Deriving the Metal and Alloy Networks of Modern Technology

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Deriving the Metal and Alloy Networks of Modern Technology Hajime Ohno, Philip Nuss, Wei-Qiang Chen, and Thomas E. Graedel Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b05093 • Publication Date (Web): 29 Feb 2016 Downloaded from http://pubs.acs.org on March 15, 2016

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Environmental Science & Technology

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Deriving the Metal and Alloy Networks of Modern Technology

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The authors:

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Hajime Ohno *

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Center for Industrial Ecology, Yale School of Forestry & Environmental Studies, 195 Prospect St, New Haven, CT 06511, USA

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Graduate School of Engineering, Tohoku University, 6-6-04, Aramaki Aza Aoba Aoba-ku, Sendai, Miyagi 980-8579, Japan [email protected] +81+22-795-8569

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Philip Nuss

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Center for Industrial Ecology, Yale School of Forestry & Environmental Studies, 195 Prospect St, New Haven, CT 06511, USA [email protected]

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Wei-Qiang Chen **

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Center for Industrial Ecology, Yale School of Forestry & Environmental Studies, 195 Prospect St, New Haven, CT 06511, USA Institute of Urban Environment, Chinese Academy of Sciences, 1799 Jimei Road, Fujian 361021, P.R.China [email protected] +86-592-6190-763

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Thomas E. Graedel

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Center for Industrial Ecology, Yale School of Forestry & Environmental Studies, 195 Prospect St, New Haven, CT 06511, USA [email protected]

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* Corresponding Author: Tel.+81-22-795-5869, Email: [email protected] ** Co-Corresponding Author: Tel. +86-592-6190-763, Email: [email protected]

1 ACS Paragon Plus Environment


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Abstract

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Metals have strongly contributed to the development of the human society. Today, large amounts

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of and various metals are utilized in a wide variety of products. Metals are rarely used

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individually but mostly together with other metals in the form of alloys and/or other

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combinational uses. This study reveals the inter-sectoral flows of metals by means of

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input-output (IO) based material flow analysis (MFA). Using the 2007 United States IO table, we

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calculate the flows of eight metals (i.e., manganese, chromium, nickel, molybdenum, niobium,

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vanadium, tungsten and cobalt) and simultaneously visualize them as a network. We quantify the

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interrelationship of metals by means of flow path sharing. Furthermore, by looking at the flows

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of alloys into metal networks, the networks of the major metals iron, aluminum, and copper

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together with those of the eight alloying metals can be categorized into alloyed-,

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non-alloyed-(i.e. individual), and both mixed. The result shows that most metals are used

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primarily in alloy form and that functional recycling thereby requires identification, separation,

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and alloy-specific reprocessing if the physical properties of the alloys are to be retained for

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subsequent use. The quantified interrelation of metals helps us consider better metal uses and

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develop a sustainable cycle of metals.

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Key words: input-output analysis, material flow analysis, alloying metals, alloys

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TOC

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1. Introduction Metals have been indispensable in our lives since the first invention of metal goods during

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the Stone age1. The use of bronze during the Bronze Age marks the starting point for the use of

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metals in alloy form1. For example, raw steel (an iron-based alloy containing up to 2% carbon) is

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oftentimes used with varying alloying elements (e.g., chromium, manganese, molybdenum, and

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vanadium) to obtain various physical and chemical properties, such as hardness, workability,

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corrosion resistance, and heat resistance.

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Because modern society is highly dependent on the use of various minerals and metals,

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various studies in recent years have investigated the topic of resource criticality2-6. The goal of

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these criticality studies is to provide insights into the geological distribution of metals and related

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geopolitical, social, and regulatory aspects in the sourcing countries, companionality (i.e., the

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fraction of an element obtained as a byproduct with another metal)7, environmental implications8,

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aspects of substitutability9, recycling potential10, and the overall importance of the resource to

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the global economy. Increasing recycling of metals can support the sustainable use of metals.

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However, recovering an individual metal from its alloyed form can be difficult under current

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technical and economic conditions11, 12. Several studies on the thermodynamic behavior of metals

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in pyro-metallurgical processes discuss the difficulties associated with metal recovery from

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major metal-based alloys (e.g. steel or aluminum- and copper-based alloys)12-15. These are

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related to a metal’s thermodynamic behavior in pyro-metallurgical processes, e.g., whether a

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metal; remains in the metal matrix, is being oxidized to the slag phase, or vaporized to the gas

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phase. Except metals vaporization (e.g. zinc in steel recycling)16, commercial base technologies

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for recovering individual metals from alloys have not yet been well developed. Therefore, as

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long as alloys are recycled for the purpose of mainly recovering base metals, alloyed elements


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are unintentionally dissipated as contaminants and/or by-products17. To prevent the dissipation of

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alloying metals during recycling, recent research points out the importance of the

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quality-oriented scrap allocation sorting scrap according to contents of metals for the sustainable

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metals use, especially for aluminum alloys18, 19. However, in order to implement the appropriate

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scrap allocation for various metals and alloys, understanding metals and alloys usages in a

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society would be necessary.

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A potential tool for the detailed study of inter-sectoral flows in an economy is the use of

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input-output tables (IOT) which are constructed on a regular basis by national statistical

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offices20. In such tables, the rows and columns indicate individual sectors of the economy and

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the matrix elements reflect transactions between two sectors in a given year. The level of detail

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differs from country to country – in the United States the IOT is given at 389 x 389 matrix

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resolution in 200721. Although the use of some 400 sectors would seem more than adequate to

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describe a national economy, the 2007 IOT of the United States contains independent sectors for

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only three metals, i.e., iron, copper, and aluminum, and even for these metals the entries are in

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monetary rather than physical units. Nonetheless, it is possible to convert the monetary

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transactions in IOTs to physical flows of metals22, 23 and thereby generate an inter-sectoral

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network for metals characterized by individual sectors (see our companion paper 24 where we

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derive a metal network for aluminum in the 2007 US economy).

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For metals without specific IOT sector entries (i.e., elements other than aluminum, iron,

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and copper), a different approach is required. For those metals, the IOTs provide only aggregated

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information, e.g., the “Nonferrous metals” sectors which comprise data about several metals

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within a single sector.



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However, IO based material flow analysis (MFA) provides some methods to help with the

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disaggregation of sectors in an IOT based on the waste input-output material flow analysis

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(WIO-MFA) model22, 23. Specific examples include plastics25, steel alloying elements17, 26, and

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automobile parts27. Of particular interest here is the work of Nakajima et al.26, which visualized

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flows of chromium, nickel, and molybdenum of automobile production in Japan.

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Based on the above work and the approach described in our companion paper24 for

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aluminum, we derive the metal networks of eight “alloying” metals (i.e., manganese, chromium,

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nickel, molybdenum, niobium, vanadium, tungsten and cobalt) in the 2007 US economy. The

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results are visualized using a Sankey diagram covering the entire economy-wide supply chain of

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these metals. The eight metals were chosen because they have large consumptive uses and

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because they are typically related to the three major metals in the form of alloys28 (Some relevant

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characteristics of these metals are given in Table S1 in the Supporting Information). As

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Nakamura et al.29 pointed out, “Sankey diagrams may become too complex for effective

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visualization” for several hundreds of sectors. An additional challenge is that we have multiple

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metals to be simultaneously visualized in a Sankey diagram. However, by applying the approach

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of Chen et al.24 (a companion paper) to aggregate and simplify the number of sectors as well as

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distributing sectors according to their degree of fabrication, the readable simultaneous picture of

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metal flow can be visualized. The diagram then provides a comprehensive view of major metal

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uses in society. In addition, by regarding sectors and flows as nodes and edges (directed and

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weighted) respectively, the flows of metals can be regarded as inter-sectoral networks. “Edge” is

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common terminology in network analysis to express the flow of resources or information

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between two nodes30. Here the nodes are sectors and the edges represent either monetary or mass

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flows. As Nuss et al.31 (another companion paper) demonstrates, various measures of network


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analysis can then be applied to the IO-based material flow networks (IO-MFNs) of metals to gain

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insights into sector “importance”, supply chain risk, and the overall network structure. This

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information is therefore also relevant in the context of resource criticality analysis31. In this

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paper, we derive and compare metal IO-MFNs in terms of the sharing of edges. Besides showing

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the overall network diagrams, we quantitatively study to what degree the metals coexist with

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each other in the economy by analyzing the edge sharing among metals. The coexistence of

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metals measured by edge sharing then reflects the challenges of any subsequent separation of

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metals and alloys in recycling operations.

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2. Methodology

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2.1 Conversion of the monetary IOT to a metal IOT

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The multi-step processes of converting the monetary IOT to a metal IOT and finally

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obtaining an IO-MFN are outlined in Figure 1. A very detailed description of applying these

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processes to aluminum has been provided in Chen et al24. Here we provide a shorter and general

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version for the convenience of readers. The first step involves the disaggregation of sectors and

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unit conversion of IO table from monetary to physical units to obtain a hybrid IO table ∗ .

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Details are provided in section 2.2. Secondly, an input coefficient matrix is calculated20.

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Thirdly, the input coefficient matrix is multiplied with two filtering matrices, i.e., (1) a physical

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flow filter Φ which is a binary matrix removing non-physical flows (e.g., services) and physical

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flows that do not incorporate the studied metal into the final product (e.g., process catalysts), and

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(2) the yield loss filter matrix Γ that removes the mass of inputs that become process waste. The filtered input coefficient matrix = Γ ⊗ (Φ ⊗ ) then consists of (which represents input coefficients whose ( , )-element is the monetary or physical input of Product to 7 ACS Paragon Plus Environment


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Product ) and (which represents input coefficients whose ( , )-element is the physical

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input coefficient of Material to Product ). The unit of is tonne per monetary unit (but

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see below for a discussion on IO-MFN units). In the fourth step, the waste input-output material

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flow analysis (WIO-MFA) model23 is computed to calculate the matrix of material composition

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of products ( ) by:

= ( − )

(1)

As Nakamura et al.23 noted, the IOT representing inter-sectoral transactions can readily be converted into the corresponding flow of materials. Consequently, during the fifth step the

hybrid IO table can be simply transformed into a physical IO table for metals and alloys by formulating the product of the diagonalized of a material (i.e. metal) and the IOT as: ∗ diag ( (,∙)) = ∗

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∗ Here, ∗ represents the endogenous IO matrix obtained in the second step, consisting of ∗ and with the same classification as (for the detailed definition, see Supporting

Information). (,∙) represents the th row of the matrix . Let

be the vector of the

net trade of products and !(,∙) the mass of waste material generated in the supply chain. Then the IO-MFN of metal in an economic system can be expressed as: ∗ diag ( (,∙)) = ∗

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(2)

diag ( (,∙)) (, )

!(,∙) 0

We address the calculation sequence in more detail in the Supporting Information.

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2.2 Sector disaggregation and arrangement for the model application to the U.S. IOT

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2.2.1 Definition of sectors


(3)

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Although a large variety of metals are used by modern society, their trade in the economy

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is highly aggregated in the original IOT for the U.S. into only five sectors (the five sectors listed

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in the first column of Table 1). The sector for “Iron and steel mills and ferroalloy manufacturing”

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includes sub-sectors producing raw materials based on iron, many types of ferroalloys, crude

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steels, and finished steels. Similarly, the sector “Primary smelting and refining of nonferrous

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metals” aggregates industries producing many different metals. The sector, “Nonferrous metal

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rolling, drawing, extruding, and alloying” aggregates the nonferrous processing industries. In

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order to disaggregate flows from those sectors into flows related to a specific nonferrous metal,

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these sectors were disaggregated into the sectors indicted in the second column of Table 1. As a

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consequence of the disaggregation, the five metal-related sectors were disaggregated into 34

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sectors related to individual metals, metal materials, scrap, and products. The disaggregation

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made the iron flow clear as well because iron sources were separated from the original

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aggregated sector for iron.

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Sectors of metal raw materials such as ferroalloys and metals themselves were

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categorized as "Material" sectors for the analysis. The ferroalloys in the “Material” category

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were considered as sources of both iron and corresponding alloying elements according to their

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chemical composition28. Consequently, flows of iron and an alloying element incorporated in a

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ferroalloy were separately analyzed. In addition, sectors of three different grades of crude steels

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and nonferrous alloys were defined as "Fabricated material", which is midway between Material

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and Product in the model. The distinction of this intermediate category enables us to analyze the

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flows of alloys defined as “Fabricated material” by setting their inputs as products in

instead of inputs as “Material” in the model23. In other words, when we describe direct inputs of



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"Material" sectors in , we can obtain individual metal flows; when we utilize "Fabricated material" sectors in , alloy flows can be obtained.

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2.2.2 Disaggregation of sectors The disaggregation of sectors is conducted for both rows and columns of the IOT. In

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addition to the disaggregation, values in the rows are converted to physical units. An exception

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to this approach relates to the sector “Nonferrous metal (except copper and aluminum) rolling,

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drawing, extruding, and alloying”, which is disaggregated into two sectors but remains in

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monetary units because the total production of nonferrous alloys and superalloys in physical

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units could not be obtained from the available data (Supporting Information).

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The approach to the disaggregation of sectors highly depends on the data availability in the

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region for which the IOTs are provided. Nakajima et al.26 and Ohno et al.17, 27 used the Japanese

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IOT 32. In this work we used the U.S. IOT21. These tables have the highest resolutions compared

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to IOTs of other economies, and can be used together with data such as the year book of iron and

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steel for Japan 33 and the minerals year book for the U.S.28, respectively. If only lower IOT

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resolution is available, similar disaggregation of sectors could be challenging for other countries

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or regions. The disaggregation of sectors provides many benefits for metal flow analysis, but

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introduces uncertainties as well, because assumptions and estimations are necessary when

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adjusting the available data into the form of an IOT having around 400 sectors. The detailed

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operations of the disaggregation taken in this study are explained in the Supporting Information.

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Because the assumption of unique sectoral prices34 for metals is generally not satisfied in the sectors of the IOT, the direct conversion of monetary unit to physical unit may introduce


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uncertainties into the analysis. For example, when the aggregated “Iron and steel mills” sector

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sells 1 million USDs of products to two different downstream sectors such as pig iron and

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stainless steel, the physical flow distribution will vary depending on price differences between

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pig iron and stainless steel, respectively. This problem can be partly reduced by further

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disaggregating the economic sectors. However, given the current resolution of the US IO table

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used in this study (~400 sectors), direct conversion of monetary units to physical units using

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homogeneous sectoral prices will likely cause some inconsistences between the analysis and

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reality. In this regard, rather than expressing the transformed metal units (TMUs) in mass terms,

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calculated units are formally designated in “hektes” as discussed in our companion paper24. This

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new unit expresses the relative magnitudes of physical flows without implying that an actual

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physical unit such as kilograms is appropriate.

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2.3 Comparison of IO-MFNs

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The resulting networks for the eleven metals and seven alloys can be studied by regarding

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each sector in the IOT as a node and the input of each sector to another as an edge. Because the

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networks were built in the same inter-sectoral structure, we can compare the IO-MFNs in terms

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of edge sharing. One edge property involves the number of shared edges, in which the degree of

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edge sharing among metals represents their potential coexistence in technological uses. For

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example, when the networks of Fe and Cu (having 57,321 and 31,654 edges, respectively, see

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Table 2), share 31,654 edges with each other, the degrees of edge sharing between Fe network

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and Cu network are calculated as 55% and 100% for Fe and Cu respectively. A second network

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property takes the total strength of shared edges into account, thus representing the significance

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of the relationships among metals in the whole network. This measure takes into account the



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weighting of edges (i.e., the quantity of physical flow of metal between sector as expressed in

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hektes). For example, Fe and Cu are found to have 307 kh (kilohektes) and 5.4 kh of total edge

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strength, respectively. If shared edges have 114 kh of edge strength in the Fe network and 5.4 kh

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of edge strength in the Cu network, the weighted degree of edge sharing will be 37% for Fe and

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100% for Cu. In this case, 37% of the total mass of iron appears to be related to the network of

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copper.

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For clarity in examining the flows of metals, we applied a threshold cutoff of 1 hekte

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(otherwise almost all edges are shared by all metals, because nearly all sectors employ tiny

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amounts of all metals). The quantitative effect of applying this threshold to the networks is

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summarized in Table 2. There is substantial coherence across the metals in terms of edge

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strength, but not of total edges. This indicates that the preponderance of metal flows occurs

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together from early to late sector flows, but that small amounts of metals such as cobalt and

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tungsten see diverse use in sectors other than those involving the major metals.

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∗ We utilize = diag( (,∙)) in which represents a metal IOT including

Product to Product of the metal flow (i.e. inter-sectoral supply chain) to compare the IO-MFN of metals with each other. From set theory, edge sharing between two different metal ( ∈ α, β) networks (N % , N & ) can be expressed as follows:

Edge sharing = N % ∩ N &

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(4)

Hereafter, metal IO-MFNs themselves are expressed as N to distinguish them from the supply chains of metals, .

To quantify the degree of edge sharing based on the IOT that was obtained, let V be

the edge detecting binary matrix for metal “m”, having the ( , )-element v01 defined as


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v01 =2

253 254 255 256

1 ( , ) − element of >1 0 otherwise

(5)

> 1 represents the threshold for removing edges with strengths less than 1 hekte from the

network. (This table is also defined as the adjacency matrix or Boolean matrix20). By comparing matrices V of each metal pair, the degree of edge sharing can be calculated. Here, ∑0 ∑1 v

represents the numbers of edges in an IO-MFN for metal . Because V contains only 1 and 0,

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the result of subtraction of V for metal α and metal β provides 1, 0, and -1 values defined as

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follows: %& ∆v01

1 N> ∖ N@ BBBBBBBBBBB > ∪ N@ = = 0 N > ∩ N @ or N −1 N@ ∖ N>

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By summing ∆V %& = C∆v01

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Finally, the degree of edge sharing can be calculated:

%&

D∆v01

%&

S = G1 −

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= 1E, the numbers of unshared edges can be determined.

∑0 ∑1 ∆V %& H × 100 ∑0 ∑1 ∆V %

element-wise product of with V , representing metal flows over 1 hekte and ∆J %& the

element-wise product of ∆V %& with J , including the weights of shared edges. The

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weighted degree of edge sharing is then ∑0 ∑1 ∆J %& SL = G1 − H × 100 ∑0 ∑1 ∆J %

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(7)

The degree of weighted edge sharing can be calculated as well. Let J be the

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(6)

(8)

We can distinguish the two types of coexistence by comparing the networks of metals with those of alloys. Because alloys contain metals, metals contained in an alloy share the same



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network as the related alloy. Thus, the supply chain of a metal in alloy forms, N 0M NOOPQ , can be

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calculated as follows: N ∗ = diagR (S,∙)T

0M NOOPQU

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W

N = V (,∙) NX

(9)

(10)

N where S denotes a specific alloy and represents the supply chain of alloy S. For metal

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networks not contained in alloys, the network Y MPMNOOPQ can be obtained based on the

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supply chains of metals not contained in alloys:

MPMNOOPQ

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= −

0M NOOPQ

(11)

These two networks and the original networks satisfy the following relationship: N = N 0M NOOPQU ∪ N MPMNOOPQ

(12)

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According to this relationship, the edge sharing among metals can be categorized into three

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groups; A: sharing edges only as alloy forms, either alloyed together or combined physically as

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alloy forms (i.e., A = N 0M NOOPQU ∖ N MPMNOOPQ ); B: sharing edges only in non-alloy form (i.e.,

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B = N MPMNOOPQ ∖ N 0M NOOPQU ); and C: sharing edges in both alloy and non-alloy forms (i.e., C = N 0M NOOPQU ∩ N MPMNOOPQ ).

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3. Results and Discussion

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3.1 IO-MFN visualization

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The derived IOTs are commonly presented as numerical spreadsheets. However, graphical

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approaches are useful methods for illustrating some of the most interesting features of the tables.

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An example is the IO-MFN for cobalt, shown in Figure 2. For all network diagrams in this paper,


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sectors in the IOT were aggregated into 106 nodes (which is more than the 99 nodes in Chen et

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al24 due to sector disaggregation). The layout of the nodes is according to their place in the

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fabrication sequence, that is, sectors at the left side of the diagrams represent early stages of

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fabrication while those at the right side reflect later stages. The U.S. did not mine cobalt in 2007

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of the figure). The imported cobalt had two principal destinations. One was its use in Batteries

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(the pale blue arrow from lower left to the right center of the network). The other was the

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formation of non-ferrous alloys (largely nickel-based superalloys) (the light blue line from lower

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left to left-center), followed by Forging & Stamping and then by the flow to the Aerospace sector

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for use in aircraft engines. More careful examination reveals such features as imports of batteries,

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flows of cobalt-containing products to the Machinery sector, the transfer and reuse of new scrap,

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and a web of cobalt-containing flows to a very large number of sectors in the national economy.

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Similar diagrams for manganese, chromium, nickel, molybdenum, niobium, vanadium, and

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tungsten appear in the Supporting Information (Figure S2 to S8). The flows coming directly from

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a metal node correspond to relatively well known flows of metals because their values are

, but imported a significant amount (the pale orange arrow from the top left to the bottom left

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∗ included in the IOT based on use statistics (i.e., in equation (2)). However, flows to

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metal-containing products could not be directly obtained from statistics or by process

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based-MFA. Thus, Figure 2 demonstrates that more detailed flow paths and end-uses were

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uncovered in this research than have traditionally been identified. This feature of the results,

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which is present over all parts of the metal supply chain, will help to understand how metals flow

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through industrial networks, and to anticipate where metals tend to accumulate as potential

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“urban mines”.



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Similar diagrams can be constructed for the metals in alloys, providing that metal-specific

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IO-MFNs have been derived for all of the alloying metals of interest. As pictured

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diagrammatically in the TOC art, the task is to combine common matrix elements and flows for

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each of the alloying metals, continuing until all matrix elements have been addressed. When this

310

is done, the results are as shown in Figure 3(a). This simultaneous visualization helps us

311

recognize the coexistences of metals in products and society, and reveals that most metals flow

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together via alloy sectors. In the present set of eight alloying metals most of the nodes of the

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network are involved, but some metals are clearly more important than others. Figure 3(b) shows

314

an enlarged version of the right side of Figure 3(a); it demonstrates that most of the metals are

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involved in flow to the Motor Vehicle sector and thus to Road Transportation. The Construction

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sector is also important in that regard, and both of those important sectors utilize metals

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primarily in alloy forms. In contrast, Machinery consumes less alloyed tungsten provided by the

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Metalworking Machinery sector: that sector largely employs tungsten as tungsten carbide for

319

metal-cutting tools 28. This result implies that the potential tungsten recovery from the

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Metalworking Machinery sector will be in the form of tungsten carbide rather than as a

321

constituent of an alloy.

322

In addition to following each metal in an alloy group independently, the metal flows can be

323

summed to create a network for a small number of alloy groups (Supporting Information: Figure

324

S9). This approach provides information specific to each alloy group, such as stainless steel or

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alloy steel. For stainless steel, for example, the two largest flows include the one to Architectural

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Metals through to the Construction sector, and the other to Motor Vehicle Parts through to the

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Motor Vehicle sector. However, smaller flows go to many other sectors, as can be better seen in

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the enlarged version of the center of Figure S9(a) shown in Figure S9(b). The network diagram 16 ACS Paragon Plus Environment

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from the perspective of alloy groups implies that alloys coexist as such in products. However, the

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important difference in the coexistences between co-existing metals and the alloys themselves is

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that different metals flowing to the same sectors may not be chemically combined (i.e., alloyed)

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with each other but rather are physically combined in products. Physically combined (e.g.,

333

bolted) metals would be expected to be more recyclable than those that are chemically

334

combined12.

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3.2 Comparison of IO-MFNs

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Because most of the metals addressed in this study flow together and share edges, metal

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relations of N % ∩ N & is summarized in Figure 4 by quantifying the degree of edge sharing and

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weighted edge sharing including IO-MFN of base metals obtained as a consequence of the sector

339

disaggregation. Edges are weighted in units of hektes (see above). Figure 4(a) clearly

340

demonstrates that the degree of edge sharing is related to the total consumption of metals. Major

341

metals’ networks tend to be shared by minor metals, but iron is a central component of most

342

metal networks because other metals share virtually all their edges with iron (i.e. N ]^ ⊃ N ).

343

Looking at other combinations of metals, for example, nickel shares 3% of its edges with those

344

of cobalt, and cobalt shares 86% of its edges with those of nickel. This reflects that a large

345

portion of cobalt is jointly used with nickel as a superalloy. However, this joint use represents a

346

tiny part of total nickel use as the main use of nickel is for stainless steel, which generally does

347

not contain cobalt. In the weighted edge sharing results shown in Figure 4(b), we find that some

348

metals share large fractions of weighted edges with other metals, while sharing much smaller

349

fractions of numbers of edges. For example, iron shares 86% of edge weight (metal flow) with

350

vanadium, but just 2% of edges. Because vanadium contents in carbon steel and tool steel are so

351

small, the flows of vanadium tend to be cut off by the threshold whereas the edges are shared 17 ACS Paragon Plus Environment


352

with iron. However, this result also demonstrates that some alloying metals are likely to be

353

dissipated by being involved in the flow of mass-produced metals.

354 355

The relationships in the network shown in Figure 4 include both chemically and physically combined coexistences of metals. Figure 5 shows the degree of edge sharing and weighted edge

356

sharing within the whole network N for the three categories. Although most metals tend to

357

share edges in alloy-related networks (i.e., the categories A and C) rather than in the non-alloy

358

network, tungsten has 78% and 55% of edges and edge weight in its own non-alloy network.

359

Furthermore, tungsten shares fewer edges with other metals in the non-alloy network. This

360

reflects the fact that tungsten in modern technology exists in relatively pure forms without

361

significant contamination by other metals (e.g., tungsten carbide cutting tools). Because

362

relationships among metals in category B include only physical coexistence, this implies

363

enhanced potential for metal recovery in the recycling phase. Metals other than tungsten tend,

364

however, to be highly combined with each other in alloy-related forms, especially in category A.

365

In this case, any subsequent recycling must consider the metals as largely part of alloy

366

combinations. Recycling thereby requires identification, separation, and alloy-specific

367

reprocessing if the characteristics of the alloys are to be retained for subsequent use. If this is not

368

done, the result is likely to be the incorporation of the alloy into a composite recycling flow of

369

(for example) carbon steel, in which case the physical and chemical properties for which the

370

alloy was designed will be lost.

371 372

373 374

3.3 Future directions We have demonstrated in this work a methodology to use IOTs as a starting point from which to construct IOTs and IO-MFNs for those metals that lack sectors of their own in 18 ACS Paragon Plus Environment

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375

economic IOTs. We have presented the results for eight metals that are associated with iron,

376

copper, and aluminum, the only three metals with designated sectors in the U.S. IOTs. Together

377

with the work of Chen et al.24 , this results in eleven different metals for which U.S. 2007

378

networks are available. Similar results for other regions and years can be expected. We have also developed approaches to combine sets of metals into IO-MFNs for alloy

379 380

groups of interest. This information, which is complementary to the networks of individual

381

metals, permits the analysis of the principal and subsidiary flows of alloys in an economy. This

382

work also shows by the degree of edge sharing that all the metals analyzed herein are

383

predominantly used in alloy forms and thus must be recycled in those forms rather than as

384

individual metals. This result has important implications for the recovery of metals in discarded

385

products. In connection with efficient scrap treatment and sorting for end-of-life (EoL) vehicles19,

386

27

387

included in EoL products would seem to be required for the sustainable use of metals.

388

, the development of metal scrap recycling strategies that consider combinations of metals

More complex network analysis approaches can reveal additional features of the networks

389

generated in this work31. For example, we anticipate that triangulated physical IOTs35, 36 for

390

metals will reveal more complex interrelationships among both metals and industrial sectors. In

391

addition, as Kagawa et al.37 and Okamoto38 have demonstrated, the identification of important

392

industry clusters for metal uses will be a potential application as well. While we have carried out

393

this type of detailed clustering analysis for aluminum31 doing similar analysis for the metals

394

reported in the present remains a task for the future.

395



396 397

Supporting Information The detailed methodologies for the conversion of monetary IO table to a metal IO table, the

398

disaggregation of sectors, the results for individual IO-MFN of metals, and the figure for the

399

network of alloys can be found in the Supporting Information. This material is available free of

400

charge via the internet at http://pubs.acs.org.

401

402

Author Information

403

Corresponding Authors

404

*Phone: +81-22-795-8569; email: [email protected]

405

*Phone: +86-592-6190-763; e-mail: [email protected]

406

Notes

407

The authors declare no competing financial interests.

408

409 410

Acknowledgements We would like to thank the Yale Criticality Project for funding this research.

411

This research was supported by Japanese Society for the Promotion of Science (Grant-in-Aid for

412

JSPS Fellows 258801).

413


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414 415

Table 1. Disaggregated sectors and their category definition for WIO-MFA Original sector

Iron and steel mills and ferroalloy manufacturing

Alumina refining aluminum production

and

primary

Primary smelting and refining of copper

Primary smelting and refining of nonferrous metal (except copper and aluminum)

Sector after disaggregation Pig iron and DRI (direct reduced iron) Iron and steel scrap Ferromanganese Ferrochromium Ferronickel Ferromolybdenum Ferroniobium Ferrovanadium Ferrotungsten Other ferroalloys Crude steel-Carbon steel Crude steel-Stainless steel Crude steel-Alloy steel Hot-rolled steel-carbon steel Hot-rolled steel-stainless steel Hot-rolled steel-alloy steel Primary aluminum Aluminum scrap Aluminum alloy Primary copper Copper scrap Copper alloy Manganese Chromium Nickel Molybdenum Niobium Vanadium Tungsten Cobalt Nickel scrap Stainless steel scrap Nonferrous metal alloy*1

Nonferrous metal (except copper and aluminum) rolling, drawing, extruding, Superalloy*1*2 and alloying *1 Expressed in monetary units *2 Analyzed with special treatment (see SI) 416 417


Category of sector Material Material Material Material Material Material Material Material Material Material Fabricated material Fabricated material Fabricated material Product Product Product Material Material Fabricated material Material Material Fabricated material Material Material Material Material Material Material Material Material Material Material Fabricated material Fabricated material


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418 419 420 421

Table 2. Numbers of edges and edge strengths of the metal networks Fe

Cu

Mn

Cr

Ni

Mo

Nb

V

W

Co

Total edges

74,608

73,948

73,948

74,608

74,608

74,606

74,608

74,278

74,608

74,278

74,278

>1 h (threshold) Remaining edges ratio (%)

57,321

39,590

31,654

20,052

17,733

12,835

3,533

1,778

1,123

1,401

738

76.83

53.54

42.81

26.88

23.77

17.20

4.74

2.39

1.51

1.89

0.99

306,890

20,572

5,458

1,626

1,255

560

46.7

26.7

13.6

10.6

13.7

Total >1 h (kh) 306,886 Remaining edge weight ratio(%) 100.00

20,565

5,451

1,618

1,247

553

42.8

24.1

11.6

8.4

12.1

99.97

99.87

99.52

99.39

98.75

91.57

90.38

85.17

77.81

88.02

8,660

2,270

588

260

196

21

9.9

5.3

11

9.0

Total edge * weights (kh )

Consumption (kt)

422

Al

*

96,500

kh = kilohekte (see text)

423


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424 425 426

Figure Captions

427 428

Figure 1. The process of filtering the network for metal M in an economic system defined by a sectoral input-output table.

429 430 431 432

Figure 2. The cobalt input-output network for the United States, 2007. The pale orange dots at the top of the diagram are origin locations for flows of cobalt or cobalt-containing products into the U.S. economy. Arrow widths indicate approximate percentages of flows (i.e., edge strengths). The units of flow are hekhtes, discussed in the text.

433 434 435

Figure 3. (a) Networks of eight metals commonly used in alloys in the U.S. economy, 2007. Colors represent the individual metals; arrow widths represent edge strengths; (b) Expanded view of (a) to show detail in the Motor Vehicle and Construction sectors.

436 437 438 439 440

Figure 4. Percentage of shared edges between networks of the eleven metals disaggregated in this work. (a) Shared edge percentages for networks of the individual metals [e.g., for non-alloy uses]; (b) Shared edge percentages for alloy networks. By reading numbers for the horizontal direction of the tables, the degree to which a metal shares edges with other metals can be observed.

441 442 443 444 445 446 447

Figure 5. (top row): Percentages of shared edges for metals either alloyed together or combined physically as alloy forms(left top panel), for metals sharing edges in both alloy and non-alloy forms (center top panel), or for metals sharing edges only in non-alloy form (right top panel); (bottom row): Percentages of shared edge strengths for metals either alloyed together or combined physically (left bottom panel), for metals sharing edge strengths in both alloy and non-alloy forms (center bottom panel), or for metals sharing edge strengths only in non-alloy form (right bottom panel).

448



449 450

Figure 1

451


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Figure 2



Figure 3 (a)


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Figure 3 (b) 27 ACS Paragon Plus Environment


(a) Degree of edge sharing

(b) Weighted degree of edge sharing

% Fe Al Cu Mn Cr Ni Mo Nb V W Co

Fe Al Cu Mn Cr Ni Mo Nb V W Co 100 37 37 100 99 40 92 86 86 24 20 100 100 58 99 99 98 69 34 30 61 51 100 100 100 98 99 98 57 28 22 63 44 100 40 39 100 100 53 92 80 83 31 27 100 43 43 100 100 99 92 85 77 28 23 100 50 49 100 100 100 90 80 73 36 31 100 45 45 100 100 91 100 61 82 65 56 100 35 35 100 100 51 100 100 94 35 31 100 29 29 100 100 55 100 75 100 48 44 100 86 85 99 99 97 86 59 56 100 65 100 62 62 98 100 100 91 78 78 79 100

Figure 4 (a) and (b)


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Figure 5



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Deriving the Metal and Alloy Networks of Modern Technology

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