3.1 XRD: Mineral modes of red chalks
All chalk samples are composed of varying proportions of quartz, clay minerals (illite, kaolinite, and/or dickite) and hematite (Fig. 3a; Appendix, Fig. 3b). Additional rutile, TiO2, is a minor phase in most analyzed samples. Remarkably, the Theley1 and 2 natural chalks contain significantly more hematite and less quartz than the Frankenalb and fabricated chalks. The Theley2 sample additionally contains goethite, which presumably formed at the expense of former hematite during weathering in a near-surface environment. The Frankenalb chalk tends to contain more quartz and clay minerals and significantly less hematite than samples from Theley. In the fabricated chalk, dickite and kaolinite are the dominant clay minerals whereas illite is absent. Quartz contents are remarkably high. The additional presence of corundum in the fabricated chalk is likely attributable to an abrasion of the grinding gear used during production of the chalk sticks. The chalks also display differences with respect to the proportions of amorphous material: The lightest-colored chalk (Frankenalb), which has greater amounts of silicates, shows the highest contents of amorphous material, and the fabricated chalks the lowest. The variability in the mineral modes is generally higher in the natural than in fabricated chalk samples.
3.2 SEM-EDX: Mineral composition, textures and topography of the chalks
3.2.1 Mineralogical composition
The mineral phases of the three chalk types Frankenalb, Theley1, and fabricated, identified via SEM-EDX, correlate well with the XRD results (see 3.1). At high magnifications, it was possible to identify individual mineral grains of quartz and illite, present in variable but mostly highest proportions. Grain sizes are mostly in the micrometer to sub-micrometer range. Minor phases are kaolinite and rutile (Fig. 4). Hematite is present as small platelets, with strongly variable grain sizes, ranging from sub-millimeter up to 5 micrometer.
For each phase, the grain size and amount vary strongly both within individual samples and among different samples. Frankenalb chalk exhibits grain sizes from < 1 µm for the round hematite particles, up to 15 µm for the flaky illite and 10 µm for the kaolinite (Fig. 4a). Theley1 featured only a few large grains (average = 1 µm); overall, it consisted of small, uniform grains that contributed considerably to a closed, compact surface of the chalk stroke (Fig. 4b). In the fabricated chalk sample, angular quartz fragments exhibit a large grain size of up to 20 µm. The sub-rounded hematite and clay mineral particles, in contrast, are only about 0.5–2 µm in size and homogenously distributed (Fig. 4c). It was not possible to detect an accumulation of hematite in any of the samples.
3.2.2 Effect of smudging on chalk distribution
In all of the red chalk strokes, the mineral particles accumulated along the papermaking fibers on the paper surface. The degree to which the particles were dispersed during smudging varies as a function of the grain form and size, an effect most easily discernible in the areas between the red-chalk strokes. The coarse-grained Frankenalb chalk shows some grains scattered between the chalk strokes, although most of the grains remain where they had been laid down (Fig. 5a). The fine-grained Theley1 shows only a few grains scattered by smudging (Fig. 5b), due to the greater adhesive forces between the small-sized particles. In comparison, the grains in the fabricated red chalk are scattered to the greatest degree (Fig. 5c). The variability of the grain sizes in the sample, with particle sizes of up to 20 µm in diameter, results in significantly lower adhesive forces among the grains.
3.2.2 Effect of wet application on chalk topography
It is evident from the SE images that the wet application method results in a change in the dispersion of the mineral grains. The application of the chalk strokes resulted in a more extensive abrasion of the chalk and therefore thicker coating of the paper. Chalk banks are not – in contrast to the chalk strokes in the dry applications – oriented in the direction of the papermaking fibers. The surface of the chalk strokes of both natural samples, Frankenalb and Theley, is relatively even and massive. A fragile topography is found only in the marginal areas of the chalk applications (Figs. 6a and b). In contrast, the wet application surface of the fabricated chalk is uneven and rough, probably due to the abundant coarse quartz particles (Fig. 6c). These different topographical features of the three red chalks will have a major impact on their lightness and color saturation. Smooth surfaces (e.g., wet chalk strokes) tend to appear darker because they show a greater amount of light reflection than rough (e.g., dry chalk strokes, fabricated chalk) surfaces that show a greater amount of light scattering [26].
3.3 FORS: Spectral features of the red chalk drawing mockups
The four chalk types (see Table 1) show slightly different spectral properties, influenced by their composition, application technique, and the paper support. First, the differences between the types of chalk were observed; for the sake of readability, here they are represented by the median spectra of the dry application on modern paper (Fig. 7). The curve shapes of the reflectance spectra of the red-chalk mockups differ most significantly at the start of the rise at 550 nm, and with respect to the form of the slope of the rise between 600–750 nm, as well as following the second rise, between ca. 760–950 nm (indicated by arrows).
The red chalk types could not be divided into groups solely based on the values for the maximum in the first derivate, even though trends were identified (Fig. 8a; breakdown regarding application technique and chalk type, see Fig. 8b in the Appendix). The peak heights and positions for the natural chalks were found to be similar, and in general, they were more widely dispersed than those of the fabricated chalks; the latter tend to display higher values with respect to these two points, with the smallest variation in the peak shift. The shift in the peak of the first derivative was overall quite small and occurred between 577 nm and 589 nm. With our samples, there was no link between the hematite content and the position or the height of the maximum, as implied by studies using mixtures of synthetic sediments and very minor parts (up to 1%) of hematite and goethite [17 p631]. The shift induced by application technique was greater than that which was induced by compositional differences of the chalk type. In samples with a lower maximum, this maximum tends to move towards the higher wavelengths (see Fig. 8b, Appendix). All of the wet and oiled chalk applications have lower peaks at higher wavelengths, whereas all of the dry and smudged applications have higher peaks at lower wavelengths. The fabricated red chalk with synthesized hematite was the only sample that displayed notably higher maximum readings. The production process of this chalk, optimized for color brightness and a more homogeneous product, assumedly could explain this.
The form of the first derivative of the spectra differed in accordance with the type of chalk and bundled sufficiently to facilitate their classification using PCA. The spectral curves could be best distinguished in the measurements taken from the smooth and dense applications of wet chalk strokes (Fig. 9a; other applications, see Figs. 9b–d in the Appendix).
The shape of the spectral curves was also influenced by the chalk application technique (dry, smudged, wet, and oiled), as illustrated for the Theley1 measurements (Fig. 10a; other chalks, see Figs. 10b–d in the Appendix). Compared to the dry chalk strokes, the ones compacted by wetted or oiled application shifted the first slope rise towards higher wavelengths (see left arrow), and increased the absorption maximum in the near-infrared range (see right arrow). The spectra of the smudged chalks that featured more paper show-through displayed a steeper slope rise that started at lower wavelength (ca. 610 nm) and flattened out at 750 nm with a lower minimum in the subsequent higher area.
The paper type has an effect primarily on the dry and smudged red chalk samples, which can probably be attributed to the paper partially showing through the chalk. The blank modern paper features a higher reflectance in the low nm range than the blank historical paper, and a lower reflectance in the high nm range (Fig. 11). As can be expected, these trends influence the spectral curves of the dry chalk applied to the two papers. In the first derivative, the historical paper, in contrast to the modern paper, tends to give rise to a lower peak with a shift at higher wavelengths in the dry application types.
3.4 FORS: Interpretation of FORS spectra on the basis of CIELAB
The visual color perception of the red chalk mockups can be expressed in CIELAB values (Fig. 12).
Based on this system, it is possible to detect differences between the red chalk types. The Frankenalb chalk exhibits overall high L*a*b* values. They scatter less than the Theley chalks, which show the greatest variance and the lowest values for all three color properties of all the chalk types, caused by oiled and wet applications. The notable differences in hematite content cannot be seen expressed in the a*-values. As other research groups studying hematite-deferrated soil mixtures have shown [27], this could be due to amounts of hematite close or above a saturation point (10%), where only little fluctuation in color can be observed. However, the hematite-rich Theley samples exhibit readings with clearly lower L*a*b*-values than the other two samples and therefore appear darker and less saturated. It is notable that a higher content of non-tinting minerals are indicated by higher trending L*-values for the Frankenalb and fabricated red chalks. It is possible that, at these high hematite concentrations, other factors (topography, particle shape) have stronger influence on the color appearance of red chalks than the hematite content. The fabricated chalk shows the least scattering which can be explained by its homogeneous composition (see 3.1 and 3.2). The greatest variation between the color values, however, can be explained by the different application techniques. Within each of the chalk types, the measuring points for the dry and smudged application techniques tend to have higher L*a*b* values than those for the wet and oiled applications.
3.5 Principal component analysis of red chalk mockups
For all chalk application techniques and paper types, PCA sorts the chalks into well-defined clusters in keeping with the chalk type (Fig. 13). Overall, three principal components explain 99% of the variance, whereby PC-1 explains 58%, but PC-2 and PC-3, taken together, still explain a significant amount, namely 41% of the variance. The Theley1 and Theley2 chalks, which stem from the same geological area, make up one point cloud. The differences between these two and the two other chalk types are represented primarily in PC-2 and PC-3. The fabricated chalks showed more pronounced clustering than the natural red chalks, indicating lower variance of surface topography within this red chalk type.
Within each group, the measuring points are dispersed in an elongated point cloud, sorted by the chalk application technique. The points spread along the axis of PC-1, which explains most of the variance. The dry chalk applications can, to an extent, be differentiated from the wet chalk applications. It is also possible to distinguish the applications on historical paper (the unfilled symbols) from the samples on modern paper.
The loadings plot (Fig. 14a) was used to interpret the scores plot. It shows which wavelength ranges of the first derivative have an impact on the scores for each PC. In sum, PC-1 indicates differences in peak height (Fig. 14b in the Appendix), PC-2 differences in peak width and PC-3 differences in peak position (Fig. 14c in the Appendix).
For PC-1, the loadings plot, which followed the curve shape of the first derivative, showed that values around the maximum (at about 570 nm) of the investigated wavelength range had the greatest impact: Samples with positive PC-1 scores in these areas had higher than average values. This value is directly related to the chalk application technique: For PC-1, the chalk strokes with rough surface (dry) or low coverage (smudged) showed the highest values, and the chalk applications that were compact and featured high coverage show the lowest values. Where the loadings plot for PC-1 showed a maximum, the loadings plot for PC-2 described a minimum in the negative region of the y-axis, slightly shifted toward the higher wavelengths (at 584 nm). The loadings plot curve intersects the x-axis at 564 nm and at 603 nm. There are two maxima, one at 545 nm, and one at 623 nm, whereby the maximum in the higher wavelength range has a higher impact on the PC-2 scores than the lower one. The two maxima in the PC-2 loadings plot mark differences in the width of the first derivative’s maxima of the samples. High impact loadings values in those ranges next to the actual maximum in the first derivative make it possible to describe the width of the curve, which was the important attribute for the determination of the chalk type in the analysis of the mockups. In the loadings plot for PC-3, the maximum from the loadings plot for PC-1 describes the curve’s point of inflection (at 578 nm). The reflectance values before that point positively correlate with PC-3, with a maximum at 553 nm, and the values after that point correlate negatively, with a minimum at 604 nm. Thus, PC-3 explains differences in the peak position. The higher the wavelength range of the maximum, the lower the value is for PC-3. Variances in the FORS spectra that could be visualized with PCA are also reflected in the CIELAB values. PC-1 correlates directly with the chromaticity values of the same measuring points and to a lesser degree with the lightness values: The higher the CIELAB values, the higher the PC-1 values (Fig. 14d in the Appendix).
Since it was also possible to determine the impact of the application technique and paper type within a particular chalk, these factors were subjected to PCA analysis with the exclusion of other factors (that is to say, all of the application techniques for one chalk type on the same paper; or both paper types with the same application type and chalk type; or different types of chalk on the same paper type and with the same application technique). In all cases, 95% of the variance could be expressed with only two principal components, and often the share contributed by PC-1 alone amounted to more than 90% of the variance. This implies that a sole factor accounts for most of the differences.
In most of the samples, it was possible using PCA to identify slight differences for a single chalk type on the basis of the application technique and the paper support. The differentiation of the application technique occurred primarily between dry and wet drawing techniques, in the positive and negative regions of PC-1 (Fig. 15a, see also Figs. 15b–d in the Appendix). In three cases, groups formed loosely based on the chalk application technique. It was also possible to differentiate the paper a type wherever their show-through was a contributing factor in the measurements; however, in two cases the effect falls within the differentiation axes of PC-2, with an explained variance of 9–18%. It is thus possible for PCA to analyze differences in the application type or paper for a single red-chalk type and thereby cause “false positive” results.
3.6 Differentiation of the red chalks in the Karlsruhe drawings
FORS measurements of 79 red-chalk drawings were taken and analyzed using PCA to group them according to their spectral similarity. This allows drawing conclusions about the diversity of the red chalks used in the Piranesi workshop and in Rome. For drawings with more than 10 measured spectra, in each case the 10 spectra with maximum values closest to the median of the maximum values in the first derivative were used, to exclude outliers. In these cases, it was assumed that only one type of red chalk was used per drawing. For individual drawings, however, it should be considered that outliers might point toward different chalk types used on the same drawing.
The positions of the peaks in the first derivatives of the average spectra of the historic red-chalk samples were found between 571 and 589 nm, and the height was between 0.00305 and 0.00658 (Fig. 16). The spectra of the historical samples resemble mostly those from Theley.
In the loadings plot, PC-1 describes the peak height of the spectra in the first derivative, PC-2 correlates with the peak position, and PC-3, which accounts for 6% of the variance, shows differences in the width of the curve, which is the main differentiating factor among the red chalks in the mockups (Fig. 17a). Plotting the principal components with CIE L*a*b* values (Fig. 17b in the appendix) supports this interpretation. PC-1 correlates with the a* and b* values of the historic drawings, i.e., red and yellow (Fig. 17c in the Appendix). The L* value correlates with the peak position and tends to be projected onto PC-2 (Fig. 17d in the Appendix). A high PC-2 value indicates there is a particularly light color and that the position of the maximum is found in the lower wavelengths.
In the PCA score plot (Fig. 18a–c; 2D scatter plots see Fig. 18d-f in the Appendix) the measuring points in the aggregate constitute a large, coherent point cloud, in which the respective drawings each take up clearly located and distinctly demarcated sub-spaces; individual drawings, however, exhibit more extensive scattering. The combined point cloud for all the drawings can be clearly differentiated from the clouds for the Frankenalb red chalk and the fabricated red chalk, but the measuring points of the aggregate cloud lie close to the elongated point cloud of the Theley chalks. The measuring points for the Frankenalb, Theley1 and Theley2 and Faber-Castell chalks are concentrated in the positive region of PC-1, and primarily in the negative region of PC-2. PC-3 is needed to separate the mockups into groups in regards to their chalk types. In an attempt to interpret the score plot based on the greatest overlaps; groups of same-colored symbols were assigned to the historical drawing measurements, which consisted of red-chalk drawings that were the most similar to each other. At the negative end of PC-1, there is a clear overlapping of the measuring points from several drawings, which cluster and form a compact group (violet symbols). Set apart from this group, a second (beige symbols) forms, slightly offset toward the right on PC-1, and displaying a clear shift on PC-3. Some of the drawings from these two groups could also be connected regarding their historical use and content, through the identification of several counterproofs that were made from them for architects visiting Rome, and which at present are attributed to the French draftsman Nicolas François-Daniel Lhuillier [1]. Counterproofing a freshly made drawing involved moistening it, which was advantageous because it fixed the remaining media on the paper, thereby prevented loss and smudging [5]. This facilitates the characterization of the chalks, as expressed in a lesser degree of data scattering, and a clear gab between their respective clusters. The red chalks that are not as easy to characterize are found in the center of the PC-1 scale. Their data points have a greater tendency to scatter, and they cannot be assigned to a compact overall group (symbols in pink, purple, green and other colors). Yellow symbols mark red-chalk drawings featuring a low coverage with paper show-through, which also scattered to a great degree toward PC-2. At the positive end of PC-1 of the point cloud of historical red chalk samples, a number of red chalks, in turn, clearly overlap each other (red symbols).
We chose selected original drawings (Fig. 19a) to show how differences in the reflectance spectra and the first derivative (Figs. 19b–c) impact the score plot. Red chalks with negative PC-1 values (beige and violet symbols) display a flatter spectrum with higher initial reflectance values (35-13-1 in Figs. 19b–c). The chalks on the positive end of PC-1 (in red) are characterized by the steeper rise of their spectra with lower initial reflectance values (35-10-2 in Figs. 19b–c). The chalks in the middle of PC-1 that have distinctly positive values for PC-2 have a spectrum with a similarly steep slope, but markedly higher initial reflectance values. In the first derivative this feature is expressed as a high peak accompanied by a shift of the maximum into the lower wavelength regions; this correlation was observed for the mockups, in connection with applications that featured lower coverage or smudging.