Irradiation- vs. vitrification-induced disordering: The case of 𝜶-quartz and glassy silica

Quartz is an archetypical silicate mineral abundantly found in a large variety of aggregate rocks. Understanding the effect of irradiation on the structure and properties of quartz is of importance in applications involving exposure to high energy radiation, including as an aggregate-forming mineral in concrete that is used for the construction of, e.g., nuclear power plants (NPP)^1,2 or nuclear waste repositories.³ In its glassy form, SiO₂ (i.e., glassy silica) is also used in optical fibers and diagnostic windows in NPPs.⁴ Intermediate amorphous-crystalline forms of silica, such as a reactive chert, can also be found in concrete. When exposed to high-energy radiation, quartz undergoes significant structural damage,^5,6 which, at a macroscopic scale, results in changes in mechanical, optical, and thermal properties.^5–13 At the atomic level, the exposure to radiations induces irreversible displacements of atoms,⁹ which, ultimately, results in the disordering of the atomic network.⁹ 

Disordered SiO₂ materials can also be formed from a silica melt wherein they are quenched fast enough from the liquid state to avoid crystallization,¹⁴ to form a silica glass. However, although they both yield non-crystalline atomic networks, it remains unclear whether irradiation and vitrification have a similar structural effect or not.¹⁵ Indeed, although irradiated materials have been proposed to show a structure that is similar to that of a quenched liquid,^16,17 some differences have been noted between the structures of irradiated quartz and glassy silica.^5,7,9 This raises the following question: can the upper limit of irradiation-induced disordering, in terms of the final density and structure, be predicted by considering the properties and structure of the isochemical glass?

Here, based on reactive molecular dynamics (RMD) simulations, we report a comparison between the structures of irradiated α-quartz and glassy silica. We show that although the structure of irradiated quartz presents some similarity with that of glassy silica, the effects of irradiation and vitrification are not mutually equivalent. Through a detailed structural analysis, we demonstrate that various structural features of irradiated quartz and glassy silica differ from each other, both in terms of their short- and medium-range orders.

To simulate the effect of irradiation on α-quartz, we rely on RMD simulation. All simulations are carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package.¹⁸ Neutron irradiation is simulated following a well-established methodology^15,19,20 that is detailed below. Initially, an atom, randomly chosen from the crystal lattice, is accelerated with a kinetic energy (600 eV herein) in a random direction. This corresponds to the energy acquired by the primary knock-on atom (PKA) after the elastic collision with an incident neutron particle. The varying propensities for atoms to attract neutrons are accounted for by using the neutron cross sections of Si and O atoms to determine the probability of each atom to be chosen as the PKA. The PKA, accelerated with the velocity corresponding to the incident energy, then collides with the other atoms in the lattice, thereby resulting in a ballistic cascade.

Note that applying a thermostat to the system can have spurious effects on the dynamics of the ballistic cascade. To alleviate this issue, a spherical region with a radius of 20 Å is created around the impacted zone within which atoms are treated in the microcanonical (NVE) ensemble. Outside the spherical region, atoms are maintained at a constant temperature of 300 K by a Nosé-Hoover thermostat.²¹ Further, a ballistic cascade involves atoms moving with high velocities. This results in excessive collisions, which could potentially lead to numerical errors in the time integration of the equations of motion. To avoid such errors, a variable time step is used for the whole system, which ensures that any atom in the system is not displaced by more than 0.05 Å during one time step. Following the collisions, the relaxation of the ballistic cascade is simulated for 15 ps with the variable time step, which allows the temperature and energy of the system to converge after each collision. The system is further equilibrated in the isobaric (NPT) ensemble at 300 K and zero pressure for another 5 ps, using a constant time step of 0.5 fs. This enables the system to reach its equilibrium density and energy after the ballistic cascade associated with a single PKA. Thus, a total simulation time of 20 ps is used per PKA to ensure the full relaxation of the system under irradiation. The process is continued with different PKAs, until both enthalpy and density show a plateau. It is worth noting that the sequential irradiation method presented herein yields a cumulative damage that is similar to that of simultaneous multiple particles’ irradiation.²² Hence, the results presented herein do not depend on the irradiation methodology, that is, irradiation by sequential or simultaneous energetic particles.

A large region of the crystal lattice is affected during each ballistic cascade. Consequently, an appropriate minimum system size needs to be determined for a given deposited energy per PKA to avoid potential spurious self-interactions arising from the periodic boundary conditions. However, extremely large system sizes might be computationally prohibitive. Thus, a minimum system size is determined for a given incident energy by using the following methodology. First, we accelerate each of the atomic species present in the pristine quartz (Si and O atoms) in randomly chosen directions with the desired incident energy. The maximum atomic displacements corresponding to a time interval of 1 ps, in each of these cases, are recorded. Finally, the system size is chosen to be at least twice as large as the maximum distance among all the recorded ones. In the present case, the initial system size is obtained as a 10 × 10 × 9 α-quartz supercell comprising 8100 atoms (2700 Si atoms and 5400 O atoms). Choosing the system size based on the methodology presented here is found to decrease the system size significantly as compared to previous studies, wherein an arbitrarily large system size was chosen.

It is worth noting that the accuracy of molecular dynamics simulations depends highly on the ability of the chosen inter-atomic potentials to appropriately describe the structure and dynamics of the system. In the case of irradiation simulations, this is further complicated by the fact that the system undergoes a structural disordering, that is, altering from crystalline to a completely disordered state. In particular, the inter-atomic potential must (1) be able to describe both the pristine and disordered structures with a fixed set of parameters, (2) provide a realistic description of ballistic cascades resulting from high-energy collisions, that is, wherein atoms potentially explore the short-distance part of the potential, and (3) be able to handle the formation of local structural defects—e.g., over- or under-coordinated atoms—which are likely to form upon irradiation. To this end, we use the reactive force field ReaxFF potential,²³ with parameter calibrations from Manzano et al.,²⁴ as it can correctly describe the structure of both pristine α-quartz and glassy silica with a constant set of parameters, and features robust potential forms that can dynamically adjust the potential energy based on the local atomic environment of each atom.²⁵ 

In order to compare the structure of irradiated quartz to that of its glassy counterpart, a silica glass is prepared following the conventional “melt-quench” method.²⁵ To ensure a meaningful comparison with the irradiated quartz, we use the same potential, time step, and system size (8100 atoms). First, an initial system consisting of 2700 Si and 5400 O atoms is generated by randomly placing atoms in a cubic box. Care is taken to maintain charge neutrality and ensure the absence of any unrealistic overlap. The system is then melted at 4500 K at zero pressure for 1 ns in the NPT ensemble. This ensures the loss of memory of its initial configuration leading to an equilibrium liquid state that of a silica melt. After equilibration, the melt is cooled from 4500 K to 300 K with a cooling rate of 1 K/ps in the NPT ensemble at zero pressure. The final glass structure formed is further equilibrated at 300 K and zero pressure for 1 ns in the NPT ensemble to ensure the complete relaxation of the structure. We observe that the final density of the glassy silica is close to 2.3 g/cm³, slightly higher than the experimental value (2.2 g/cm³). This could be attributed to the cooling rate used herein for the preparation of the glass, which is significantly higher than that typically achieved experimentally. Note that although the thermodynamic properties, such as the density or thermal expansion, are found to be sensitive to the thermal path followed upon cooling, the short- and medium-range order structures (bond lengths, coordination numbers, pair distribution function (PDF), structure factor, etc.) only weakly depends on the thermal history.^26,27 Further, the structure of the glass generated here shows a good agreement with experimental data.²⁵ 

The collisions of neutrons with the atoms induce some ballistic cascades within the network, which, in turn, results in the formation of locally disordered regions. The events associated with a single ballistic cascade are as follows. A high-energy neutron particle collides elastically with the PKA, which, due to the high kinetic energy absorbed during the collision, is accelerated and displaced significantly from its original position. Along the way, the PKA collides with other atoms in the crystal lattice, called secondary knock-on atoms (SKAs), displacing some of them from their original lattice positions. The displacements of the PKA and SKAs result in the formation of a disordered region through the accumulation of crystal defects, such as vacancy, interstitial, and coordination defects for Si and O atoms, e.g., tri-cluster O atoms (O^III) and three- and five-coordinated Si (Si^III and Si^V) atoms.¹⁵ These high-energy defects increase the overall energy of the system. Subsequently, the formation of disordered regions results in an overall increase in the volume of the system. A detailed analysis of the defects formed during ballistic cascades due to a single PKA has been presented elsewhere.¹⁵ 

Upon further irradiation, the system tends to get increasingly disordered, ultimately leading to a non-crystalline structure. Figure 1 shows the evolution of the density and enthalpy of an α-quartz crystal exposed to sequential radiation. We observe that the density of quartz decreases monotonically until it plateaus at around 2.2 g/cm³. This density value is close to that of glassy silica,²⁸ which suggests a similarity in their overall structures. In the initial region, the slope of the density curve is steep, corresponding to a sharp decrease in the density associated with each damage-cascade. However, the slope gradually decreases with the amount of deposited energy, before the density eventually saturates. The decrease in density observed herein is found to be in good agreement with previous experimental results^5,13 (see Fig. 1). Note that the experimental and simulated deposited energy cannot easily be compared. This arises from the fact that while the energy is deposited per unit of volume in the simulations, the neutron flux is applied to a face of quartz in the experiments. As such, the response of a material to a given surface neutron flux depends on its geometry and on the ability of the neutrons to penetrate through the material—which is not explicitly accounted for in the present simulations. Further, the fraction of the deposited energy that is actually transferred to the crystal in experiments is not a priori known, since some neutrons may pass through the crystal while transferring only a part of their kinetic energy to the atoms. Despite the difficulty of meaningfully comparing experimental and simulated results, we observe that the final density reached by irradiated quartz exhibits a close match with previous experimental results,^5,7,10 which confirms the realistic nature of the present results.

Next, we focus on the evolution of enthalpy upon irradiation. The enthalpy initially exhibits a sharp increase, thereby confirming the formation of a large number of high-energy short-range defects. The overall change in the enthalpy of the system is close to 0.25 eV/atom, which is two orders of magnitude smaller than the deposited energy required for saturation. Thus, it can be inferred that most of the deposited energy is dissipated in the form of heat, whereas only a small amount is absorbed by the system to form short-range defects. We note that enthalpy and density saturate after significantly different amounts of deposited energy (around 5 and 20 eV/atom, respectively). This is in line with recent results showing that energy relaxes faster than density.²⁹ This has been attributed to the fact that energy relaxes through short-range structural reorganizations, whereas density relaxation requires medium-range collective motions of atoms—similar to displacive actions.^29–31 To ensure that the results of the irradiation simulation do not significantly depend on the incident energy per neutron, but rather on the total deposited energy, we conducted multiple simulations for varying system sizes and neutron energies. We observe that the obtained results do not exhibit any significant dependencies on either the system size or the incident energy (see the supplementary material).

We now compare the atomic structure of irradiated quartz, after saturation of both the energy and density, to that of glassy silica. We first rely on the pair distribution function (PDF), which captures structural correlations within the short- and medium-range orders. Figure 2 shows the PDFs of the crystalline, irradiated, and glassy states of quartz. In the case of crystalline quartz and glassy silica, the peak around 1.6 Å corresponds to the nearest neighbor (Si–O) distance,³² whereas the second peak close to 2.65 Å arises from second neighbor O–O correlations.³² We note that although glassy silica presents broader peaks than the crystalline system—due to an increased degree of disorder—no significant differences in the short-range order structure (i.e., for distances d < 3 Å) are observed. In contrast, due to the periodic nature of the structure of crystalline quartz, its PDF features a series of sharp peaks which are only weakly defined in glassy silica. As expected, this shows that the medium-range order (3 < d < 10 Å) of glassy silica strongly differs from that of crystalline quartz and that glassy silica does not present any long-range order d > 10 Å. Altogether, the PDF confirms that glassy silica has a well-defined short-range order structure with no long-range order.

As expected, the PDF of irradiated quartz presents the typical features of that of a glassy material (i.e., a well-defined short-range order combined with the absence of a long-range order). In particular, the two short-range order peaks at 1.6 and 2.65 Å—reminiscent of Si–O and O–O correlations in quartz—are present at the same positions. However, the second peak is found to be notably broader that in glassy silica, which denotes a decreased degree of order in the short range. In addition, the PDF of irradiated quartz shows two secondary peaks around 2 Å and 1.4 Å. The existence of these peaks, which are absent in both quartz and silica glass, has been suggested in experimental observations.³³ Further, we note that the minor peaks found in the medium-range order of the structure of glassy silica are virtually absent from that of irradiated quartz. This shows that the medium-range order in irradiated quartz is not as well defined as that of glassy silica. Overall, despite its similarities with glassy silica, irradiated quartz presents an increased degree of disorder, both in terms of its short- and medium-range orders.

We now focus on the connectivity of the atomic network. Despite being non-crystalline, glassy silica shows a well-defined atomic environment for each species, similar to that observed in quartz. Namely, the silicate network comprises 4-fold coordinated Si tetrahedra, which are linked to each other by 2-fold coordinated bridging O atoms.²⁵ SiO₄ tetrahedra are found to be connected through their corners only—i.e., only corner-sharing polytopes are observed. In contrast, as suggested from the presence of secondary peaks in the PDF (see Fig. 2), the atomic structure of irradiated quartz comprises some coordination defects, which are listed in Table I. We observe the existence of defective under-coordinated 3-fold and over-coordinated 5-fold Si atoms, as well as small fractions of 2-fold and 6-fold coordinated Si. On the other hand, defective 1-fold (non-bridging) and 3-fold (tri-cluster) O atoms are found, as well as a small fraction of isolated free O. The nature of defects and local structure of glassy silica have been extensively studied in previous works.^27,34,35 Overall, a comparison shows that irradiated quartz features a large variety of coordination defects,¹⁵ which are largely absent from glassy silica.

These coordination defects result in the appearance of additional peaks within the PDF of irradiated quartz (see Fig. 2). We first investigate the origin of the secondary peak centered around 2 Å. By analyzing the partial PDF associated to each pair of atomic species, we note that this peak arises from strained Si–O bonds. The contribution of the O neighbors to the peak is investigated using the following methodology. First, we compute the O neighbors of each Si atom by fixing a cutoff distance. The cutoff is chosen as the point where the Si–O partial PDF goes close to zero (2.3 Å). The O neighbors for each of the Si atoms are then ranked as first, second, etc., based on their absolute distance from the central Si atom. Figure 3 shows the Si–O partial PDF for the Si atoms contributing to this peak, as well as the contributions of the five first O atom neighbors. We note that these units are highly asymmetric, the three closest O neighbors being systematically at a distance lower than 1.8 Å, whereas one or two other O atoms are at a distance of around 2 Å from the central Si atom. This suggests that two main types of mechanism contribute to the formation of this peak. (1) Nearly 30% of the Si–O bonds contributing to the peak belong to 5-fold coordinated Si (Si^V) units. However, note that the SiO₅ units observed herein differ from those that are typically observed, e.g., in silicate crystals subjected to high-pressure.³⁶ As shown in Fig. 3, SiO₅ units consist of nearly pristine SiO₄ tetrahedra—with four Si–O bonds of around 1.6 Å—attached with an additional O neighbor (at 2 Å) at the vicinity. As such, in this case, O mostly acts as an interstitial defect rather than being strongly bonded to the central Si. (2) The remaining Si–O bonds contributing to the 2 Å peak belong to 4-fold coordinated Si atoms (Si^IV). The SiO₄ polyhedra then consist of under-coordinated SiO₃ units—with three Si–O bonds of around 1.6 Å—attached with an additional O neighbor (at 2 Å) at the vicinity. In this case, the fourth oxygen neighbor can be connected to one or two other Si units. These two types of defects mostly arise when the PKA is an O atom. In this case, the permanent displacement of the O atom results in the formation of an oxygen vacancy (SiO₃) near the initial collision and a permanently displaced interstitial free oxygen. In most cases, these defects are quickly relaxed via local atomic reorganizations, namely, free oxygen atoms “attach” to a pristine SiO₄ tetrahedron at their vicinity (defect type 1) and undercoordinated SiO₃ units tend to attract a neighboring bridging or non-bridging O atom (defect type 2).

Next, we investigate the origin of the secondary peak centered around 1.4 Å in the PDF of irradiated quartz (see Fig. 2). First, by analyzing the partial PDF associated to each pair of atomic species, we note that this peak arises from O–O correlations. This is found to originate from the existence of edge-sharing Si tetrahedra—i.e., adjacent Si atoms sharing two O neighbors—which are not found in glassy silica. Here, 4.5% of Si atoms are found to belong to edge-sharing units. No face-sharing units are observed.

We now turn our attention to the characterization of the angular environments of each atomic species, that is, inside and between SiO₄ tetrahedra. Figure 4 shows the bond angle distributions (BADs) of the O–Si–O and Si–O–Si angles. In agreement with previous observations, the O–Si–O and Si–O–Si BADs observed in quartz are sharp and symmetric and centered around 109° and 140°,³² respectively. On the other hand, the O–Si–O BAD of glassy silica is centered around the same value but is broader than that of the crystal. However, the Si–O–Si BAD of glassy silica significantly differs from that of quartz, as it is broader, centered around lower angles values (around 135°), and features some asymmetry, the peak being skewed towards smaller angles. The asymmetry observed herein is supported by experiments³⁷ and molecular orbital (MO) calculations^37–39 and has been attributed to the competing effects of covalent interactions and strong Si–Si repulsions at lower angles (<120°). Note that such an asymmetry is typically not predicted by classical potentials,²⁵ which further confirms the ability of the reactive inter-atomic potential used herein to predict realistic structures for crystalline quartz and glassy silica. In addition, the broadening of the inter-tetrahedral angle upon vitrification is in line with the fact that this angle is associated to a thermally broken constraint in silica.^40,41

As in the case of glassy silica, the BADs of irradiated quartz appear broader than those of quartz. In particular, the O–Si–O BAD is found to be largely similar to that of glassy silica, although slightly broader. We observe the existence of a shoulder at around 90°, which arises from the contribution of the distorted SiO₅ units (see Sec. III C). In addition, the Si–O–Si BAD exhibits an asymmetric character reminiscent of that of glassy silica. However, the Si–O–Si BAD of irradiated quartz differs from that of glassy silica as it is broader and centered around lower angle values. Note that the reduction in the average Si–O–Si angle is in agreement with previous experimental observations.⁷ We also observe the existence of a shoulder around 110°, which arises from the tri-cluster O and edge-sharing units. In addition to the intra- and inter-tetrahedral angles, the dihedral (or torsional) angle is also of interest as it captures the mutual flexibility between SiO₄ tetrahedra.¹⁴ Figure 5 shows the dihedral angle distribution in pristine and irradiated quartz and glassy silica. We observe that the dihedral angle follows a trimodal distribution in α-quartz, with three peaks centered around 15°, 105°, and 135°. In contrast, both glassy silica and irradiated quartz exhibit weakly defined bimodal distributions, with two peaks centered around 60° and 180°. Hence, the absence of a well-defined orientational order between SiO₄ tetrahedra contributes to increase the extent of medium-range structural disorder in glassy silica and irradiated quartz.

We now compare the medium-range order structure of irradiated quartz with those of crystalline quartz and glassy silica. To this end, we compute the partial structure factors S_ij(Q) from the Fourier transformation of the partial PDFs g_ij(r) as⁴² 

where Q is the scattering vector, $ϱ0$ is the average atomic density, and R is the is the maximum cutoff distance used to compute the PDF. Here, we choose a value of 10 Å for R. To reduce the effect of the finite cutoff R in the integration, we use a Lorch-type³³ window function $FL(r)=sin(πr/R)/(πr/R)$⁠. Note that this function, while suppressing spurious ripples at low wave vectors, can induce a broadening of the structure factors. The total neutron structure factor is then computed as

where c_i is the fraction of atoms of type i (i = Si, O) and b_i are the neutron scattering lengths of each of the species. Although it contains the same information as the PDF, the structure factor tends to emphasize the contribution of the medium-range order. In particular, the first sharp diffraction peak (FSDP) of the structure factor captures structural correlations within the medium-range order.^43–45 The FSDP is typically observed around 1-2 Å in disordered materials and is usually narrower than the following peaks. Note that including or not, the FSDP when back-calculating the PDF from the Fourier transformation of the structure factor does not yield to any notable difference.⁴⁶ This confirms that the FSDP is more related to the medium-range rather than to the short-range. Although the origin of the FSDP remains controversial, it is usually attributed to some structural correlations between voids and atomic clusters within the medium-range.^45,46 Furthermore, the full width at half maximum (FWHM) of the FSDP is related to a coherence length L as L = 7.7/FWHM,⁴⁵ which is usually associated with the average size of rigid atomic clusters within the network.^45,47 Note that this expression is analogous to the Scherrer equation⁴⁸ for poly-crystals, wherein the coherence length is linked to the average size of the individual crystallites.

Figure 6 shows the structure factors of pristine and irradiated quartz and glassy silica. The structure factors of pristine quartz of glassy silica compare well with previous observations.^25,49,50 Namely, the structure factor of pristine quartz comprises several sharp peaks at small reciprocal distance (that is, around 1-2 Å) due to the long-range periodicity of the structure. In contrast, the structure factor of silica only shows a broad FSDP centered around 2 Å⁻¹.⁴⁹ Upon irradiation, we observe that the structure factor of quartz gradually broadens, loses any contributions from the long-range order (i.e., short reciprocal distance), and eventually becomes fairly similar to that of glassy silica. In particular, the position of the FSDP coincides with that of glassy silica. However, the FSDP observed in irradiated quartz appears notably broader than that of glassy silica. Note that the full-width at half-maximum (FWHM) of the FSDP is related to a coherence length L within the medium-range as L = 7.7/FWHM, which has been suggested to represent the average length of the rigid atomic clusters within the network.^45,47 To assess the extent of medium-range disorder in irradiated quartz and glassy silica, we compute the FWHM by fitting the FSDP by a Lorentzian function. The FWHMs are found to be 2.432 and 1.487 Å⁻¹ in irradiated quartz and silica glass, respectively. These values yield coherence lengths L of 3.167 and 5.176 Å, respectively, which further confirms that irradiated quartz exhibits a more disordered medium-range order than glassy silica.⁵¹ More specifically, we note that the coherence length obtained for irradiated quartz becomes close to 3.2 Å, that is, the average size of the Si tetrahedra. This suggests, in irradiated quartz, that the Si polyhedra constitute the only “rigid” structure of the network, whereas more extended rigid clusters, probably small rings, are observed in glassy silica.

Finally, we further investigate the origin of the increased disorder observed in the medium-range order of irradiated quartz with respect to that of glassy silica by computing their ring size distributions.⁵² All the ring size distribution computations are carried out using the RINGS package.⁵³ Here, rings are defined as the shortest closed paths within the silicate network, their length being defined as the number of Si atoms belonging to a given ring (see Fig. 7(a)). Figure 7(b) shows the ring size distribution in crystalline and irradiated quartz and glassy silica. First, we note that crystalline quartz presents only two types of rings, namely, 6- (see Fig. 7(a)) and 8-membered rings. In contrast, glassy silica glass shows a broader distribution of ring sizes centered around an average size of 6, in agreement with previous simulations^49,52 and recent experiments.⁵⁴ We then note that irradiation also results in the formation of a broad ring size distribution within the silicate network. However, the ring distribution of irradiated quartz is found to be significantly different from that of glassy silica. In particular, we find that the distribution of rings is fairly uniform between ring sizes of 6 and 10 and is followed by a long tail. The largest ring size observed in irradiated quartz is found to have a length of 19 Si atoms, that is, significantly higher than the largest ring found in silica glass. Overall, this highlights once again the fact that irradiated quartz shows an increased degree of disorder at the medium-range as compared to glassy silica.

Altogether, the present results show that, upon irradiation, although the structure of quartz gradually evolves towards one that resembles glassy silica, irradiation- and vitrification-induced disordering result in distinct structural effects. Overall, irradiated quartz is found to feature an increased degree of disorder, both in terms of its short- and medium-range orders. This manifests by the presence of coordination defects, edge-sharing units, and large silicate rings, which are all absent from the structure of glassy silica. This suggests that, although isochemical glasses offer a convenient way to roughly estimate the upper limit of the irradiation-induced disordering of crystals, vitrification and irradiation fundamentally differ from each other. Based on this insight, it is clear that a better understanding of materials’ structural damage under irradiation and their ability to relax structural defects through recrystallization is needed to enable the design of radiation-resistant materials.

See supplementary material for the effect of system size and incident energies on the irradiation-induced swelling in quartz.

This research was performed using funding received from the DOE Office of Nuclear Energy’s Nuclear Energy University Programs. The computational facility was in part provided by the San Diego Supercomputer Center as part of the HPC@UC program. The authors also acknowledge financial support for this research provided by The Oak Ridge National Laboratory operated for the U.S. Department of Energy by UT-Battelle (LDRD Award Nos. 4000132990 and 4000143356), National Science Foundation (CMMI: 1235269, CAREER Award No. 1253269), Federal Highway Administration (No. DTFH61-13-H-00011), and the University of California, Los Angeles (UCLA). This manuscript has been co-authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).