# X-ray Dating of Ancient Linen Fabrics

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}, exploiting new table-top X-ray micro-sources. A theoretical formula is derived for dating linen samples directly from wide-angle X-ray scattering measurements. Our preliminary results show that X-ray dating results are in agreement with other dating sources, such as the radiocarbon method and historical records, if some conditions are satisfied. Indeed, this new dating method can be applied only to threads not older than about thirty centuries because of the saturation of the structural degradation with age. Moreover, the method can be applied only on textiles in which cellulose degradation is mainly due by natural aging arising from thermal, hydrolytic, photolytic, photochemical, and oxidative processes. Analyses can be repeated several times on the same sample, which remains unaltered for other complementary characterization procedures. The proposed X-ray dating of some ancient linen fabrics opens the way to explore limits and potentialities of this new approach and to further develop a new dating method, alternative to the existing ones for specific applications in archeological studies.

## 1. Introduction

^{14}C) or Historical Records (HR). In the discussion of the results, we analyze expected limits of application of the proposed new dating method by verifying the WAXS-derived aging times of linen’s threads also from a statistical point of view.

## 2. Degree of Polymerization as a Function of the Aging Time

## 3. WAXS Characterization of Ancient Linen Threads

^{14}C/HR dating are reported in Figure 1 and in the following text. The main data of the characterized samples are summarized in the first two columns of Table 1.

^{2}, with 100 μm effective pixel size) with an offline Rigaku RAXIA-Di reader was employed to collect WAXS data. WAXS data were collected for each linen sample directly mounted on the sample holder with an acquisition time of 1800 s. The spot size at the sample position was about 200 μm. The image plate detector was placed at about 10 cm from the sample, giving access to a range of scattering vector moduli (q = 4π × sinϑ/λ) from 1.5 to around 35 nm

^{−1}. Two-dimensional (2D) patterns were then converted into one-dimensional (1D) data profiles after the calibration procedure.

^{−1}, i.e., the region of the incident beam tail. After this rescaling, it is evident that the diffraction WAXS intensity peaks depend on the age of the linen threads. This dependence was used to date the ancient linen threads from WAXS data.

## 4. X-ray Aging Parameter

_{q}

_{∊[0.9,1.3]}in the scattering vector q-range = 9.0–13.0 nm

^{−1}(yellow region of Figure 3); the maximum intensity in the entire q-range, dominated by the intensity of the (200) peak (I

_{M}); and the minimum background intensity between the (1–10) and (200) diffraction peaks (I

_{m}). The symbol <...> stands for the average of the scattered intensities in the indicated q-range. The term <I>

_{q}

_{∊[0.9,1.3]}stands for the intensity in an angular sector of 10 degrees around the hk0 axis averaged in the scattering q-range from 0.9 to 1.3 nm

^{−1}and is referred in the following as I

_{D}.

_{D}, i.e., proportional to the inverse of DP(t). The integrated intensity under every diffraction peak is also proportional to the number of crystalline cellulose chains, which diffract photons in well-defined scattering directions, defined by the Bragg law. Therefore, in the definition of AF, it is necessary to insert a quantity proportional to the number of cellulose chains, which cause diffraction. In turn, this quantity depends on the actual thickness of the sample, which changes for every sample and comprises a different number of fibres, as shown in Figure 1. This contribution to the intensity of the peaks can be taken into account by the maximum-to-minimum ratio of the main (200) peak, evaluated as follows:

_{M}is the maximum intensity corresponding to the (200) diffraction peak and I

_{m}is the minimum scattered background intensity that occurs at about q = 13.3 nm

^{−1}between the (1–10) and (200) peaks.

_{Mm}values larger than 4. Let us note that the maximum-to-minimum ratio of the main (200) peak R

_{Mm}can be also indirectly related to the degree of crystallinity of the cellulose through the following relation [19]:

_{Mm}values smaller than 4, causes other than natural aging have probably contributed to the degradation of cellulose. Indeed, the DP maximum fractional loss and the DP activation energy values change under the action of enzymes or acid/basic solutions, which strongly accelerated cellulose degradation. Our tests indicate that even an empirical and approximated evaluation of C, through Equation (6), allows a rapid comparison of cellulose samples [20] to make a preliminary judgement if the linen fabric has suffered mainly a natural aging process and so to discard samples that could have suffered more aggressive degradation processes.

^{14}C/HR dating up to about 25–30 centuries, after which saturation occurs, is evident. This finding can be related to the evolution equation of CB, reported in Appendix A [3,4], as a function of the aging time t.

_{min}, a quantity that is proportional to 1/DP(t) − 1/DP(t = 0), where AF

_{min}is the minimum value of the aging factor, corresponding to the maximum value of DP, that is DP(t = 0), without any degradation due to natural aging. This value could be obtained by the contemporary linen sample of raw flax, for which we can put the aging time t = 0 on the scale of centuries. Therefore, AF − AF

_{min}is proportional just to CB(t). Moreover, we have introduced a normalized CB

_{nor}in Equation (2) to have an a-dimensional quantity to evaluate natural aging of cellulose.

_{min}is the minimum value corresponding to contemporary raw flax and AF

_{max}is the maximum value obtained for very long aging times.

_{nor}obtained by WAXS. Thus, the evolution equation of CB

_{nor}can be used to fit the aging parameter AP values derived from AF values determined by the WAXS measurements (see Figure 4) as a function of the aging time t. In this way, we can experimentally determine the DP maximum fractional loss, ${\omega}_{DP}^{*}$, and the DP activation energy, ${E}_{DPa}$, for the natural aging of linen that occurred during very long periods of time at about stationary conditions over a time scale of many centuries. The evaluation of these quantities is a prerequisite to perform an X-ray dating of ancient linen threads. Whenever the fraction of maximum CB, i.e., the CB

_{nor}values, can be quantitatively derived by AP, the X-ray aging times obtained can be compared with those obtainable by other dating methods.

## 5. X-ray Determination of Linen Aging Parameters

^{14}C/HR dating. Sample A has been discarded by the analysis because bleaching processes have introduced a nonnatural aging, i.e., an accelerated DP reduction due to the chemical action of oxygen used for the decolorization of the textile [2]. This finding is evident also by our WAXS characterization, which gives an AP value of the bleached thread (sample A) larger than that obtained by the raw flax sample (sample B). Indeed, the oxidative bleaching of the fiber has introduced a number of CB, causing a certain level of structural degradation of the fabric. For further considerations about the action of acid, basic, enzymatic chemical processes on the structural degrade of cellulose, see the Discussion Section.

^{−1}(denoted in the following as h

^{−1}), is reported to be ${k}_{DP}\left(273.15+90\right)=0.0022{h}^{-1}$ [4]. Natural aging depends on the average room temperature at which cellulose degradation occurs. To evaluate the temperature excursions for longer time periods, we can rely on a detailed analysis of tree rings’ growth [21]. A 100-year spline filter shows that the global mean temperature oscillations in the last two millennia have been contained in a range of ±0.9 °C. The duration of these warmer or cooler periods of large temperature variations has been at most about two centuries. Moreover, a long-term cooling trend of about 0.6 °C has been manifested in the last two millennia, from the beginning of the Christian Era until the beginning of 1900 [21]. The average room temperature of the last century is very similar to that of the Roman period about 2000 years ago. The average room temperature in the last century is available today for many countries [22]. For Egypt, West Bank, and Israel the average temperatures in the last century have been 22.5 °C, 19.4 °C, and 19.5 °C, respectively. Therefore, due to the results reported in weather data banks [22], these values can be considered the average room temperatures of the last two millennia within small variations, indeed, with a reduction of about 0.6 °C in the last two millennia, divided between twenty centuries, leading to 0.03 °C variations per century. The variations of ±0.9 °C with a maximum duration of about two centuries averaged over a longer period of two millennia, as it was applied a 1000-year spline filter to climate data, are equivalent to a fluctuation of about 0.09 °C per century. Therefore, within an indetermination of about ΔT

_{r}= 0.1, the temperature of the last century can be considered representative to the last two millennia.

_{nor}obtained by WAXS, a relation between the aging time t and the other quantities involved in the natural degradation process of the cellulose can be obtained:

_{nor}, the linear growth of AF values in the aging time’s region of the D and FII samples will be related to the slope of $C{B}_{nor}\left(t,{T}_{r}\right),$ at half of its maximum value. In Appendix A, we have derived a relation which relates the DP activation energy ${E}_{DPa}$ to this slope (Equation (A10)):

## 6. X-ray Dating

^{14}C dating of sample D.

^{14}C dating values of the other samples DII, NII, E, and HII have not been used. Therefore, they are useful for a reliability check of X-ray dating obtained by Equation (8), based on the WAXS experimental evaluation of CB

_{nor}given by AP. Sample LII is not useful for the check of reliability of X-ray dating because it is too ancient and has reached the maximum AP value. In addition, the contemporary sample B is not useful for the check of reliability of X-ray dating because it has not suffered any aging degradation process. In fact, because DP degradation has an asymptotic behavior as a function of t, we can associate a finite aging time value only up to a maximum AP value of 0.99 because, for AP→1, Equation (8) is indeterminate. For this reason, for sample LII, we cannot obtain any X-ray dating, and for AP values very close to 1, the uncertainty interval of the determined aging time is expected to be very large.

_{nor}curve towards 1 for large aging times. Indeed, these two samples are both characterized by very large AP values of about 0.98, and the width of their +2σ uncertainty interval (right-hand value) is about 70% larger than the −2σ interval (left-hand value). Further statistical insight about this point will be discussed in Appendix B.

^{14}C confirms that the X-ray dating reported in Table 3 could be a valid and reliable new method to estimate the time when ancient fabrics, which have suffered natural aging, were made because any information about the dating of samples DII, NII, E, and HII has not been used to perform the corresponding X-ray dating. In fact, the obtained X-ray dating can be considered conditioned almost totally by the HR dating of sample FII and almost completely independent by the

^{14}C dating of the other samples. Indeed, the estimate of the slope of the $C{B}_{nor}$ curve, i.e., of the fraction of maximum CB, at half of its maximum is partially dependent only on the

^{14}C dating of sample D. In the third column of Table 3, for X-ray aging times, we show in parentheses the [−2σ,2σ] interval which, for older samples, is not symmetric with respect to the median value due to saturation effects in the decreasing degree of polymerization of cellulose, which seems to stop after several thousands of years. For details about the

^{14}C date ranges reported in the third column of Table 1, one can refers to previous works [13,15]. To facilitate the comparison with the X-ray dating results, the

^{14}C dating values reported in the second column of Table 3 have been obtained by expressing the data ranges of the third column of Table 1 as a median value with a [−2σ,2σ] interval. However, it should be noted that, due to the non-monotonic nature of the

^{14}C calibration curve,

^{14}C dating very often leads to the impossibility to summarize the data range interval as a median value with symmetric left and right 95% confidence level limits, since the calculated age distribution can be also bi- or trimodal. Therefore, the

^{14}C aging time median values reported in Table 3 have to be considered only as equivalent values to allow a direct comparison with the X-ray corresponding dating values.

^{14}C and X-ray dating have been further analysed by a suitable statistical analysis of data.

## 7. Discussion

^{14}C dating. Additionally, the measurements are not destructive. These findings allow comparison of different dating methods on the same piece of textile, if needed.

^{2}. However, this possibility is based on the assumption that the ancient textile fabric is homogeneous in its physical/chemical/structural characteristics, i.e., the analyzed small thread is representative of the full textile. This important assumption is critical for other dating methods too. For example, in some cases,

^{14}C dating of textile fabrics suffers from the impossibility to eliminate all textile carbon contaminants through the standard procedure of sample cleaning, thus leading to possible wrong dating [16]. Therefore, the possibility to perform dating of a textile by using complementary sources of information could be very useful to solve eventual doubtful cases.

^{14}C/HR dating) should be available.

^{14}C dating. This result shows that

^{14}C and X-ray methods, if necessary, could be used together to increase the reliability of dating measurements in order to determine the possible presence of either inhomogeneity or impurity in the sample, which could affect the dating resulting by a specific method. The agreement obtained among

^{14}C and X-ray dating has been also quantitatively analysed by a novel statistical analysis of the data (see Appendix B), showing that the two methods of estimating the aging time are compatible within the experimental uncertainties for the linen samples analyzed here.

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Evolution Equation of Chain Breaks in Cellulose

## Appendix B. Noise-to-Signal Ratio Statistical Analysis of the X-ray Dating

^{14}C aging time should be linear before saturation occurs, and a novel analysis of its results considers a suitable “noise” and a noise-to-signal ratio and its geometrical representation. We first consider the prediction of the

^{14}C data from the X-ray and then the opposite. We exclude by the following analysis sample FII, characterized by a HR dating, because it has been used to calculate linen aging quantities used in the X-ray dating.

^{14}C aging time reported in the second column of Table 3.

**Figure A1.**Scatter plots and their best-fit regression lines between (i) the central values of $x$ vs. $y$ (black); (ii) the +2σ values of $x$ vs. $y$ (blue); and (iii) the −2 of $x$ vs. $y$ (red).

**Figure A2.**From X-ray to

^{14}C measurements: Square root of the noise-to-signal ratio (NSR) as a function of the square root of the regression ${\mathrm{NSR}}_{a}$ (abscissa) taken as the absolute value $\left|a-1\right|$ and the square root of the correlation ${\mathrm{NSR}}_{r}$ (ordinate): The black line is the central values of column 3 in Table 3. The blue line is +2σ. The red line is −2σ. The 45° line shows where ${\mathrm{NSR}}_{r}={\mathrm{NSR}}_{a}$.

_{nor}. The different widths of +2σ and −2σ uncertainty intervals for large CB

_{nor}values close to 0.98 have the same origin. The association of an asymmetric −2σ,+wσ uncertainty interval at the central value, with w < 2, in case of very large aging times (CB

_{nor}close to 0.98) would partially reduce the effect of CB

_{nor}saturation on the statistical noise which, in these cases, is dominated by ${\mathrm{NSR}}_{r}$. In any case, the central values of the X-ray dating minimizes the NSR and is practically not polarized, with a negligible ${\mathrm{NSR}}_{a}$ because $a\cong 1$. Therefore, it gives an accurate estimate of the aging time, at least in terms of comparison with the

^{14}C dating.

^{14}C data of Table 3. Figure A3 shows the regression lines fitted to the data, while Figure A4 reports the NSR Cartesian quadrant. The

^{14}C data are less scattered around the central values, as Table 3 reports and Figure A3 clearly shows in the estimate of the X-ray prediction bounds.

**Figure A3.**Scatter plots and their best-fit regression lines between: (i) the central values (black); (ii) the +2σ values (blue); and (iii) the −2σ values (red).

^{14}C and the X-ray, are practically indistinguishable. If we consider ±2σ bounds, the X-ray dating can be affected by statistical polarization for large CB

_{nor}values close to 1 due to the saturation of the cellulose degradation for large aging times. This finding leads to reliable X-ray dating only when the linen fabrics have suffered a natural aging at an average room temperature of 21–23 °C for not more than 25–30 centuries. For smaller average room temperatures, linen fabrics also older than 25–30 centuries could be reliably dated by the proposed X-ray method.

**Figure A4.**From

^{14}C to X-ray measurements: Square root of the noise-to-signal ratio (NSR) as a function of the square root of the regression ${\mathrm{NSR}}_{a}$ (abscissa) taken as the absolute value $\left|a-1\right|$ and the square root of the correlation ${\mathrm{NSR}}_{r}$ (ordinate): The black line is the central values of column 2 in Table 3. The blue line is +2σ. The red line is −2σ. The 45° line shows where ${\mathrm{NSR}}_{r}={\mathrm{NSR}}_{a}$.

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**Figure 1.**Low-magnification optical microscopy images of some of the analyzed samples under the same illumination conditions: The central sample is of our age (2000 AD). For the ancient samples, in parentheses are shown the average

^{14}C/HR dating. The analyzed threads are 0.2–0.6 mm wide and a few mm long.

**Figure 2.**Two-dimensional Wide-Angle X-ray Scattering (WAXS) pattern measured on sample D (575 AD): The main axes of the fiber-diffraction pattern are shown (white lines) together with indexing of main cellulose diffraction peaks.

**Figure 3.**One-dimensional WAXS profiles extracted from the relevant 2D patterns after integration in the angular sector of 10 degrees around the hk0 equatorial fiber-diffraction axis in arbitrary units: The cellulose (110) and (1–10) diffraction peaks have been indexed and rescaled to have the same integrated intensity in the q-range 1.5–4.0 nm

^{−1}. See the main text for further details and Table 1 for symbols.

**Figure 4.**Aging Factor (AF) values as a function of the

^{14}C/HR dating of the investigated linen threads: Error bars are four standard deviations (−2σ, 2σ).

**Figure 5.**Comparison between

^{14}C/HR and X-ray dating: CB

_{nor}curves corresponding to the different average room temperatures of the samples have been plotted with different colors. Error bars (blue) correspond to the

^{14}C/HR dating (blue circles). Error Bars of X-ray dating (red circles) have not been shown for clarity.

Sample Name | Sample Description of Fabric (Provenience) | Year of Manufacture Based on ^{14}C Dating or Historical Records | Scattered Intensity under the (110)–(1–10) Peaks | Maximum Main Diffraction Peak Intensity | Minimum Main Diffraction Peak Intensity | Main Diffraction Peak: Max-to-Min Ratio | Aging Factor |
---|---|---|---|---|---|---|---|

I_{D}<I> _{q∊[9.0,13.0]} | I_{M}I _{(200)} | I_{m}I _{q = 13.3} | R_{Mm}I _{M}/I_{m} | AF $\frac{{I}_{M}}{{I}_{m}}\times \frac{1}{{I}_{D}}$ | |||

B | New, raw flax | 2000 AD | 0.948 ± 0.009 | 3.63 ± 0.01 | 0.507 ± 0.002 | 7.16 ± 0.03 | 7.56 ± 0.08 |

A | New, bleached | 2000 AD | 0.996 ± 0.008 | 4.186 ± 0.009 | 0.517 ± 0.005 | 8.1 ± 0.1 | 8.1 ± 0.1 |

DII | Medieval, ^{14}C dating, Jericho (Israel) | 997–1147 AD | 0.732 ± 0.009 | 2.941 ± 0.007 | 0.471 ± 0.004 | 6.24 ± 0.04 | 8.5 ± 0.1 |

D | Medieval, ^{14}C dating, Fayyum (Egypt) | 544–605 AD | 0.833 ± 0.008 | 3.57 ± 0.01 | 0.460 ± 0.002 | 7.76 ± 0.04 | 9.3 ± 0.1 |

FII | From a mummy, HR dating (Siege of Masada), (Israel) | 55–74 AD | 0.641 ± 0.008 | 2.41 ± 0.01 | 0.366 ± 0.004 | 6.58 ± 0.07 | 10.3 ± 0.2 |

NII | From a mummy, ^{14}C dating, Engedi (Israel) | 350–230 BC | 0.538 ± 0.007 | 1.91 ± 0.01 | 0.308 ± 0.004 | 6.20 ± 0.09 | 11.5 ± 0.2 |

E | From a mummy, ^{14}C dating, Egypt | 405–345 BC | 0.416 ± 0.005 | 1.799 ± 0.007 | 0.380 ± 0.004 | 4.7 ± 0.1 | 11.4 ± 0.2 |

HII | From a mummy, ^{14}C dating, Thebes (Egypt) | 1000–720 BC | 0.825 ± 0.007 | 3.90 ± 0.01 | 0.41 ± 0.005 | 9.5 ± 0.1 | 11.5 ± 0.2 |

LII | From a mummy, ^{14}C dating, Egypt | 3500–3000 BC | 0.649 ± 0.007 | 2.76 ± 0.01 | 0.367 ± 0.002 | 7.52 ± 0.05 | 11.6 ± 0.1 |

**Table 2.**Age of the samples derived by the

^{14}C/HR dating, normalized aging parameter AP values obtained by the WAXS measurements, and average room temperature (°C) at which the samples have been degraded.

Sample Name | Aging Time (centuries) | Aging Parameter AP ± 2σ_{AP} | Average Room Temperature T_{r} (°C) |
---|---|---|---|

B | 0.2 ± 0.1 | 0.00 ± 0.01 | / |

DII | 9.5 ± 0.8 | 0.23 ± 0.01 | 21.5 |

D | 14.4 ± 0.3 | 0.43 ± 0.01 | 21.0 |

FII | 19.55 ± 0.1 | 0.68 ± 0.02 | 21.0 |

NII | 23.1 ± 0.6 | 0.98 ± 0.025 | 23.5 |

E | 23.9 ± 0.4 | 0.95 ± 0.025 | 22.5 |

HII | 28.8 ± 1.4 | 0.98 ± 0.025 | 22.5 |

LII | 52.7 ± 2.5 | 1.00 ± 0.01 | 22.5 |

Sample Name | ^{14}C/HR Aging Time(95% Confidence Level; 2 Standard Deviations Each Side) | X-ray Aging Time Obtained by Equation (8) (in Parentheses: Left and Right 95% Confidence Levels; 2 Standard Deviations Each Side) |
---|---|---|

DII | 9.5 ± 0.8 | 9.4 [−0.7,0.7] |

D | 14.4 ± 0.3 | 14.5 [−1.0,1.0] |

FII | 19.55 ± 0.1 | 19.6 [−1.5,1.5] |

NII | 23.1 ± 0.6 | 23.5 [−2.9,5.1] |

E | 23.9 ± 0.4 | 23.9 [−2.3,2.8] |

HII | 28.8 ± 1.4 | 27.7 [−3.6,6.0] |

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**MDPI and ACS Style**

De Caro, L.; Giannini, C.; Lassandro, R.; Scattarella, F.; Sibillano, T.; Matricciani, E.; Fanti, G.
X-ray Dating of Ancient Linen Fabrics. *Heritage* **2019**, *2*, 2763-2783.
https://doi.org/10.3390/heritage2040171

**AMA Style**

De Caro L, Giannini C, Lassandro R, Scattarella F, Sibillano T, Matricciani E, Fanti G.
X-ray Dating of Ancient Linen Fabrics. *Heritage*. 2019; 2(4):2763-2783.
https://doi.org/10.3390/heritage2040171

**Chicago/Turabian Style**

De Caro, Liberato, Cinzia Giannini, Rocco Lassandro, Francesco Scattarella, Teresa Sibillano, Emilio Matricciani, and Giulio Fanti.
2019. "X-ray Dating of Ancient Linen Fabrics" *Heritage* 2, no. 4: 2763-2783.
https://doi.org/10.3390/heritage2040171