Supplementary Material for

Correlation between Local Structure and Boson Peak in Metallic Glasses

Azkar Saeed Ahmad1 ∙ Xiangnan Zhao1 ∙ Mingxiang Xu2 ∙ Dongxian Zhang3 ∙ Junwen Hu4 ∙ Hans J. Fecht5 ∙ Xiaodong Wang1 ∙ Qingping Cao1 ∙ J. Z. Jiang1

1 International Center for New-Structured Materials and Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, P. R. China.

2 Department of Physics, Southeast University, Nanjing 211189, P. R. China.

3 State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, P. R. China.

4 Hangzhou Workers Amateur University, Hangzhou, 310027, P. R. China.

5 Department of Materials, Faculty of Engineering, University of Ulm, Albert-Einstein Allee 47, D-89081 Ulm, Germany.

Corresponding Authors:

J. Z. Jiang ([email protected])

Mianxiang Xu ([email protected])

1 Figure Captions

Figure A1: The graph between 3 versus for six studied Zr-based metallic glasses along with red fitted curves that have been obtained by assuming 3 Einstein’s type oscillators exist besides the Debye’s type oscillator. It is cleared that if number of the vibratory modes are reduced then it is impossible to fit and reproduce boson peak. This proves that the best fitting can only be obtained by considering 5 Einstein’s vibratory modes along the Debye’s vibratory mode as shown in Fig. 2b of the main manuscript.

Fig. A1 A.S. Ahmad et al.

2 Table Captions

Table A1: The numerical values of the weight factors α, β, γ, δ and η are listed below.

β γ δ η Sample α 1.58E- 1.09E-35 8.57E-21 1.81E-20 S1 9.47E-34 20

1.87E- 3.04E-21 7.04E-21 9.46E-21 S2 5.51E-32 20

2.94E- 5.67E-37 8.63E-21 8.64E-21 S3 3.24E-59 20

2.87E- 1.55E-21 6.67E-21 1.97E-21 S4 6.82E-29 20

3.31E- 2.52E-21 6.99E-21 9.03E-30 S5 1.51E-31 20

2.09E- 1.34E-30 1.31E- 2.76E-20 S6 2.13E-31 20 20

3