Local decomposition induced by dislocation motions inside precipitates in an Al-alloy

Transcription

1 Supplementary information Local decomposition induced by dislocation motions inside precipitates in an -alloy B. Yang, Y. T. Zhou, D. Chen, X. L. Ma* Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Wenhua Road 7, Shenyang, China * Correspondence and request should be addressed to X.L.Ma (xlma@imr.ac.cn) Materials and Methods Sample preparation Master alloy with nominal composition of -4wt.%Cu was prepared by arc melting. The alloy ingot was sealed in quarts tube and experienced a solution treatment at 50 o C, then ageing at 300 o C for days, shown in Fig.S1. The as-received sample is a dual-phase material which is composed of tetragonal θ- Cu precipitate embedded in matrix (Fig.S). Plastic deformation of the dual-phase plate was performed by using surface mechanical attrition treatment (SMAT). During the SMAT process, a large number of steel balls impact onto the sample surface at a high flying speed, that generate a large plastic strain at a very high strain rate in the topmost surface layer. With an increasing depth from the topmost surface, a gradual decreasing strain and strain rate are applied resulting in a gradient variation of microstructure, ranging from nano-grained structures to deformed coarse-grained structures. Below a certain depth (about 40 μm in this sample), no plastic deformation is induced and the microstructure remains original (Fig.S3). Therefore, the SMAT technique is able to generate a gradient variation of plastic strain (and strain rate) from a high value to zero within the thin surface layer. In this work, the -alloy sample was treated under vacuum (6x10 - Pa) at liquid nitrogen temperature for 60 minutes with a vibrating frequency of 50 Hz. Structural characterization 1

2 X-ray diffractions at lower scanning angle of 3 o were performed to determine phases in the μm thick layer from the top. For small angle XRD with the incidence angle α, the penetration depth (t) is estimated from the equation 1 : t 1 1 α sinα = sinα μ ρμ ρμ Where μ is absorption coefficient of the sample; μ m is mass absorption coefficient of the sample, and ρ is density of the sample. When the incidence angle α is small, t is proportional to α. According to C. E. Foerster et al., the estimated penetration depth for sample is about 700 nm with grazing incidence XRD of Cu K α radiation at the incidence angle of 0.5 o. In the present work, X-ray diffractions of Cu K α radiation at lower scanning angle of 3 o ( α=3 o ) were performed to determine phases in SMAT -4wt.% Cu alloy. Considering the magnitude of ρ and μ m in this work rather similar to that in previous study, the penetration depth is estimated to be about μm. m By comparing the intensity of the corresponding peaks before and after SMAT, it is seen that the volume of Cu precipitates in the sample is largely reduced after SMAT (Fig.S4). For a semi-quantitative measurement, we first confirmed there is no texture in the sample before SMAT. Then we carried out small angle (3 o scanning) diffraction from the same area before and after SMAT deformation. After removing the background of XRD data, the strongest peak of each phase, (110) Cu and (111) are selected for calculating the peak areas. The volume fraction of Cu phase relative to is expressed by the following equation: W I Cu Cu Cu = =, Cu Cu I I I Cu K I Cu + K + O3 K O 3 I m where K is an absorption correction factor. Cu K O3 and K O 3 can be found in the PDF database as.8 and 4.3 3,4, respectively. Hence, Cu K =.8/4.3 = By comparison of Cu fraction before (7.6%) and after (4.89%) deformation in the same area, we can estimate that Cu is largely reduced by 35.6% after SMAT deformation (table S1).

3 Table S1. Measurement of Cu fraction based on X-ray diffraction I Cu I W Cu (%) Before SMAT After SMAT ΔW Cu (%) 35.6 The cross-sectional foil samples for TEM observations were prepared. A Tecnai G F30 transmission electron microscope, equipped with Gatan imaging-filter (GIF), high-angle-angular-dark-field (HAADF) detector, and X-ray dispersive spectroscopy (EDS) systems, was used at 300kV for electron diffraction, HAADF imaging, and elemental mapping. The probe size for EDS line-scan is less than nm and the step size about 3 nm. During the TEM observation, dislocations with slip system of [001](110) are frequently observed inside the Cu precipitates. Therefore, high-resolution imaging was performed along [110] direction of Cu. Structural details along this projection are displayed as seen in Fig.S5. Molecular dynamics simulations To monitor the microstructural development along the slip plane under the application of external stress, MD simulations with Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) 5, are performed using the embedded atom method (EAM) interatomic potential. This is an analytical EAM potential function including a long range force 6. In the EAM potential, the electron-density function is taken as a decreasing exponential function, a two-body potential is defined as a function 7, and the embedding energy is assumed to be a universal form 8. This potential has been successfully applied in various different studies Based on the experimental results 1,13, and that in the present study, the dislocation of 1 [001](110) is constructed with 1144 atoms. The x axis denotes [110] direction, the y axis [001] direction, and the z axis [110] direction. A periodic boundary condition applied in the x direction ensures that the short dislocations remain straight during their motions. The total energy minimization criterion, which is based on the conjugate gradient algorithm, 3

4 is used to optimize the atomic structure and relax the system to equilibrium. To avoid thermal disturbance in the simulation, the temperature of 0.1 K is controlled by Nose/Hoover thermostat 14,15. The maximum temperature reaches.0 K for the case of an NVT ensemble (constant number of particles, volume and temperature) in all simulations (using a constant time step equal to ps). The Velert velocity integration algorithm 16 is used, and the stress is applied to keep the velocity of 0.1 m/s for the Top atoms. In addition to monitor the atomistic processes during dislocation motion, we also applied the centrosymmetry parameter to analyze the large amount of data in such atomistic simulations (Fig.S6). The centrosymmetry parameter is a measure of the local lattice disorder around an atom and can be used to characterize whether the atom is part of a perfect lattice, or a local defect (a dislocation or stacking fault) in solid state systems. The centrosymmetry parameter is computed using the following equation 17. CSP = N / i= 1 r r R i + R i + N / (1) where the N nearest neighbors are identified and R i and R i+n/ are vectors from the central atom to a particular pair of nearest neighbors. The unit is Å. There are N (N-1)/ possible neighbor pairs that can contribute to the equation (1). If the atom does not have N neighbors (within the potential cutoff), then its centrosymmetry parameter is set to 0.0. Fig.S6b shows that, at 14,000 timesteps, the force on atoms along [001] direction is mainly accumulated on the dislocation core. In Fig.S6c-e, the atoms are colored according to the value of the centrosymmetry parameters from 14,000, 00,000, to 400,000 timesteps. In the bulk of a tetragonal Cu lattice, for reference, the centrosymmetry parameter is 1Å for Cu atoms. When Cu atoms depart from the lattice for segregation during dislocation motion, the centrosymmetry parameter tends to zero for atoms within the decomposition region. These values assume that the Cu nearest-neighbor distance does not change in the vicinity of these defects, in which the centrosymmetry parameter is about 6Å for atoms halfway between tetragonal and decomposition sites. Our MD simulations on the extended dislocation inside Cu indicate that the equilibrium separation distance of the two partials is 14.4 nm after optimization. 4

5 Correspondingly, this value ranges from 10 to 0nm in experiments. Our experiments also indicate that the (110) slip plane of Cu precipitate is composed of a number of extended dislocations. The characteristic of the dislocation motion is that two partials move towards each other in the scale of 10-0nm (corresponding to the width of stacking faults), schematically illustrated in Fig.S7. References 1. Cullity, B. D. & Stock, S. R. (eds) Elements of X-Ray Diffraction, 3 rd edition (Englewood Cliffs, NJ: Prentice-Hall, Inc., 001).. Foerster, C. E. et al. Carbon ion implantation into pure aluminium at low fluences. Surf. Coat. Technol. 19, (005). 3. Bradley, A. J., Jones, P. An x-ray investigation of the copper-aluminium alloys. J. Inst. Met. 51, (1933). 4. Straumanis, M. E. The Precision Determination of Lattice Constants by the Powder and Rotating Crystal Methods and Applications. J. Appl. Phys., 0, (1949). 5. Plimpton, S. J. Fast Parallel gorithms for Short-Range Molecular Dynamics. J. Comp. Phys. 117, 1-19 (1995). 6. Cai, J., Ye, Y.Y. Simple analytical embedded-atom-potential model including a long-range force for fcc metals and their alloys. Phys. Rev. B 54, (1996). 7. Rose, J.H., Smith, J.R., Guinea, F., Ferrante, J. Universal features of the equation of state of metals. Phys. Rev. B 9, (1984). 8. Banerjea, A., Smith, J.R. Origins of the universal binding-energy relation. Phys. Rev. B 37, (1988). 9. per, H. E., Politzer, P. Molecular dynamics simulations of the temperaturedependent behavior of aluminum, copper, and platinum. Int. J. Quant. Chem. 76, (000). 10. Pal, U., Sanchez Ramirez, J. F., Liu, H. B., Medina, A., Ascencio, J. A. Synthesis and structure determination of bimetallic Au/Cu nanoparticles. Appl. Phys. A 79, (004). 5

6 11. Cheng, H., Lü, Y. J., Chen, M. Interdiffusion in liquid Cu and Ni Cu alloys. J. Chem. Phys. 131, (009). 1. Bonnet, R., Loubradou, M. Crystalline defects in a B.C.T. Cu(θ) single crystal obtained by unidirectional solidification along [001]. Phys. Stat. Sol. (a) 194, (00). 13. Galy, D., Boulanger, L. Transmission electron microscopy study of plastic deformation in NiZr. J. Mater. Sci. 30, (1995). 14. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, (1984). 15. Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 31, (1985). 16. Swope, W. C., Andersen, H. C., Berens, P. H., Wilson, K. R. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 76, (198). 17. Kelchner, C. L., Plimptom, S. J., Hamilton, J. C. Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, (1998). Fig.S1. The ageing curve of the sample used in this study. 6

7 Fig.S. Low-magnification bright-field TEM image showing the microstructures of the dual-phase -Cu alloy which experienced a solution treatment at 50 o C, and then ageing at 300 o C for days. The Cu precipitates are in black in the image. X-ray diffraction and electron diffraction indicate that the θ- Cu precipitate has a body-centered tetragonal structure with a = 0.61nm and c = 0.49nm. Fig.S3. Cross-sectional scanning electron microscopic image showing the deformation layer in the SMAT sample (the area between two opposite arrows). The microstructures are gradually varied ranging from nano-grained structures to deformed coarse-grained structures. 7

8 Figure S4. X-ray diffractions patterns of samples before and after deformation. Based on the consideration of comparison, low scanning angle of 3 o was performed to all the samples. Scanning at this angle is believed to be able to get the information in μm thick layer from the top. The profiles in black are from the sample before deformation, where and tetragonal Cu are identified; while the profiles in red are from the SMAT sample. It is seen that the intensity of some of the Cu diffractions in SMAT sample became much lower compared with that of the undeformed sample, namely, some Cu phase is dissolved during the severe deformation. Figure S5. (a) Structural projection of tetragonal Cu along [110] direction. This crystal has eight sub-layers stacked along <110> direction, namely, A 1 B 1 CB A B CB 1 (note that [110] and [110] are equivalent in the tetragonal structure). (b) uminum atoms in layer A forming a network of hexagons. (c) uminum decoration in layer B, each atom is located above the hexagonal center of A. (d) Copper distribution in layer C. 8

9 Figure S6. (a) Schematic of the computational cell used for MD simulations. The stacking fault is in the left area of the partial dislocation (indicated with ). (b) Snapshots of the atomic configuration projected on the ( 1 10) plane are displayed where atoms, at 14,000 timesteps, are colored by the force value on atoms along the horizontal ([001]) direction ranging from ev/å to ev/å. (c) At 14,000 timesteps, a display of centrosymmetry parameters ranging from 13.0 Å to 5.0 Å. (d) Atoms, at 00,000 timesteps, are colored by the centrosymmetry parameters ranging from 13.0 Å to 5.0 Å. (e) Atoms, at 400,000 timesteps, are colored by the centrosymmetry parameters ranging from 14.0 Å to 0.0 Å. 9

10 Figure S7. (a) Schematic representation showing an extended dislocation array along the (110) planes of Cu phase. Each extended dislocation is composed of two partials with stacking faults in between. Note that the widths of stacking fault are variant, ranging from 10 to 0nm according to the experiments. (b) The characteristic of the dislocation motion: two partials move towards each other, making Cu deviation in the area the partials passed by. (c) The contraction of extended dislocation finally results in a combination of two partials. The Cu displacement and segregation leave a Cu-poor area in its vicinity. 10