Nature 448, 787-790 (16 August 2007) | doi:10.1038/nature06044; Received 5 February 2007; Accepted 21 June 2007

Vitrification of a monatomic metallic liquid

M. H. Bhat1, V. Molinero1,2, E. Soignard1, V. C. Solomon1, S. Sastry3, J. L. Yarger1 & C. A. Angell1

  1. Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
  2. Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
  3. J. Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560064, India

Correspondence to: C. A. Angell1 Correspondence and requests for materials should be addressed to C.A.A. (Email: caa@asu.edu).


Although the majority of glasses in use in technology are complex mixtures of oxides or chalcogenides, there are numerous examples of pure substances—'glassformers'—that also fail to crystallize during cooling. Most glassformers are organic molecular systems, but there are important inorganic examples too1, 2, such as silicon dioxide and elemental selenium (the latter being polymeric). Bulk metallic glasses can now be made3; but, with the exception of Zr50Cu50 (ref. 4), they require multiple components to avoid crystallization during normal liquid cooling. Two-component 'metglasses' can often be achieved by hyperquenching, but this has not hitherto been achieved with a single-component system. Glasses form when crystal nucleation rates are slow, although the factors that create the slow nucleation conditions are not well understood. Here we apply the insights gained in a recent molecular dynamics simulation study5 to create conditions for successful vitrification of metallic liquid germanium. Our results also provide micrographic evidence for a rare polyamorphic transition preceding crystallization of the diamond cubic phase.

It has been argued that any liquid can be vitrified if the cooling rate is sufficiently high6, and even ideal gases can be vitrified if the molecules are allowed complex shapes7. It seems that the crystal nucleation time can be made long with respect to amorphous form assembly times in a variety of ways, for instance by making sure that not more than a few atoms are hot at any time. Thus amorphous forms of metals like Bi and Pb have been made by deposition from the vapour at very low temperatures8. However, these prove to have no kinetic stability, and crystallize when the temperature is raised even 15 K above absolute zero. In spite of the conclusions of ref. 6, vitrification of single-component metals by cooling from the liquid might therefore seem improbable.

On the other hand, we demonstrated recently5 by molecular dynamics that an atomic liquid, Stillinger–Weber silicon, becomes non-crystallizing in 'slow' molecular dynamics cooling runs when the interaction potential is modified, without reducing the attractive potential, so as to lower the melting point by approx50% and put isoenergetic crystals in competition with each other against increasingly stabilized liquid. We found that ability to vitrify on the computational timescale was established when the diffusivity of the liquid at the crystallization temperature was reduced to 1.0 times 10-5 cm2 s-1, and the excess free energy, which provides the drive to crystallize below the melting temperature Tm, rose most slowly during supercooling. These turn out to be the same conditions established9 in experiments on binary alloys such as Ni-P (ref. 10) and Zr2Ni, which are vitrifiable by melt spinning. (In these cases, the melting point of Ni is lowered by 35%, and Zr by 42%, as a result of chemical mixing in which an optimum negative deviation from ideal mixing is exploited3, 6. In Zr-Cu, a 'bulk' glassformer at 1:1, a metastable eutectic4 lies lower still).

These results suggested to us that another variable, pressure, might be used to achieve the same conditions for a single-component metal of the right initial properties. Pressure can only lower the melting point if the melting is accompanied by a volume decrease, so the possibilities, starting at zero pressure, are limited to Bi, Ga, Ce, Si and Ge. Having used liquid Si as the starting point in our 'potential tuning' study5, it was natural to choose liquid Si for initial tests of the new proposal, using molecular dynamics simulation of the Stillinger–Weber silicon potential11.

At the solid–solid–liquid triple point T3 of Si, T3/Tm(1 atm) is 0.5 (see Methods and Supplementary Information), and simulations with the Stillinger–Weber potential have found12 (see Methods and Supplementary Information) that its diffusivity at T3 was 0.9 times 10-5 cm2 s-1, as in the Ni-P eutectic. Encouraged by these relations and also by Brazhkin's observations on In-Sb (ref. 13), and Tanaka's arguments14, but having failed to vitrify Si with multianvil cell quenching at 9 GPa (see Supplementary Information), we turned our attention to experiments conducted in a high-pressure diamond anvil cell (DAC).

In DACs, the transparency of the compressing diamonds permits the use of pulsed-laser-beam melting methods. The high thermal conductivity of the diamonds ensures rapid cooling of the samples. The optimum melting conditions were determined by variation of laser pulse duration, sample size, and thickness of the pressure-transmitting (NaCl) medium.

As sample for the diamond cell study, we chose Ge for several reasons. First, we thought Ge, which has a larger effective hard core than Si but the same sp3-based tetrahedral bonding, might be closer in character to the model monatomic glassformer of our earlier (zero-pressure) study5, as indeed we verify below. Second, Ge, in the normal-pressure (1 atm) liquid state, has a higher first-shell coordination number than liquid Si, and is considered to resemble a disordered beta-tin structure15. It has a metallic value and temperature coefficient of electrical conductivity16, and should behave more obviously like a metal under high-pressure conditions where the electron delocalization must be higher still. Third, partial vitrification of Ge in belt-type anvil press quenches has been reported17. Finally, Ge has little affinity for carbon, and hence is less likely to chemically damage the DAC windows during melting experiments. Subsequently, the molecular dynamics of liquid Ge (discussed later) yields a diffusivity of only 0.76 times 10-5 cm2 s-1 at T3, even lower than for Si.

Using the sample mountings described in the Methods section, we prepared 20-mum-diameter Ge samples, melt-quenched from pressures in the range 5–11 GPa (the upper limit for our diamond culets), for in situ Raman, and ex situ transmission electron microscope (TEM) examination. The Raman spectra for pressures above 7.9 GPa (by ruby fluorescence) showed the disappearance of the sharp intense line at 326 cm-1 (298 cm-1 at 0 GPa) and its replacement by a featureless broad fluorescence band, from which no structural details could be obtained.

The pressures, after the quench, were found to differ from the initial value by plusminus0.8 GPa, so we report results as the initial pressure with the final pressure in parentheses. In repeat experiments, glasses are always obtained at 7.9 GPa and above, approx11 GPa being our maximum. Four trials at approx5 GPa (including one using green laser heating) failed to vitrify. Attempts to characterize a vitreous sample in situ (under pressure) by X-ray diffraction using the Sector 1 Advanced Photon Source (APS) at Argonne, unfortunately were not successful owing to the very small sample size. The TEM results, by contrast, provided detailed evidence that vitreous Ge was produced directly from the melt in the case of quenches of small samples at pressures near T3.

Figure 1a and b shows twin optical microscope images of the DAC aperture with embedded Ge crystals before, and spread glass after, the melting pulse. The TEM image in Fig. 1c shows a approx300-nm-tall section of a 2 mum sample from a quench at 7.9(7.1) GPa, with two adjacent electron diffractograms (Fig. 1d and e). Figure 1d is from one of several electron-thin regions that gave the same diffraction pattern. Also, in subsequent studies of samples melt-quenched in the favourable pressure range, the same pattern is obtained. It is clearly an 'amorphous' pattern, being devoid of any irregularities or inhomogeneities that could be attributed to nanocrystals. Figure 1e is taken from a small area that includes a globule of interest to our discussion (at arrowhead), and contains a number of spots in addition to the diffuse rings. The spots are due to a single diamond-cubic Ge crystal originating within the globule (see high-resolution image in Fig. 1f). Globules with and without similar embedded crystals were seen in other sections of the 2 mum fragment (Fig. 1c, which is a small part of the sample in Fig. 1b). The TEM image (Fig. 1c) was chosen over those from other successful runs (all of which gave the same amorphous diffractograms), because of the presence of the globular features—see our discussion below. The globular sample, the importance of which we discuss below, was obtained at the low-pressure limit (7.9(7.1) GPa) of the range for successful vitrifications. All other vitrified samples had uniform textures. The structure factor for the glassy phase has been derived from the diffractogram and is compared with other relevant data in Fig. 2.

Figure 1: Optical and electron micrographs of vitrified Ge.
Figure 1 : Optical and electron micrographs of vitrified Ge. Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com

a, b, The Ge sample through the gasket aperture (between the diamond anvils) before and after the melting pulse. c, 300 nm segment of the 2 mum sample fragment of vitrified Ge quenched at 7.9(7.1) GPa, showing globules in matrix. Energy-dispersive X-ray analysis of both shows only Ge and Cu (from the grid) to be present. d, Amorphous diffraction pattern obtained from all areas except the area including the globule indicated by the arrowhead. e, Amorphous diffraction pattern for the globule area. Laue spots, indicating crystalline character, are obvious. The crystal–glass boundary (at the arrow tip) is seen in the high-resolution image of f. The crystal has grown within a globule. Energy-dispersive X-ray analysis of both shows only Ge and Cu (from the grid) present (see Supplementary Information). Other globules in c are fully amorphous. This is reminiscent of the preferential crystallization of the LDA in Al2O3–Y2O3 polyamorphic transitions29, and also in the molecular triphenyl phosphite case30. Annular dark-field imaging (see Supplementary Information) proves that the globules in c are darker because they are thicker, protruding from the matrix as seen at the right edge of c. In the annular dark field they appear bright.

High resolution image and legend (293K)

Figure 2: Comparisons of structure factors for vitreous and liquid states of Ge from laboratory and molecular dynamics simulation studies.
Figure 2 : Comparisons of structure factors for vitreous and liquid states of Ge from laboratory and molecular dynamics simulation studies. Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com

a, Structure factor S(Q) (that is, the scattered intensity at the scattering vector Q) for glassy Ge derived from the electron diffraction pattern of Fig. 1 (thick solid line) compared with the corresponding TEM electron-diffraction-based S(Q) for vapour-deposited amorphous Ge20 (thin solid line). The thick dashed line is S(Q) at 1,273 K from liquid Ge19. The similarity of the present S(Q) to that of the vapour-deposited value confirms the LDA character, while the displacement of the peaks to higher Q for our sample reflect its formation at pressure exceeding zero. b, Our Ge simulation results for the liquid at zero pressure (thick solid line), and at 7.5 GPa (thin solid line) showing agreement with laboratory results19 at zero pressure and 1,273 K (dashed line). Small Q changes reflect mainly changes in second-, third- and higher-shell coordination numbers.

High resolution image and legend (86K)

Thus far we have tested the vitrifiability of liquid Ge near its triple point. Clearly metallic, even at normal pressure, liquid Ge yields vitreous states when melt-quenched in the DAC from near and somewhat above the triple point pressure, but not from much below it. The possibility that the quench product is a beta-tin-like (or other high-density) crystal, which then amorphizes during decompression is eliminated by our temperature of decompression, 25 °C, because much work has shown that ambient decompression of metastable metal crystals of this type, including Ge18, yields crystalline semiconductors. Details on five such possible paths for Ge, all documented, all with the same conclusion, are given in Supplementary Information. We conclude that our successful quenches have yielded the first examples of vitrification of a monatomic metallic liquid.

However, just as the high-pressure crystals are known not to survive decompression to ambient pressure unless first cooled below 100 K, so also a metallic glass does not survive our ambient-temperature decompression. Rather, it transforms from a high-density amorphous (HDA) glass to a low-density amorphous (LDA) glass. We now verify that we have observed the LDA (in Fig. 1). To aid our analysis we use additional simulations on a model of Ge (V.M., manuscript in preparation) similar to one used to study Ge surfaces (see Supplementary Information) for which no comparisons with experiments were made. We make comparisons in Fig. 2.

Figure 2b shows the excellent agreement of calculated and observed19 structure factors of liquid Ge at normal pressure, and also the effect of pressure increase to 7.5 GPa. The latter effect is confirmed by ab initio molecular dynamics studies15 analysed in terms of increasing metallicity. A glass formed from this liquid should be unambiguously metallic. However, the Fig. 2a structure factor for our glass, derived from the Fig. 1d diffraction pattern, is strikingly different from that of the liquid19. As anticipated above, it closely resembles that obtained from electron diffraction of vapour-deposited Ge20 (the LDA non-metallic form), and also from X-ray scattering for vapour-deposited21 and electrodeposited Ge (see Supplementary Information). The differences between the high- and low-density forms are shared by water, Si and Ge22.

The identification of our glass with the previous LDAs seems unambiguous. Our finding is consistent with that of ref. 13 in the only parallel of our work—the high-pressure vitrification of liquid GaSb. (GaSb at 1 atm is a zincblende phase with a low melting point of 970 K, decreasing with increasing pressure to 670 K at T3). Again, the dense polyamorph does not survive decompression at room temperature. Indeed, this is expected from the theoretical model23 which first predicted the liquid–liquid transitions: Aptekar23 showed a spinodal limit on the stability of both HDA Ge and Si at 2–4 GPa (see also Supplementary Information).

To identify the liquid–liquid transition, we turn to a composite phase diagram (Fig. 3) that combines what we know from the earlier simulation study5 with what we know from laboratory high-pressure24 and supercooling studies25. Figure 3 shows a temperature–pressure phase diagram for Ge, whose vertical axis is projected from the temperature–lambda phase diagram5 at lambda = 20 (versus lambda = 21 for Si), as shown to be appropriate by the (S(Q) comparisons in Fig. 2b. (lambda is the 'tetrahedrality parameter' in the Stillinger–Weber potential5, 11.) We emphasize the projection of the liquid–liquid transition line of the temperature–lambda phase diagram into the pressure plane of the temperature–pressure diagram.

Figure 3: Relation of temperature–pressure phase diagram for Ge to the temperature–lambda potential diagram for Stillinger–Weber systems.
Figure 3 : Relation of temperature|[ndash]|pressure phase diagram for Ge to the temperature|[ndash]||[lgr]| potential diagram for Stillinger|[ndash]|Weber systems. Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com

The temperature–pressure phase diagram for Ge24 is shown in relation to the temperature–lambda phase diagram of ref. 5 by which the relation of Ge to Si in the temperature–lambda diagram is understood. The temperature scale changes for Ge, and becomes that of the laboratory Ge phase diagram, and the gap between Tm and the liquid–liquid transition temperature TLL has been set to the experimental supercooling limit found by cooling small levitated samples25. Projections of the temperature–lambda diagram at lambda = 20 into the pressure plane show how the Tm and TLL transition lines of Ge change with pressure. The TLL line is shown approaching the vertical at the T3 pressure, for thermodynamic reasons given in ref. 5. In water polyamorphism32, TLL, which goes vertical at the T3 pressure, tracks the homogeneous crystal nucleation line Th. Th, much studied in solution systems where composition replaces the pressure axis, goes almost vertical near the eutectic composition (the equivalent of the T3 pressure), intersecting the ideal glass and Kauzmann temperatures T0 and TK at the eutectic temperature (see Supplementary Information). Therefore, LDA cannot form during cooling above the T3 pressure, for example, along line 'c'. For a description of the vertical dashed lines 'a', 'b' and 'c', see text. The numbers '4' and '6' indicate the coordination numbers of crystal phases.

High resolution image and legend (107K)

Pressure increases depress not only the melting point of Ge, but also the liquid–liquid transition26, as predicted in refs 23 and 27 and as observed by molecular dynamics for Stillinger–Weber Si (ref. 12; V.M., S.S. and C.A.A.,unpublished work). We represent the glass transition temperature Tg by a thick square-dotted line, using the observation12 (for Stillinger–Weber Si) that isothermal diffusivity passes though a maximum below the T3 pressure and that Tg must be above 473 K at 8.1(8.9) GPa, because heating an in situ vitrified sample up to 473 K (the pressurized cell safety limit) for one hour did not cause crystallization (according to Raman spectra). We represent the quenches of this study on the phase diagram of Fig. 3 (see lines a, b and c).

The lower-pressure, crystallizing, melt-quenches of our current experiments are represented by the vertical dashed line 'a' that passes through the liquid–liquid line while the liquid is still well above the extension of the Tg line. Crystals form rapidly as they cross the liquid–liquid line5, 12, 26 because the gap in configuration space between LDA and crystal is so much smaller than that between HDA and the crystal5.

The melt-quenches that produce amorphous Ge without globules are represented by vertical line 'c'. Above T3, the liquid–liquid line is almost vertical (see caption and Supplementary Information). Thus, above T3 there is no possibility that the liquid can transform to LDA before it vitrifies. The homogeneous glass obtained at 10.6(10.1) GPa must therefore be the HDA metallic form. Thus we have vitrified a metallic liquid into a metallic glass. As argued above (see details in Supplementary Information), this metallic glass transforms to LDA during ambient decompression, via spinodal collapse23, 28.

The vertical line 'b' is the cooling trajectory of the sample that yielded the globule phase as a consequence of passing the liquid–liquid line and the Tg line almost simultaneously. Then, as seen in Y2O3–Al2O3 glass29 and also in triphenyl phosphite30, nucleated droplets of the LDA phase are vitrified as they form (LDA being less diffusive than HDA. Given the propensity of low-temperature liquid polyamorphs to crystallize29, 30, the existence of nanocrystals within many, but not all, of the amorphous globules then provides circumstantial microscopic evidence for the controversial liquid–liquid transition in Si-like supercooled liquids12, 26, 31.


Methods Summary

DAC studies

Crystalline Ge samples were embedded in a thin layer of pressure-distributing NaCl inside a 210 mum hole in a T-301 stainless steel gasket, which was mounted in a Merrill-Bassett DAC. Ruby chips were included for pressure determination using the fluorescence spectrum frequency shift. A Synrad 60-1 CO2 laser provided 125 W pulses of duration 2–100 mus in trial experiments. Glass formation was initially inferred from the disappearance of the strong Raman signal for diamond-cubic Ge at 326 cm-1 (7.9 GPa). The Ge sample (Fig. 1b), embedded in NaCl, was then carefully transferred onto a TEM copper grid (Ted Pella, Inc.) with lacey carbon support, and the NaCl carefully dissolved away using distilled water, which usually leaves the Ge on the grid. The high-resolution images and selected area diffraction patterns were recorded with a Philips CM200 field emission gun electron microscope operated at 200 kV. The instrument is equipped with a Gatan slow-scan charge-coupled device (CCD) camera, an energy-dispersive X-ray detector (EDAX) and the Gatan-Digital Micrograph and ES Vision acquisition systems.

Data treatment

Diffraction data for amorphous Ge were collected on the above-mentioned high-resolution TEM and calibrated using an Au standard. The two-dimensional diffraction image was radially integrated and scaled to the Dirac–Fock atomic form factors (200 keV electrons)33. The resulting structure factor S(Q) is shown in Fig. 2.

Molecular dynamics simulations summary

The Stillinger–Weber Si simulations11 were performed with protocols described in ref. 4. For Ge, periodic isobaric-isothermal simulations of 5,000 atoms modelled with the Stillinger–Weber11 potential modified with lambda = 20, epsilon = 45 kcal mol-1 and sigma = 2.1836 Å were carried out using the LAMMPS code (see Methods and Supplementary Information).

Full methods accompany this paper.



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Supplementary Information

Supplementary information accompanies this paper.



We thank C. Benmore and Q. Mei for the attempted in situ studies of melt-quenched samples at the Argonne APS. We acknowledge the allocation of computer time at the Center for High Performance Computing at the University of Utah, where the simulations on Ge were carried out. The cooperation of D. Matyushov and his group (whose Arizona State University computing facilities were used for the Si simulations) is also appreciated. We also thank our NSF-CRC colleagues P. Debenedetti, G. Stanley and P. Rossky for discussions. This work was supported by NSF grants from the Chemistry CRC (to C.A.A.), the DMR Solid State Chemistry (to C.A.A.), the NSF Chemistry (to J.L.Y.), the Carnegie/DOE Alliance Center (DOE-NNSA CDAC) (to J.L.Y.) and the Swarnajayanti Fellowship, DST, India (to S.S.). The TEM studies depended on the John M. Cowley Center for High Resolution Electron Microscopy.

Author Contributions C.A.A., V.M. and S.S. conceived the project as part of previous work5. J.L.Y. recommended and directed the DAC investigation, M.H.B. and E.S. executed the sample mounting, laser pulse melting, and Raman characterization experiments, V.C.S. and M.H.B. performed the TEM studies, V.M. carried out both preliminary Si and later Ge molecular dynamics simulations, and wrote the results analysis given in the Supplementary Information, and C.A.A. wrote the paper (with advice and criticism from all co-authors).


Competing interests statement

The authors declare no competing financial interests.


Online Methods

Molecular dynamics simulations on Stillinger–Weber Si and Ge

Molecular Dynamics (MD) simulations of Si with the Stillinger–Weber11 potential were executed at different pressures from 0 to 16 GPa, and those carried out in the vicinity of the triple point (approx11 GPa) and up to 16 GPa never crystallized. Higher pressures were not investigated. The diffusivity at the triple point was 0.96 times 10-5 cm2 s-1.

The simulations presented in the letter were carried on a model of Ge based on the Stillinger–Weber potential for Si with tetrahedrality parameter lambda = 20, and scaling the two-body attraction term to reproduce the crystal energy of Ge, epsilon = 45 kcal mol-1 and sigma = 2.1836 Å (V.M., manuscript in preparation). These runs were executed using a fast parallel-processing MD code (LAMMPS code34), and periodic boundary conditions, with isobaric–isothermal simulations on 5,000 atoms. A similar model with lambda = 19.5 has been used to study solid Ge surfaces35, and was recently applied to liquid Ge-Si alloys36.

As seen in Fig. 2b, the agreement of the Ge simulations with experiment is very good, minor differences only showing up at small Q, where the second and third and higher neighbour shells are involved. According to this model, the diffusivity at the triple point, 0.76 times 10-5 cm2 s-1, is even lower than it is for Si, implying that crystallization would never be observed on any computational timescale.


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