Archaeological and Anthropological Sciences
The Ties that Bind: Archaeometallurgical typology of architectural crampons as a method for reconstructing the iron economy of Angkor, Cambodia (10th to 13th c.).
S. Leroy*, M. Hendrickson, S. Bauvais, E. Vega, T. Blanchet, A. Disser, E. Delque-Kolic
*Corresponding author: ; LAPA-IRAMAT, NIMBE, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Gif-sur-Yvette, France.
Additional comments on the Curve of iron-carbon alloys heterogeneity
Since several years, researchers in iron archaeometallurgy look for a rapid and relevant method to describe the qualities of iron-carbon alloys and especially to be able to apply this method to a large set of samples. This method should be capable to express the mechanical properties of an iron-carbon alloy such as a craftsman could comprehend it by his empirical knowledge. These properties are based on the proportion of carbon: the more the alloy is rich in carbon, the more it is hard and fragile and the less it is rich in carbon, the more it is flexible and ductile. Certain plateaux of composition are also important, knowing that under a value of 0.2 % of carbon, the metal is “not quenchable” (hardening of the alloy by fast cooling). On the other hand, the majority presence of ferrite in an alloy lower than 0.2 % of carbon allows a hardening by strain hardening (cold hammering). Finally, an important parameter lies in the distribution of the rates of carbon within the metal. A metal composed of an average of 0.4% carbon, comprising 50 % of hypereutectoid steel (0.8% of C) and 50 % of pure iron (0.02 % of C), does not have the same mechanical properties as a metal completely made up of a 0.4% carbon steel. Finally, the organisation between the various more or less carburised zones implies also very different mechanical properties. A metal made up of strips of hypereutectoid steel and of strips of soft iron will have properties of hardness, elasticity and resilience much better than a metal made up of two juxtaposed zones of 0.8 and 0.02% of carbon.
Until now, researchers had proposed an interpretative framework based on the rate of average carbon and on the proportion of the surface higher or lower than 0.2% of carbon, this value indicating if the steel can be quenched or not (Pagès et al., 2008, Pagès et al., 2011, L'Heritier et al., 2013). Even if it rested on valid theoretical bases, this system was however not efficient and answered only half problems asked by the characterisation of iron-carbon alloys in archaeometallurgy. First, the domains of existence of the proposed groups were not coherent and second, it did not take into account the heterogeneousness of the distribution of the carbon. That's why we propose a new interpretative framework that allows taking into account the carbon distribution within the metal in order to describe better the intrinsic heterogeneity in the direct process of iron-steel making.
This new framework also bases on the rate of average carbon content weighted on the surface (`X) but this time in connection with the standard deviation of the mean always weighted on the surface (s), such as:
X=1i=1nWii=1nWiXi
and as:
σ= 1i=1nWii=1nWiXi-X2
Where Xi is the mean value of each of the carbon rates categories and Wi is the weight assigned to each of the carbon rates categories. This new framework has the form of a bell, defining a domain of distribution of the analysed objects. It possesses superior and lower limits which are imposed by the context of the study. In this work, it is limited to 0.9% of carbon, what corresponds to the limits of the metal forgeability and to the highest rate detected in our set of sample. Inside this bell-shape, the more an object is situated on the top, the more the metal which makes it up is heterogeneous, i.e. the more it is composed of metallic zones for which the rate of carbon contents are distant (max. s=0.37). So, in the vertical axis, the bell can be divided into four zones indicating degrees of homogeneity as followed:
· Degree 1 - Homogeneous: standard deviation lower than 0.1. It is the maximum standard deviation for an object composed of two categories of very close carbon rates and of identical surfaces (for example 50% of 0.1/0.3% and 50% of 0.3/0.5%);
· Degree 2 – Slightly heterogeneous: standard deviation from 0.1 to 0.2. This upper limit is the maximum standard deviation for an object having two categories of carbon rates distant from one category and of identical surfaces (for example 50% of 0.1/0.3% and 50% of 0.5/0.7%);
· Degree 3 – Moderately heterogeneous: standard deviation from 0.2 to 0.3. Tis upper limit is the maximum standard deviation for an object having two categories of carbon rates distant from two categories and of identical surfaces (for example 50% of 0.1/0.3 % and 50% of 0.7/0.9%);
· Degree 4 - Heterogeneous: standard deviation from 0.3 to 0.37. This limit is the maximum standard deviation for an object (for example 50% of 0.02/0.1% and 50% of 0.7/0.9%).
Given that the graph represents a mean rate of carbon and a standard deviation and given that several combinations of compositions can give an identical mean rate of carbon, it is not possible to define a strict existence domain of certain alloys. Nevertheless, big tendencies emerge. Domains proposed in this article are defined according to limits arbitrarily fixed at 80 %, given that a composition of 80 % and more of the surface of an object can be considered as characteristic of the global properties of the object. It is necessary to note that in the previous attempts of alloys characterisation, the threshold had been fixed to 70 % and that we are more restrictive here (Pagès et al., 2011, L'Heritier et al., 2013). The chosen limits respect the usual definitions of iron-carbon alloys with between 0.02 and 0.2%C Low Carbon Steel, between 0.2 and 0.6%C Medium Carbon Steel and High Carbon Steel for metal from 0.6 to 0.8%C.
The combination of both parameters allows us to define existence domains of the studied alloys. These domains represent tendencies because it is not possible to represent strict limits between them (see Figure).
Figure: Definition of the existence domains of alloys, based on the heterogeneity of the carbon distribution (standard deviation) and on the mean rate of carbon.
References
Pagès G, Long L, Fluzin P, Dillmann P (2008) Réseaux de production et standards de commercialisation du fer antique en méditerranée : les demi-produits des épaves romaines des Saintes-Maries-de-la-Mer (Bouches-du-Rhône, France). Revue archéologique de Narbonnaise, 261-283
Pagès G, Dillmann P, Fluzin P, Long L (2011) A study of the roman iron bars of Saintes-Maries-de-la-Mer (Bouches-du-Rhône, France). A proposal for a comprehensive metallographic approach. Journal of Archaeological Science 38:1234-1252
L'Heritier M, Dillmann P, Aumard S, Fluzin P (2013) Iron? Wich iron? Methodologies for metallographic and slag inclusion studies applied to ferrous reinforcements from Auxerre Cathedral. In: Humphris J, Rehren T (eds) The World of Iron. Archetype Publications, London, pp 409-420