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By applying first principles density functional theory (DFT) methods, different metal fluorides and their surfaces have been characterized. One of the most investigated metal fluorides is AlF₃ in different polymorphs. Its chloride-doped analogon AlCl_<i>x</i>F_{3&#8722;<i>x</i>} (ACF) has recently attracted much attention due to its application in catalysis. After presenting a summary of different first-principle studies on the bulk and surface properties of different main group fluorides, we will revisit the problem of the stability of different <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-AlF₃ surfaces and extend the investigation to chloride-doped counterparts to simulate the surface properties of amorphous ACF. For each material, we have considered ten different surface cuts with their respective terminations. We found that terminations of (<inline-formula> <math display="inline"> <semantics> <mrow> <mn>01</mn> <mover accent="true"> <mn>1</mn> <mo stretchy="false">&#175;</mo> </mover> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>) and (<inline-formula> <math display="inline"> <semantics> <mrow> <mn>11</mn> <mover accent="true"> <mn>2</mn> <mo stretchy="false">&#175;</mo> </mover> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>) yield the most stable surfaces for <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-AlF₃ and for the chlorine substituted surfaces. A potential equilibrium shape of the crystal for both <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-AlF₃ and ACF is visualized by a Wulff construction.