We have performed a series of elastic neutron scattering measurements on 1/8-hole doped La1.875Ba0.125−xSrxCuO4 single crystals with x = 0.05, 0.06, 0.075 and 0.085. Both charge-densitywave (CDW) and spin-density-wave (SDW) orders are found to develop simultaneously below the structural transition temperature between the low-temperature orthorhombic (LTO) and lowtemperature tetragonal (LTT) or low-temperature less-orthorhombic (LTLO) phases. In the ground state the CDW order is observed only in the LTT/LTLO phase and drastically degrades towards the LTO boundary. The x-dependence of Tc strongly suggests a direct effect of the CDW order on the suppression of superconductivity. Results are discussed in comparison with those from the La1.6−xNd0.4SrxCuO4 system within the framework of the stripe model. PACS numbers: 74.72. Dn, 71.45.Lr, 75.30.Fv, 74.25.Dw The interplay between magnetism and superconductivity is a central issue in high-T c superconductivity [1]. Neutron scattering measurements on the superconducting La 2−x Sr x CuO 4 (LSCO) system have shown dynamical incommensurate (IC) magnetic correlation [2][3][4]. The linear doping dependence of incommensurability with the superconducting transition temperature (T c ) in the under-doped region suggests a relationship between magnetic correlation and superconductivity [5].On the other hand, it is well known that superconductivity in the La 2−x M x CuO 4 (M=Ba, Sr) system is anomalously suppressed at the specific hole concentration of x ∼1/8. For the La 2−x Ba x CuO 4 (LBCO) system, this 1/8-anomaly is accompanied by an occurrence of the lowtemperature tetragonal (LTT) phase with P4 2 /ncm symmetry [6][7][8]. Superconductivity in the low-temperature orthorhombic (LTO) phase of LSCO with Bmab symmetry is weakly suppressed in comparison with the LBCO system [9,10]. Maeno et al. initiated systematic studies on La 1.875 Ba 0.125−x Sr x CuO 4 (LBSCO) using polycrystalline samples to clarify the relation between T c and crystal structure [11]. We comprehensively studied the same system using single crystals and revealed a drastic change in x-dependence of T c [12,13]. In the present study we demonstrate a close relation between T c and crystal structure as shown in Fig.4.Recently, the IC spin-density-wave (SDW) and the charge-density-wave (CDW) orders were discovered in La 1.6−x Nd 0.4 Sr x CuO 4 (LNSCO) with x ∼ 1/8. These provide important clues for understanding the mechanism of the 1/8-anomaly based on the stripe model [14,15]. In the framework of the stripe model it is recognized that the orders are a manifestation of dynamical spin/charge correlation and that stabilization of the orders competitively induces instability of superconductivity [16]. In the LTT phase stripe-shaped orders parallel or perpendicular to Cu-O bonding are favorably stabilized by the corrugated pattern of the in-plane lattice potential. Hence, T c is suppressed to a greater extent in the LTT phase than in the LTO phase. Whether visible signs, such as the anomalous suppression of T c , app...