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PROBLEM TO BE SOLVED : To provide a garnet-type compound designed to make substitution ion such as of Pr easily solid-soluble in the matrix compound. SOLUTION : The garnet-type compound is represented by the general formula : A1(III)3-2xA2(II)xA3(III)xB(III)2C1(III)3-xC2(IV)xO12(wherein, each of the Roman numerals in the parentheses represents the valence number of ion; each of A1, A2, and A3 represents the element at the A site; B represents the element at the B site; each of C1 and C2 represents the element at the C site; each of A1, A2, B, C1, and C2 represents at least one kind of element exhibiting the corresponding valence number of ion defined above; A3 represents at least one kind of element selected from the group consisting of trivalent rare earth elements of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu; A1 and A3 represent different elements; x represents a number satisfying a condition 0
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