A lithium ion-conducting compound, having a garnet-like crystal structure, and having the general formula: Lin[A(3-a′-a″)A′(a′)A″(a″)][B(2-b′-b″)B′(b′)B″(b″)][C′(c′)C″(c″)]O12, where A, A′, A″ stand for a dodecahedral position of the crystal structure, where A stands for La, Y, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and/or Yb, A′ stands for Ca, Sr and/or Ba, A″ stands for Na and/or K, 0a′2 and 0a″1, where B, B′, B″ stand for an octahedral position of the crystal structure, where B stands for Zr, Hf and/or Sn, B′ stands for Ta, Nb, Sb and/or Bi, B″ stands for at least one element selected from the group including Te, W and Mo, 0b′2 and 0b″2, where C and C″ stand for a tetrahedral position of the crystal structure, where C stands for Al and Ga, C″ stands for Si and/or Ge, 0c′0.5 and 0c″0.4, and where n=7+a′+2·a″−b′−2·b″−3·c′−4·c″ and 5.5n6.875.
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