Structural and electronic properties of the PbCrO₄ chrome yellow pigment and of its light sensitive sulfate-substituted compounds

Abstract

Chrome Yellows (CY) are a family of synthetic pigments of the formula PbCr_(1−x)S_xO₄, used by van Gogh and other nineteenth-century masters, whose photo-degradation threatens the conservation of invaluable works of art. Experimental studies have demonstrated that the darkening of the pigment is provoked by the formation of superficial layers of Cr(III) oxides and sulfates due to the reduction of the native Cr(VI) to the Cr(III) oxidation state. A strong correlation between CY degradation and its chemical composition (sulfate richness) and structure (orthorhombic vs. monoclinic) was also experimentally put forward. Here we investigate a possible sulfate pathway to CY degradation, and investigate PbCr_(1−x)S_xO₄ (x = 0, 0.25, 0.5, 0.75, 1) compounds in both orthorhombic and monoclinic phases by first principles DFT calculations. Our results show that the mixed PbCr_(1−x)S_xO₄ and the native PbCrO₄ share a similar electronic structure, though an energy up-shift of the conduction band is computed by both increasing the amount of sulfate and passing from the monoclinic to the orthorhombic phase. Our calculations suggests that, under a purely electronic picture, the Cr(VI) photo-reduction is more difficult for compounds with high sulfur concentration and an orthorhombic phase. Therefore, we conclude that degradation should be ascribed to other factors, such as different solubility and morphology.

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1. Introduction

Chrome Yellows (CY) are a family of synthetic yellow pigments of PbCr_(1−x)S_xO₄ formula, which were introduced in 1809 by Vaquelin and made commercially available since around 1815.^1,2 CY suddenly entered into the palette of nineteenth-century masters, including J. Constable,³ J. M. W. Turner,⁴ V. van Gogh,^5,6 G. Seraut,⁷ C. Pissarro,⁸ P. Cezanne,⁹ J. Ensor,¹⁰ who highly appreciated its bright and opaque colour ranging from deep yellow to lemon yellow. Pure PbCrO₄ is the reference compound, CrO₄²⁻ being responsible for the characteristic deep yellow colour of the pigment; it shows a monoclinic crystal structure (Scheme 1, left). Upon substitution of chromate anions with sulphates, the colour of PbCr_(1−x)S_xO₄, solid solutions gradually shifts towards lemon yellow while the structure changes from the monoclinic to the orthorhombic phase typical of PbSO₄. Sulphate-poor CY pigments, with x < 0.4, maintain a prevalence of monoclinic phase while the orthorhombic phase prevails by further increasing the sulphate amount, since the pure PbSO₄ only exists in the orthorhombic anglesite-type crystal structure (see Scheme 1, right).

Scheme 1 Left: PbCrO₄ in monoclinic (P121n1) phase. Right: PbSO₄ in orthorhombic (Pbnm) phase.

A number of paintings where CY were employed, comprising some iconic works by Van Gogh, have shown with time a perceptible darkening of colour which raises serious concerns for their conservation. The penchant for degradation of chromate-based pigments has been extensively investigated in the last few years by employing synchrotron radiation (SR)-based X-ray microprobe techniques as well as electronic and vibrational spectroscopies on both original paint micro-samples and artificially aged paint models.^11–21 It has been found that the pigment darkening is likely due to the formation of a superficial micrometric layer made of amorphous Cr(III) oxides (Cr₂O₃) along with Cr(III) sulphates and/or organo-metallic Cr(III) compounds; the alteration process has been accordingly ascribed to reduction of the native Cr(VI) to the Cr(III) oxidation state.

Both environmental (light, temperature, humidity) and intrinsic (composition of the CY solid solution, paint additives, organic binding media) aspects have been evaluated as potential triggering factors of the formation of superficial Cr(III)-compounds.^{11,14–16,19,21} It has been proved that the reduction process is mainly photo-activated (by both UV and visible light), although a role can be played also by Cr(V) intermediate compounds thermally formed by interaction of CY with the binding medium (typically a drying oil).^19,21 Behind these environmental factors it has emerged, however, that the primary role is ascribable to the chemical composition and structure of PbCr_(1−x)S_xO₄ solid solutions. As a matter of fact, orthorhombic sulphate-rich CY are much more prone to photochemical reduction than the sulphate-poor analogues having a monoclinic crystal phase.^14,19

To shed some light on the nature of the material structure/properties relationship and to analyze how the electronic structure of CY is affected by compositional and structural changes, here we investigate the CY pigment and its sulphate-substitution products by first principles electronic structure computational analyses. Theoretical modeling can provide accurate information at the microscopic level of colouring materials used in paintings^22–30 and in different applications.^31–38 In this study, we have taken into account well defined models and have investigated the interplay between structural and electronic properties as a function of the composition and the crystalline phase. The pure PbCrO₄ and PbSO₄ reference structures have been investigated by employing Density Functional Theory (DFT) calculations, including both scalar relativistic (SR) and spin–orbit coupling (SOC) effects. After having tested different levels of theory on the reference lead chromate and sulphate compounds, we have focused on the intermediate binary structures PbCr_(1−x)S_xO₄ with x = 0.25, 0.50 and 0.75, in both monoclinic (m-PbCr_(1−x)S_xO₄) and orthorhombic (o-PbCr_(1−x)S_xO₄) phases. These theoretical models can be related to the CY laboratory synthesized samples, with increasing amount of sulphate and proved to have different grades of light fastness.¹⁴ Our study shows that due to the peculiar electronic structure of PbCrO₄ and of the related PbCr_(1−x)S_xO₄, the Cr(IV) to Cr(III) reduction process becomes less energetically favored for sulphate-rich species or within the orthorhombic phase, thus suggesting that the role of sulphate in the degradation is possibly limited to factors different from pure electronic ones, such as its different solubility and morphology (i.e. smaller particle size).

2. Models and computational details

All the calculations have been carried out using the PWSCF code as implemented in the Quantum-Espresso program package, without any symmetry constraint.³⁹ The PBE exchange-correlation functional was used and the electron–ion interactions were described by ultrasoft pseudopotentials (USPP) from the Pslibrary.⁴⁰ Pb 5d, 6s and 6p electrons; Cr 3s, 4s, 3p and 3d; S 3s and 3p; O 2s and 2p shells were explicitly included in the calculations. Plane-wave basis set cutoffs of 50 Ry and 400 Ry were used for the smooth part of the wavefunctions and the augmented density, respectively. Both scalar relativistic (SR) and full relativistic calculations including spin–orbit coupling (SOC) have been performed. A 4 × 4 × 4 Monkhorst Pack grid⁴¹ was used to sample the Brillouin zone of the tetragonal systems.

We optimized the structure of PbCrO₄ using as reference the available experimental data. At room temperature PbCrO₄ assumes a P121n1 monoclinic phase (m-PbCrO₄)⁴² while at high temperatures an orthorhombic (Pnma) structure (o-PbCrO₄) has been reported⁴³ very similar to that of PbSO₄ (o-PbSO₄), which is found in an anglesite structure with an orthorhombic conformation (Pbnm), see Scheme 1.⁴⁴ Since a similar change of phase, from the monoclinic to the orthorhombic, has been observed for the mixed systems upon increase the sulfur concentration, the electronic properties of the o-PbCrO₄ and o-PbSO₄ have also been investigated and compared to that of m-PbCrO₄.

The investigated cells of PbCrO₄ and PbSO₄ contain a total of 24 atoms: 4Pb, 4Cr/S and 16O. The cell of m-PbCrO₄ has an angle β of 102.42° while the α and γ angles are equal to 90°. The a and b cell parameters are measured 7.12 and 7.34 Å, respectively, while c is 6.79 Å, being the total volume of the cell 350.80 ų. The orthorhombic phase of this species, o-PbCrO₄, is slightly larger, 367.00 ų is the cell volume and a, b and parameters measure 8.80, 5.73 and 7.27 Å, respectively. o-PbSO₄ is very similar to the analogous chromate, showing smaller a, b and c parameters 6.96, 8.48 and 5.40 Å, respectively, accounting for a total volume of 318.49 ų.

Geometry optimization of these structures has been performed both by leaving the cell parameters fixed at the experimental values and optimizing the ions (experimental cell), and by allowing both the cell and the ions to relax (optimized cell). Calculations have been performed using a SR-DFT approach and a full relativistic one, including SOC effects. To investigate how the changes in the chemical composition and crystalline phase are reflected on the electronic structure of CY, we have taken into consideration mixed Cr and S materials (i.e. PbCr_(1−x)S_xO₄) which have also experimentally studied.^14,18,19,21 We investigated mixed structures with composition range x = 0, 0.25, 0.5, 0.75, 1; for the x = 0.5 substitutions we have taken into account the three possible distributions of the CrO₄²⁻ and SO₄²⁻ octahedra in the crystal, see discussion below. The compounds have been modeled by subsequently replacing the chrome by sulfur atoms in the m-PbCrO₄ structure and re-optimizing both cell and ions for the monoclinic phase, and making the reverse process (substitution of sulphate by chromate) starting from o-PbSO₄ for the orthorhombic phase.

3. Results and discussion

3.1 PbCrO₄ and PbSO₄ reference structures

In Fig. 1 the SOC-optimized structures of m-PbCrO₄, o-PbCrO₄ and o-PbSO₄ are reported. Negligible differences have been computed in the optimized geometrical parameters obtained using the experimental and optimized cell parameters, with the exception of o-PbCrO₄ that is not stable at room temperature^45,46 and indeed undergoes a strong reorganization upon cell relaxation (see ESI†). The inclusion of SOC only slightly affects the optimized structures suggesting that SOC has a minor impact on the geometry of the investigated systems (see ESI†).

Fig. 1 Optimized structures of m-PbCrO₄ (P121n1), o-PbCrO₄ (Pnma) and o-PbSO₄ (Pbnm).

The SOC-DFT band structures calculated on the optimized geometries employing experimental cell parameters are reported in Fig. 2, see ESI† for the corresponding SR-DFT data. A summary of indirect and lowest direct band gaps are reported in Table 1.

Fig. 2 SOC-DFT band structures of m-PbCrO₄, o-PbCrO₄ and o-PbSO₄ employing the experimental cell parameters. The zero has been set in both cases at the top of the valence band.

Table 1 Direct and indirect band gaps (eV) computed for m-PbCrO₄, o-PbCrO₄ and o-PbSO₄ using SR- and SOC-DFT. Band gaps have been computed employing the experimental cell parameters and upon atomic + cell parameters optimization

		m-PbCrO4		o-PbCrO4		o-PbSO4
		Exp. cell	Opt. cell	Exp. cell	Opt. cell	Exp. cell	Opt. cell
SR	Dir.	1.81 (A–B)	1.79 (A–B)	1.96 (Γ)	1.53 (Γ)	4.29 (U)	4.29 (Γ–Z)
		1.82 (A)	1.81 (A)			4.55 (Γ–Z)	4.56 (U)
	Ind.	1.73	1.71	1.96		1.52
SOC	Dir.	1.74 (A–B)	1.71 (A–B)	1.86 (Γ)	1.45 (Γ)	3.81 (U)	3.81 (Γ–Z)
		1.75 (A)	1.72 (A)			3.82 (Γ–Z)	3.82 (U)
	Ind.	1.65	1.63	1.85	1.44	3.59	3.59

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An indirect band gap of 1.73 and 1.65 eV is computed for m-PbCrO₄ using SR- and SOC-DFT, respectively. SOC thus induces a small (0.08 eV) decrease in the computed band gap suggesting a moderate involvement of the lead atoms in the band edges. On overall, the results are quite underestimated with respect to the experimental ones reported at ca. 2.3 eV (ref. 47) as expected for standard GGA-DFT calculations.^48–50 The top of the valence band is computed between A and B while the bottom of the conduction band is computed at A, the direct band gap in A lays ca. 0.10 eV above the indirect one. The presence of a direct band gap close to the indirect band gap is in line with the previous computational analyses by Errandonea et al.^47,51 who found m-PbCrO₄ to be an indirect band gap semiconductor, with the direct band gap easily accessible. As it can be noticed from Table 1, the differences between the band gaps computed using the experimental cells or the optimized ones are negligible.

The band gap of o-PbCrO₄ is computed to be 1.96 and 1.86 eV by SR- and SOC-DFT, respectively. Here the band gap can be considered as being direct at the Γ point of the Brillouin zone, almost degenerate with the computed indirect ones. Upon cell relaxation, the orthorhombic phase slightly deviates from orthogonality and while the b axis remains unchanged, the a and c axis are reduced and increased by 8% and 6%, respectively, resulting in a total reduction of the volume of ca. 4%. Structural changes lead to a dramatic drop of the band gap by as much as 0.4 eV, bringing it below that of the monoclinic phase. These variations are not surprising when considering that o-PbCrO₄ has been only reported at high temperatures and is not stable at standard conditions. The band gap of the relaxed cell structure is still computed at Γ and the structure of the band is very similar to that computed for the experimental cell, with a very flat region of the valence band and a clear minimum of the conduction band at Γ.

The indirect band gap of o-PbSO₄ is computed 4.05 and 3.59 eV by SR- and SOC-DFT, respectively, and lays ca. 0.2 eV below the lowest direct band gap computed at U. The bottom of the conduction band is computed at U while the top of the valence band is computed between Γ and Z. In o-PbSO₄ SOC lowers the band gap by ca. 0.5 eV, a stronger effect than what found for PbCrO₄ due to the larger Pb character of the conduction band with respect to the lead chromates, as discussed below. The SOC-DFT band gap is overestimated by ca. 0.4 eV with respect to the experimental one, reported at ca. 3.2 eV.⁵² While the origin of such overestimate is presently not clear, we notice that a comparable discrepancy was found for similar oxides.^47,51

The density of states (DOS) of the investigated pure phases is reported in Fig. 3. The valence band has a similar composition for the three compounds and is mainly due to the oxygen orbitals, with a minor involvement of the Pb s orbitals, a contribution which decreases passing from m-PbCrO₄ to o-PbCrO₄ and o-PbSO₄. The valence band of o-PbCrO₄ phase is up-shifted by ca. 0.25 eV with respect to the monoclinic phase (alignment done considering the Pb 5d states), it is shown as a more structured band with a higher energy low intensity peak. This up-shift in the o-PbCrO₄ valence band is responsible for the decrease of the band gap discussed previously and it is due to the structural reorganization and the decrease of the cell volume. This is confirmed by looking at the valence band structure of o-PbCrO₄ using the experimental cell parameters, which does not show a band gap lowering, see ESI.†

Fig. 3 Total density of states for m-PbCrO₄ (top), o-PbCrO₄ (middle) and the o-PbSO₄ (bottom) structures. Contribution of the main orbitals to the valence and conduction bands. The DOS have been aligned using the Pb d peaks (spin down) and the zero has been set to the top of the m-PbCrO₄ valence band.

The conduction band of PbCrO₄, in both crystalline phases shows mainly contributions from Cr d orbitals and O p orbitals and a low but meaningful amount of Pb p states. In o-PbSO₄, the conduction band is essentially delocalized on the Pb and O centers and is up-shifted by ca. 2 eV with respect to PbCrO₄. This change reflects in an opening of the band gap as experimentally found to go from 2.3 eV for m-PbCrO₄ to 3.2 eV for o-PbSO₄. The larger involvement of lead atoms in the conduction band of o-PbSO₄ than in PbCrO₄ accounts for the larger SOC effects computed for the sulphate with respect to the chromate analogue, as discussed above. A conduction band character similar to that of o-PbSO₄ has been also observed for PbMoO₄ and PbWO₄, tetragonal oxides, both showing a larger computed band gap than PbCrO₄, 3.3 and 3.9 eV, respectively.⁵³

The electronic structure of PbCrO₄ presents a few peculiarities with respect to the previous cited metal oxides. The CrO₄²⁻ ion shows a weaker crystal field splitting compared to the MoO₄²⁻ and WO₄²⁻ tetrahedral anions. The antibonding combination of the Cr d orbitals and oxygen lone-pairs lies at lower energies with respect to the unoccupied localized Pb states, thus becoming the final states of charge transfer excitations. In addition, the Pb contribution to the conduction band of PbCrO₄ seems to have implications on the CY pigment colour. This contribution is obviously absent in SrCrO₄, an oxide in the monazite crystal structure, which, even presenting similar contributions of Cr and O in the valence and conduction bands, has a larger band gap with respect to the analogue Pb ternary oxide.^51,53 The Pb presence in the conduction band is due to hybridization of deep occupied Pb and O states; and the antibonding Pb–O component shifts to lower energies the conduction band, mainly of Cr–O character, making it more accessible and easier to be (photo) reduced. In the case of sulphate, the Pb character of the conduction band changes completely the nature of charge-transfer transitions and the chemical–physical properties of this compound.

3.2 Mixed PbCr_(1−x)S_xO₄ structures

The pathway to gradually replace chromate with sulfate anions in monoclinic PbCrO₄ has been simulated to elucidate how the introduction of an increasing amount of sulfate may influence the structural and electronic proprieties of CY.^14,18,19 Mixed Cr/S structures of formula m-PbCr_(1−x)S_xO₄ (with x = 0.25, 0.5, 0.75) have been analyzed. Since experimentally a change of phase from monoclinic to orthorhombic is observed when synthesizing lead chromate in the presence of more than 50% of sulfur, we optimized the mixed o-PbCr_(1−x)S_xO₄ materials and the analogous monoclinic phase. The monoclinic and orthorhombic optimized structures are reported in Fig. 4. The mixed structures are formed by CrO₄²⁻ and SO₄²⁻ tetrahedra with a nine-fold coordination of the Pb in distorted polyhedra. We compute very similar stabilities and electronic parameters for the three considered x = 0.5 structures, see ESI.† Therefore hereafter only the most stable conformation of both phases (c) will be reported. In Table 2 the optimized main cell parameters and the valence and conduction band edges relative to those of m-PbCrO₄ are reported.

Fig. 4 Optimized structures of the investigated mixed m-PbCr_(1−x)S_xO₄ and o-PbCr_(1−x)S_xO₄.

Table 2 Computed cell parameters, band gap (SR and SOC) and position of the top and bottom of the valence and conduction bands, respectively, for the m-PbCr_(1−x)S_xO₄ and o-PbCr_(1−x)S_xO₄ structures. The electronic structures have been aligned using the Pb d (spin down) peak taking as reference that of the m-PbCrO₄ and zero has been set to the top of the valence band of m-PbCrO₄

	m-PbCr(1−x)SxO4					o-PbCr(1−x)SxO4
	x = 0	x = 0.25	x = 0.5	x = 0.75	x = 1	x = 0	x = 0.25	x = 0.5	x = 0.75	x = 1
Volume (Å^3)	2351	2319	2293	2261	2232	2354	2280	2221	2181	2141
A (Å)	7.107	7.097	7.066	7.034	7.000	7.633	7.414	7.178	7.188	7.124
B (Å)	7.427	7.376	7.344	7.297	7.259	8.391	8.503	8.691	8.622	8.632
C (Å)	6.762	6.726	6.715	6.692	6.669	5.835	5.741	5.653	5.587	5.530
A (°)	89.9	89.8	90.0	90.0	90.0	90.0	90.0	90.0	89.7	90.0
B (°)	102.5	102.6	102.8	102.7	102.6	90.0	90.0	90.0	90.0	90.0
Γ (°)	90.1	90.4	90.0	89.9	90.1	90.0	90.0	90.0	90.0	90.0
VB (eV)	0.00	−0.10	−0.11	−0.12	−0.10	0.21	0.19	0.08	0.13	0.10
CB (eV)	1.63	1.74	1.84	1.97	3.75	1.71	1.99	2.22	2.34	3.69
Egap (eV)	1.63	1.84	1.95	2.09	3.85	1.50	1.80	2.14	2.21	3.59

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Upon increasing the amount of sulfur a reduction of the cell volume is predicted, nicely matching the experimental observations;^54,55 the volume contraction is 5% for the monoclinic phase, while for the orthorhombic phase the volume contracts by 9%. To get insight into the possible changes of the structural parameters which accompany the substitution of chromate with sulfate, the PbO, CrO and SO distances of the polyhedrons have been analyzed but no relevant effects have been noticed, ESI.†

The band gap is strongly influenced by the presence of sulfur. For the monoclinic phase the band gap increases by 0.21 eV (x = 0.25), 0.35 eV (x = 0.50) and 0.46 eV (x = 0.75) with respect to PbCrO₄, while the band gap of the orthorhombic phase markedly increases by 0.30, 0.64 and 0.71 eV for x = 0.25, 0.50 and 0.75, respectively, see Table 2. Despite the known flaws of PBE in computing absolute band gap energies, we are confident that the methodology is accurate enough to qualitatively, at most, reproduce the band gap evolution as a function of sulphate richness. For pure m-PbSO₄ (o-PbSO₄) the band gap is computed to be 2.22 eV (2.09 eV) larger than that of m-PbCrO₄ (o-PbCrO₄) due to a completely different conduction band composition, in line with that discussed above for the pure phases. For the mixed monoclinic structures, the valence band is stabilized by 0.10 eV with respect to the pure m-PbCrO₄, while the conduction band is progressively up-shifted by increasing the sulfur amount, see Table 2, being both shifts responsible of the band gap opening. The same trend is found for the orthorhombic species.

Except for the conduction band of PbSO₄, the valence and conduction bands of the orthorhombic structures are up-shifted with respect to their monoclinic counterparts. For the valence band we computed shifts in between 0.2 and 0.3 eV, while the variations of the conduction band is far more pronounced, see Table 2. It can be noticed that the conduction band of the reference pure species are very similar in both crystalline phases, with computed differences below 0.1 eV, while for x = 0.25, 0.50 and 0.75 we compute an up-shift of 0.25, 0.38 and 0.37 eV, respectively, of the conduction band going from monoclinic to orthorhombic phase, see Table 2. These changes deliver band gaps in the orthorhombic phase that are lower for x = 0 (−0.13 eV) and x = 1 (−0.26 eV) compared to their monoclinic counterparts, while they are almost unchanged for x = 0.25 and larger for x = 0.5 and x = 0.75, see ESI.†

The total and projected DOS of the investigated oxides are reported in Fig. 5. Since the oxygen atoms of chromate and sulfate are not electronically equivalent, we have analyzed separately those belonging to the CrO₄²⁻ tetrahedra, hereafter O_Cr, from those coming from SO₄²⁻, hereafter O_S. On overall, for the mixed m-PbCr_(1−x)S_xO₄ species the valence band is mainly composed of p orbitals of both O_Cr and O_S in different ratios depending on the composition, with a small contribution from Pb s orbitals.

Fig. 5 Total and projected density of states for the m-PbCr_(1−x)S_xO₄ and o-PbCr_(1−x)S_xO₄ structures. Contribution of the main orbitals to the valence and conduction bands. PDOS have been aligned using the Pb d (spin down) peak taking as reference that of m-PbCrO₄. The zero has been set to the top of the valence band of m-PbCrO₄. O_Cr and O_S are referred to the oxygen bonded to Cr and S, respectively.

The composition of the conduction band of the mixed species is quite stable with the progressive substitution of chromium by sulfur and show almost exclusively contributions from the O_Cr p and the Cr d states with a minor participation of the Pb p orbitals, analogously to that found for the reference m-PbCrO₄. For the m-PbCr_(1−x)S_xO₄ species, we therefore find, up to a minimal Cr concentration (0.25), a conduction band up-shifted with respect to pure m-PbCrO₄ due to the reduced density of the contributing Cr states. In m-PbSO₄ the composition of the conduction band completely differs from that containing chromium being mainly due to the Pb p orbitals, as discussed above for the orthorhombic phase, o-PbSO₄.

To analyze in details the partial DOS (PDOS) of the mixed species, the areas of the PDOS with respect to the total DOS in defined regions of energy have been integrated (see the integration limits in ESI†) and expressed in percentages with reference to the total areas of the accounted band. For the monoclinic phase, in the region of the valence band in between ca. −1.2 and 0.4 eV PDOS of O_S contribute for 0%, 6%, 49%, 72% and 93% to the total DOS going from x = 0 to x = 1 while the PDOS of O_Cr contribute for 89%, 84%, 42%, 19% and 0, showing a good correlation with the CrO₄²⁻ amount in the crystalline cell. The contribution of Pb 6s orbitals in this energy region is constant at ∼5%. In the conduction band region between ca. 1.5 and 3 eV, for all the species containing CrO₄²⁻, the PDOS of Cr is constant contributing 51–52%, independently from the amount of CrO₄²⁻, also the PDOS of O_Cr consistently contribute to the conduction band (36–31%) while the Pb d orbitals contribute for 8%. This Pb contribution is originated from the antibonding counterpart of the Pb–O_Cr mixing induced by Cr, as discussed for m-PbCrO₄, and is therefore not present for PbSO₄. Indeed, for the PDOS of m-PbSO₄ only a single band at ca. 10.2 eV is observed, 93% O_S p and 7% Pb, whose character is similar to that of the orthorhombic phase.

For the o-PbCr_(1−x)S_xO₄ systems, the highest-energy peak in the valence band, characteristic of the total DOS o-PbCrO₄ structure is maintained, even though smoothed, only for the species with x = 0.25. The valence band character is essentially oxygen and in the intermediate mixed species the composition in terms of O_Cr/O_S reflects the ratio of chromate/sulfate of the considered system. For the o-PbCr_(1−x)S_xO₄ species (x = 0.00–0.75), we evaluated the contribution of the Cr, O and Pb by integrating the conduction band areas of the PDOS, with integration limits 1.5–3.0 eV. The Cr states constantly contribute for ∼51% to the conduction band of all the oxides, 37–35% is the contribution of O_Cr, and 9–10% is that of Pb. It is interesting to notice that independently to the presence of S or Cr, the character of the conduction band of the mixed o-PbCr_(1−x)S_xO₄ species (x = 0.0–0.75) is the same, analogously to that of the monoclinic phase; we observe only a decrease in the density of the Cr and O_Cr states.

The composition of the orthorhombic valence and conduction bands is very similar to that retrieved for the monoclinic structure, the up-shift of the conduction band is essentially related to the lower number of Cr and O_Cr states contributing to the conduction band and this decrease is probably related to the lightening of the CY pigment by increasing the amount of sulfate.¹⁴ Incidentally, SR-DFT calculations provide a qualitatively similar electronic properties as calculated including spin–orbit coupling, see ESI.†

On overall, our calculations do not show any peculiar electronic features between monoclinic and orthorhombic series which could explain the different inclination to degradation. We therefore believe that other reasons, probably related to the morphology of the materials, make the orthorhombic phase, with an amount of SO₄²⁻ larger than x = 0.4, more prone to photo-induced blackening.

4. Summary and conclusions

We have investigated the interplay of structural, chemical composition and electronic factors in determining the properties of the Chrome Yellow (CY) pigments. PbCr_(1−x)S_xO₄ compounds (x = 0, 0.25, 0.5, 0.75 and 1) have been taken into account both in a monoclinic and an orthorhombic phase. To shed some light on the reduction of chrome from Cr(VI) to Cr(III) that takes place at high sulfur concentration and that is associated to the pigment darkening we have investigated in depth the changes of the structural and electronic properties of the studied species. The band gap of the lightfast and deep yellow m-PbCrO₄ reveals that the valence band is mainly composed by O with minor contributions of the Pb s orbitals, while the conduction band is instead formed by Cr d and O p orbitals with a small contribution from the Pb p orbitals. The introduction of sulfur leads to a slight decrease of the volume cell and a progressive increase of the band gap, which accounts for the shift of color toward lemon yellow. In all the mixed species, the composition of the valence and conduction bands are very similar to that of pure m-PbCrO₄. Interestingly, while both the oxygen bounded to sulfur and to chromium participate in the valence band, only those from the CrO₄²⁻ octahedra are involved in the conduction band. The conduction band of PbSO₄, stable in the orthorhombic phase, has an obviously different character being mainly contributed by Pb p orbitals. An energy upshift of ca. 2 eV compared to that of m-PbCrO₄ is associated to this compositional change. The orthorhombic phase of the mixed species also shows an increase of the band gap upon increasing the amount of sulfur. The band gap of o-PbCr_(1−x)S_xO₄, is lower, equal and higher than their monoclinic counterparts for x = 0, 0.25 and >0.5, respectively. The compositions of the bands are very similar to those of their monoclinic counterparts but the conduction band shows a progressive increase/decrease of the p O_Cr/Pb orbitals.

Both the introduction of sulfur and the change of phase induce an up-shift of the conduction band. Taking the top of the conduction band as an estimate of the material reduction potential, our data suggest that (photo) reduction becomes more difficult for the species with high sulfur concentration or with an orthorhombic phase. On overall, we can conclude that in a purely electronic picture, PbCrO₄ is more prone to light induced reduction than the sulfate analogues. A possible explanation of the higher light sensitivity of sulfate-rich CYs (x > 0.4) pigments may then lay in an higher tendency to release CrO₄²⁻ anions into the paint matrix which could be the actual responsible of the photoredox process experimentally observed. Thus, other properties of the PbCr_(1−x)S_xO₄ system will be modeled such as the effect of sulfate substitution on both thermodynamic and kinetic solubility of the pigment into the organic binding medium. We hope that our study, providing a quantitative description of the electronic structure of the pigment models, being able to follow how the electronic properties respond to compositional and structural modifications, may complement the analytical and spectroscopic data and provide an alternative perspective in the pigments analysis.

Acknowledgements

AA and SF thank MIUR-PRIN 2010–2011 Project No. 20104XET32 “DSSCX” and the CINECA award under the ISCRA initiative for the availability of high performance computing resources and support. Authors thank Paolo Umari for helpful discussions.

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Footnote

† Electronic supplementary information (ESI) available: Cell parameters for the experimental and optimized cells. Relative stabilities of the m–o-PbCr_0.5S_0.5O₄ compounds. Band structure and DOS of the limit structures at the experimental cells. Composition of the first peaks of the valence and conduction bands for all the studied species. Valence, conduction band and band gap energies vs. composition for the monoclinic and orthorhombic mixed structures. Main geometrical parameters for all the mixed structures. See DOI: 10.1039/c6ra01444e

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