SYDNEY — Attempts by Australia and others to boost their role in rare-earth elements face numerous challenges even though China’s grip is expected to loosen in the coming decade.

Australia announced this month that it will back a second large rare-earth project, providing a loan of 840 million Australian dollars ($550 million) to the Australian miner Arafura to build a mine and processing facility in the Northern Territory. The loan, provided largely by the government’s Critical Minerals Facility, comes two years after another miner, Iluka, was given AU$1.25 billion to build a rare-earth processing plant in Western Australia.

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