Refinement of the crystal structures of (\mathrm{Ba}{2} \mathrm{CrO}{4}) and (\mathrm{Ba}{3} \mathrm{CrO}{5}) using powder neutron diffraction data has confirmed that the former is isostructural with (\beta-\mathrm{K}{2} \mathrm{SO}{4}) and the latter isostructural with (\mathrm{Cs}{3} \mathrm{CoCl}{5}). (\mathrm{Ba}{2} \mathrm{CrO}{4}) is orthorhombic, (P_{n m a}) (No. 62), (Z=4) with (a=7.6285(5) \AA, b=5.9136(5), c=10.4639(8)), and (V=472.04(5) \AA^{3} ; \mathrm{Ba}{3} \mathrm{CrO}{5}) is tetragonal, (14 / \mathrm{mcm}) (No. 140), (Z=4) with (a=7.3033(3) \AA, c=) (11.6704(6), V=622.48) (4) (\AA^{3}) from powder Guinier X-ray diffraction data. Magnetic properties of (\mathrm{Sr}{2} \mathrm{CrO}{4}, \mathrm{Ba}{2} \mathrm{CrO}{4}), and (\mathrm{Ba}{3} \mathrm{CrO}{5}) were examined down to (2-5 \mathrm{~K}). The structures and magnetic properties of (\mathrm{Sr}{2} \mathrm{CrO}{4}) and (\mathrm{Ba}{2} \mathrm{CrO}{4}) are compared with their vanadium analogues (\beta-\mathrm{Sr}{2} \mathrm{VO}{4}) and (\beta-\mathrm{Ba}{2} \mathrm{VO}{4}). Unlike isostruclural (\beta-\mathrm{Sr}{2} \mathrm{VO}{4}) which contains the (\mathrm{V}{2} \mathrm{O}{8}^{8-}) dimer, (\mathrm{Sr}{2} \mathrm{CrO}{4}) contains truly isolated (\mathrm{CrO}{4}^{4}) tetrahedra and its magnetic behavior can be best described as a dimerized chain. (\mathrm{Ba}{2} \mathrm{CrO}{4}) and (\mathrm{Ba}{3} \mathrm{CrO}{5}) also contain isolated (\mathrm{CrO}{4}^{4-}) tetrahedra. (\mathrm{Ba}{2} \mathrm{CrO}{4}) is paramagnetic down to (5 \mathrm{~K}). (\mathrm{Ba}{3} \mathrm{CrO}{5}) undergoes longrange magnetic order at (\sim 8 \mathrm{~K}), a temperature range significantly higher than that of isostructural (\mathrm{Rb}{3} \mathrm{CoCl}{5}) and (\mathrm{Cs}{3} \mathrm{Co} X{5}(X=\mathrm{Cl}, \mathrm{Br})). 1993 Academic Press. Inc.