Abstract
AbstractCopper (Cu) is one of the most popular fcc metals in recent researches and applications. The smaller the electronic devices become, the more important is to study the structures and properties of grain boundaries in Cu in order to yield better performances for the processes of semiconductor production. In this research, an artificial Cu bicrystal with a symmetric tilt misorientation of [011](12-2) / [011](-12-2) was made and then the atomic structure of the grain boundary (GB) of the bicrystal was investigated using high resolution transmission electron microscope (HRTEM). Σ = 9 [011]/(-17-7)(7-55) asymmetric tilt grain boundary and Σ = 9 [011]/(12-2) symmetric tilt one were found to be connected. Corresponding to the simulations of Lennard-Jones (LJ) or embedded atomic method (EAM), the asymmetric tilt grain boundary of (-17-7)L / (7-55)R which is deviated from the symmetric tilt one of (12-2)L / (1-22)R by 25.24 °can exist stably and become an essential transitional grain boundary for the transition from high-energy (12-2)L / (1-22)R grain boundary to the lowest-energy (-5-11)L / (11-1)R one.The boundary structure in the segment of Σ = 9 [011]/(12-2) symmetric tilt grain boundary (STGB) was analyzed using HRTEM to be a glide-mirror symmetric structure which is the same as those observed in Al, Si and Ge. Simultaneously, the structure is also corresponding to the structural model of EAM which was simulated by Seidman et al. On the principle of EAM, the larger values of dΦij(Rij) / dRij and bulk modulus of Cu imply a steep bonding-energy curve near the equilibrium position. The repulsive energy in Cu may increase more dramatically than in Al if the atoms come closer. In other words, Al may have more tolerance for two atoms being closer than their equilibrium distance to make the mirror symmetric structure present (observed by Mills), but it has not been found in this research.The volume expansion per unit GB area, δV / A, of the Σ = 9 [011]/(12-2) GB in Cu can be obtained as 0.0036 nm, which represents a little wider gap between both grains than 0.1205 nm, twice the lattice spacing of {244}. Compared to the dilation of Σ = 3 [011]/(11-1) STGB in Cu-Bi alloy, δV / A = 0.04 ±0.005 nm, and that of Σ = 3 [011]/(11-1) STGB in Cu, δV / A = 0.001 ±0.004 nm, it is reasonable to postulate that the glide-mirror symmetric structure is a stable structure without any alloy atom interfered in the GB core. According to the displacement map of the glide-mirror symmetric structure, it is apparent that the atoms at the tops of the periodic pentagons have relatively large displacements and relax towards the core of the GB. Large displacement of these atoms may have something to do with missing of a {244} plane in the boundary core. The atoms, however, next to the core of the GB relax outwards the core because they are highly influenced by the Coulomb’s repulsive force of the opposite grain. These atoms possess relatively small relaxation displacements because of the positiveδV / A . If the levels of the atoms of the glide-mirror symmetric structure in the [011] direction were considered, the glide-mirror symmetric structure interpreted by relaxation displacements and bonding lengths would be conflicting with that proposed by Seidman et al.The glide-mirror symmetric structure translates into modified mirror symmetric structure through a step structure. As a result of that, the boundary plane shifts to left for four to five {244} spacings. The modified mirror symmetric structure is somewhat different from that observed in Al by Mills.The borderline between both grains in the step structure is measured as (11-1)L[-21-1]L and (-1-33)R[6-11]R and is similar to (75-5)L / (-1-77)R with deviations of 7.5 °and 9.4 °, respectively. It is the same as (-17-7)L / (7-55)R asymmetirc tilt GB which holds relatively low GB energy.There is a partial displacement-shift-complete (DSC) dislocation in the step structure. The Burgers vector of this partial DSC dislocation is the combination of two mutually perpendicular partial DSC vectors of the Σ = 9 [011]/(12-2) STGB. b = a/18 [12-2]L + a/36 [-41-1]L = a/36 [-25-5]L, or b = a/18 [1-22]R + a/36 [41-1]R = a/12 [2-11]R. Due to the nature of DSC, the lattice points will not occupy the DSC lattice sites if the rigid-body translation is not the multiple of perfect DSC vectors. The translation in the step structure does not preserve the glide-mirror symmetric structure but forms modified mirror symmetric one because the components of the Burgers vector of the DSC dislocation are only half the perfect DSC vectors.The dilation (δV / A) of the glide-mirror symmetric structure near the step is measured as –0.0024 nm and is smaller than that of the same structure far away from the step, 0.0036 nm. It means that a compressive stress field is endured in this area where the glide-mirror symmetric structure is above the partial DSC positive edge dislocation. On the other hand, the dilation of the modified mirror symmetric structure is evaluated as 0.0322 nm which is corresponding to a tensile stress field. The modified mirror symmetric structure is different from that observed by Mills in Al. Based on the principle of EAM and the concept of effective charge, Al has more tolerance than Cu to get closer with little elevation of repulsive energy. The mirror symmetric structure can exist in Al, but only modified mirror symmetric one can be present in Cu.The atomic model of the modified mirror symmetric structure of which both grains have a relative translation of a/4 [011] were proposed according to the relaxation displacements and the DSC lattice.From the EDX information of Co, no Co segregation was found in the Σ = 9 [011]/(12-2) STGB in Cu. The concentrations of Co in the GB and near the GB were determined as 0.7 at% and 0.8 at%, respectively, by means of EDX spectroscope. The grain boundary structure of the Co-doped Σ = 9 [011]/(12-2) STGB in Cu was verified to be mirror symmetric structure, which is very similar to that in Al proposed by Mills, but is different from the modified mirror symmetric one.The mirror symmetric structure of the Co-doped Σ = 9 [011]/(12-2) STGB in Cu translates into another mirror symmetric structure through a step structure. The step structure is also different from that either in pure Cu or in Al. As a result of that, the boundary plane shifts to left for six {244} spacings. The orientation of the step is close to (-5-11)L / (11-1)R, which is of the lowest energy among all of the Σ = 9 [011]/(12-2) symmetric and asymmetric tilt GB. The step structure is also influenced by the Co doping.Both grains translate each other by a perfect DSC vector, maintain the same mirror symmetric structure and then induce a secondary grain boundary dislocation (SGBD) at the step. The components of the Burgers vector, a/18 [-25-5]L or a/6 [2-11]R, of the SGBD in the axes of DSC lattice are both perfect DSC vectors. The multiplicity of the Co-doped Σ = 9 GB was not formed by the rigid-body translation.The GB dilation,δV / A, of two set of mirror symmetric structures are calculated as 0.0614 nm and 0.0681 nm, respectively. BecauseδV / A is close to half a DSC vector, Co atoms with smaller atomic size may insert into the looser sites at the core of the GB, and then are treated as secondary coincident sites.