As background, rare earth elements (REE) are crucial materials in an incredible array of consumer goods, energy system components, and military defense applications. Major market segments that rely on REE-based products or technologies include health care, transportation and vehicles, lighting, renewable energy systems, communications systems, audio equipment, military defense technologies, and modern electronics. In recent years, the markets for rare earths have been shifting from the more mature applications mainly for the LREE, such as catalysts, to more high-tech newer applications mainly for the HREE, such as permanent magnets that are used in wind turbines and hybrid/electric vehicles. However, the global production and entire value chain for REE is dominated by China, with the U. S. currently 100% import reliant for these critical materials. Traditional mineral ores including those previously mined in the U. S., however, have several challenges. Chief among these is that the content of the most critical and valuable of the rare earths is deficient, making mining uneconomical. Further, the supply of these most critical rare earths is nearly 100% produced in China from a single resource that is only projected to last another 10–20 years. The U. S. currently considers the rare earths market an issue of national security. It is imperative that alternative domestic sources of rare earths be identified and methods developed to produce them. Recently, coal and coal byproducts have been identified as one of these promising alternative resources. Two options are being intensively explored: 1) extraction from lignite and 2) extraction from coal ash".

a) Based on the compositions of these materials, suggest a method with supporting (chemical) rationalization for extraction of rare earth elements. Note: For each source you may need to first identify the composition of each potential resource.
b) Prepare a table (in word) listing the primary resources (fuels, chemicals, solvents, etc.) necessary for each approach (assuming a different method for each resource), listing in an adjacent column costs. Scale to 1 ton of total recovered REEs. Compare costs, required starting resource tonnage to reach a conclusion as to best path forward. For your reference, two articles are posted to canvas under Supplementary Materials II providing representative REE concentrations in lignite and coal ash.