The coefficient of variation
In probability theory and statistics, the Coefficient of Variation (CV) is used as a measure of standardized variability for each element. This was calculated by dividing the standard deviation by the mean for each element of the Yuehe nephrite data set (n = 230) (Table 1).When the CV is low, the data have less variability and higher stability.
For this case, the major element Ca has the lowest value of CV, which is also in line with the usual perception. The major element content is very large and is itself less influenced by impurity minerals in nephrite and factors in the soil micro-environment. In contrast, the trace element content is not only affected by the surrounding rocks of nephrite, but also causes stronger fluctuations due to intrusive effects of random element in the soil . As expected, the trace elements in the nephrite samples exhibit a significantly higher level of variability than the nephrite major elements. If 1 is set as the cutoff, the elements below this values in the order from smallest to largest are Ca, Cr, V, K, Fe, Mn and Ba. And the elements greater than 1 are S, Cu, Zn, Ti and Hg. This grouping could correspond to the results of the cluster analysis very well.
Cluster analysis can categorize elements with similar geochemical characteristics, and can identify elements with close performance. Theoretically, a hierarchical R-type cluster analysis of the elements from the pXRF scans (normalized data) can visually represent the degree of similarity in terms of the order of coalescence and the distance between groups. More specifically, in the elemental clustering analysis pedigree chart (by single linkage), the vertical coordinate represents the distance between different variables, and the similarity between variables increases as the distance gets closer (Fig. 4). Back to the current case, the different elemental assemblages correspond to a large extent to the different primary geochemical features and factors such as weathering, erosion and alteration that affected the appearance of nephrite .
In Fig. 4, the specificity of Cu is remarkable, and its distance from other elements is much greater than that between other elements. Apart from Cu, the remaining elements can be roughly divided into two major groups. First, Ca, Cr, V, K, Mn, Fe and Ba are classified as the same group, which can be considered as elements in the primary and impurity minerals of nephrite . Second, S, Hg, Zn and Ti are common trace elements in the soil or minerals [32, 33]. As for Cu, the tomb also had a large number of bronzes, where the loss and flow of copper elements would more or less make the copper content of nephrite increase. Certainly the occurrence of elemental exchange (possibly only unidirectional) triggered by the co-placement of bronze and jade deserves further attention.
Moreover, the fact that S and Hg are grouped together implies that, in addition to the trace elements of the soil itself, other exogenous elements have intruded into the nephrite. The compound of S and Hg, cinnabar, is precisely one of the striking features of the Yuehe Tomb No.1, and its large-scale use has caused many red particles still remaining in the decorative grooves of many nephrite objects to this day (such as M1:129, M1:161 and M1:316 in Fig. 3). In general, these three types of clusters reflect both the affinity of geochemical properties among elements, and the regularity of elemental migration and deposition.
Correlation analysis can help to reveal the relevance between elements, and then to identify the possible sources of various elements. The higher the correlation between chemical elements in nephrite, the higher the possibility that the elements come from the same stable input. Therefore, it serves a similar function as cluster analysis, but focuses more on the commonality between elements two by two.
As shown in Table 2, there are three groups of elements with correlation coefficients higher than 0.6, including S and Hg, Mn and Fe, as well as Ca and Cr. They are almost the groups whose distance is less than 0.6 in the cluster analysis (in Fig. 4), thus further confirming that the elements within these groups have more similar mode of occurrence. However, the correlation coefficient of Ca and Cr is not the largest, although they are the first elements to cluster. The peculiarity is probably due to the fact that Ca is the major element, although it has a similar geochemical background to some of the common elements in nephrite as displayed in Fig. 4, it is supposed to have stronger correlation reasonably with other major elements, and its correlation to trace elements is relatively less significant . The case of Fe is different. In some sense, Fe is considered a major element since it can often substitute for Mg, especially if the nephrite is green (serpentine-related genesis). In this batch of samples, the Fe content of most of the tested parts is less than 1%, implying that Fe may be present in the impurity minerals. Inclusions in nephrite are not only magnetite, limonite, pyrite, but also a type of inclusion containing Fe–Mn which usually manifests itself as fern-like, which is most likely the source of Mn . Besides, neither S nor Hg is a common element in nephrite inclusions, as can be barely seen from their respective negative correlation coefficients with Ca. Their contents are more than typical trace elements, and the high correlation indicates that they may be bound together in some compound form. And this requires taking into account whether their level is commensurate. Moreover, the nephrite objects from Yuehe Tomb No. 1 appear generally dark in hue, unlike other excavated nephrite, and it is reasonable to wonder if these two elements, not commonly found in other cases, played an important role in this color change.
Elements and secondary colors
The ancient Chinese also noticed this phenomenon of jade darkening, and they may have imaginatively referred to it as mercury alteration, based on the burial practice of using mercury for embalming. Mercury alteration is unique among the several types of alteration that occur in Chinese ancient jades and often appears on ancient jade artifacts unearthed from high-grade tombs of the pre-Qin period (before 221 BCE) . Previous studies have speculated the similar darkening phenomenon on jade may result from carbon, manganese, iron and copper, but a closer examination of Yuehe jade again links blackening and mercury, and stimulated more intense discussion on the blackening mechanism of ancient jade . Some related simulated experiments have also been conducted and confirmed that the black HgS was immersed inside the jade, forming a black elemental mercury, rather than the metallic mercury element dipped in the jade or red mercury causing black mercury alteration . Moreover, a recent systematic scientific analysis of these nephrite objects from Yuehe Tomb No. 1 indicate the coloring factor is metacinnabar (-HgS), which might be converted from cinnabar (-HgS) in the influence of bromine and alkali .
However, the point that was overlooked before is that the contents of Hg and S do not seem to match well into the compound HgS. We make a scatter plot of the data obtained by scanning the black area (n = 109), and add a regression line y = 0.25x + 327.46 (Fig. 5). According to the relative atomic masses of S (= 32.07) and Hg (= 200.59), the ratio between them should be approximately 6.25 based on a 1:1 atomic number combination, which is 25 times different from the actual result. Therefore, it can be assumed that the source of Hg is almost from HgS, but there are other sources of S. The human body (vertebrates) contains about 0.25% elemental sulfur (plants also contain elemental sulfur, but less than animals), the slow decay of the body in the sealed burial environment of the tomb releasing sulfur (or hydrogen sulfide) in the process . It is suggested that the close or even direct contact between jade and body will make it easy for S to seep inside the jade . Hence, there is also the view that the cause of black HgS is the combination of sulfur (or hydrogen sulfide) and mercury . The sever imbalanced content between Hg and S also serve as a reminder that the current study about mercury alteration could not reach a definitive conclusion.
Although the Ca content range of this batch of data is 3.7–13.6%, most of the nephrite is fairly stable in terms of Ca at different tested points. This can only demonstrate that the purity of the tremolite component in some of these nephrite samples is not very good. However, there are still some nephrite pieces that have been affected by weathering, which led to obvious changes in the Ca content of some parts. There is an early claim that the whitening of jade is related to the increase in Ca content, and this has been referred to as calcification . Microscopic observation on the whitening parts shows no significant change in the thickness of the crystal fibers of the constituent minerals, but there is a tendency for the structure to loosen, thus turning from translucent to opaque and fading to white . Then many studies have since shown that Ca is actually lost due to qualitative changes, thus some scholars urged the elimination of the concept of calcification . But recent research have revised these views, suggesting that the ‘calcification’ of the jade whitening actually occurs, usually in neutral and alkaline environments, where the soil pH is closely related to different calcium salts [CaCO3 or Ca(HCO3)2, etc.]. The deposition process of calcium salts is relatively easy while the penetrating is comparatively hard, which makes this calcification phenomenon rare and the whitening mostly appears as a dotted distribution .
To determine the whitening mechanism of Yuehe nephrite, we plotted the Ca content of whitening nephrite in the white and non-white regions for comparison (n = 16) (Fig. 6). The majority of cases show an approximate 10–20% increased Ca content in the whitening part of the nephrite. This is also confirms the rationality of the so-called calcification. In addition, although they are all in a relatively uniform soil micro-environment, there are still 4 samples showing varying weathering performance with a decreased Ca percentage, which probably implies different whitening mechanisms. Most previous studies have been conducted on individual samples [9, 37], with little analysis of the overall condition of jade excavated from a certain site, to the extent that regular insights may have been missed. The relationship between this not-identical deviation of Ca and jade whitening deserves further study.
Combined with cultural factors
As a class of objects made of precious materials, many nephrite artifacts do not appear individually, but in combinations. Examples include the six auspicious jade implements mentioned earlier and complicated hangings consisting of a number of pedants, ornaments and tubes. On the other hand, some jade pieces are used in pairs due to the aesthetic need for symmetry, which has resulted in twin objects with extremely similar appearance (in terms of shape, material, decoration, engraving technique, etc.). It is interesting to note that these twin artifacts may take on a completely different color after being buried in the soil for thousands of years. Various cultural sources of twin samples are available among Yuehe nephrite (Table 3). They provide a case for examining such different secondary variations on almost the same material.
In order to present the similarities and differences of these twin nephrite artifacts in a more integrated way, a principal component analysis was performed on a total of 57 data from 27 samples (see Additional file 3: Table S3 for details). All 11 elements were included in the statistics, as this allowed for a comprehensive representation of the native properties and weathering conditions of each sample. The results are displayed in Fig. 7. The cumulative explained variance ratio is not very satisfactory, and these two principal components only occupy 50% of the contribution, which can barely reflect the potential information of the data. Some types of nephrite samples are more concentrated in distribution, or even independently grouped, such as Animal ornament, Flake ornament B and Yue style artifacts. Even under the influence of weathering and alteration, some nephrite pieces still have common properties.
Examining these samples with regional styles, they almost do not intersect individually, which seemingly suggests somewhat a discernible provenance for the nephrite material. On the contrary, there is a remarkable variation within each group, especially the Dongyi and Chu group, making it difficult to characterize the geochemical elements within a certain range. Many previous analyses of ancient jade (almost exclusively nondestructive) have discussed the issue of distinguishing provenance by elements . They are difficult to exclude visually indistinguishable elemental variation in the jade caused by secondary changes. However, most cases in Fig. 7 still show significant differences between samples of the same nephrite material at different test points (see Additional file 3: Table S3). Some of the test points actually have almost the same hue and other sensory effects. This hints at a very important point in the detection of ancient jade, where visual similarities may in fact contain differences in the elements. This situation reminds of the risk to reveal the geochemical characteristics of ancient jade materials purely from the perspective of the elements. Previous practice could only compare these elemental data with known deposits of nephrite, and tend to seek sources in the neighboring geography of the corresponding territory according to cultural factors . This is rather reckless when nephrite deposits of comparable quality to ancient jade had not yet been identified in the Central Plains (see Fig. 1). Only by clarifying the specific mechanisms of secondary changes can we understand the elemental indicators that represent the ancient jade itself, and thus further discriminate the provenance of the jade material.