In LiCoO2, lithium ions diffuse in 2 dimensional planes. It is the most widely used cathode material in consumer electronics since SONY first introduced it in lithium ion batteries in 1991.
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In LiCoO2, lithium ions occupy octahedral sites (shown in yellow in the animation) in the 2 dimensional lithium diffusion planes between the CoO2 layers. Lithium ions move by hopping through neighbouring tetrahedral sites (shown in blue in the animation). Thus, lithium ions diffusion in LiCoO2 is 2 dimensional.