when microcrystals fall through the liquid oil under the gravitational force, they tend to lay down with their largest face horizontal (Fig. 11a). Consequently, microcrystals adopt a preferred orientation with the normal to the largest face perpendicular to the sample plane. The piling of the crystals is not perfect, some crystals being tilted or aggregated in larger grains. This is mostly the case with the droplet or dabbing deposition. When a horizontal mechanical stress is applied with an applicator or a paint brush, the polymer chains of the oil become aligned along the stress direction (Fig. 11b). This may have two effects: first, a dissociation of the aggregates into separate microcrystals, second a better alignment of the crystal tablets in the horizontal plane by polymer–crystal surface interactions. This could explain why the preferred orientation seems to be enhanced when such a mechanical stress is applied during film deposition.