Anomalous compressibility of silica

Scientific problem

Silica, SiO₂, has the unsual property that it gets softer as you pressurise from atmospheric pressure, reaching a maximum in its compressibility (the parameter that quantifies how soft somthing is, defined as -(1/V)dV/dP, where V = volume and P = pressure) at around a pressure of 2 GPa in experiments.

The task is to see if this can be explained. Previous attempts have sught link it to a phase transition in the glass, but our work shows no existence of a phase transition (pdf reprint). Our approach is to use classical molecular dynamics wih what are through to be reasonable potentials (two models, both based on ab initio quantum chemistry calculations).

Our hypothesis is that at high pressure one expects the material to become stiffer on increasing pressure for the normal reasons of atoms getting closer and being squashed together. This is the high-pressure side of the maximum in the compressibility, and this is easy to understand. The challenge is to understand why silica gets softer on increasing pressure on the low-pressure side of the maximum in the compressibility. The question revolves around how easy is it to buckle the structure, and this comes down to how flexible the silica network is. We know that there is an intrinsic flexibility from our work on rigid unit modes (pdf reprint), and the existence of this flexibility should mean that the structure can buckle under pressure with minimal energy cost. So at low pressure we expect to have a flexible network, which stiffens on increasing pressure. But on reducing the pressure into the negative pressure regime, we expect to end up stretching the silica network. Much of the network will then be taught, and further reduction in pressure leading to expansion of the volume can be be accomplished by stretching the bonds within the SiO₄ tetrahedra. Because this will be cost more energy, we then have a much smaller volume change for a given change in pressure, corresponding to a lowering of the compressibility.

Typically one might calculate something over around 20 pressures or so. However, since we want a derivative, and since we are looking at quite a subtle effect, we actually need a lot of points. This is a grid problem in several respects

• the need for grid computing;
• the need for some job creating and workflow management;
• the need for data management.

The fruits of the eMinerals project are ideal for this.

Methods

We ran DL_POLY3 jobs with two different silica potentials at a temperature of 50 K, initially using the NPT ensemble. Figure 1 shows the configuration.

Figure 1: View of the 512-tetrahedra silica sample used in this work.

The grid work involved

• setting up jobs to sweep across a range of pressures;
• managing all data within the SRB;
• Having all output in the SRB, enabling us to generate SVG plots such as volume vs timestep in order to check equilibration, and to gather the results from all jobs in order to construct plots of volume vs pressure. These plots are stored within the SRB, and by using TobysSRB interface we can quickly see these plots rather than having to download data and copy into a spreadsheet or other plotting program.

The analysis steps were as follows

• We extracted mean volume vs pressure, and fitted a polynomial. From this polynomial we were able to extract the compressibility.
• We extracted the nearest-neighbour Si-O, O-O and Si-Si pair distribution functions.
• We saved several snapshot configurations for each pressure, and used a program called GASP to quantify the structural fluctuations in terms of tetrahedral displacements and rotations, and tetrahedral distortions.

Scientific results

The results can be summarised as

• Figure 2 shows one example of the volume vs pressure curve. Note the sigmoidal shape which means that the modulus of the gradient will to have a maximum.

Figure 2: Plot of the pressure-dependence of the volume of amorphous silica.

• Figure 3 shows the compressibility derived from these data. The maximum is clearly seen. This result is obtained from two model potentials, suggesting that it is reasonably robust behaviour.

Figure 3: Plot of -dV/dP of amorphous silica, which directly gives the compressibility.

• Figure 4 shows the mean interatomic distances obtained from the pair distribution functions, and cube-root of the volume, all normalised to equal 1 at zero pressure. Bars show the widths of the pair distribution functions. The key points are that the Si-O and O-O distances hardly change, but that the Si-Si distances follow much more closely the size of the sample. The latter reflects the buckling of the network without the tetrahedra distorting very much (although they do expand ever so slighly on decreasing pressure).

Figure 4: Plot of the pressure-dependence of the interatomic distances of amorphous silica, normalised to their values at zero pressure. Also shown is the cube root of the sample volume.

• Figure 5 shows the fluctuations in the SiO₄ orientations vs pressure. This is a proxy for the flexibility of the silica network: the more flexible it is, the more they can fluctuate. In fact this analysis is limited to small-scale fluctuations: there is another set of larger-amplitude flip-flop motions which occur as rare events.

Figure 5: Plot of the pressure-dependence of the rotational fluctuations in amorphous silica, coupled with the distortions of the SiO₄ polyhedra.

Discussion

The results taken above are broadly consistent with our working hypothesis outlined above, namely that the tetrahedra do not distort, and that the structure is more flexible around the pressure of the compressibility maximum.

The work clearly highlighted the value of the escience methods. Specifically,

• Grid computing with data management methods enabled us to work with very large numbers of simulations;
• CML was invaluable for gathering data and rapid view of results.

Credits

• This work was carried out as part of a Cambridge third year project by Lucy Sullivan - Lucy showed that it is possible to make use of all the tools developed by the eMinerals project.
• The science side of the project was carried out by Andrew Walker, Kostya Trachenko and Martin Dove (Cambridge).
• Richard Bruin (Cambridge) worked on the job submission process.
• Toby White (Cambridge) developed the XML/CML to HTML and SVG transformations
• Ilian Todorov and Bill Smith (CCLRC Daresbury)developed the DL_POLY_3 simulation code used in this work.
• Rik Tyer (CCLRC Daresbury) developed the metadata tools used in this study.