Can X-ray Diffraction Distinguish Natural from Anthropogenic Hematite? Replication of the Conversion of Natural Goethite in Both Furnace and Campﬁre

: Hematite, the mineral that gives color to bright red iron ochres, occurs naturally, but there is much evidence that early humans sometimes artiﬁcially produced hematite by heating a related mineral, goethite, in wood ﬁres. This represents an important cognitive and technological advance in early human prehistory. Thus, there is a need to distinguish natural hematite from hematite generated by heating goethite in a wood ﬁre. Measuring the line widths of powder X-ray diffraction (XRD) in hematite has been explored, and synthetic goethite heated in a modern furnace has been used as a model system for studying this process. We now show that to be an inappropriate model. Although chemically identical, natural goethite is physically different from and much more variable than goethite produced in a laboratory. Furthermore, by replicating the process using Stone Age technology, we show that heating goethite in a wood ﬁre complicates the interpretation of XRD line widths of the resulting hematite. We conclude that strategies other than powder XRD are necessary to draw conclusions about the ancient processing of iron ochres. lines in natural goethite is more variable than has been widely appreciated, that line broadening is less intense for goethite that of goethite. through the replication of the process in ﬁres, we show that the non-uniform or line broadening is not a promising strategy for estimating the of the ﬁres which

While the term "ochre" is used in a variety of contexts, an excellent definition for the context of this study is "a geological product containing iron oxide and/or oxyhydroxides", which "leaves a colored streak when rubbed against a harder material" [23] (p. 1). A range of color terms are often used, including red, yellow, orange, and brown, [2,20,22,23], and the presence of other minerals, especially silicates, carbonates, and/or quartz is often noted.
The two most common minerals in ochre are goethite (FeO(OH)), which forms a yellowish-brown pigment, and hematite (Fe 2 O 3 ), which forms a bright red pigment. A frequent observation by archaeologists is that humans often preferred red ochres, and several explanations for this have been offered [1,13,16]. Historical documentation establishes that humans have known at least since early Roman times that yellowish-brown ochre can be converted to a bright red one by heating [24]. Material scientists demonstrated that yellowish-brown goethite, FeO(OH), is converted to red hematite Fe 2 O 3 , by heating above 300 • C (Equation (1)).
FeO(OH) (s) → Fe 2 O 3(s) + H 2 O (l) (1) painted stones. The characterizations of the artifacts using Raman spectroscopy, TEM, and SEM-combined with a comparison of their results with those of natural goethite, which the researchers heated in the laboratory-were all consistent with the red pigment being hematite prepared by heating goethite [7,39]. Furthermore, careful geological prospecting around Riparo Dalmeri demonstrated that no sources of natural hematite were available to the artists [7]. Similarly, in the Aurignacian layers in Fumane Cave and the Late Epigravettian layers at the Tagliente rock shelter, the accessory minerals mixed with hematite pigments correspond to local goethite sources, not the sources of natural hematite. By firmly establishing the provenance of the ochre, the authors demonstrated that it resulted from heated goethite [5,[36][37][38]. Using the non-uniform broadening of the 104 peak in XRD and the results reported by Pomiès et al. [28,29] for synthetic goethite, they estimated heating temperatures ranging from 300 to 950 • C [37].
Conversely, similar strategies can be used to demonstrate that hematite pigments are natural and were not produced by heating goethite. For example, using Raman spectroscopy, XRD, SEM, and geological prospecting, the ochre found in a Magdalenian burial in Mirón cave was shown to result from natural hematite in local outcrops, not from heated goethite [40].
Replication is an important experimental strategy for understanding ancient technologies. To test hypotheses about lost technologies, researchers often attempt to recreate ancient processes, and they then compare the resulting materials to those found by archaeologists. Replication experiments have proven invaluable in understanding the ancient technology of fire, e.g., [22,25,41,42]. Similarly, replication experiments have revealed much about the processing and use of ochres [4,20,23,26,[43][44][45]. Thus, it is surprising that studies using the replication of the heating of ochres in natural fires are relatively few. Lorblanchet [46] demonstrated that natural ochre can be rubified in a wood fire. In a remarkably thorough and controlled series of experiments, Wojcieszak et al. [22] used Raman spectroscopy and SEM to characterize the effect of wood fires on manganese minerals and clays in dark ochres. In a very influential paper, Wadley [26] demonstrated that brown ochres become red even when buried under wood fires.
Recently, we heated natural goethite in wood fires using Stone Age technology and recorded the Munsell colors and diffuse reflectance spectra of the goethite and the resulting hematite [47]. We found that clean, red hematite pigments were easily generated, and heating solid lumps of goethite rather than its powder makes it easier to avoid the contamination of the pigment in the fire. Subjective color terms are widely used in virtually all the literature on ochres. However, recent studies have recorded Munsell colors, e.g., [5,20,23,26], which is a coded system of reproducibly printed colors that can be consulted by scientists around the world. Even better, the reflectance profile of visible light can be measured as the percent of light reflected as a function of the wavelength of light (i.e., the visible reflectance spectroscopy), and several recent papers have made use of this technology [47][48][49]. For example, Elias et al. used λ m , the wavelength at which the increase in reflectance is at its steepest, to characterize ochres [48]. For the natural goethite that we studied, the Munsell color of heated ochre is consistently 2.5YR 3/4-6 and λ m = 582-590 nm [47].
To further explore the heating of natural goethite, we now report the replication of the process in the laboratory and in outdoor wood fires, and we describe the X-ray diffractograms of the resulting hematites. To our knowledge, no one has integrated XRD with experimental replication in natural fires. In this study, we present two lines of investigation of heating ochres. First, we show that the selective broadening of the XRD lines in heated natural goethite is more variable than has been widely appreciated, and that line broadening is often much less intense for natural goethite than that of synthetic goethite. Second, through the replication of the process in wood fires, we show that the non-uniform or selective line broadening is not a promising strategy for estimating the temperature of the fires in which ochre was heated.

X-ray Diffractometry (XRD)
Powder X-ray diffractograms (XRD) were recorded in air at ambient temperature (22 ± 2 • C) on a Rigaku diffractometer with a Multiplex goniometer and a RINT fixed monochromator (Applied Rigaku Technologies, Inc., Austin, TX, USA). A copper anode operating at 40 kV and 30 mA generated the X-rays, and the monochromatic K α1 line (1.54 angstroms) was selected. Scan speed was 1.0 • /min, and the range was from 2θ = 15 • to 80 • (65 min acquisition time). Scans were analyzed using the Materials Data Jade 6.0 software (MDI Materials Data; Livermore, CA, USA) including FWHMs, which are calculated by fitting the peaks and reporting the widths in tabular form. All measurements are reported as 2θ.

Ochre Samples
Natural goethite was purchased from Wards Scientific (mined in Hibbing, MN, USA), and it came as lumps of approximately 100 g. Through macro-and microscopic inspection, the goethite was variable in purity, cementation, and crystallinity. Thus, to measure the dependence of line width on temperature, it was necessary to make a homogeneous sample from which multiple, identical subsamples could be taken. A single lump was crushed between hardened steel plates, ground in a mortar and pestle, and passed through a 200-micron sieve. Using XRD and polarized light microscopy (PLM), the homogenized sample was shown to contain only goethite and quartz. No carbonates or silicates were detected using PLM or FT-IR spectrometry. Using gravimetry, the sample was found to contain 63% goethite and 37% quartz [47]. Initial experiments were performed using this homogenized powdered subsample, and follow-up experiments involved heating solid lumps of the ochre. The lumps were all from the same lot purchased from Wards but contained different percentages of goethite and quartz. In no case was the natural goethite purified.
To name samples, we used the same system as in [47]. For each sample, a unique integer was assigned, followed by N for natural goethite, Fire or Furn(ace) for the method of heating, and P for powder or L for solid lump. For example, 10-NFireP is sample 10 with the appended abbreviation indicating that it is natural goethite heated in a fire as a powder.

Sample Heating
The details of the fires have been described [47] but are summarized here. In the laboratory, samples were heated in a thermostat-controlled Fisher Isotemp Muffle Furnace. Outdoors, the fires (60-80 cm in diameter) were made of well-seasoned wood in a simple, flat hearth [25,26,41,42]. The diameters of the fuel were from 4 to 12 cm, and the lengths were from 40 to 80 cm. Except for Fire 1, the temperatures of the samples were measured every 15 min in triplicate using an Etekcity Lasergrip 800 IR Thermometer; accurate measurements required being within 50 cm of the sample. Fire temperature was controlled by the amount of wood and the rate of stoking. In this configuration, the fires were slightly reducing in the flames, and they were strongly reducing in the coals [47]. Figure 1 illustrates a fire with samples at its center. Figure 2 shows an unheated sample of natural goethite (on the right) and four lumps that had been heated in the fire. A color card from the International Federation of Rock Art Organizations is included as a reference and scale.

Results
Eight XRD lines of hematite were selected for study (see Table 1) usin criteria: sufficient intensity to measure widths accurately and precisely, a terfering lines, and comparability to measurements reported in the litera location of hematite lines had a standard deviation of ±0.003°.

Results
Eight XRD lines of hematite were selected for study (see Table 1) usin criteria: sufficient intensity to measure widths accurately and precisely, a terfering lines, and comparability to measurements reported in the litera location of hematite lines had a standard deviation of ±0.003°. h k l d/Å 2θ

Results
Eight XRD lines of hematite were selected for study (see Table 1) using the following criteria: sufficient intensity to measure widths accurately and precisely, avoidance of interfering lines, and comparability to measurements reported in the literature. The peak location of hematite lines had a standard deviation of ±0.003 • . As examples of our analysis, the XRD pattern for natural goethite powder heated at 450 • C is illustrated in Figure S1, and the data are listed in a tabular form in Table S1. Similarly, the XRD pattern for natural goethite powder heated at 900 • C is illustrated in Figure S2, and the data are listed in a tabular form in Table S2.
For optimum precision and accuracy in the XRD measurements, we found it necessary to dry samples at 150 • C for two hours immediately before loading them into the diffractometer. All reported measurements are from one-hour scans. For the furnace-heated samples, the reported FWHMs are the average of two or three replicates. In this way, the standard deviation on replicate peak widths was ±0.007 • . (Exposure to ambient air for more than an hour allowed humidity to artificially increase peak widths by up to 0.05 • and increased the standard deviation on peak widths by up to a factor of four).
To establish the accuracy, resolution, and precision of the instrument independent of the complications of iron oxides, we measured the locations and widths of four quartz lines in 42 ochre samples. The average width of all four lines was 0.135 • , comparable to literature values and indicating the excellent resolution of our Rigaku diffractometer. The standard deviation of the location of the quartz lines was ±0.004 • and of the width was ±0.02 • , indicating excellent precision. The widths of quartz peaks were independent of ambient humidity and the temperature at which samples were heated.
We converted natural goethite into hematite in a furnace at 300, 450, 600, 750, and 900 • C and then measured the peak widths for the eight selected lines. These widths (FWHM) are plotted vs. temperature in Figure 3. All the lines at all temperatures are wider than expected for well-crystallized hematite, and the FWHM values show little or no dependence on temperature. In fact, to our surprise, the widths of only two of the lines (012 and 024) demonstrated a narrowing trend from 300 to 600 • C.
These results for natural goethite are dramatically different from the results from heating synthetic goethite [14,28,32]. In the studies of synthetic goethite, the FWHM vs. T plots of synthetic goethite show a steady decrease in peak width from 300 to 600 • C over a range from about 1.0 to 0.3 • for four of the lines (012, 104, 214, 204), lines, which correspond to those predominantly resulting from the lattice of iron ions [28,32]. (For easy comparison, Figure 3 in our study is at approximately the same scale as the corresponding figure in [28].) In contrast, well-crystallized hematite shows widths of 0.13 to 0.15 • for these lines [14,32].
In Figure 4, we display the dependence on temperature for the width of line 012 for three natural goethites: our sample (black square), that of Löffler and Mader (red diamond) [32], and the sample used in Cavallo et al. (yellow triangle) [33]. Two synthetic goethites are also plotted: that of Löffler and Mader (purple circle) [32] and Pomiès et al.
(blue dash) [28]. The comparison of results from five different goethites clearly illustrates two points: 1. the three natural goethites are highly variable (purple, red, and yellow lines), ranging from a dramatic dependence of FWHM on temperature to almost no dependence, and 2. the two synthetic samples (black, blue) are similar to each other in that both show a strong dependence of FWHM on temperature.
literature values and indicating the excellent resolution of our Rigaku diffractometer. The standard deviation of the location of the quartz lines was ±0.004° and of the width was ±0.02°, indicating excellent precision. The widths of quartz peaks were independent of ambient humidity and the temperature at which samples were heated.
We converted natural goethite into hematite in a furnace at 300, 450, 600, 750, and 900 °C and then measured the peak widths for the eight selected lines. These widths (FWHM) are plotted vs. temperature in Figure 3. All the lines at all temperatures are wider than expected for well-crystallized hematite, and the FWHM values show little or no dependence on temperature. In fact, to our surprise, the widths of only two of the lines (012 and 024) demonstrated a narrowing trend from 300 to 600 °C. These results for natural goethite are dramatically different from the results from heating synthetic goethite [14,28,32]. In the studies of synthetic goethite, the FWHM vs. T plots of synthetic goethite show a steady decrease in peak width from 300 to 600 °C over a range from about 1.0 to 0.3° for four of the lines (012, 104, 214, 204), lines, which correspond to those predominantly resulting from the lattice of iron ions [28,32]. (For easy   Figure 3 in our study is at approximately the same scale as the corresponding figure in [28].) In contrast, well-crystallized hematite shows widths of 0.13 to 0.15° for these lines [14,32].
In Figure 4, we display the dependence on temperature for the width of line 012 for three natural goethites: our sample (black square), that of Löffler and Mader (red diamond) [32], and the sample used in Cavallo et al. (yellow triangle) [33]. Two synthetic goethites are also plotted: that of Löffler and Mader (purple circle) [32] and Pomiès et al.
(blue dash) [28]. The comparison of results from five different goethites clearly illustrates two points: 1. the three natural goethites are highly variable (purple, red, and yellow lines), ranging from a dramatic dependence of FWHM on temperature to almost no dependence, and 2. the two synthetic samples (black, blue) are similar to each other in that both show a strong dependence of FWHM on temperature.  [32], red diamond; synthetic, Löffler and Mader [32], purple circle; synthetic, Pomiès et al. [28], blue dash; natural, Cavallo et al. [33], yellow triangle.
For a semi-quantitative comparison of the dependence of temperature for all the four selectively broadened lines, we calculated approximate slopes of the plots of FWHM vs. T from 300 to 600 °C where the relationship is quasilinear for the five heated ochres (see Table 2). We achieved this by minimizing the deviation in the y-axis between the points and a straight line. These slopes indicate that the trends illustrated in Figure 4 Table 2 indicate that synthetic goethite makes a poor model for understanding the XRD of natural goethites.  [32], red diamond; synthetic, Löffler and Mader [32], purple circle; synthetic, Pomiès et al. [28], blue dash; natural, Cavallo et al. [33], yellow triangle.
For a semi-quantitative comparison of the dependence of temperature for all the four selectively broadened lines, we calculated approximate slopes of the plots of FWHM vs. T from 300 to 600 • C where the relationship is quasilinear for the five heated ochres (see Table 2). We achieved this by minimizing the deviation in the y-axis between the points and a straight line. These slopes indicate that the trends illustrated in Figure 4 for line 012 are repeated for 104, 024, and 214. The dramatic differences documented in Figures 3 and 4 and in Table 2 indicate that synthetic goethite makes a poor model for understanding the XRD of natural goethites.  Chemically, all five goethites are FeO(OH), so these results are initially surprising. However, iron oxide formation is notoriously complex [31] and very dependent on the conditions under which they are formed. Crystallinity [47,50], crystal size [51], crystal morphology [39,[51][52][53], and impurities [31] all significantly affect the physical properties of goethite, so the variability in XRD line widths demonstrated here is consistent with these observations.
To extend our findings to Stone Age ochres, we replicated the heating of natural goethite in wood fires. We compared the XRD peak widths of natural goethite heated in a furnace to the widths of samples heated in a wood fire. To our knowledge, these are the first XRD results reported for fire-heated goethite.
In our first effort (Fire 1), we heated two samples of the homogenized, powder goethite (described in Section 2) in a campfire for one hour (samples 10-NFireP and 11-NFireP). The XRD lines of goethite had completely disappeared and been replaced by the expected lines for hematite, indicating complete conversion. The widths of those lines are recorded in Table 3. We then compared these widths to those of goethite heated in a furnace (illustrated in Figure 3) to determine the apparent temperature of the fire. The results varied wildly, and different lines led to grossly different predictions of temperatures, including some that are too high for a campfire or too low to have led to complete conversion to hematite in an hour. The difference between furnace-heated and fire-heated samples may be due to the varying temperatures achieved in a fire (see below for more on fire temperatures) or to the complex chemical environment of a fire. In either case, these data suggest that XRD line width is not a promising strategy for determining the temperature at which ochres were heated, especially for goethite that shows little dependence of FWHM on temperature, like the goethite here. Table 3. Widths (FWHM) of four XRD lines for two powder samples heated in a fire in crucibles and the apparent fire temperatures as estimated from the width using plot in Figure 3. As we had not measured the temperature of Fire 1, we followed this initial effort by recording the XRD patterns for samples in four additional fires. The sample names and fire temperatures are listed in Table 4. The first two, 14-NFireP and 20-NFireP, were from the large batch of the homogenized natural goethite powder. Similar to the results of the powders in Table 3, the width of the lines of the XRD lines did not serve as an accurate proxy for determining the temperature at which the samples were heated. In fact, most of the lines were outside the range of the widths recorded in furnace-heated samples (Table 5).  We then took two new lumps of goethite from the same box of goethite purchased from Wards, 27-NFireL and 28-NFireL, and heated them as lumps directly in a fire (as opposed to heating ground and sieved powders). After heating, we brushed the ash from their surfaces and ground and sieved them. As previously reported, this produced pigments of virtually the same color as those produced by heating in a furnace [47]. We recorded the XRD, and again, the widths did not accurately predict the temperature of the fire ( Table 5). Half of the lines were outside the range of the widths recorded in furnace-heated samples.
To measure the variability in three different lumps of goethite taken from the same source of natural goethite independent of any effect of fire, we took two more new lumps from the same box of goethite purchased from Wards, and we heated them in the furnace at 600 • C (samples 36-NFurnL and 37-NFurnL). Although ground via the same procedure and heated for the same amount of time in the same furnace, these samples had XRD line widths very different from those of the first sample. The widths are listed in Table 6. Differences ranged from +0.22 • (the 214 line in 36-NFurnL) to −0.21 • (the 104 line in 37-NFurnL). These differences are much larger than can be explained by the uncertainty of the measurement, which is better than ±0.01 • (see Section 2). This demonstrates that hematite made by heating different pieces of goethite from a single source may have very different line widths due to the natural variability within the source. Table 6. Line widths in degrees measured for three different subsamples of the same natural goethite after heating at 600 • C for one hour in a furnace.

Discussion
Taken together, these results demonstrate that the selective broadening of XRD lines of heated natural goethite is much less dependent on temperature than for the lines of heated synthetic goethite, questioning the use of synthetic goethite as a model. Furthermore, there is dramatic variation among different sources of natural goethite, probably resulting from differences in crystal size, crystallinity, impurities, and accessory minerals [24,31,32,39,48,52]. To use selective broadening at all requires the measurement of the broadening in the same source of natural goethite as the artists used [33], but, due to the high variability in a single geological source, even this strategy is risky. Furthermore, heating in wood fires yields quite different degrees of broadening than heating in laboratory furnaces. Instead of relying on XRD, a combination of careful archaeology, sourcing of local goethite, and a battery of analytical methods, as exemplified by research groups in Europe, is necessary for firm conclusions [5,7,17,[33][34][35]53,54].
The mineralogy of iron oxides is very complex, partly because so many varieties are possible (in addition to goethite and hematite, there are magnetite, maghemite, lepidocrocite, ferrihydrite, etc.) [31]. As emphasized in the literature, the reproducible synthesis of iron oxides requires careful control of pH, reagent concentrations, reagent purity, temperature, convection, and even the material of the container (plastic versus glass), again because of the complexity of their chemistry, e.g., [31,32,50]. In contrast with the clean, controlled environment in laboratories, the formation of natural goethites occurs over geological time scales in complex and uncontrolled environments. We hypothesize that the complex and changing environments in which natural goethites form may disrupt the crystalline structure sufficiently to affect ion rearrangement during the goethite-to-hematite transition. Rietveld's refinement of X-ray diffractograms may offer a strategy to test this hypothesis in the future.
Although the interpretation of the XRD of iron oxides is so fraught with complications, several other strategies have proven effective in identifying whether hematite ochres found in archaeological contexts are natural or result from the anthropogenic heating of goethite. As reviewed in the Introduction section, a provenance study (the characterization of the total mineral content in ochres combined with geological prospecting) is an excellent strategy. For example, red ochre found in the Tagliente shelter contained a mix of hematite, quartz, and calcite in proportions that did not exist in any local sources. However, goethite, quartz, and calcite were found in a local source. In combination with careful archaeology and other analyses, the evidence is very persuasive that the ochre was intentionally heated [37]. In another case, the complex mineral composition of hematite ochre found in a Magdalenian burial in El Mirón Cave corresponded closely to a nearby source, demonstrating that the hematite did not result from heated goethite [40].
Another strategy that may prove helpful is the determination of pore size using transmission and scanning electron microscopies [5,[32][33][34][35], even possibly to estimate the temperature at which the goethite was heated. However, more work is needed. In some studies of pore size, as for the broadening of XRD peaks, synthetic goethite was used as a model [14,29]. In contrast, the studies comparing laboratory-heated natural goethite to archaeological ochres have yielded more promising results [5,33,39].

Conclusions
The XRD line widths of hematite produced by heating natural goethites are very different from those of heated synthetic goethite. Within natural goethites, line widths are highly variable between sources and even within a single source. Heating goethite in a fire complicates selective line broadening compared with heating in a furnace, probably because of the variability in temperatures achieved in an open, wood fire. Thus, the XRD results from heating synthetic goethite in a furnace are shown to be an inappropriate model for understanding natural goethites heated in a wood fire. Whether the TEM and SEM studies of pore size and crystal morphology of heated synthetic goethite are appropriate as models for naturally heated goethite remains a question for future work.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/colorants1030022/s1, Figure S1: XRD pattern of natural goethite powder heated at 450 • in oven for 1 h; Figure S2. XRD pattern of natural goethite powder heated at 900 • in oven for 1 h; Table S1: XRD data in tabular form of natural goethite powder heated at 450 • in oven for 1 h; Table S2: XRD data in tabular form of natural goethite powder heated at 900 • in oven for 1 h.

Data Availability Statement:
The data presented in this study are available in this article.