What is thermodynamic rarity?

Thermodynamic rarity (TR) is an indicator of raw material scarcity based on physical aspects of the minerals where the different elements are produced [1]. A given element has a high thermodynamic rarity value when it is scarce in the crust and/or when the processes required to mine and beneficiate it are very energy intensive. It is defined as the amount of exergy that would be required to extract and beneficiate an element from ordinary rocks (i.e. not from ore), using the best prevailing technologies. Thus, TR is composed by two terms:

• Mining and concentrating cost: it is the “real” cost associated with the conventional beneficiation processes from current mines to refined metal. As mines are depleted, this real cost becomes increasingly higher [2].
• Exergy replacement cost: the second term relates to the fact that having minerals concentrated in ore bodies (and not dispersed throughout the crust) represents a “free bonus” provided by nature, which reduces the otherwise required energy costs of mining. The reduction of this bonus when mines are depleted is quantified as so called exergy replacement costs (ERC). These are defined as the cumulative exergy that would be needed to reconcentrate a mineral from a completely dispersed state (denoted Thanatia) [3] to the conditions of concentration and composition found in the original mines using prevailing technology. Hence, ERC can be seen as the ultimate future effort that society would need to put into play when all mineral deposits become depleted [2].

How can it be calculated?

To calculate the TR of a device, it is necessary to know its elemental composition (in g), i.e. the mass of each element it embodies. The 𝑇𝑅 [𝑘𝐽] of a device will be the sum of all the individual contributions of the individual elements in thermodynamic rarity terms, as indicated by the following equation, where 𝑤𝑖[𝑔], refers to the mass of each element in grams, and TR_i [kJ/g] the thermodynamic rarity of each element (provided by the calculator) [4].

How does the calculator work?

1. Click on the chemical element to enter values.
2. Enter the mass of the chemical element in grams.
3. The calculator displays the TR of the element (if the TR of the element is not known, it is considered zero).
4. The calculator displays the TR and the total mass of the device.
5. The calculator displays on a bar chart the relative contributions of each element in mass (chart on the left) or in TR terms (chart on the right). Only the seven most relevant elements (either in mass or in rarity terms are shown). The remaining element are added and displayed in the item called “Rest”.
6. Initially, the graphs show the 7 most relevant elements according to their weight contribution. Alternatively, the 7 most relevant elements according to their TR value can be displayed by clicking the “Order rarity by value” button.

The following figure shows an example.