In order to create a painting, an artist must carefully select his painting materials and especially those materials that convey color to the painting and help create other optical effects. In the 15^th-17^th century, most colored pigments were inorganic in nature, many of them powdered minerals Among painters’ pigments, commonly available materials are present such as earth colours, and bone black, but also fairly rare ones such as the red pigment vermillion/cinnabar or the blue pigment ultramarine.

The most expensive pigment of many historical periods is without any doubt natural ultramarine, sometimes referred to by its mineral names lazurite or lapis lazuli [1]. Lazurite is an alumino-silicate mineral containing zeolite cages in which sulphur polyanions are present that give it its characteristic blue colour. In the 15-17^th century, natural ultramarine was a material more expensive than gold. It derived its scarcity and hence its very high price from the fact that the only known mines of natural ultramarine were located in a remote northeastern Afghan province called Badakhshan. In the 15-17^th century, most natural ultramarine was transported along the silk road and reached Europe via Venice [2]. What was traded in this manner were either large lumps of the blue/white lazurite-rich rocks (that also contain other minerals) or already (partially) purified lazurite powder. In Venice and other locations in Europe, by means of the application of various crushing and particle selection techniques [3], the purity of the blue pigment was then improved, creating different grades of ultramarine of widely different price.

By means of Macroscopic X-ray powder diffraction (MA-XRPD), it is possible to record the distribution of crystalline materials in historical paintings and thus to identify which inorganic pigments were employed by an artist to create a specific work of art. In recent years, this method has been employed by our group to identify the inorganic pigments present in masterworks by artists such as Vincent Van Gogh [4],(19^th century), Johannes Vermeer [5] (17^th century) and Jan Van Eyck [6] (15^th century).

Of particular usefulness for highly specific pigment mapping of oil paintings is reflection mode MA-XRPD. Although dependent on the diffraction characteristics of the pigments studied and on the measurement conditions, in this mode, the detection limit of scanning MA-XRPD is of the order of 2-5%. Next to allowing for a direct identification of the pigment mixtures that constitute the paint of a particular hue, this ability to detect and identify minor components in a complex mixture makes it also possible to employ MA-XRPD to record fingerprints of specific pigments and highlight art historically relevant differences between pigment subtypes. For example in Vermeer’s Girl with the Pearl Earring, it was possible to establish that Vermeer used at least two distinctly different subtypes of lead white to paint the Girl’s face: one hydrocerussite-rich (2PbCO₃.Pb(OH)₂) to paint the lighter/highlighted facial areas and another, poorer in hydrocerussite and richer in cerussite (PbCO₃) which is used in the shadow areas [5,7].

Since natural ultramarine pigment powder is invariably prepared by purification of (heat-)crushed lazurite-rich Afghan rocks, the resulting powder not only contains microcrystals of the blue mineral lazurite, but also of its accessory minerals such as albite, sodalite, diopside, pyrite, quartz, sanidine etc. Some of these share the structure and overall chemical composition of the blue alumino-silicate mineral while others are quite different. All of these accessory minerals, however, lack the intense blue color of lazurite and thus alter the color intensity and tone of the blue pigment when they are (too) abundantly present.

Through MA-XRPD mapping of blue areas of a series of Netherlandish paintings by well-known 15^th and 17^th century artists from various museums in Belgium and the Netherlands, we have made a non-exhaustive survey of the presence of the pattern of accessory minerals that are present in 15^th and 17^th century natural ultramarine. The aim of the survey was to answer questions such as: (a) does the fingerprinting pattern of the accessory mineral change with time?, (b) and if so, does it change gradually or erratically? and (c) is the pattern significantly affected by the application of the purification methods? In the presentation, preliminary answers to some of these questions will be discussed by means of examples from the oeuvre of 15^th-17^th century artists Petrus Christus, Albrecht Bouts, Jan Steen and Johannes Vermeer.

[1] Kirby, J., Nash, S., Cannon, J. (eds.) (2010) Trade in Artists’ Materials. London: Archetype Publications.

[2] Matthew, L. and Berrie, B., in [1], pp. 245-252.

[3] Gambardella A. et al. (2020). Science Advances 6, eaay8782.

[4] Vanmeert et al. (2018). Angewandte Chemie Int. Ed. 57, 7418-7422.

[6] De Meyer et al. (2019). Science Advances 6, eaax1975.

[7] Van der Snick et al. (2020). Science Advances 6, eabb3379.

[8] Van Loon A. et al. (2019). Heritage Science 7, 102.

Cultural heritage objects are affected by various corrosion processes during decades and centuries of storage in museums and collections. Atmospheric gases like CO₂, moisture or - as wood emits significant amounts of formic and acetic acid¹ - the storage furniture itself can induce corrosion. Calcareous heritage objects like historic Mollusca shells², eggs³, ancient pottery (Figure 1, a) or marble reliefs (Figure 1, c, d) are very sensitive to acetic and formic acid vapours. The corrosion process leads to the formation of efflorescence crystals sometimes crystallizing in pores and cracks, which can cause severe damage to the artifacts. This phenomenon has been known as “Byne’s disease” since the end of the 19^th century.⁴ Both, simple salts like Ca(CH₃COO)₂∙H₂O⁵ or Ca(CH₃COO)₂∙½H₂O⁶ and complex compounds like calclacite (Ca(CH₃COO)Cl·5H₂O)⁷ or thecotrichite (Ca₃(CH₃COO)₃Cl(NO₃)₂·6H₂O)^8-9 were found as corrosion phases on calcareous historic objects. Many of these efflorescence phases, however, still remain poorly characterized due to their microcrystalline character and the occurrence of polyphase mixtures.

Our work focuses on the characterization of unknown or hitherto poorly characterized efflorescence phases found on herriatge objects. As the amount of substance that can be removed from the artifacts is usually very small, we also describe the synthesis of the corrosion phases by model experiments. In this study we present the characterization and structure elucidation of complex efflorescence salts like Ca₂(CH₃COO)(HCOO)(NO₃)₂·4H₂O¹⁰, Ca(CH₃COO)(HCOO)·2H₂O and Ca₃(CH₃COO)₄(HCOO)₂· 4H₂O¹¹ that were found on ancient amphorae (Figure 1, a) or historic birds eggs⁵ and seemingly simple corrosion phases like Ca(CH₃COO)₂∙½H₂O¹² which crystallizes on marble reliefs (Figure 1, c, d) or ceramics⁶. A systematic structural investigation of these efflorescence phases revealed calcium carboxylate zig-zag chains (Figure 1, b) as the common structural motif, which shows the crucial role of the carboxylic acids in the corrosion processes and explains the great chemical variety of these compounds. The seemingly simple Ca(CH₃COO)₂·½H₂O was found to crystallize in a 11794.5(3) ų unit cell with a triple helix motif (Figure 2, e) analogous to the collagen proteins.

In summary, the investigations on corrosion phases found on cultural heritage objects led to the discovery of many hitherto unknown or only poorly characterized solid phases with complex crystal structures. In addition, global structural motifs that were revealed in these studies indicate that a lot more compounds are to be discovered.

References

(1) Gibson, L. T.; Watt, C. M., Acetic and formic acids emitted from wood samples and their effect on selected materials in museum environments. Corrosion Science 2010, 52 (1), 172-178.

(2) Tennent, N. H.; Baird, T., The deterioration of Mollusca collections: identification of shell efflorescence. Stud. Conserv. 1985, 30 (2), 73-85.

(3) Bette, S.; Mueller, M. X.; Eggert, G.; Schleid, T.; Dinnebier, R. E., Efflorescence on calcareous objects in museums: crystallisation, phase characterisation and crystal structures of calcium acetate formate phases. Dalton Trans. 2019, 48, 16062-16073.

(4) Byne, L. F. G., The corrosion of shells in cabinets. Journal of Conchology 1899, 9, 172-178.

(5) Tennent, N. H.; Baird, T., The deterioration of Mollusca collections: identification of shell efflorescence. Studies in Conservation 1985, 30 (2), 73-85.

(6) Boccia Paterakis, A.; Steiger, M., Salt efflorescence on pottery in the Athenian Agora: A closer look. Studies in Conservation 2015, 60 (3), 172-184.

(7) Giuseppetti, G.; Tadini, C.; Ungaretti, L., La struttura cristallina della calclacite/ Crystalline structure of a triclinic phase of the compound corresponding to calclacite, Ca(CH3COO)​Cl.5H2O. Periodico di Mineralogia 1972, 41, 9-21.

(8) Gibson, L. T.; Cooksey, B. G.; Littlejohn, D.; Linnow, K.; Steiger, M.; Tennent, N. H., The Mode of Formation of Thecotrichite, a Widespread Calcium Acetate Chloride Nitrate Efflorescence. Studies in Conservation 2005, 50 (4), 284-294.

(9) Wahlberg, N.; Runčevski, T.; Dinnebier, R. E.; Fischer, A.; Eggert, G.; Iversen, B. B., Crystal Structure of Thecotrichite, an Efflorescent Salt on Calcareous Objects Stored in Wooden Cabinets. Crystal Growth & Design 2015, 15 (6), 2795-2800.

(10) Bette, S.; Eggert, G.; Fischer, A.; Stelzner, J.; Dinnebier, R. E., Characterization of a new efflorescence salt on calcareous historic objects stored in wood cabinets: Ca 2 (CH 3 COO)(HCOO)(NO 3 ) 2 ·4H 2 O. Corrosion Science 2018, 132, 68-78.

(11) Bette, S.; Müller, M. X.; Eggert, G.; Schleid, T.; Dinnebier, R. E., Efflorescence on calcareous objects in museums: crystallisation, phase characterisation and crystal structures of calcium acetate formate phases. Dalton Transactions 2019, 48 (42), 16062-16073.

(12) Bette, S.; Stelzner, J.; Eggert, G.; Schleid, T.; Matveeva, G.; Kolb, U.; Dinnebier, R. E., Corrosion of heritage objects: collagen-like triple helix found in the calcium acetate hemihydrate crystal structure. Angewandte Chemie International Edition 2020.

Seven and fivefold point symmetries are incompatible with three-dimensional translation symmetry and thus very rare as symmetry elements of building blocks in tilings and pavings. Heptagonal symmetry elements as local symmetry elements in isolated objects in art, architecture and nature appear surprisingly much less frequently than pentagonally shaped designs. This presentation aims to give some objective, but also subjective reasons why architects, designers and artists rarely choose for local heptagonal symmetry in their creations. It is argued that reasons that are commonly put forward as explanation for the choice for heptagonal symmetry are too simplistic and probably not true. A number of examples is presented where the designer has chosen for heptagonal symmetry as a key element for creation and reasons for these choices are proposed where possible. Special emphasis will be given to two outstanding heptagonal religious edifices in French Occitany and larger heptagonal urban geometries in the low countries.

Beauty of our world we can see everywhere, but always two points of view are among scientists and artists, who is better: nature or human in the process of creativity. In our work we present three-shell clusters in intermetallic compounds and compare it with ivory puzzle balls. The crystal structures of all these intermetallic compounds were studied by single crystal method and confirmed by X-ray powder diffraction. Li₂₀Mg₆Cu₁₃Al₄₂ [1] (sp. gr. Im-3, a = 13.8451(2) Å) crystallizes as an ordered version of Mg₃₂(Al,Zn)₄₉, Mg₉Ni₆Ga₁₄ (sp. gr. Fd-3m, a = 19.8621(1) Å) and Mg₃Ni₂Ga (sp. gr. Fd-3m, a = 11.4886(17) Å) crystalizes in the own structure types. All these structures can be described as three-shell clusters: [CuAl₁₂@Li₂₀Cu₁₂@Al₆₀] (fig. 1a) for the Li₂₀Mg₆Cu₁₃Al₄₂, [Ni₆Ga₆@Mg₂₀@Ni₁₈Ga₄₂] (fig. 1b) for the Mg₉Ni₆Ga₁₄ and[Mg₆@Ni₁₂Ga₆@Mg₃₆] (fig. 1c) for the Mg₃Ni₂Ga. Very easy to see, that the kind of packing of core shells for all these clusters is very similar to well-known human masterpiece ivory puzzle balls which are very popular in China (fig. 1d), but also known in Europe as “contrefait Kugeln” (fig 1e), which are created on the base of Johannes Kepler’s Platonic Solids model of the Solar system from Mysterium Cosmographicum (fig 1f) [2]. The last one consists as second and third spheres octahedron and icosahedron like in first and second spheres of [Mg₆@Ni₁₂Ga₆@Mg₃₆] cluster and as forth spheres dodecahedron with pentagons and hexagons which also form third sphere of [CuAl₁₂@Li₂₀Cu₁₂@Al₆₀] and [Ni₆Ga₆@Mg₂₀@Ni₁₈Ga₄₂] clusters.

Figure 1. Atomic structure of a three-shell clusters [CuAl₁₂@Li₂₀Cu₁₂@Al₆₀] (a), [Ni₆Ga₆@Mg₂₀@Ni₁₈Ga₄₂] (b), [Mg₆@Ni₁₂Ga₆@Mg₃₆] (c), Chinese ivory puzzle ball (d), Ivory puzzle ball from German workshop (e), Johannes Kepler’s Platonic Solids model of the Solar system (f).

The results of electronic structure calculations for Li₂₀Mg₆Cu₁₃Al₄₂, Mg₉Ni₆Ga₁₄ and Mg₃Ni₂Ga confirm the three-shell clusters.

[1] Pavlyuk, N., Dmytriv, G., Pavlyuk, V., Ehrenberg, H. (2019). Acta Crystallogr. B75, 168.

[2] Sparavigna, A. C. (2018). hal-01825008.

Keywords: three-shell cluster; single crystal; intermetallic compound; lithium; magnesium

Funding for this research was partially provided by National Science Centre, Poland (No. 2017/25/B/ST8/02179).

Possibly for recreational purposes, the very well established crystallographer Emil Makovicky has for the last 30 to 40 years turned his formidable analytical skills to the classification of the symmetries that underlie patterns of Islamic building ornaments and Hans Hinterreiter’s graphical art. These patterns can be characterized as being more or less periodic in two dimensions (2D), see e.g. [1-5]. He stated in [2] that “in performing the symmetrological analysis, we should stay on the same level of accuracy on which the creator of the pattern worked”. He had to concede, however, more than 30 years ago that this “certainly brings a certain subjectivity into the process: we should not shun away from it because such a degree of abstraction from imperfections of certain degrees and kinds underlies the entire practice of natural sciences wherefrom the science of symmetry originated” [2]. Utilizing recently developed information theory based approaches to crystallographic symmetry classifications in 2D [6,7], one can now replace that subjectivity with the objectivity that comes from calculations that involve all pixel intensity values of digital images of such patterns.

These information theory based approaches to crystallographic symmetry classifications utilize geometric Akaike Information Criteria (G-AICs), which are in essence first-order geometric bias corrected sums of squared residuals between the raw image data and symmetrized versions of this data. G-AIC value ratios are used for the selection of symmetry models to represent the raw data, whereby the need to estimate the level of the “generalized noise“ is removed by algebraic means whenever non-disjoint models are involved. Performing the symmetry model selection in reciprocal/Fourier space and basing it exclusively on the structure-bearing complex-valued Fourier coefficients of the image intensity has the advantage of suppressing much of the generalized noise just by calculating the discrete Fourier transform, which is the first step of translation averaging. Symmetrizing the Fourier coefficients and transforming them back into direct space is equivalent to averaging over the asymmetric units.

A simple definition of generalized noise is that it sums up all variations of the intensities of all individual image pixels that are left unexplained by a correct plane symmetry classification. This type of noise is the sum total of all effects of the recording and processing of the digital image and also includes all disturbing effects of “structural defects” in the underlying patterns. For the methods to work (at their current state of development), this kind of noise needs to be considered as approximately Gaussian distributed. Given that there are many sources of that kind of noise with different distributions and that the contribution of none of these sources dominates, this assumption is justified by the central limit theorem.

The new methods allow for objective, i.e. researcher independent, classifications of the full range of crystallographic symmetries, i.e. Bravais lattice type, Laue class, and plane symmetry group, of “noisy” real-world patterns. The identification of the plane symmetry group that can with the highest likelihood, i.e. minimized Kullback-Leibler information loss [6,7], be assigned to a noisy digital 2D periodic image of that pattern by an information theory based method enables the most meaningful crystallographic averaging in the spatial frequency domain.

Considering that it is fundamentally unsound to assign an abstract mathematical concept such as a single symmetry type, class, or group with 100 % certainty to a piece of art or the work of artisans, the information theory based approaches to crystallographic symmetry classifications deliver probabilistic (rather than definitive) classifications. This means that numerically derived confidence levels of the classifications within individual symmetry hierarchy branches are provided with each classification result so that the researcher is presented with objectively derived information, which may be used at the researcher’s discretion.

The paper demonstrates the objective classification of a few Islamic building ornaments and examples of Hans Hinterreiter’s graphical art. It is hoped that this will be helpful to the recreation of busy conference participants at the 25^th World Congress and General Assembly of the International Union of Crystallography. Using some of Emil Makovicky’s words from the second direct quote above, information theory based crystallographic symmetry classifications are poised not only to help resolve controversies in the symmetrology of art and cultural artifacts field [8], but also in the “natural sciences wherefrom the science of symmetry originated” [2].

[1] E. Makovicky, The crystallographic art of Hans Hinterreiter, Zeits. für Kristallogr. 150 (1979) 13–21.

[2] E. Makovicky, Symmetrology of art: coloured and generalized symmetries, Computers Math. Applic. 12B (1986) 949–980.

[3] E. Makovicky, Ornamental Brickwork, Theoretical and applied symmetrology and classification of patterns, Computers Math. Applic. 17 (1989) 955–999.

[4] E. Makovicky, Symmetry through the eyes of the old masters, Berlin: De Gruyter, 2016.

[5] E. Makovicky and M. Ghari, Neither simple nor perfect: from defect symmetries to conscious pattern variations in Islamic ornamental art, Symmetry: Culture and Science 29 (2018) 279–301.

[6] P. Moeck, Towards generalized noise-level dependent crystallographic symmetry classifications of more or less periodic crystal patterns, Symmetry 10, paper 133 (46 pages) (2018), DOI: 10.3390/sym10050133, open access.

[7] P. Moeck, On classification approaches for crystallographic symmetries of noisy 2D periodic patterns, IEEE Transactions on Nanotechnology 18 (2019) 1166–1173, DOI: 10.1109/TNANO.2019.2946597, see also http://arxiv.org/abs/1902.04155, August 31, 2019 for an expanded version of this review.

[8] E. Makovicky, Comments on decagonal and quasi-crystalline tilings in medieval Islamic architecture, Science 318, Art. no. 1383a, (2 pages) 2007, DOI: 10.1126/science.1146262.

Fully non-invasive multi-analytical approach combining spectroscopic (FT-IR, Raman) and X-ray-based (MA-XRF, XRPD) techniques was used to study a number of miniature portraits from Czech collections.

The portrait miniatures of the late sixteenth to the nineteenth century represent a highly specific and significant field of European fine art. After 1700, ivory plates were introduced and became the most frequent support of the eighteenth and the nineteenth centuries. Watercolour and gouache were the most common techniques; however, the use of oil has also been recorded.

It is the ivory-painted miniatures that are a special challenge for XRPD - not only because the painting layers are very thin and the ivory signal can interfere the signal from the phases in the painting layer, but also because ivory is a hygroscopic material whose dimensions and curvature respond to changes in environmental conditions (temperature, relative humidity) even during the measurements. We have therefore created a special methodological procedure for measuring miniatures painted on ivory, which we plan to present together with the most interesting results. XRPD helped to identify rare pigments, degradation products and even the binder used thanks to the evidence of metal soaps’ formation in paint layers.

Figure 1 X-ray pattern measured in yellow-green curtains in the background. The XRPD identified lead white (H), mixed Pb-Sb-Sn yellow (Y), earth pigments represented by mica (M) and kaolinite (K) and lead soaps (S) formed by interaction of fatty binder (oil) with Pb-based pigments.

Keywords: X-ray diffraction, X-ray microdiffraction, non-invasive analysis, miniature painting, metal soaps

The study was supported by the Ministry of Culture of the Czech Republic, NAKI II programme, project No. DG18P02OVV034.