Fig. 1 a Schematic of the Cu/complexions multilayer model. b Illustrating how compression loading is performed and loading details

Fig. 2 Side view of the fcc{111}//{110}bcc and fcc{111}//{111}fcc interface models after the introduction of crystalline complexions. Interface models are Cu/Nb interface with a KS and b NW orientation; Cu/Ag interface with c cube-on-cube and d hetero-twin orientation; Cu/Ni interface with e cube-on-cube, f hetero-twin orientation. The red and black lines represent two sets of compact planes

Fig. 3 Relaxed atomic structure and misfit dislocation networks of the a KS Cu/Nb interface, b NW Cu/Nb interface, c cube-on-cube Cu/Ag interface, d hetero-twin Cu/Ag interface, e cube-on-cube Cu/Ni interface, f hetero-twin Cu/Ni interface. The atoms are colored according to excess potential energy. Solid lines of different colors represent dislocation lines with different Burgers vectors

Fig. 4 a Side view of the interface models after the introduction of amorphous complexions. b In-plane atomic structure of Cu3 to Am2 layers at the C/A interface. The yellow and blue atoms indicate Cu and Nb atoms. c RDF analysis for the Cu3 to Am2 layers. d Disregistry vectors of the Cu1 layer at the relaxed C/A interface and the colors are scaled by the vector magnitude

Fig. 5 Open Thompson tetrahedron showing all possible slip systems in the a fcc and b twin fcc crystalline, in which the three slip planes are denoted by ABD (ABD′), ACD (ACD′) and BCD (BCD′), and the ABC plane corresponds to the interface. The open polyhedron shows all possible slip systems in the bcc crystalline with c KS, d NW orientation, in which the five slip planes are indicated by ${\text{A}}^{\prime } {\text{B}}^{\prime } {\text{F}}^{\prime }$, ${\text{A}}^{\prime } {\text{C}}^{\prime } {\text{G}}^{\prime }$, ${\text{A}}^{\prime } {\text{C}}^{\prime } {\text{G}}$, ${\text{B}}^{\prime } {\text{C}}^{\prime } {\text{E}}^{\prime }$ and ${\text{B}}^{\prime } {\text{C}}^{\prime } {\text{E}}$, and the plane ${\text{A}}^{\prime } {\text{B}}^{\prime } {\text{C}}^{\prime }$ plane corresponds to the interface

Fig. 6 Nucleation characteristics of Shockley partial dislocations from the a KS Cu/Nb interface, b NW Cu/Nb interface, c cube-on-cube Cu/Ag interface, d hetero-twin Cu/Ag interface, e cube-on-cube Cu/Ni interface, f hetero-twin Cu/Ni interface under y compression loading. The yellow and green atoms indicate Cu and Nb atoms in a and b. The red atoms indicate local hcp structure; the blue atoms indicate local hcp structure; the white atoms indicate unknown structure

Fig. 7 Stress-strain and dislocation density curves for a Cube-Ag and c Twin-Ag complexions model. The configuration of the dislocation evolution for b Cube-Ag and d Twin-Ag complexions model at different strains (i)-(iv) marked by arrows in a and c. Cyan atoms indicate Ag atoms in complexions. Red atoms indicate local hcp structure, and white atoms indicate unknown structure in matrix Cu. Perfect fcc and bcc atoms are not shown. The colored solid lines within the model indicate the dislocations with different Burgers vectors

Fig. 8 a Stress-strain and dislocation density curves for Cu50Zr50 amorphous complexions model. b Configuration of the dislocation evolution for Cu50Zr50 amorphous complexions model at different strains (i)-(iv) marked by arrows in a. Blue atoms indicate Zr atoms, and yellow atoms indicate Cu atoms in complexions. Red atoms indicate local hcp structure and white atoms indicate unknown structure in matrix Cu. Perfect fcc and bcc atoms are not shown. The colored solid lines within the model indicate the dislocations with different Burgers vectors

Fig. 9 Relative orientation of the gliding planes for different complexions models to indicate possible transmission pathway. Schematic diagrams of fcc/fcc system with a cube-on-cube and b hetero-twin orientation, and the fcc/bcc system with c KS, d NW orientation

Fig. 10 Top view of the atomic structure and the traces of the gliding planes at the Cu /Nb interface with a KS, b NW orientation. The red ${\text{A}}^{\prime } {\text{B}}^{\prime } {\text{C}}^{\prime }$ is for the Nb side and the blue ABC is for the Cu side. The atoms are colored according to excess potential energy

Fig. 11 Geometric schematic of slip system transmission across the interface used in Eqs. (1) and (2)

Fig. 12 Snapshots of the multilayer with amorphous complexions at the strain of a 6.5%, b 7.0%, c 7.5%. Atom colors in the amorphous layer represent the magnitude of the von Mises shear strain. Crystalline Cu layers are colored according to the CNA method, green atoms indicate fcc structure, pink atoms indicate local hcp structure, and white atoms indicate unknown structure

Fig. 13 a Dislocation density and STZs atomic percentage curves of Cu50Zr50 amorphous complexions model during loading. b STZs atomic percentage curves for amorphous complexions models with different compositions during loading