Determining alloying practices from chemical composition

The first attempt to understand alloying practices (i.e. the formulation of the copper alloy) from chemical composition was made by Caley (Reference Caley1939) using Greek bronze coinage. He based his argument on a set of analyses of 86 closely dated Greek coins (from the second half of the fourth century BC to the third century AD). He observed systematic variations in the proportions of copper, tin and lead over time and between issues—for example, the early coins (mid fourth to mid third century BC) had uniformly high copper (80–90 per cent), with varying proportions of lead and tin, while the level of copper was lower but more variable from the second half of the third to the second half of the second century BC. The highest proportion of tin occurred in the earliest period and the percentages of lead varied more erratically than either copper or tin (from <2 per cent to a maximum value of 36.76 per cent). Up to 2 per cent lead was considered as unintentional, but deliberate addition was dominant from the second century BC onwards. The overall trend identified by Caley was a gradual decline in average tin and a rapid rise in lead from the second century BC onwards.

The main purpose of Caley's analysis was to understand how this variation in lead and tin came about. In order to achieve this, Caley (Reference Caley1939: 111–35) discussed the composition of these coins in terms of three ratios:

$$R = \displaystyle{{( {{\rm \% }Sn + {\rm \% }Pb} ) } \over {{\rm \% }Cu}}$$

$$r1 = \displaystyle{{{\rm \% }Sn} \over {{\rm \% }Cu}}$$

$$r2 = \displaystyle{{{\rm \% }Pb} \over {{\rm \% }Cu}}$$

Caley divided the observed variation into two types of change:

• • Type I: change in tin percentage compensated by an equal change in lead (R remains constant but r1 and r2 change).

• • Type II: change in tin percentage accompanied by much greater change in lead, resulting in an increase in R.

Type I change implies substitution of tin by lead in a controlled way and only occurs in early series of coins of the same type, issued within a short period. In general, however, the ratio of %Sn to %Pb is greater than 50 per cent (i.e. tin is the dominant alloying element). Caley postulated a series of recipes for replacing tin with lead, either by adding an amount of lead or replacing the tin with a tin/lead alloy, citing Pliny to support the second suggestion.

Type II coins are different and are conventionally seen as replacing copper with lead (e.g. Hammer Reference Hammer1908). Caley defined two patterns of alloying that could be employed in Type II change—‘addition’ (the addition of lead to an existing ternary bronze) and ‘replacement’ (the substitution of copper with lead)—and used the values of the three defined ratios to distinguish between them. In ‘addition’, r1 would remain constant (since both %Cu and %Sn are equally diluted), but r2 and R would increase. In ‘replacement’, both r1 and r2 would increase, as would R. Caley (Reference Caley1939: 133) concluded by stating:

This is an important and ingenious way of distinguishing between the different possible practices of the coin-casters at the point of manufacture—in the Greek case, it appears that the later alloys were made by diluting existing ternary bronze with additional lead, rather than making the alloys afresh from three components (copper, tin and lead), and gradually increasing the amount of lead at the expense of the copper.

Alloying of pre-Qin Chinese coinage

Caley's work demonstrates that a careful study of the ratios of copper, tin and lead can reveal important insights into bronze alloying practice. In a recent study of the chemical composition of pre-Qin (before 221 BC) Chinese copper coinage (Pollard & Liu Reference Pollard and Liu2021), rather than trying to produce representative averages for a particular coin type, we used a similar methodology to that of Caley (Reference Caley1939), considering ratios r1 and r2 and focusing on trend lines within the analytical data. Plotting the available data shows that the three main alloying elements (Cu, Sn and Pb) vary widely, even within a specific type of coinage, so that the recipe for the casting alloy is inadequately characterised by a set of averages of copper, lead and tin.

As an example, Figure 1 shows a plot of %Sn vs %Pb for the knife-coins (刀币) of the Warring States period (475–221 BC), divided typologically by Zhou (Reference Zhou2004) into four types: Yan knives (n = 178); Qi knives (n = 35); straight knives (n = 16); and other knives (n = 6). The Qi and Yan knives are linked to their use in the Qi and Yan States, perhaps indicating a more similar production procedure. The figure shows a strong negative correlation between tin and lead. An average composition for the Qi knives, for example, would be an inadequate description of their composition as a group, and suggests that it is best described by a trend line, reflecting the linear relationship between lead and tin. Moreover, it is apparent that the Qi knife-coins are very similar in composition (strictly, ranges of composition) to other contemporaneous coinage, despite slightly different trend lines for Yan knives, Qi knives and straight knives. This is potentially relevant in the context of the Kaogong ji, since some authors (e.g. Zhou Reference Zhou1978) have suggested that the six recipes only applied to the Qi state during the Warring States period. Although Figure 1 applies to coins and not to the categories of object defined in the Kaogong ji, it does suggest that the practice of metal casting in the Qi state was similar to that of other states during the Warring States period.

Across the entire dataset of pre-Qin coins produced by Zhou (Reference Zhou2004), the correlations calculated by Pollard and Liu (Reference Pollard and Liu2021) between the major elements are:

$$\eqalign{& {\rm Cu}{\hbox-}{\rm Pb}\colon \;r = -0.965 \cr & {\rm Cu}{\hbox-}{\rm Sn}\colon \;r = 0.443 \cr & {\rm Sn}{\hbox-}{\rm Pb}\colon \;r = -0.597} $$

These correlations can be interpreted as follows: the strong negative correlation between copper and lead shows that as lead increases copper decreases, indicating that copper is replaced by lead in a dilution process. The weaker positive relationship between copper and tin shows that the coins with the highest copper also tend to have the highest tin. This weak positive association between tin and copper indicates that the alloying is not a simple dilution of copper with lead and tin (in which case tin would correlate negatively with copper, and tin and lead would correlate positively) but is more likely to be one of bronze (copper plus tin) diluted with lead, which would give the correlation trends observed in the data.

If we are correct in assuming that the process is a dilution of bronze with a lead alloy, then those coins with the highest values of tin and the lowest values of lead should be closest to the composition of the bronze component before the lead is added. Inspection of the entire dataset suggests that the highest tin values in the pre-Qin coinage are approximately 18 per cent, and the corresponding lead value is approximately 15 per cent. This composition is reasonably close to that of the Eastern Zhou ritual vessels that have the highest tin values—10 per cent lead, 18 per cent tin and 72 per cent copper (data from So Reference So1995). For the purposes of modelling the effect of mixing various combinations, we have therefore assumed that they might approximate the composition of the undiluted, raw ‘stock bronze’. This does not necessarily imply that coins were made from ‘recycled’ ritual vessels (although this could be true)—simply that the stock bronze alloy for coins was similar to that used for making ritual bronzes.

We have previously suggested that the simplest explanation for the alloy compositions of many of the pre-Qin coins is that they fit a mixing line between two starting components (Pollard & Liu Reference Pollard and Liu2021): one containing copper, lead and tin (i.e. a leaded bronze of approximately 80 per cent Cu, 15 per cent Sn and 5 per cent Pb), and one containing only copper and lead. For the latter, we used a 50/50 copper-lead alloy, which approximates the composition of ‘crude lumps’ of metal recovered archaeologically from hoards (Dai & Zhou Reference Dai, Weirong, Oddy and Cowell1988) and initially interpreted as primitive coinage. This suggestion that the composition of most of the pre-Qin coinage could be explained by a binary mixing model of two components was surprising, since the previous (and natural) assumption was that these ternary alloys were made from three independent starting components. The correlation structure within the major element data, however, indicates that this is unlikely.

Implications for the six recipes

The results summarised above focus on coinage, which are not the subject of the six recipes, and which are likely to have been produced in specialised mints, probably under centralised administrative control. Casting practices may therefore have been quite different in foundries producing bronze vessels and weapons. Nonetheless, the significance of casting leaded bronze (i.e. ternary metal) objects from a binary composition of pre-alloyed components is of great relevance to a reconsideration of the six recipes. If correct, it immediately solves the main question: how were ternary alloys produced from two components, Jin and Xi? Can we therefore make the leap and assume that Jin was a tin-bronze (or leaded tin-bronze), and that Xi was a predominantly lead alloy?

Table 2 shows a re-interpretation of the compositions in the six recipes, assuming that Jin is a bronze alloy with a composition of 80 per cent copper, 15 per cent tin and 5 per cent lead, and Xi is a binary 50/50 copper-lead alloy. As in Table 1, Model I assumes that Jin is the final resulting alloy, and Model II that Jin is a separate component. Figure 2 shows a plot of these data against an accumulated database of the chemical analyses of Eastern Zhou objects (data sources listed in the online supplementary material (OSM)).

Figure 2. Plot of %Pb (lead) vs %Sn (tin) for analysed metal objects from elite Eastern Zhou tombs, and predicted compositions for the six recipes from Table 2 (Model I) (summarised and plotted by the authors; for the background data, see the online supplementary material).

Table 2. The six recipes reinterpreted assuming Jin = 80 per cent Cu (copper): 15 per cent Sn (tin): 5 per cent Pb (lead) and Xi = 50/50 Cu/Pb.

This shows that interpreting the two components in the six recipes as pre-prepared alloys is at least plausible—in all six cases, the modelled data fit within the distribution of the analytical data. If Jin and Xi were pure copper and tin, respectively, then the modelled points would lie on the tin axis, with no lead present. Granted, some objects have no lead and could have been produced from such a recipe, but the vast majority contain large quantities of lead. Figure 2 also demonstrates that the model proposed by Liang (Reference Liang and Wang1925) and subsequent researchers—that Jin is copper and that Xi is a tin-lead alloy—is unlikely for most cases, since this would give an overall positive correlation between lead and tin starting at the origin, as shown from the modelled data in Figure 3. The key feature here for any combination of copper with a binary tin-lead alloy is the positive correlation of the mixing lines, radiating from the origin (which, in this case, corresponds to 100 per cent Cu). Also shown in Figure 3 are two other models: one starting with a binary copper-tin alloy (80/20) diluted with pure lead, and also a binary copper-lead alloy (60/40) diluted with pure tin. The first of these shows a correlation that could be accommodated by the distribution in Figure 2, suggesting that this combination, or some variant of it, could also be involved in Eastern Zhou alloy production. Clearly, this does not define conclusively the nature of Jin and Xi—the hypothesis that Jin and Xi could represent a leaded bronze diluted by a binary copper-lead alloy, as identified in the study of pre-Qin coinage, is certainly plausible, in that it reflects the structure of the analytical data. This is not to say that it is the optimal model or even the only plausible one. It does, however, mitigate against the previous view that Jin and Xi are copper and tin, respectively, or even that Xi is a tin-lead alloy.

Figure 3. Model data for pure Cu (copper) diluted with increasing amounts of: 75 per cent Pb(lead)/25 per cent Sn (tin); 50 per cent Pb/50 per cent Sn; 75 per cent Sn/25 per cent Pb; binary Cu-Sn (80/20) diluted with pure Pb; and binary Cu-Pb (60/40) diluted with pure tin (summarised and plotted by the authors).

Another significant observation from Figure 3 is that most of the analysed objects from the Eastern Zhou do not conform well to any of these formulaic recipes, which calls into question the interpretation or applicability of the six recipes. If the data are broken down into object type and plotted against the appropriate formula, we see little correspondence. Figure 4, for example, shows a plot of the analysed Eastern Zhou objects from Shandong Province (approximating to the ancient Qi state, where the six recipes were assumed to have been recorded), with the two interpretations of the composition of objects from Table 2. It is evident that the lead content of either model appears unanimously higher than the chemical analyses of the excavated objects, regardless of object types. Meanwhile, a few objects show much lower levels of lead or tin, which cannot fit to any interpretation of the six recipes. This lack of correspondence should come as no surprise, as it has been observed since at least the 1970s (Zhou Reference Zhou1978; Wu Reference Wu1986) and has been eloquently summarised by von Falkenhausen (Reference von Falkenhausen2014), who, as noted above, suggests that the clarity of the ratios outlined in the six recipes are an administrative fiction, at best.

Figure 4. Plot of Eastern Zhou objects from Shandong Province (circles), together with calculated compositions from Table 2 (triangles) (summarised and plotted by the authors; for the background data, see the online supplementary material).

The identity of Jin and Xi

Even if the detail of the six recipes is not reflected in the analytical data, it remains important to understand what Jin and Xi were. The existence of these six formulae clearly indicates an administrative desire for a systematic and regulated approach to metal production during the Zhou Dynasty, although the scatter of the analytical data shows that this was not universally achieved. This could be related to the organisation of Eastern Zhou metal production, and no doubt discussion of this will continue. The idea that pre-prepared complex alloys were used as the raw materials for casting bronzes in pre-Qin China at a time when, from the archaeological evidence, relatively pure copper, tin and lead ingots were also available, requires a re-evaluation of the technological choices made by early Chinese bronze-casters. We have suggested, extrapolating from our study of pre-Qin coinage, that a bronze approximating to 80 per cent copper:15 per cent tin:5 per cent lead and a diluting component corresponding to an approximate 50/50 copper-lead alloy might have been suitable starting materials, and may therefore have corresponded to Jin and Xi, respectively. We are not suggesting that these are the precise compositions of Jin and Xi, merely that they are examples of what Jin and Xi might have been. If this is the case, then it would imply an additional step in the chaîne opératoire of metal casting—the production of prefabricated alloys for casting, to be supplied to the metal-casters. The obvious question is where did this prefabrication take place—the smelting site, the casting site, or elsewhere—and who performed this step, and why?