Structural Signature of β-Relaxation in La-Based Metallic Glasses

Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 4308−4313

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Structural Signature of β‑Relaxation in La-Based Metallic Glasses X. D. Wang,*,† J. Zhang,† T. D. Xu,† Q. Yu,† Q. P. Cao,† D. X. Zhang,‡ and J. Z. Jiang*,† †

International Center for New-Structured Materials (ICNSM), Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, and School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China ‡ State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, People’s Republic of China

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S Supporting Information *

ABSTRACT: The secondary β-relaxation is an intrinsic feature in glassy materials. However, its structural origin is still not well understood. Here we report that the βrelaxations in La50Al15Ni35 and La50Al15Cu35 metallic glasses (MGs) mainly depend on the vibration of small Ni and Cu atoms in local cages. By using advanced synchrotron X-ray techniques and theoretical calculations, we elucidate that the tricapped-trigonalprism-like polyhedra with more large La atoms in shells favor the local vibration of center Ni atoms, leading to the pronounced β-relaxation event. In contrast, the in-cage vibration of Cu atoms is somehow suppressed by the appearance of more shell Cu atoms. Nevertheless, they could easily diffuse out of the cages compared with Ni, thus triggering the onset of α-relaxation. This work provides a pathway to understand the different structural relaxation behaviors in MGs and other disordered materials from their local atomic packing and dynamics points of view.

he secondary relaxation, also called Johari−Goldstein βrelaxation, is considered as an intrinsic feature of glassy materials,1−5 which usually exhibits an excess wing in the loss modulus spectrum in metallic glasses (MGs).6−8 The βrelaxation is closely related to the physical aging, the glass transition, and the formation of shear transformation zones, therefore being of great importance for understanding the properties of MGs.9−12 In a Pd43Cu27Ni10P20 MG, the movement of small P atoms was suggested to play an important role in the β-relaxation because the activation energy for the P hopping measured by nuclear magnetic resonance is comparable to that for the β-relaxation.13 In contrast, in a Zr−Cu-based MG, the β-relaxation was proposed to be related to the behavior of large Zr atoms by breaking long Zr−Zr bonds to form short Zr−Cu bonds.14 The local rotational and translational diffusion of atoms, formation of string-like structures, and spatial heterogeneity in glasses were also reported for the origin of the β-relaxation.15−17 Recently, La−Al−Ni MGs were reported to exhibit an isolated hump below the glass transition Tg in the loss modulus spectrum measured by dynamical mechanical analysis (DMA), whereas the hump becomes unpronounced when Ni atoms are replaced by Cu atoms,18−20 providing an opportunity to understand the origin for β-relaxation behaviors from their structure perspective. Although this issue has been studied for decades,1−20 it is still not fully understood how the βrelaxation happens at the atomic level. Here we report structural results obtained from high-energy synchrotron Xray diffraction (XRD), X-ray absorption fine structure (XAFS), and ab initio molecular dynamics (AIMD) simulations for two La50Al15Ni35 and La50Al15Cu35 MGs, clearly demonstrating different responses of Ni and Cu atoms to the β-relaxation

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© XXXX American Chemical Society

behaviors (Figure S1 in Supporting Information). The origin for the pronounced β-relaxation in the La50Al15Ni35 MG is elucidated at the atomic level. Figure 1a shows the structure factors S(q) for as-quenched La50Al15Ni35 and La50Al15Cu35 MGs, indicating that they are fully amorphous. From their DSC (PerkinElmer diamond) traces in Figure 1b at a heating rate of 20 K/min, it is found that the Tg of the as-quenched La50Al15Ni35 MG (∼487 K) is much higher than that (∼432 K) of the as-quenched La50Al15Cu35 MG, indicating that the average bond strength in the La50Al15Ni35 MG should be stronger.21 The exothermic event below Tg of the as-quenched La50Al15Ni35 MG is much broader than that of the as-quenched La50Al15Cu35 MG, suggesting that the as-quenched La50Al15Ni35 MG contains more excess free volume as compared with as-quenched La50Al15Cu35 MG.22 Figure 1c gives the pair distribution functions G(r) of both as-quenched MGs, in which the first peak displays the average distribution of different atomic pairs in the nearest neighbor shell in real space. On the basis of the facts of atomic bond lengths and only 15% Al content, the two peaks in the G(r) curve of La50Al15Ni35 MG are mainly contributed from Ni−La pairs (peak area of 37%) and La−La pairs (peak area of 63%). In contrast, the peak area of La−La pairs greatly reduces to 39% in the La50Al15Cu35 MG together with 44% Cu−La pairs and 17% Cu−Cu pairs. The average bond length of La−La pairs (∼3.68 Å) in La50Al15Ni35 MG is longer than that (∼3.65 Å) in La50Al15Cu35 MG. More excess Received: June 26, 2018 Accepted: July 17, 2018 Published: July 17, 2018 4308

DOI: 10.1021/acs.jpclett.8b02013 J. Phys. Chem. Lett. 2018, 9, 4308−4313

Letter

The Journal of Physical Chemistry Letters

Figure 1. (a) Structure factor S(q). (b) DSC traces at a heating rate of 20 K/min. (c) First-principle peak in pair distribution functions G(r). (d) Local atomic distribution around Ni and Cu atoms in the nearest-neighbors obtained from XAFS spectra (without phase shift correction) for asquenched La50Al15Cu35 and La50Al15Ni35 MGs, respectively. All data for the as-quenched La50Al15Ni35 MG are shifted along the y axis for clarity.

Figure 2. (a) Fractions of total major Voronoi polyhedra. (b) Fractions of Ni- and Cu-centered polyhedra in as-quenched La50Al15Ni35 and La50Al15Cu35 MGs, respectively. (c) Topological atomic packing of polyhedra and centered by Ni atoms and centered by Cu atom in as-quenched La50Al15Ni35 and La50Al15Cu35 MGs, respectively.

ing mainly to Cu−Cu and Cu−La pairs with different bond lengths, are clearly separated in La50Al15Cu35 MG. Surprisingly, only one major peak for atoms distributing around Ni atoms is detected in La50Al15Ni35 MG, corresponding to the dominant Ni−La pairs or strongly overlapping with Ni−Ni and Ni−Al pairs. These results clearly demonstrate that local atomic environments around Ni and Cu atoms are quite different in

free volume detected in Figure 1b could mainly exist between large-sized La−La atoms in the La50Al15Ni35 MG. The average bond length of Ni−La pairs (∼2.98 Å) is shorter than that of Cu−La pairs (∼3.11 Å), indicating that Ni atoms tend to closely bond with La atoms. To uncover Ni- and Cu-centered local packing structures, we further carry out Ni and Cu Kedge XAFS measurements in Figure 1d for La50Al15Ni35 and La50Al15Cu35 MGs, respectively. Two main peaks, correspond4309

DOI: 10.1021/acs.jpclett.8b02013 J. Phys. Chem. Lett. 2018, 9, 4308−4313

Letter

The Journal of Physical Chemistry Letters

Figure 3. Vibrational MSD of Ni and Cu atoms using different time periods: (a,b) 0.45 ps and (c,d) 2.1 ps for measuring the MSD of Ni and Cu atoms in as-quenched La50Al15Ni35 and La50Al15Cu35 MGs, respectively.

ment (MSD), , of each atom as a function of time in asquenched La50Al15Ni35 and La50Al15Cu35 MGs is calculated by using AIMD (Figure S3a). Generally speaking, the values for small-sized Ni and Cu atoms are larger than those for La and Al atoms in both MGs. When the time is longer than 1 ps, the average values for Cu, La, and Al atoms in the asquenched La50Al15Cu35 MG are larger than those for Ni, La, and Al atoms in the as-quenched La 50 Al 15 Ni 35 MG, respectively. The intermediate scattering functions (ISFs), 1 N defined as F(q , t ) = N to characterize the density fluctuation of atoms between time zero and time t, show that the β-relaxations in both MGs are quite similar, roughly happen on the time scale from 0.01 to 1 ps, and finally merge with the α-relaxation (Figure S3b). The ISF curves give a hint that the atomic movement at ∼1 ps time scale is the key factor in controlling β-relaxations in both MGs. Because of the sluggish movements of La and Al atoms, it is not unreasonable for us to focus on the behaviors of Ni and Cu atoms that have relatively larger vibrations. Figure 3 shows vibrational MSD of each Ni and Cu atom in both as-quenched La50Al15Ni35 and La50Al15Cu35 MGs with time periods of 0.45 and 2.1 ps, respectively. It is found that although most Ni and Cu atoms have small MSD values ( 1.0 Å2 in the time period of 0.45 ps. Moreover, the amplitude of Ni atoms over 1.0 Å2 is generally larger than that of Cu atoms in this time period, as shown in Figure 3a,b. With time extension to 1.5 ps (Figure S4) and 2.1 ps, values of such Ni atoms (Figure S4a and Figure 3c) do not change much, indicating that they are mainly confined within the cages in the as-quenched La50Al15Ni35 MG. However, several Cu atoms have increased values with time extension, even beyond 3.0 Å2 within the time period of 2.1 ps, as shown in Figure S4b and Figure 3d, suggesting that these Cu atoms could diffuse out of their cages. More details of the evolution of local atomic packing with time (before and

both as-quenched La50Al15Ni35 and La50Al15Cu35 MGs, which could affect the dynamic behaviors of both MGs. To further dig out the atomic structure origin for βrelaxation behaviors in as-quenched La 50 Al 15 Ni 35 and La50Al15Cu35 MGs, we perform AIMD calculations to simulate the quenching process of both MGs. The pair correlation functions g(r) and structure factors obtained from AIMD simulations almost capture the main features of the experimental data (Figure S2a,b). The contributions of weighted partial g(r) to the total and the major bond length of Ni−La pairs (∼2.90 Å) shorter than Cu−La pairs (∼3.03 Å) (Figure S2c) are consistent with the above experimental results in Figure 1c, suggesting that the AIMD-produced atomic configurations are reliable to analyze the local structure differences between both MGs. Figure 2a shows total Voronoi polyhedron distributions with high abundances in both MGs. It is found that in La50Al15Ni35 MG, the and polyhedra are rich, whereas in La50Al15Cu35 MG, the polyhedron becomes dominant. These major differences mainly come from the variations between Ni- and Cu-centered polyhedra, as shown in Figure 2b. Such Nicentered and polyhedra are mainly tricapped-trigonal-prism (TTP)-like (Figure 2c), in which the Cu-centered polyhedron is also illustrated. By carefully examining various polyhedra, it is found that the Ni atoms are mainly surrounded by large La atoms in and polyhedra, whereas in polyhedron, some La atoms in trigonal prisms tend to be replaced by small Cu atoms, leading to a local denser packing around the center Cu atoms in the La50Al15Cu35 MG. These simulation results are also consistent with the results in Figure 1c,d, in which the fraction of the first shell Cu atoms around center Cu atoms in the La50Al15Cu35 MG is more than that of the first-shell Ni atoms around center Ni atoms in the La50Al15Ni35 MG. The β-relaxation in MGs could be correlated with the vibration of atoms.23,24 The vibrational mean square displace4310

DOI: 10.1021/acs.jpclett.8b02013 J. Phys. Chem. Lett. 2018, 9, 4308−4313

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The Journal of Physical Chemistry Letters

with the time scale for happening of the β-relaxation reflected from the ISF curves. From the atomic structure perspective, three major features exist in the as-quenched La50Al15Ni35 MG compared with the La50Al15Cu35 MG, that is, (1) there is relative loose packing due to the high fraction of large-sized La−La pairs, (2) the Ni atoms are mainly surrounded by La and Al atoms, forming more TTP-like polyhedra, and (3) Ni atoms surrounded by eight to nine large-sized La atoms often have large vibrational displacements in cages. Although the average bond strength is much stronger in the as-quenched La50Al15Ni35 MG, it still locally has more “soft spots”,25 for example, several Ni atoms in loose-packed TTP-like and polyhedra, exhibiting the pronounced β-relaxation. Usually, the βrelaxation is regarded as the precursor of the α-relaxation, at which major atoms in the sample can vibrate largely. Our results indicate that the β-relaxation, confined by vibrations of Ni atoms in local cages, could be relatively independent from α-relaxation. However, as shown in the as-quenched La50Al15Cu35 MG, the α-relaxation could be triggered if the large-vibrated atoms diffused out of the cages with large displacements due to breaking of weak bonds. Besides the temperature, the mechanical strain was also found to induce the structural relaxation in shear bands by initiating shear transformation zones (STZs),26 which is the resulting of interaction between stress and local structure of MGs and possibly related to the fast secondary relaxation.27 More studies are strongly needed to explore this relationship. In summary, we observe a pronounced β-relaxation in the asquenched La50Al15Ni35 MG, whereas it gets unpronounced and almost overlapped with the α-relaxation in the La50Al15Cu35 MG. We elucidate that such different relaxation behaviors between La50Al15Ni35 and La50Al15Cu35 MGs are closely related to their specific atomic structures, mainly determined by the local atomic packing around Ni and Cu atoms. Composed of more large La atoms in the shells, the loose-packed TTP-like and polyhedra favor the atomic dynamics of center Ni atoms, whose hopping time is almost comparative to the β-relaxation time. In contrast, with more Cu atoms locating in the shells, the local atomic packing around Cu atoms gets denser, suppressing their atomic dynamics in cages. Nevertheless, some Cu atoms in and polyhedra with seven La, one Al, and three Cu as neighbors more easily escape out of the cages to trigger the α-relaxation, causing the β-relaxation to be partially overlapped with the αrelaxation. Therefore, our findings will shed new insight into the understanding of the relationship between the local structure and the β-relaxation in MGs and other glassy materials.

after) for one Ni-centered polyhedron with nine La and one Ni shell atom and one Cu-centered polyhedron with seven La, one Al, and three Cu shell atoms are displayed in Figures S5a−c and S5d−f, respectively. Both are dominant Ni- and Cu-centered polyhedra with large MSD values (Figure S6a,b). Concerning the issue that for the same TTP-type atomic packing, for example, Ni-centered polyhedron in the as-quenched La50Al15Ni35 MG, some exhibit large MSD values, whereas other have small MSD values, it is found that some shell atomic configurations, for example, eight to nine large La atoms in the shell, generally favor the large MSD values of the center Ni atoms, whereas seven La, one or two Al, and two or one Ni atom in the shell favor the small MSD values of the center Ni atoms in Figure S7a. This means that the longer La−La bonds in the shell might give more freedom to the center Ni atoms, whereas the shorter Ni−La and Ni−Al bonds could suppress the vibration of the center Ni atoms. Unlike Ni, the mobile Cu atoms usually have seven La, one Al, and three Cu in their shells for and polyhedra in Figure S7b,c. To further evaluate the differences in vibrations of Ni and Cu atoms, we count the number of atoms having > 1 Å2 within different periods (Δt) in the whole time period of 24 ps in Figure 3. The vibration frequency for Ni atoms to have > 1 Å2 in Figure 4a is generally larger than that for Cu atoms in

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Figure 4. (a) Vibration frequency for Ni and Cu atoms with larger than 1.0 Å2 in different time periods in both as-quenched La50Al15Ni35 and La50Al15Cu35 MGs. (b) Distribution of time between two nearest independent hopping ( > 1.0 Å2) for Ni atoms. The dominant time values are less than ∼1.5 ps, which is well consistent with the β-relaxation time on the ISF curve.

EXPERIMENTAL METHODS Ribbon samples of ∼0.03 mm thick and 3 mm wide with nominal compositions of La50Al15Ni35 and La50Al15Cu35 were prepared by single-roller melt spinning on a rotating Cu wheel with a surface velocity of 30 m/s in an atmosphere. The temperature-dependent loss modulus E″ of ribbon samples was measured on a TA Q800 DMA using the film tension mode with a frequency of 1 Hz and a heating rate of 3 K/min in a nitrogen-flushed atmosphere. The synchrotron XRD measurements were performed at the 11-ID-C beamline of APS, Chicago with an energy of 105.7 keV (λ = 0.1173 Å) to ensure the diffraction data within a wide q range. The diffraction patterns were recorded by a PerkinElmer Si 1621 detector and

the early ∼1.2 ps and then almost keeps a constant after ∼1.2 ps. In contrast, the vibration frequency for Cu atoms further increased beyond ∼1.2 ps, in good agreement with the data in Figure 3. Figure 4b shows that the time intervals between two nearest independent atomic hopping of Ni atoms with > 1.0 Å2 are mainly less than ∼1.5 ps, which is well consistent 4311

DOI: 10.1021/acs.jpclett.8b02013 J. Phys. Chem. Lett. 2018, 9, 4308−4313

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The Journal of Physical Chemistry Letters

(5) Tanaka, H. Origin of the excess wing and slow beta relaxation of glass formers: a unified picture of local orientational fluctuations. Phys. Rev. E 2004, 69, 021502. (6) Ngai, K. L.; Paluch, M. Classification of secondary relaxation in glass-formers based on dynamic properties. J. Chem. Phys. 2004, 120, 857−873. (7) Hachenberg, J.; Samwer, K. Indirections for a slow β-relaxation in a fragile metallic glass. J. Non-Cryst. Solids 2006, 352, 5110−5113. (8) Wang, W. H.; Wen, P.; Liu, X. F. The excess wing of bulk metallic glass forming liquids. J. Non-Cryst. Solids 2006, 352, 5103− 5109. (9) Ruta, B.; Chushkin, Y.; Monaco, G.; Cipelletti, L.; Pineda, E.; Bruna, P.; Giordano, V. M.; Gonzalez-Silveira, M.; et al. Atomic scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopy. Phys. Rev. Lett. 2012, 109, 165701. (10) Yu, H. B.; Wang, W. H.; Samwer, K. The β-relaxation in metallic glasses: an overview. Mater. Today 2013, 16, 183−191. (11) Yu, H. B.; Shen, X.; Wang, Z.; Gu, L.; Wang, W. H.; Bai, H. Y. Relating activation of shear transformation zones to in β-relaxation metallic glasses. Phys. Rev. Lett. 2012, 108, 015504. (12) Qiao, J. C.; Wang, Y. J.; Pelletier, J. M.; Keer, L. M.; Fine, M. E.; Yao, Y. Characteristics of stress relaxation kinetics of La60Ni15Al25 bulk metallic glass. Acta Mater. 2015, 98, 43−50. (13) Yu, H. B.; Samwer, K.; Wu, Y.; Wang, W. H. Correlation between β-relaxation and self-diffusion of the smallest constituting atoms in metallic glasses. Phys. Rev. Lett. 2012, 109, 095508. (14) Liu, Y. H.; Fujita, T.; Aji, D. P. B.; Matsuura, M.; Chen, M. W. Structural origins of Johari-Goldstein relaxation in a metallic glass. Nat. Commun. 2014, 5, 3238. (15) Johari, G. P. Localized molecular motions of beta-relaxation and its energy landscape. J. Non-Cryst. Solids 2002, 307, 317−325. (16) Yu, H. B.; Samwer, K.; Wang, W. H.; Bai, H. Y. Chemical influence on β-relaxations and the formation of molecule-like metallic glasses. Nat. Commun. 2013, 4, 2204. (17) Zhu, F.; Nguyen, H. K.; Song, S. X.; Aji, D. P. B.; Hirata, A.; Wang, H.; Nakajima, K.; Chen, M. W. Intrinsic correlation between βrelaxation and spatial heterogeneity in a metallic glass. Nat. Commun. 2016, 7, 11516. (18) Wang, Z.; Yu, H. B.; Wen, P.; Bai, H. Y.; Wang, W. H. Pronounced slow beta-relaxation in La-based bulk metallic glasses. J. Phys.: Condens. Matter 2011, 23, 142202. (19) Liang, D. D.; Wang, X. D.; Ma, Y.; Ge, K.; Cao, Q. P.; Jiang, J. Z. Decoupling of pronounced beta and alpha relaxations and related mechanical property change. J. Alloys Compd. 2013, 577, 257−260. (20) Wang, X. D.; Ruta, B.; Xiong, L. H.; Zhang, D. W.; Chushkin, Y.; Sheng, H. W.; Lou, H. B.; Cao, Q. P.; Jiang, J. Z. Free-volume dependent atomic dynamics in beta relaxation pronounced La-based metallic glasses. Acta Mater. 2015, 99, 290−296. (21) Yang, B.; Liu, C. T.; Nieh, T. G. Unified equation for the strength of bulk metallic glasses. Appl. Phys. Lett. 2006, 88, 221911. (22) Van Den Beukel, A.; Sietsma, J. The glass transition as a free volume related kinetic phenomenon. Acta Metall. Mater. 1990, 38, 383−389. (23) Douglas, J. F.; Pazmino Betancourt, B. A.; Tong, X.; Zhang, H. Localization model description of diffusion and structural relaxation in glass forming Cu-Zr alloys. J. Stat. Mech.: Theory Exp. 2016, 2016, 054048. (24) Ding, J.; Cheng, Y. Q.; Sheng, H.; Asta, M.; Ritchie, R.; Ma, E. Universal structural parameter to quantitatively predict metallic glass properties. Nat. Commun. 2016, 7, 13733. (25) Schoenholz, S. S.; Cubuk, E. D.; Sussman, D. M.; Kaxiras, E.; Liu, A. J. A structural approach to relaxation in glassy liquids. Nat. Phys. 2016, 12, 469−472. (26) Argon, A. S. Plastic deformation in metallic glasses. Acta Metall. 1979, 27, 47−58. (27) Wang, Q.; Liu, J. J.; Ye, Y. F.; Liu, T. T.; Wang, S.; Liu, C. T.; Lu, J.; Yang, Y. Universal secondary relaxation and unusual brittle-toductile transition in metallic glasses. Mater. Today 2017, 20, 293−300.

then integrated after subtracting the background by program Fit2D.28 Subsequently, the output data were normalized to get the total structure factor S(q) after standard corrections in PDFgetX2.29 The corresponding pair distribution function G(r) was obtained by Fourier transform of S(q). Ni and Cu Kedge XAFS spectra were collected in the transmission mode at the 1W1B-XAFS beamline of BSRF, Beijing. The standard data analysis was conducted by using the software Athena of Ifeffit package.30 After the model system approached the equilibrium, Voronoi tessellation,31 vibrational mean square displacement (MSD), ,32 and intermediate scattering function (ISF) were adopted to identify the static and dynamic structural differences between both MGs in the as-quenched states.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b02013. DMA results and AIMD calculations to build the atomic configurations of two as-quenched MGs. MSD, ISF, and Voronoi tessellation analyses for the configurations to show their static and dynamical structure difference. Major polyhedra centered by mobile and immobile Ni and Cu atoms as well as the differences in their element constitutions. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (X.D.W.). *E-mail: [email protected] (J.Z.J.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the staff of 11-ID-C at APS, Chicago and 1W1BXAFS at BSRF, Beijing for the assistance during measurements. Financial support from the NNSFC (51671169, U1532115, and 51671170), the National Key Research and Development Program of China (nos. 2016YFB0701203, 2016YFB0700201, 2017YFA0403401, 2017YFA0403403, and 2017YFA0403404), the NSF of Zhejiang Province (grant Y4110192), and the Fundamental Research Funds for the Central Universities is gratefully acknowledged. The computer resources at National Supercomputer Center in Tianjin and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (grant no. U1501501) are also gratefully acknowledged.

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REFERENCES

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The Journal of Physical Chemistry Letters (28) Hammersley, A. P.; Svensson, S. O.; Hanfland, M.; Fitch, A. N.; Hausermann, D. Two-dimensional detector software: From real detector to idealized image or two theta scan. High Pressure Res. 1996, 14, 235−248. (29) Jeong, I. K.; Thompson, J.; Proffen, Th.; Turner, A. M. P.; Billinge, S. J. L. PDFgetX: A program for obtaining the atomic pair distribution function from x-ray powder diffraction data. J. Appl. Crystallogr. 2001, 34, 536. (30) Newville, M. IFEFFIT: interactive XAFS analysis and FEFF fitting. J. Synchrotron Radiat. 2001, 8, 322−324. (31) Finney, J. L. Random packing and the structure of simple liquids. Proc. R. Soc. London, Ser. A 1970, 319, 479−493. (32) Starr, F. W.; Sastry, S.; Douglas, J. F.; Glotzer, S. C. What do we learn from the local geometry of glass forming liquids? Phys. Rev. Lett. 2002, 89, 125501.

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