Glass phase cracked

Tap a solid object such as a desk, and you will generate a sound – a pressure wave that spreads out with a certain speed. The faster you tap, the shorter the wavelength, but the speed of sound remains constant. This is the basis of the 100-year old Debye model, which allows us to calculate the degrees of freedom (or the number of vibrational states) in a system and therefore the heat capacity of any solid, just from the speed of sound and the number of atoms in the sample.

When the wavelength of sound waves becomes comparable with the period of the crystalline lattice, however, this picture starts to break down and the Debye theory predicts an accumulation of vibrational states at certain frequencies and thus an increased heat capacity. Unlike a crystalline solid, glasses are disordered and therefore are not expected to exhibit this short wavelength behaviour: the Debye model should hold.But experiments in the 1960s revealed otherwise. At temperatures of around 10 K where, oddly, crystals do not show much deviation from the Debye model, the heat capacity of glasses rises significantly above the Debye prediction. This extra heat capacity means that one needs to put extra energy into a glass to heat it to a given temperature, and suggests that a glass has additional vibrational states into which you can put that additional energy. The additional vibrational states became know as the “boson peak”.

For the past 50 years, physicists have tried to understand the physical origin of the boson peak, and thus how disorder in atomic positions makes glasses so different thermodynamically from ordered crystals. But despite dozens of theoretical models and hundreds of experimental results, no unified picture emerged. “If you Google ‘boson peak glass’ you will have over 100,000 hits,” says Alexander Chumakov, scientist on the ESRF’s ID18 beamline. “Some people call it the last puzzle of solid state physics.”

Unexpected result

In experiments carried out at the ESRF on beamlines ID18, ID27 and ID28, Chumakov and co-workers claim to have solved the riddle of the boson peak. The international team compared atomic motions in a glass with those in a corresponding crystal using nuclear inelastic scattering, a technique that determines the exact number of vibrational states. Remarkably, the number of states measured around the boson peak turned out to be exactly the same as the number of the corresponding acoustic degrees of freedom in a crystal (Phys. Rev. Lett. 106 225501).

“The very concept of these extra degrees of freedom where you have to put the energy of the extra heat capacity turned out to be incorrect,” says Chumakov. “The additional heat capacity is not because of additional vibrational states but because the same states are located at lower energy and, thus, are more efficiently activated at lower temperatures. The behaviour is not anomalous, it is the same as for crystals but just appears at lower temperatures.”

Convincing the community?

The team’s dramatic conclusion, which stemmed from pioneering investigations of glass dynamics in the mid-1990s at former inelastic X-ray scattering beamline ID16 by the ESRF’s Giulio Monaco and Francesco Sette, emerged from careful comparisons between an iron-containing sodium silicate glass, Na₂FSi₃3O_8.5, and a crystal of a similar composition and density. To some, that’s a relatively exotic form of glass. So the ESRF-led team has recently performed the same experiment with the very material that launched the boson-peak mystery 50 years ago: plain old window glass, SiO₂. Exactly the same agreement between the number of vibrational states in glass and its corresponding crystal was observed.

The work is a big leap forward, but the book is not closed on the boson peak, according to Reiner Zorn of the Jülich Center for Neutron Science in Germany. “Although the ESRF results leave open the possibility that there is something in addition to transverse waves, there is now no necessity to assume such boson-peak specific vibrations,” he says. “Such measurements have a long tradition in inelastic neutron scattering, but for that method the high pressures necessary here are currently out of reach.”

The glass phase has further riddles in store, says Chumakov. “Glasses possess many other intriguing features still waiting for clarifications, for instance the so-called “fast processes”, correlated diffusion, dynamic heterogeneities, and many others that will be attacked soon by ESRF researchers and users.”

Matthew Chalmers

This article originally appeared in ESRFnews, December 2012. 

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Top image: The reduced density of states (g(E)/E2) should be a straight line. But glasses exhibit an excess of g(E)/E2 compared to crystals, although the total number of states is the same: the boson peak in the glass has no additional modes over the crystal.