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A main source of capacity fading in lithium-ion batteries is the degradationof the active cathode materials caused by the series of volume changes duringcharge and discharge cycles. The quaternary colquiriite-type fluoridesLi$_x$CaFeF$\mathrm{_6}$ and Li$_x$CaCoF$\mathrm{_6}$ were reported to havenegligible volume changes in specific Li concentration ranges, making theunderlying colquiriite structure a promising candidate for so-calledzero-strain behavior. Using first-principles electronic structure calculationsbased on density functional theory with a Hubbard-$U$ correlation correction onthe transition-metal ions, we systematically investigate the equilibriumvolumes of the colquiriite-type fluorides Li$_x$CaMF$\mathrm{_6}$ with M =Ti,V, Cr, Mn, Fe, Co, and Ni at the Li concentrations $x$=0, 1, and 2. Weelucidate the connection between the total volume of the structures and thelocal volumes of fluorine coordinated octahedra around the cations, and we findtrends along the series of the 3d transition-metal elements. In the lithiationstep from $x$=1 to $x$=2 we find volume changes of about 10 %, and we discussthe discrepancy to the experimentally reported smaller value forLi$_x$CaFeF$\mathrm{_6}$. The suitability as cathode material was furhterinvestigated by calculating the theoretical voltages and capacities. From $x$=0to $x$=1 we describe the compensating structural mechanisms that lead to anexceptionally small volume change of Li$_x$CaMnF$\mathrm{_6}$, which posseses ahigh theoretical voltage and moderate capacity. This compound is therefore aparticularly promising zero-strain cathode material.

First-principles analysis of the interplay between electronic structure and volume change in colquiriite compounds during Li intercalation