Two new compounds were found in the K-Si-As system. One of them, K[subscript]2SiAs[subscript]2, is isostructural with K[subscript]2SiP[subscript]2 with infinite [subscript]sp[infinity]1 (SiAs[subscript]2) [superscript]-2 chains, while KSi[subscript]3As[subscript]3 adopts a new structure type with infinite puckered [subscript]sp[infinity]2 (Si[subscript]3As[subscript]3) [superscript]- layers. The structure of KSi[subscript]3As[subscript]3 can be related to that of the compound, SiAs, while the structure of K[subscript]2SiAs[subscript]2 is completely different from SiAs[subscript]2 owing to the different content of cations. The sodium analogue of KSi[subscript]3As[subscript]3 was also synthesized through cation exchange reaction;In the study of the structures of M[subscript]5X[subscript]3 (M = Ca, Sr, Ba; X = Sb, Bi), we found that the pure binary M[subscript]5X[subscript]3 in the Mn[subscript]5Si[subscript]3 structure can exist without any interstitial element in the octahedral site. They follow the valence rule strictly as interstitial elements are introduced. Three structures, filled with Mn[subscript]5Si[subscript]3, filled [beta]-Yb[subscript]5Sb[subscript]3, and anti-Th[subscript]3P[subscript]4, were observed on changing interstitial elements from Cl or Br to F to I. It is believed that this phenomenon is caused by an anion size effect;Also, an unusual stoichiometric compound Ca[subscript]16Sb[subscript]11, which violates the valence rule, was found as a new member of R[subscript]5 n + 6 T[subscript]3 n + 5 (R = rare earth metal; T = transition metal) series during the study of M[subscript]5X[subscript]3Y systems (Y = interstitial element). This series is related to the W[subscript]5Si[subscript]3 structure. A relationship between r[subscript] R/r[subscript] T and [delta]V was established to explain this series. Based on this relationship, the Sr[subscript]16Bi[subscript]11 analogue was also synthesized;The mixed cation effect was examined in Sr-Mg-Ge system. Two non-stoichiometric compounds, Sr[subscript]2 + xMg[subscript]12 - xGe[subscript]7 and Sr[subscript]5 + yMg[subscript]19 - yGe[subscript]12, were found to be isostructural with Zr[subscript]2Fe[subscript]12P[subscript]7 and Ho[subscript]5Ni[subscript]19P[subscript]12, respectively. Two other compounds, SrMg[subscript]3Ge[subscript]3 and Sr Mg[subscript]2Ge[subscript]2, also have been synthesized with new structure types. The similar powder patterns and reasonable postulation support the idea that the structure of SrMg[subscript]3Ge[subscript]3 might be related to that of Rh[subscript]4P[subscript]3.