In a method for vapor-depositing a substrate with a layer of a needle-shaped x-ray fluorescent material containing at least one alkali metal, alkali halide phases and an alkali halide are mixed in a vapor phase and are vapor-deposited on the substrate. A needle-shaped fluorescent material is thereby produced having the formula'.times.'.times.''.times.''.times..times..times.'.times..times.'.t- imes..times.'''.times.''.times..times.''.times..times.'''.times.'.times..t- imes.''.times..times.'''.times.''.times..times.'.times..times.''' ##EQU00001## wherein M.sup.+ is at least one metal ion from the group Na, K, Rb and Cs, H.sup.- is at least one halide from the group F, Cl, Br and I and S.sup.z+ is at least one lanthanide ion from the group La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb or Lu.
