Supplementary Materials for
“In-situ Atomic Force Microscopy Observation Revealing Gel-like Plasticity on a Metallic
Glass Surface”
Y.M. Lu1, 2,†, J.F. Zeng1,†, J.C. Huang3,*, S. Y. Kuan3, T.G. Nieh4, W.H. Wang2, M.X. Pan2, *, C.T.
Liu1, Y. Yang1,*
1.
Centre for advanced structural materials, Department of mechanical and biomedical engineering, City
University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong, P.R. China
2
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China.
3
Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung
80424, Taiwan, Republic of China (R.O.C.)
4
Department of Materials Science & Engineering, The University of Tennessee, Knoxville, TN 379962200, USA
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1
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Supplementary Figures
Figure S1 The correlation lengths of Au70Si30 TFMG obtained at different times of scans and
different forces.
2
Figure S2. (a) and (b) show the distribution of the nano-sized regions on Au70Si30 TFMG
surface at the force of 3.49 nN with unmarked units for type I and marked units for type II and
type III. Type I, II and III represent the energy dissipation behavior of (c) stochastic change, (d)
continuous increase and (e) decrease with scan numbers, respectively. The solid lines in (c)-(e)
are drawn for eye guides.
3
Figure S3. Distribution of the nano-sized regions on Au70Si30 TFMG surface at the force of
(a)-(b) 4.21 nN, (c)-(f) 6.75 nN and (g)-(h) 10.53 nN. On figure (a), only one type of energy
dissipation behavior with (b) continuous decrease (type III) was found. On figure (c), unmarked
units for type I and marked units for type II and type III. Type I, II and III represent the energy
dissipation behavior of (d) stochastic change, (e) continuous increase and (f) decrease with scan
numbers, respectively. On figure (g), only one type of energy dissipation behavior with (h)
continuous increase (type II) was found. The solid lines in (b), (d)-(f) and (h) are drawn for eye
guides.
4
Figure S4. Magnified view of energy dissipation images obtained at the force of (a)-(d) 4.21 nN
and (e)-(h) 10.53 nN. The nano-sized shrinkage ((b)-(d)) and proliferation ((f)-(h)) of high
dissipation regions can be clearly seen from the circled regions.
5
Figure S5. The energy dissipation spectra of the crystallized Au70Si30 sample obtained in DAFM
at the force of 10.53 nN. The insert shows the XRD of the crystallized sample.
6
Viscosity calculation
In DAFM experiments, the mean total force exerted by the AFM tip in the scanning can be
calculated via the equation1 Fa  k   A0 2  Asp 2  （
/ 2 Asp  Q）, in which A0 is the free amplitude
without tip-sample interaction; Asp is the set-point amplitude; and k and Q are the spring
constant and quality factor of the AFM cantilever, respectively. In general, one may take the
mean total force ( Fa ) as the summation of the mean elastic force ( Fe ) and the mean inelastic
force2 ( Fv ), which can be calculated as Fe  kA0cos  / 2    （
/ 2Q）and Fv  Fa  Fe , respectively.
According to Ref.3, the viscosity (  ) can be estimated as   Fv /( R （d / dt）) ,
where  is viscosity,  is the displacement, R is the tip radius and t is the contact time during
scan. For our case, d / dt is approximated as  / t and t is approximated to be 10-20% of the tip
oscillation period. Here we use the hertz theory to consider the tip radius and displacement, in
which Fe  4E*  R   3/2 / 3 ( E  is the elastic modulus), and then the viscosity can be
/ 3Fe）.
estimated by the following equation:   4 Fv tE * （
In our experiments, t is about 0.3μs (the resonant frequency is 325 kHz), E  is about 80 GPa
and Fv / Fe is about 10~30. Based on these values, the surface viscosity of Au70Si30 TFMG is
estimated to be about 105~106 Pa•s, which is much lower than the bulk viscosity at the glass
transition temperature (1012 Pa•s).
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Calculation of yielding stress
The corresponding stress4 (  s ) at the force of 6.75 nN is calculated as  s  Fa / 3 A , in which Fa
is the averaged total force (6.75 nN) and k is the contact area. In DAFM, the contact area is
roughly estimated as A   R 2 with R the contact tip radius (~1nm). The yielding stress5 (  b ) for
bulk Au70Si30 MG is estimated as  s  0.02  E , in which E is bulk elastic modulus and
calculated according to the “rule of mixture”6.
References
1
S. Morita, Roadmap of scanning probe microscopy (Springer Science & Business Media,
2006).
2
Á. SanPaulo and R. García, Phys. Rev. B 64, 193411 (2001).
3
Y. H. Liu, D. Wang, K. Nakajima, W. Zhang, A. Hirata, T. Nishi, A. Inoue, and M. W.
Chen, Phys. Rev. Lett. 106, 125504 (2011).
4
D. Xu, G. Duan, W. L. Johnson, and C. Garland, Acta Mater. 52, 3493 (2004).
5
A. R. Yavari, Nature 439, 405 (2006).
6
W. H. Wang, Prog. Mater. Sci. 57, 487 (2012).
8