Raw material ‘criticality’—sense or nonsense?

The past decade has seen a resurgence of interest in the supply security of mineral raw materials. A key to the current debate is the concept of ‘criticality’. The present article reviews the criticality concept, as well as the methodologies used in its assessment, including a critical evaluation of their validity in view of classical risk theory. Furthermore, it discusses a number of risks present in global raw materials markets that are not captured by most criticality assessments. Proposed measures for the alleviation of these risks are also presented. We find that current assessments of raw material criticality are fundamentally flawed in several ways. This is mostly due to a lack of adherence to risk theory, and highly limits their applicability. Many of the raw materials generally identified as critical are probably not critical. Still, the flaws of current assessments do not mean that the general issue of supply security can simply be ignored. Rather, it implies that new assessments are required. While the basic theoretical framework for such assessments is outlined in this review, detailed method development will require a major collaborative effort between different disciplines along the raw materials value chain. In the opinion of the authors, the greatest longer-term challenge in the raw materials sector is to stop, or counteract the effects of, the escalation of unit energy costs of production. This issue is particularly pressing due to its close link with the renewable energy transition, requiring more metal and mineral raw materials per unit energy produced. The solution to this problem will require coordinated policy action, as well as the collaboration of scientists from many different fields—with physics, as well as the materials and earth sciences in the lead.


Introduction
In recent years, concerns about supply security have led to a resurgence of interest in mineral and metal availability, particularly in highly import-dependent industrialised countries Raw material 'criticality'-sense or nonsense?

Topical Review
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 4 Author to whom any correspondence should be addressed. such as Germany, Japan, and the United States. The rapidly increasing number of studies published in this field clearly reflects this trend (e.g. Glöser et al 2015, Helbig et al 2016, NSTC 2016. After a period of relatively low raw-material prices following the end of the Cold War (Humphreys 1995), the rise of China as the World's major producer and consumer of minerals, metals and energy has led to a tightening of global markets, and concomitant fears of inadequate supply Sievers 2011a, 2011b).
Ultimately, the trigger for the first new wave of government studies into non-fuel raw materials supply (NRC 2007, EU Commission 2010 was the reduction of Chinese export quotas for rare earth elements (REEs) by ~25 % from 2007 to 2009 (Tse 2011). China's use in 2010 of export restrictions for REEs as a political instrument against Japan (over tensions in the East China Sea) further aggravated these concerns Sievers 2011a, 2011b). At the time, China accounted for more than 95% of global primary REE output (Hedrick 2010, Cordier 2011. Therefore, the effects of these quota reductions were widely felt across the globe, mostly in terms of significant price increases. The concept of raw material criticality is at the core of the recent debate. It is the aim of this review to introduce this concept to a physical sciences audience, while critically discussing both its limitations and the shortcomings of current assessments in some detail. In addition, we will briefly consider those complexities of the raw material markets not captured by current assessments of criticality. We argue that generalised criticality assessments can be misleading, and might consequently not be useful to highlight the greatest (economic) risks inherent in current markets. In contrast to the simplified material-by-material approach used in current assessments, we try to identify over-arching issues and discuss a number of possible approaches for the alleviation of the corresponding risks.

Raw material criticality
Despite its central role in the current debate, it is still difficult to give a precise definition for raw material criticality. This is mainly due to two factors: (1) the variability in definitions and assessment methodologies used and (2) the vagueness of the definitions given in many studies (see Erdmann andGraedel 2011, Glöser et al 2015). For instance, Graedel and Nuss (2014) define criticality as 'the quality, state or degree of being of the highest importance', while according to Gleich et al (2013), 'criticality denotes the extent of current and future risks associated with a certain metal'. Raw mat erials with a high criticality rating are called critical.
Irrespective of this variability in definitions, two aspects are widely regarded as crucial for the identification of critical raw materials: (1) the vulnerability of a given consumer to supply disruptions, i.e. the importance of the raw material under consideration, and the consequent impact of supply shortfalls, and (2) the likelihood for the occurrence of such disruptions, often called 'supply risk' (NRC 2007, Erdmann and Graedel 2011. Critical raw materials must have a high score on both dimensions when compared to other raw materials (e.g. EU Commission 2010). Glöser et al (2015) clearly demonstrated that the basic 2D structure of most assessments reflects a fundamental equivalence between criticality and the classic definition of risk (e.g. Cox 2009). Other studies also hint at this equivalence (Buijs et al 2012, Graedel and Nuss 2014, Helbig et al 2016. Given this observation, it is possible to define the criticality of a raw material more precisely as a measure of the (economic) risk arising from its utilisation (incl. production, use, and endof-life) for a specific consumer over a certain period. A consumer can be anything from a single company or technology, to a national or multi-national economy .
Because this definition ties criticality to risk theory, and thus allows for a rigorous treatment within the framework of quantitative risk analysis (Cox 2009), we use it as the basis for the present review. Readers should note that risk, both in the definition given above as well as in quantitative risk analysis, is not limited to being economic in nature (see Cox 2009). It may also be societal or environmental, as discussed in more detail in section 3 below. Therefore, our definition preserves the 'holistic' intentions of the criticality concept (e.g. Helbig et al 2016). Nevertheless, we note that most criticality assessments focus exclusively on economic aspects in their practical implementation, and this is why we specifically included them in our definition.
As indicated above, and stressed by most authors (see Erdmann andGraedel 2011, Graedel and, the criticality of a given raw material is strongly dependent on the consumer and time-period under consideration. Criticality is therefore by no means an inherent property of a material itself, although the similarity of the term to the criticality concept in the physical sciences, where it generally refers to systems near a transformation of state, might at first suggest such a relationship (see Bradshaw et al 2013).
It is also important to note that virtually all criticality assessments are limited to non-fuel raw materials, even though their structure would in principle allow for the inclusion of fuels (coal, gas, oil). In this review, the term 'raw material(s)' therefore explicitly refers to non-fuel raw materials.

Assessment method
The most common procedure for criticality assessments is to compile sets of different indicators into aggregate scores for both the supply risk and vulnerability dimensions, and then plot them against each other to delimit the field of critical raw materials. Figure 1 illustrates such a plot. This approach is an abstraction from the classical risk matrix (see Glöser et al 2015), and was originally introduced by the National Research Council (NRC 2007). As mentioned above, some studies merely use a single final dimension (e.g. BGS 2015, NSTC 2016), while others introduce a third one to reflect e.g. environmental issues .
The detailed assessment process differs widely across different studies. In particular, there are large differences in the specific choice of indicators, their respective weightings in the final aggregate scores (Erdmann andGraedel 2011, Graedel and, and the procedures used for the aggregation of these scores (Erdmann andGraedel 2011, Glöser et al 2015).
While some of the differences in the specific choices of indicators between studies certainly reflect differences in the systems under consideration (i.e. the specific consumer, see above), there is still much variation between studies with a similar scope. In the following two subsections, we give a brief overview of the different indicators used for the vulnerability and supply risk dimensions in recent studies, as well as the ways in which they are aggregated. To ensure comparability, we focus specifically on assessments dealing with consumption at the level of national or multi-national economies. A more detailed discussion would be beyond the scope of this article. We nevertheless note that the general principles also apply to assessments at other organisational levels (e.g. single companies; Lapko et al 2016).
A critical discussion of the suitability of current assessments to adequately capture the economic risks associated to raw material supply and consumption follows in section 3.

Indicators for vulnerability
We mentioned earlier that the vulnerability dimension (sometimes called 'economic importance') is intended to provide a measure of the (economic) impact of supply restrictions on the consumer of interest. Economic impact in this sense is perhaps best defined as the additional monetary cost arising from a demand/supply imbalance (Helbig et al 2016). As discussed in more detail in the next section, there are many potential contributors to this cost, and due to the great complexity of the global manufacturing and trade system, it is inherently difficult to measure. This is why criticality studies generally use one or more easier-to-measure indicators to assign an estimated vulnerability value. The general assumption behind all such indicators is that they are either directly or inversely related to economic impact. However, concrete choices differ greatly between different studies, as illustrated by the overview in table 1. Readers will note that certain vulnerability indicators are also used for the supply risk dimension in some studies. In these cases, they are not used as vulnerability indicators. Table 1 summarises the vulnerability indicators used in nine recent assessments (see Helbig et al 2016). It shows that substitutability is the most widely used vulnerability indicator. This is a good example of an indicator that is inversely related to vulnerability: the more easily a material can be substituted, the lower the impact of supply restrictions should be, since substitutes are generally less likely to be affected by restrictions at the same time as the raw material of interest. However, substitutability alone is insufficient to assess economic impact. This is, because it does not provide a measure of the magnitude of the costs associated to supply restrictions.
The second most frequently used types of vulnerability indicators are those referring to the value of the products affected, the value of the utilised materials, or the spread of utilisation (table 1). These are good examples of indicators directly related to economic impact. This is particularly clear for the first two, i.e. the value of affected products and the value of utilised materials. Both can in principle be expected to be proportional to the potential economic impact of supply shortfalls. As such, they complement substitutability.
For many of the other indicators listed in table 1, e.g. company concentration of production or consumption volume, the relationship to economic impact is not as clear-cut. This is particularly true for those indicators also used to assess supply risk in certain studies. This issue is discussed in more detail in section 3 below.

Indicators for supply risk
The supply risk dimension is intended to provide a measure for the probability of the occurrence of supply restrictions. Again, this is difficult to quantify due to the complexities of global supply-chains and the many possible events that could result in a tightening of supply relative to demand-from mine-closures and natural disasters to political and military conflicts, or the introduction of new consumer technologies. It is not surprising, therefore, that criticality studies again resort to a set of indicators assumed to be related directly or inversely to supply risk. Just as for vulnerability, particular choices vary greatly between individual studies. This is illustrated by the overview given in table 2 for 15 recent assessments (data from Achzet and Helbig 2013).
Clearly, the most widely used supply risk indicator is country (or company) concentration of production, usually measured using the Herfindahl- Hirschman-Index (HHI;Hirschman 1964). This is often weighted in some way by 'country risk', e.g. using the Worldwide Governance Indicator (WGI; World Bank 2015). The assumption behind the use of these indicators is that the more concentrated the production of a given raw material is in a small number of countries, specifically those with poor governance, the higher will be the probability of supply disruptions due to political or military conflicts in, or with, these countries (e.g. Graedel et al 2012). A similar logic applies to company concentration in mining corporations as a supply risk indicator. Both are good examples of direct indicators.
In contrast, depletion time is a good example of an indicator with an assumed inverse relationship to supply risk: The greater the expected time-frame for the depletion of current reserves, it is argued, the lower the probability of shortages within a given period (e.g. Graedel et al 2012).
Of the other indicators, by-product dependency requires particular explanation. Many elements considered essential for modern technologies are produced as by-products from  the extraction of other metals (Campbell 1985), their so-called hosts. A good example is indium, which is mostly recovered from sulphidic zinc ores (Schwarz-Schampera 2014, Werner et al 2017). Many authors argue that this dependence on the production of the host metals results in a higher probability of supply disruptions (e.g. Nassar et al 2015). This is because the supply of the by-products is in principle limited by the amount of the host metal extracted every year, and as such, might not be able to adjust to (rapid) increases in demand, resulting in shortages. It is argued that the fraction of a given raw material produced as a by-product can be used as an indicator for the probability of supply disruptions .
Last but not least, the demand growth and import dependence indicators deserve mention. The general argument with respect to demand growth is that a higher value should be accompanied by a higher probability for the development of market-imbalances and consequently a higher supply risk.
Similarly, greater import dependence should lead to a greater probability of a country's supply being affected by political or military conflicts elsewhere in the world, also leading to higher supply risk.
Due to their relatively rare usage, the remaining indicators listed in table 2 do not warrant detailed discussion.

Indicator aggregation and calculation of criticality scores
Different procedures are used to aggregate indicators into the final vulnerability and supply risk scores. This sub-section gives a brief overview of the most important aggregation methods used in different studies. It also introduces the different procedures used to derive an overall criticality score in some studies.
Indicator aggregation methods may conveniently be subdivided into the following three groups: (1) Additive-scores are the sum of (weighted and/or scaled) indicator values (e.g. Graedel et al 2012, Panousi et al 2016. (2) Multiplicative-scores are the product of (weighted and/ or scaled) indicator values (e.g. vulnerability score by EU Commission 2014). (3) Mixed-scores are mixed sums and products of (weighted and/or scaled) indicator values (e.g. the WGI-HHI indicator used by EU Commission 2014).
The numerical results of these aggregation methods will clearly differ widely, even if the same indicator values are used.
Having arrived at the final scores, some studies use simple thresholding to delimit a field of critical raw materials in a so called criticality plot (e.g. EU Commission 2014; see figure 1), while others combine either the two dimensions, or the initial indicators, into an overall criticality score that allows for a sorting of materials from highest to lowest criticality. Again, the calculation of this overall score is done differently in different studies. The following methods are in use: (1) Sum-the overall criticality score is the (weighted) sum of the two dimensions or individual indicators (e.g. Morley and Eatherly 2013, Moss et al 2013, BGS 2015. (2) Euclidean distance-the overall criticality score is the Euclidean distance from the origin of the criticality plot (sometimes including an additional dimension; e.g. Graedel et al 2012).
(3) Geometric mean-the overall criticality score is the geometric mean of the two dimensions or of individual indicators (e.g. NSTC 2016).
We note that this list might not be exhaustive. Some studies do not provide sufficient details of the methods they use to aggregate overall scores.

Limitations and shortcomings of current approaches
In this section, we discuss the major limitations and shortcomings of current approaches to criticality assessments. We start by examining the relationship of criticality to classical risk and decision theory, and in particular, to quantitative risk analysis (Cox 2009). This gives us a theoretical framework within which an objective evaluation of different aspects of current assessments is possible. Several authors have previously voiced criticism concerning the validity of current assessments (e.g. Buijs and Sievers 2011a, 2011b, Reuter et al 2015, Reuter 2016). However, these previous contributions mostly focussed on specific aspects of the assessments, such as the specific choice of indicators, rather than developing their criticism from a more general theor etical framework. The main inspiration for this section was a recent article by Glöser et al (2015). Much of the following two subsections represents a summary of their work.

Relationship to classic risk and decision theory
Classic risk theory stems from Bayesian decision theory (BDT), as used in engineering problems involving probabilistic uncertainties about the state of nature (Benjamin andCornel 1970, Cox 2009). Benjamin and Cornell (1970) define state of nature as 'some factor which is not known with certainty, but on which the consequences of a decision depend', e.g. whether or not there exists a potentially active geological fault in the bedrock below the proposed site for a nuclear power plant. The general principle of BDT is as follows: sets of possible actions, {a i }, and states of nature, {s j }, are defined in the beginning. To every action-state of nature-pair, a numeric value describing its outcome, usually expressed in monetary terms as a cost (negative) or profit (positive), is assigned using a so-called utility function, u(a i , s j ). Assuming that the probabilities for the possible states of nature, {p(s j )}, are known, expectation values for the utility of each action can be calculated as: The action a i yielding the highest expectation value is the most preferable (Benjamin and Cornell 1970). While the above is a description of the simplified case where the amount of information on outcomes and probabilities is fixed, it is nevertheless sufficient to arrive at the classical definition of risk. In particular, the risk, R, associated to an uncertain event (accident, hazard), e i , may in analogy to (1) be expressed as the expectation value of the associated cost, A, i.e.: where p(e i ) is the probability for the occurrence of event e i . The major difference of the cost function, A(e i ), to the utility function, u(a i , s j ), described above is that the sign is reversed, such that greater risks are identified by a greater positive value even though their expected impact is negative. It should also be noted that the cost function, A(e i ), will generally represent the sum over a number of different consequences of event e i . Furthermore, the cost function is not necessarily limited to monetary costs. For instance, when public health risks are considered, a useful measure of cost may be quality-adjusted life-years (Cox 2009). For environmental risks, yet other measures are appropriate (Suter 2006). There is a long-standing debate whether or not these different measures can be harmonised (e.g. Ackerman and Heinzerling 2002). In fact, much of the current discussion about counter-measures to climate change centres around the correct pricing of carbon dioxide emissions (Grubb and Newbery 2007). While a detailed discussion of these issues is beyond the scope of this article, we note that all the different risks (economic/environmental/ societal) included in the criticality definition of section 2 are treatable within the general framework of classic risk theory. However, the harmonisation of different cost functions might not be possible such that separate assessments for e.g. economic and environmental risks might be necessary. Although we focus on economic risks in the following discussion, the same principles also apply to the other types of risk. Another important note on (2) is that it implicitly refers to a particular time frame. This is because the value of p(e i ) generally depends on the length of time under consideration (Cox 2009). A simple example illustrates this assertion: say the event under consideration is the failure of a moving part in a machine, e.g. an axle. Then p(e i ) should clearly be greater for greater time-periods since the probability of failure increases with increasing wear.
In introductory texts, (2) is often re-written as (e.g. Cox 2009): or some semantically equivalent expression. As Glöser et al (2015) demonstrated, the criticality concept as first introduced by the National Research Council (NRC 2007) is clearly an abstraction from this definition of risk. In particular, criticality is implicitly constructed to be directly proportional to the risk associated with the consumption of a given raw material. Glöser et al (2015) also showed that the two dimensions, supply risk and vulnerability commonly used to identify critical raw materials can be matched directly to likelihood and consequence, respectively, as defined by (2) and (3). Provided we assume that the respective relationships of the supply risk and vulnerability indicators with likelihood and consequence are linear we have: Glöser et al 2015). The supply risk dimension does therefore clearly not constitute a measure of risk in the classical sense, but merely of probability or likelihood. As such, the term is highly misleading. We therefore replace it by disruption probability in the following.
Before moving on to the detailed discussion of recent studies, it is necessary to stress that (2)-(4) are greatly simplified, since they refer to single types of events with a fixed effect size only.
To arrive at a generalised algebraic form for raw material criticality, one needs to consider what kinds of events actually contribute to the risk criticality describes. Unfortunately, the discussion of this fundamental aspect is exceedingly vague in most studies. Nevertheless, there is a general consensus that, irrespective of the underlying causes, the main events of interest are price-hikes (type 1), and severe physical disruptions of supply (type 2), potentially causing the shut-down of production of dependent products (e.g. NRC 2007, Sievers 2011a, 2011b).
Readers will note that: (a) the effect size of type 1 events is continuous (price can increase by an arbitrary factor, e.g. 2, 3, 4 etc), with a corresponding probability distribution, and b) type 2 events will generally coincide with (albeit prohibitive) increases in price for the consumer. As such, type 2 events may simply be taken to form the upper end of the scale of effect sizes (prohibitively high cost, equivalent to no availability). This means both types of events may in principle be captured on a single continuous scale of effect sizes. A generalised algebraic form for the criticality, C, of a given raw material can then be written as the expectation value of the vulnerability: where x is the effect size (e.g. the factor by which price increases), and p(x) and v(x) are the corresponding disruption probability (as a probability density) and vulnerability, respectively. Note that vulnerability may also be negative in cases where price decreases/supply increases (i.e. where x < 1). If vulnerability is expressed as a monetary cost, then C would be in units of e.g. U.S. dollars (USD), since x is dimensionless, as is p(x). However, (5) still neglects the time for which an event lasts and therefore implies a comparison between events of identical duration. If this is not true, then (5) must be extended to include event duration, t, in addition to effect size: where t 0 denotes the total time period under consideration (e.g. 5 years). Because p(x,t) is in units of 1/t, the resultant C in (6) is still expressed in monetary units. Note that Glöser et al (2015) only derived (4), but did not cite any generalised expressions equivalent to (5) or (6). These are first shown here. If a criticality assessment were to focus on societal or environ mental rather than economic risks, a similar expression would result for C consisting of the integral of the product of disruption probability times vulnerability (in appropriate units) over effect size and time. Only the final units of C will be different if they are not harmonised to monetary costs, e.g. quality-adjusted life-years in the case of public health risks.
Given these quantitative definitions, we are now in a position to evaluate some of the formal aspects of criticality assessments, as well as their underlying logic. In the following two sub-sections, we focus first on the identification and ordering of critical raw materials (section 3.2), and second, on the effects of the addition or omission of assessment dimensions (section 3.3). We then briefly discuss indicator choice and aggregation (section 3.4) and give a final summary in section 3.5. We focus mostly on formal aspects since a detailed discussion of individual indicators and their aggregation is beyond the scope of this article. As shown below, the focus on formal issues is entirely sufficient for our purposes.

Identification and ordering of critical raw materials
The first important question when evaluating any criticality assessment must be whether its general structure honours the formal requirements set by classic risk theory outlined above. In particular, if an overall criticality score is computed, does it comply with (2) to (6) such that the resultant ordering of raw materials reflects their true criticality? A related question is whether criticality plots (see figure 1) are a suitable tool for the identification of critical raw materials. Since the correct ordering and identification of risk factors is a key requirement for the effective allocation of resources to reduce risk, the following discussion will mostly focus on the effects of different methods on overall criticality order.
It is clear from (5) that an overall criticality score should be calculated as the integral over the product of vulnerability and disruption probability 5 as a function of effect size, x. Not a single criticality study in the available literature complies with this requirement. Instead, the dependence of both event probability and vulnerability on x is ignored, and only a single value compiled for each dimension. This is a gross over-simplification. In particular, it implies the comparison of only a single type of event with given x, which is itself never specified; or independence of p(x) and v(x) from x (see section 3.1).
This gross simplification alone highly limits the applicability of current criticality studies, and a justification for it is never given.
Even if we assume that the simplification in (4) is legitimate, it is interesting to ask whether current studies at least comply with this simpler form, i.e. whether they calculate overall criticality scores as the product of vulnerability and disruption probability. On a criticality plot (disruption probability against vulnerability) contours of constant criticality should then have the shape of hyperbolas (see Glöser et al 2015), as illustrated schematically by the boundary of the criticality field in figure 2(a).
Referring back to section 2.4, it appears that there is not a single study where the simple product is used, and a justification of this evident failure to honour (4) is also never given. We note, however, that the geometric mean (NSTC 2016) produces exactly the same criticality order and contour shapes as the simple product, although absolute criticality values differ. Therefore, its use does not have a negative impact on qualitative results (ordering). But what effect do the other methods have? In particular, how do their results differ from those of the correct method?
In order to answer these questions, it is helpful to consider a graphical illustration of how the sum and Euclidean distance methods affect the shape of criticality contours in a criticality plot. This is done in a schematic manner in figures 2(b) and (c). The boundaries between the critical and non-critical fields in all plots are designed to go through the centre of the plot as a reference point. The figure clearly illustrates how the criticality field is extended towards the axes as first the sum method (2(b)) and then the Euclidean distance method (2(c)) are used to calculate criticality scores. This means that raw materials plotting close to the axes, and therefore having low true criticality, become more likely to be identified as critical materials-an undesirable result.
In fact, if there is a negative correlation between disruption probability and vulnerability the resultant criticality order will be significantly different from the true criticality order. The broken line in figure 2 illustrates this point. The filled circle at the centre of the line marks the material with the highest true criticality. Moving away from this point towards the axes, true criticality decreases.
It is easily seen that the sum method would result in equal criticality scores for all materials on the line, i.e. a random ordering, while the Euclidean distance method would actually result in a reversal of the true criticality order. The latter result would be considered 'worse-than-useless' sensu Cox (2008Cox ( , 2009).
Since perfect negative correlation represents a limiting scenario, we might expect the sum method to always do better than a random assignment of scores for real data. The Euclidean distance method, on the other hand, would be expected to do worse-than-random in an appreciable number of cases. The overall results of any study using the Euclidean distance method (e.g. Graedel et al 2012) should therefore be regarded with the greatest scepticism. It is clearly the worst possible choice of method for the calculation of overall criticality scores.
Last but not least, it is worth noting that the incongruity between the shape of the criticality region in standard criticality plots with the shape of contours of constant criticality may also cause undesirable effects (see Glöser et al 2015). This is illustrated in figure 3 for the data published by the EU Commission (2014). It shows both the 'critical' region, as well as contours of constant criticality (product of the two axes). The main result is that materials with the same criticality as the lower left-hand corner of the square 'critical' region are not included in the list of critical mat erials. These are: baryte, Mo, Sn, natural rubber, V and bauxite. This is particularly interesting for V and natural rubber, both of which clearly have higher criticality values than borate, which is included in the list. Similarly, materials with very high criticality values (greater than those of Sb, magnesite and W), but plotting close to the upper left-hand corner of the criticality field, would not be included in a list of critical raw materials.
To briefly summarise this sub-section, not a single study complies even with the simplest formal requirements for the identification and ordering of critical raw materials set by classical risk theory. This is in accordance with the results of Glöser et al (2015).

Addition or omission of assessment dimensions
Another important aspect to consider when evaluating any criticality assessment is whether it honours the 2D structure dictated by (2) to (5). That is, whether it assesses both event probability and vulnerability (consequences) for the raw materials under consideration, and aggregates them in a suitable manner.
While most studies comply with the basic requirement of two-dimensionality (see section 3.1, Glöser et al 2015), some do not. Interestingly, deviations occur in both directions: either, additional dimensions are introduced, or one of the two original dimensions, usually vulnerability, is omitted. An excellent example for the introduction of additional dimensions is provided by the methodology of Graedel et al (2012), who introduce an additional 'environmental implications' dimension. Examples using only a single dimension are provided by the British Geological Survey's 'risk list' (e.g. BGS 2015), the JRC report (Moss et al 2013) and the Oakdene and Hollins study (Morley and Eatherly 2013).
Two important questions need to be asked with respect to these studies: first, can the introduction or omission of dimensions be justified, and second, what is its effect on the overall results of an assessment? With respect to these questions, a clear distinction must be made between the addition and omission of dimensions. In the following, we briefly discuss both cases in the context of specific examples.
As an example for the addition of a dimension, we choose the methodology of Graedel et al (2012). In the authors' own words, the additional 'environmental implications' axis is meant to 'depict the environmental burden of the various metals', i.e. the ongoing environmental effects due to their extraction and use. There are some major conceptual issues with the introduction of this aspect as an additional equivalent axis in criticality assessments. Schematic illustration of the effects of different calculation methods for overall criticality scores on the identification of critical raw materials: (a) product aggregation (correct method), (b) sum aggregation, and (c) Euclidean distance method. The boundaries between the fields of critical and noncritical raw materials represent iso-criticality contours, and are designed to go through the centre of the diagram. Note how the field of critical raw materials is extended towards the axes by the sum (b) and Euclidean distance (c) methods. The broken line represents the hypothetical case of perfect negative correlation between D and V, and the central dot the material with the highest true criticality score on this line. Its relationship with the iso-criticality contours indicates how criticality order is affected by the different aggregation methods, as discussed in more detail in the main text. For instance, the environmental damage caused by the ongoing extraction of a raw material forms part of its regular extraction costs, in the broadest sense of the term. As a normally externalised cost that is not represented in the price of a commodity, it can in principle be seen as equivalent to a risk (which is also an expectation value of a cost, see section 3.1), although it might be expressed in different units. Thus it would be on the same level as the (economic) criticality assessed via the other two axes of Graedel et al's (2012) assessment, and should not be mixed with these axes, but only with the final results for economic criticality, provided a suitable harmonisation between economic criticality and environmental risk can be achieved.
Unfortunately, the authors do not provide a justification for their decision to consider environmental implications as an equivalent third dimension. In combination with the use of the Euclidean distance method for the calculation of the overall criticality score (see above) this causes a further distortion of their results, and even greater limitations to the usefulness of their methodology.
The omission of one of the original dimensions can also have a number of unfortunate effects on the overall results. To illustrate this, consider the case where the vulnerability dimension is omitted (e.g. BGS 2015). In this case, the overall result depends greatly on the nature of the correlation between disruption probability and vulnerability. If it is strongly positive, then materials with a high disruption probability will also have a high vulnerability, and therefore a high criticality. Identification and ordering of critical materials would thus be (mostly) correct, even if only one dimension were used.
If there is no correlation, however, then a significant proportion of all materials with a high disruption probability will not be critical because they will have low vulnerability. In such a case, the expected error rate of an assessment would be on the order of tens of percent, and the result little better than a random assignment of criticality scores.
Further, if the correlation is negative, then the materials with the highest disruption probability will not include those with the highest true criticality, since these materials would lie around the middle of the range in disruption probabilities (see figure 2 and corresponding discussion in section 3.2 above). Such a result might again be considered 'worse-than-useless' (see section 3.2).
An important general note from this as well as the previous sub-section must be that the outcome for any methodology not following the prescriptions from risk theory greatly depends on the covariance structure of the data. This issue is greatly exaggerated when assessments fail to include one of the two dimensions, vulnerability or disruption probability. As discussed in detail by Sievers (2011a, 2011b), the case of negative correlation, which usually results in the worst outcomes of assessments using non-ideal methodology, might actually be expected for the global raw materials market.

Indicator choice and aggregation
In order to ensure the logical coherence and applicability of criticality assessments, the indicators used for the vulnerability and disruption probability scores, as well as their aggregation should fulfil the following general conditions in compliance with the accepted methodology for quantitative risk assessments (see Cox 2009): (1) They should have empirically demonstrable, statistically significant relationships with the quantity of interest; and (2) Be aggregated and weighted in a way that reflects these relationships. Corrections should be made where indicators are correlated, to avoid positive bias.
To fulfil both conditions, assessments would need to include an evaluation of indicator quality and scaling using empirical data. Additionally, an evaluation of causal and probabilistic links between different events should be performed.
Unfortunately, none of the recent assessments includes an in-depth analysis of suitable empirical data to verify indicator choices, or inform the weightings/scalings used in their aggregation. Instead, the particular choices and weightings generally reflect the subjective opinions of the authors (see Erdmann andGraedel 2011, Graedel and. The absence of empirically grounded assessments is by no means evidence for the absence of suitable input data. For instance, a study by Gleich et al (2013) showed that the historic evolution of market prices of mineral raw materials is reasonably well explained by combinations of different explanatory variables (including HHI) whose values are freely available from various sources for at least the past 30 years. Crucially, the exact combinations of explanatory variables, and their respective weightings differ between elements, likely as a function of different market structures. Based on these results, Gleich et al (2013) suggested that the same is to be expected for certain aspects of criticality assessments, particularly the disruption probability (supply risk) dimension, since prices are to some degree a reflection of the scarcity of a raw mat erial (see Gleich et al 2013). This means that the generalised approach used in criticality assessments, where the same indicator weightings are used for all elements, is probably a gross oversimplification that has little, or nothing, to do with reality.

Summary of evaluation
The detailed evaluation presented in the previous sub-sections illustrates that virtually all available studies on raw material criticality suffer from at least one, if not several, serious methodological short-comings that highly limit their applicability. In particular: (1) All studies ignore the fact that there is a spectrum in the severity of the events of interest (effect size), with variable consequences, and accordingly focus on a single type of event only, without considering the effects of this simplification.
(2) Even the simplified studies do not comply with the formal requirements set by risk theory for the ordering and identification of critical raw materials. Depending on the exact methods used, as well as the nature of the correlation between disruption probability and vulnerability, 'worse-than-useless' outcomes sensu Cox (2009) may result.
(3) Some studies introduce additional dimensions, or omit the vulnerability dimension from the assessment. This can again bring about 'worse-than-useless' results, depending on data structure. (4) Neither the choice of indicators, nor their aggregation and scaling are informed by empirical data on actual market behaviour, but rather by the subjective opinions of individual authors. Available empirical data suggests that these arbitrary procedures are probably not adequate.
Profound conceptual issues are apparent from these shortcomings. They suggest that many authors are aware of neither the fundamental equivalence of criticality and risk (see Glöser et al 2015), nor the true meaning of risk itself. This impression is corroborated by recent reviews , Dewulf et al 2016 whose authors are clearly aware of the work of Glöser et al (2015), but neglect to discuss its fundamental implications. Many of the shortcomings of recent criticality assessments outlined above could have been avoided with a sound understanding of risk theory.
Even without reference to risk theory, both the lack of conceptual unity between current studies, as well as their universal failure to take into account relevant empirical data, provide clear indications for the deep philosophical issues present in the field.
Despite the evident shortcomings of available work on raw material criticality, we note that criticality assessments are nevertheless important. This is for two major reasons. First, even inaccurate assessments raise awareness about the general issue of raw material supply security, a topic that until recently had mostly been ignored in western countries. Second, assessments can be amended to better reflect reality using the principles set out above. In particular, they should be based on empirical evidence, include logically coherent risk models, and be compatible with risk theory (see Cox 2009).
However, the necessary increase in complexity might pose significant challenges for assessors. Specifically, it will require extensive collaboration between different disciplines along the value chain. Geoscientists, mining and mineral process engineers, materials scientists, metallurgists, and economists all have a rôle to play. While current assessments should be regarded with healthy scepticism, improved assessments resulting from such future work would certainly be useful tools for political and industrial decision makers.

Other important aspects of risk in global metal markets
Because criticality assessments focus exclusively on single raw materials, they necessarily ignore some of the interconnected nature of global markets and the many complexities, and risk factors, arising from it. This section is devoted to a brief introduction and discussion of some of these risk factors, and their potential effects on national or multi-national economies. In particular, we focus on the following aspects: (1) Concentration of the production/supply of not one, but several or many different raw materials in a small number of countries; (2) Interdependence of the production cycles of various industrial and minor metals; (3) Growing energy requirements due to decreasing ore deposit quality.
Each will be treated in a separate sub-section. We note that some or all of these aspects are often discussed in criticality assessments, too (e.g. EU Commission 2014, Klossek 2014, Angerer et al 2016), but due to their nature are inherently difficult to incorporate into the material-by -mat erial approach of these assessments.

Concentration of the supply of many raw materials in few countries
Many studies highlight the current status of China as the largest producer of many metals as a major risk factor in global markets (e.g. EU Commission 2014). The general fear is that a dependence on a small number of countries for many raw material imports increases the probability of wide-ranging supply disruptions in the same way it supposedly does so for single raw materials (see section 2.3). But is this fear justified?
As a first point, we note that the fact that China is the main producer of many mineral raw materials does not necessarily imply its dominance for the import balance or consumption of other countries. This is exemplified by the country-specific total values of raw material imports to the EU ( figure 4). Clearly, China is only a minor supplier of raw materials to the EU. While no single other country has a strongly dominating share in EU imports, South Africa, the USA, Brazil, (Switzerland), Australia and Canada are clearly the EU's most important trading partners for raw materials. This is not an unexpected result given the strong historic ties between Europe and these countries, as well as their well-developed mining industries based on a world-class natural resource base.
The probable reason for China's relatively unimportant role as a supplier to the EU (and other countries) is its dual role as both the largest producer and the largest consumer of raw materials worldwide (Streifel 2006, Roache 2012. Only for some of the minor raw materials (e.g. rare earth elements, antimony) does China play an important role as an exporter. However, due to their comparatively low total value and specialised applications, these materials only have a very small effect on overall import balances.
Today, most of China's primary production is consumed internally, and only exported as part of intermediate or finished industrial products. In terms of total imports to the EU, China is indeed its largest trading partner (it is second in terms of exports from the EU, Eurostat 2016). This current state of affairs is a direct result of Chinese efforts to integrate manufacturing capacities along the value chain, and concentrate them in China, starting with the production of raw materials, and then moving on to industrial products. Given this trend, perhaps greater attention should now be paid to the EU's reliance on China for the provision of certain industrial products (e.g. consumer electronics) rather than specific raw materials.
The emergence of China as the largest consumer of mineral raw materials has had other important consequences for global markets. In particular, the greater competition for resources has resulted in increased overall demand, and consequently significant increases in raw material prices (Streifel 2006, Roache 2012. This general effect is quite different from the  (2014), and price data for individual raw materials taken from Kelly and Matos (2014). Note that the prominent position of Switzerland is due to its role as a major trading hub for gold and other precious metals. It does not itself produce significant amounts of primary raw materials. The other countries on the list, however, are all major primary producers for various commodities. feared supply restrictions due to individual producing countries discussed in many criticality assessments. Despite its evident importance, we are not aware of a systematic assessment of the risk posed to global raw material markets, and western economies in particular, by the rapid growth of other emerging economies, e.g. India.
A related point is the loss of primary production infrastructure and the related know-how to other countries, e.g. due to competitive disadvantages (price-dumping etc.). Since this makes the (re-)establishment of significant local production much harder, it has the potential to greatly exacerbate supply disruptions, should they occur. This poses a risk that must not be underestimated (Reuter 2016).

Interdependence of metal-cycles
While the separate treatment of different raw materials in criticality assessments suggests that each material is produced independently of all others, this is not generally the case. Many metals tend to occur together in the same geological environments due to similarities in their geochemical behaviour. Good examples of such groups are Pb-Zn-Ag, U-Th-Rare Earths and Cr-Ni-Platinum group elements (see Robb 2005). The metal wheel of Verhoef et al (2004) provides an overview of the relationships between a number of different major and minor metals (figure 5).
While many mines produce one metal as the main product, they often also produce one or several co-or by-products. The difference between these two categories is that co-products, due to their comparatively high value, still enact an influence on mining decisions, while by-products, due to their low value, do not (Campbell 1985). To an extent, the co-and byproducts may help to maintain the profitability of a mining operation.
The main issue, particularly with the co-production of different metals, is that movements in the market of one metal can have significant effects on that of another, and vice versa. Consider the simple example where for some reason the use of Pb in all branches of industry in the EU is banned, resulting in a significant drop in Pb-prices. Because virtually all Pb mines are also Zn mines, and vice versa, each element being an important co-product of the other (Reuter et al 2015; see figure 5), this would lead to a drop in Zn production due to mine closures. Therefore, the end result would be an increase in Zn prices, an outcome that would have been difficult to predict without knowledge about the close geological link between these two metals. Similar linkages exist between other metals (figure 5). The nature of these links is not incorporated into criticality assessments in a meaningful way. The percentage of a specific element produced as a 'companion' used in some assessments  does not provide useful information on the relevant peculiarities of its specific market, or the markets it is related to (e.g. the Pb-Zn linkage).
For by-products, the relationship is more one-sided. In particular, the production rate of the corresponding main products sets a relatively strong limit to their supply (e.g. Campbell 1985). This might result in supply restrictions once this limit is reached (e.g. Frenzel et al 2015, Lovik et al 2016. However, this is an element-specific problem, since the by-products do not affect the corresponding main products. As such, it is easily incorporated into criticality assessments. Only the actual determination of true supply potentials might present some difficulties due to data availability issues (e.g. Frenzel et al 2015Frenzel et al , 2016. Supply potentials, however, are not considered in any criticality assessment. As mentioned earlier, other issues are often correlated with the by-product status of some raw materials, e.g. intransparent trading and price formation, and high concentration of supplies (Wellmer et al 1990, Frenzel et al 2015. These issues are mostly a function of the small market size for these materials (see Frenzel et al 2015). Small market size (in terms of monetary value of total consumption) can be seen as a first order indicator for vulnerability. This means that for most of these materials, overall criticality is probably small, even if disruption probability is relatively high.

Decreasing ore quality
It is well established that access to mineral resources is becoming harder as time progresses (Mudd 2009, Mudd 2010, Northey et al 2014. Following the 'best first' principle (Hall and Kiltgaard 2012), the best ore deposits (near-surface, highgrade, close to major infrastructure) are already found and exploited. This has two consequences: First, new ore deposits become increasingly hard to find, and second, if found, the resources they contain are generally harder to access. The latter might be for several reasons, e.g. greater depth below surface, lower grade, or remoteness of location. A good example of this general trend is provided by the steady decline in mean copper ore grades over the last century (e.g. Mudd et al 2013, figure 6). As eloquently demonstrated by Mudd (2010) this is both a geological as well as an economic inevitability.
Both effects, but particularly the second, i.e. harder access, tend to increase energy costs per unit mass of material (e.g. Calvo et al 2016), although this may be counteracted to some degree by changes in extraction technology (e.g. Swart and DeWulf 2013). This trend is particularly problematic in view of the increased non-fuel raw material needs for decentralised energy production using renewable sources (Kleijn et al 2011, Vidal et al 2013. In particular, significantly greater needs for non-fuel raw materials per unit energy produced (e.g. figure 7) could necessitate the mining of non-fuel raw materials at ever greater energy costs which would in turn increase the total demand for energy, and therefore non-fuel raw materials, creating a positive feedback loop with potentially dramatic consequences for the global economy. Note that renewables (particularly wind and solar PV) do not just have significantly higher needs in terms the industrial metals (Fe, Cu, Al) and concrete (figure 7), but also many of the rarer elements (e.g. Ag, Ge and Sn, see Kleijn et al 2011). However, in terms of total energy requirements, the industrial metals are much more significant.
Already, the post-mine processing and refining of nonfuel raw materials to metal and mineral products account for about 12% of global energy consumption (EIA 2016). The energy consumption of mining is not included in this figure, but is probably of a similar order of magnitude (e.g. mining accounted for c. 11% of total energy demand in South Africa in 2012, DoEZA 2013).
This systemic problem cannot be studied through the lens of criticality studies, but rather requires an integrated approach to reach an assessment of the potential severity of the issue. While a number of authors have previously pointed out this problem (Kleijn et al 2011, Vidal et al 2013, Fizaine and Court 2015, a detailed study of its potential magnitude is still lacking.

Summary
In summary, there are a number of complex risk factors present in global markets, which are not, and sometimes cannot, be captured in criticality assessments as long as these are done on a material-by-material basis. The most pressing of these issues is probably the close link between the renewable energy sector and increased future raw materials demand, with potentially disastrous consequences for the global economy. As emphasised by Liebig as early as 1866, 'civilisation is the economy of power' (cited in Jevons 1866). Without a source of abundant cheap energy (Liebig went on to call coal England's source of power), human civilisation would not have progressed as rapidly as it did, nor will it be able to continue this progress into the future (Jevons 1866). If an increasing proportion of total energy production needs to be devoted to the extraction of primary raw materials, this main enabler of technological progress is under serious threat.

Alleviation of risks
While the previous sections focused primarily on the nature of the different risks present for consumers in the global raw materials markets, this section is dedicated to measures proposed for the mediation of these risks. Given the limited applicability of current criticality studies, however, it is not actually clear which individual risks are the greatest. Therefore, this section must necessarily be of a preliminary character. It will focus on those measures discussed most frequently in the recent debate.
Mediation measures can be subdivided into two main groups according to which part of the overall risk they focus on: they can reduce either disruption probability, or vulnerability. In the following sub-sections, different proposed measures are introduced and their main effects on overall risk are discussed.

Reduction of disruption probability
One traditional strategy to lower disruption probability due to high import dependence is diversification of supplies. Companies usually diversify their supplies when the main supplier either increases prices or struggles with delivery problems, or proves to be no longer trustworthy. Diversification can be a good strategy to mitigate the influence of a quasimonopoly on a market, and to lower the probability for supply disruptions. However, sometimes diversification is not easy to achieve due to unfavourable market conditions such as limited opportunities to diversify (only a small number of suppliers exist) or when investments to develop alternative resource projects demand a long time scale as is the case in the REE market (de Boer andLammertsma 2013, Klossek et al 2016). Other factors that can also have a negative effect on diversification efforts are general political instability of producing countries, civil wars and underdeveloped or unsecure trade routes.
Other than the political measures focusing on international relations and diversification of imports, another possibility for the reduction of disruption probability is to increase the share of domestic production in the total consumption of the most critical raw materials. Policymakers can directly influence the commercial success of mining operations through the amount of taxation, environmental laws or export duties. Depending on the country, political decisions can become critical factors for the mining business (Arsel et al 2014). Encouraging greater recycling rates within the framework of the so-called circular economy (Yuan et al 2006, Anderson 2007, EU Commission 2015, again to increase the share of domestic production in total consumption, might also be a viable option to decrease the probability for supply disruptions from international political conflicts. However, once primary production infrastructure and the related know-how required for its operation has been lost from a country or region, the (re-)establishment of primary production is much more difficult (Reuter 2016). Therefore, policy should also focus on avoiding such losses, as they would inadvertently stifle-or at least delay -any efforts to stimulate domestic supply chains.
Concerns about undisturbed access to land-based raw materials also opened up discussion for the potential future exploitation of marine resources (e.g. EU Commission 2012, Greenpeace 2013, OECD 2016). At the moment, deep-sea mining is technologically challenging and commercially not viable. However, if raw material prices should increase again in the future, deep sea deposits of polymetallic nodules and manganese crusts rich in cobalt, copper, nickel, manganese and even platinum, tungsten and rare earths could become valuable strategic resources (Hein et al 2013). This is why several nations as well as exploration companies have secured exploration licenses from the International Seabed Authority (International Seabed Authority 2014). These exploration activities could lead to the exploitation of deep-sea resources in the next two decades. However, industrial-scale mining on the seafloor remains a controversial issue. Critics emphasise the limited understanding of the potential impact on deep-sea ecosystems, requiring further scientific study (Greenpeace 2013). Besides these ecological concerns, the higher energy requirements for the exploitation of seabed resources again feeds into the decreasing quality of, and harder access to, natural resources discussed earlier.

Reduction of vulnerability
Besides measures to reduce disruption probability, a number of different options also exist to reduce the vulnerability to supply shortfalls. For instance, both the effects of transient Figure 7. Raw material requirements per unit energy produced for different sources of electricity. EPR-evolutionary pressurised reactor; PV-photovoltaics, CSP-concentrated solar power. Note the significantly higher demand for industrial metals and concrete for electricity produced from renewable sources. Also note that coal and gas do not include contributions from fuel extraction. In terms of total greenhouse gas emissions, renewables still do significantly better than fossil sources of electricity (Kleijn et al 2011). Data recalculated from sources in Vidal et al (2013). price-hikes and supply shortfalls can be mediated by keeping stockpiles of the required raw materials covering a few months, or even a year, of consumption. This can be done at either the company or national level. Japan and South Korea, for instance, maintain national stockpiles of raw materials they consider critical for their manufacturing industries (JOGMEC 2014, KORES 2013.
Another option to reduce vulnerability, particularly the economic impact of price-hikes, is to reduce the amount of critical materials used in the final products. This can either be done through more efficient product design or production processes, or through increased substitution where viable substitutes exist for critical raw materials (e.g. as for Co in permanent magnets in the 1970s, see Buijs et al 2011aBuijs et al , 2011b.
Of course, policymakers can have a direct influence on these processes by encouraging research into resource efficiency and material substitution. However, individual companies will also have to invest into their own research and development programmes, particularly if they are more seriously affected by the risks related to certain raw materials than the corresponding national economies. As mentioned in the beginning, criticality is dependent on the specific consumer. Raw materials critical for one or two companies might not be critical for a whole country.

The long term
It is also important to re-iterate that one of the main raw material-related long-term risks to the global economy is the prospect of increasing unit energy cost of production at increased demand. There are many options to address this risk. For instance, the effect might be counteracted to some degree by the introduction of new mining and beneficiation processes that are considerably more energy efficient than conventional options. There is a significant potential for such reductions in the mining industry (e.g. with more efficient crushing and grinding equipment; Napier-Munn 2015).
An alternative strategy is to deploy (new) means of less resource-intensive, zero-carbon energy production beyond the current drive for renewables. There are a few options, e.g. fossil fuels with carbon capture and storage, nuclear fission, and perhaps nuclear fusion (Brook 2012, Cowley 2016. While fission power is already available for largescale deployment, the other two options still require considerable future development (Boot-Handford et al 2014, Lopez Cardoso et al 2016. Movement towards a 'circular economy' (Yuan et al 2006, Anderson 2007, EU Commission 2015 where recycling rates for all non-consumable raw materials approach 100% is another important option. It should be noted, however, that perfect recycling is a physical impossibility (e.g. Reuter et al 2006, Amini et al 2007, Reck and Graedel 2012, and, therefore, that the mining of primary resources will probably never cease completely. A particular problem is that the recycling of ever more complex products will also require increasing amounts of energy per unit mass of raw material, just as for primary ores (Reuter et al 2006). Nevertheless, increased rates of recycling may serve to take some of the strain from the global primary production system. This could be complemented by reductions in raw material consumption, e.g. through better raw materials efficiency in industrial products, or substitution of the most energy-intensive raw materials by less energy-intensive ones. Materials research has an important role to play in these strategies.
The best results would evidently be achieved by a favourable combination of all of the above strategies. However, while there are obvious economic incentives for their adoption, targeted government policies will be needed to accelerate the process. Particularly in areas where basic research is required to lay the scientific foundations for new and more efficient processes, as well as to demonstrate their viability, government funding is often an essential ingredient. The importance of the adoption of suitable policies can thus hardly be understated.

The role of applied physics
Since this article is chiefly intended for an applied physics audience, we would now like to highlight some of the many areas in which physicists can make an important contribution to the mediation of risks related particularly to escalating unit energy costs of production for many raw materials. Specifically, the following areas of physics are of interest: (1) Solid state physics: first, for research into the substitution of the most energy-intensive and critical primary resources in industrial materials; second, to develop new materials with the right properties required for alternative modes of power production (e.g. in solar cells or nuclear reactors); and third, for the development of more efficient grinding techniques, which will require a detailed understanding of the physical controls on rock breakage, and innovative thinking regarding energy-efficient fracturing (Napier-Munn 2015).
(2) Nuclear physics: for the development of alternative modes of power generation (fusion/fission), to supplement renewable sources. (3) Surface physics/fluid dynamics: for the modelling and improvement of current mineral separation technologies, particularly froth flotation. (4) Exploration geophysics: for the development of new geophysical/remote-sensing techniques to improve the success rate, and therefore the efficiency, of mineral exploration efforts.
Of course, this list is by no means exhaustive. Nevertheless, it still illustrates the relevance of many areas of applied physics to the complex problem at hand.

Summary and conclusions
After a detailed evaluation of the methodology of current criticality assessments, as well as the more complex resourcerelated challenges facing the global economy, we come to the following conclusions: First, current assessments of raw material criticality are flawed in several fundamental ways. This is mostly due to a lack of adherence to risk theory, and highly limits their applicability. Many of the raw materials generally identified as critical, particularly those produced as by-products and only employed in niche, albeit high-tech, applications, are probably not critical.
Second, the flaws of current assessments do not mean that the general issue of supply security of raw materials can be ignored, but rather, that new assessments are urgently needed. These assessments should follow the principles outlined in section 3 of this review. In particular, they should be based on empirical evidence, include logically coherent risk models, and be compatible with risk theory (see Cox 2009).
Third, the results of new and improved assessments will likely include more of the traditional industrial metals in the list of critical materials, particularly those related to steelmaking (Fe ore, coking coal, Cr, Ni), and power infrastructure (Cu). Increased and sustained public investment in the raw materials sector is needed to ensure the future supply security of important raw materials. This is particularly true for those societies that are large consumers but have shown rapidly decreasing public and private investment in the resource sector (Western Europe, the United States).
Fourth, the greatest challenge in the resource sector for the longer term is to counteract the escalation of unit energy costs of production, which is inevitable if conventional production processes continue to be applied to resources of ever harder accessibility-from both primary and secondary sources. This issue is particularly pressing due to its close link to the renewable energy revolution which is set to dramatically increase the demand for raw materials per unit energy produced (Vidal et al 2013). Due to its multi-faceted nature, the close link between energy and resource efficiency is not captured in any of the current criticality assessments.
Particularly the solution to this last challenge will require coordinated policy action, as well as the collaboration of scientists from many different fields-with physics, as well as the materials and earth sciences in the lead.