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Boyce, at Eurasian Natural Resources Corp before Gemfields, will replace Derek Batorowski as finance chief of the lithium developer.
Carr arrives on the board following the departure of Martin Vidal in November.
She is currently also on the boards of Sylvania Platinum (LN:SLP) and Bunree Resources Management, and was involved with Talvivaara Mining (now Ahtium) until it dropped its London listing in 2014.
Bacanora CEO Peter Secker said the appointments reflected well on the company.
"To have secured the services of a non-executive director and a CFO who have both held senior finance positions at multi-divisional natural resources companies, reflects the significant progress made by Bacanora in the last 12 months," he said.
"I would like to take this opportunity to thank Derek Batorowski for the valuable contribution he has made to the company as finance director over the years. "
Batorowski will stay on at Bacanora as a non-executive director.
