An example of the breaking and reforming of bonds within .. the square cross section fiber is shown here. Movement of oxygen B to a new position in the structure, . within the surface of the square fiber is shown here.
Motivation
Using atomistic modeling techniques, the structure of a material can be observed visually and quantitatively, both on a material surface and in the bulk. Changes in material structure over time, under applied conditions, can be directly observed and rapid dynamic processes can be monitored in detail.
General Introduction
Using a Blue Gene/L supercomputer, we prepared and investigated the structure of silica glass fibers, down to a small experimental scale. In Chapter Two of this work, the structural characteristics of sodium silicate and sodium aluminosilicate glasses are discussed.
Molecular Dynamics Methodology
To that end, thermostat and barostat algorithms are used to control the temperature and pressure of the sample, as determined by the system constraints. Adjustments to the temperature are made by scaling up or down the kinetic energy of all the atoms of the system to bring the average closer to the target temperature.
Formation of a Glass Sample
With just the previously described sample box, a large percentage of the atoms would be affected by the surfaces, and very little bulk structure would be produced in the sample. This problem was addressed through the use of periodic boundary conditions.12 Images of the sample box were placed around the original to form an infinite lattice enclosing the formed sample.
Terminology and Analytical Techniques
As atoms moved in the sample, their images also moved in all surrounding images. Silicon tetrahedrons within the structure share corners with each other by bridging oxygen, and connect to form rings within the structure.
Introduction
The bulk structures of sodium silicate and sodium aluminosilicate glasses have been investigated using computer simulations in previous work.21,68-70 Typically, these simulations have been small in size, containing from several hundred70 to three thousand21 atoms. Simulated structures are found to agree with experimental data, but generally show that the samples may have an elevated fictitious temperature.
Sodium Silicate and Aluminosilicate Glasses
The NBO content of the glass should increase proportionally with the sodium content, and the bond lengths and angles may change and distort as the structure breaks down. Any aluminum added to the structure can be thought of as adding a bridging oxygen that the sodium in the structure had converted to a non-bridging oxygen.
Ring Structure
Ring size can be directly linked to the number of non-bridging oxygens found in the structure. As the aluminum content in the sodium aluminosilicate glasses increases, the rings become more interconnected, and the ring size distribution narrows again to consist primarily of six- and seven-membered rings.
Oxygen Coordination
The non-bridging and triplet oxygen content in the systems is shown here, given as a function of composition. As the aluminum content of the glass increases, the triple-bridged oxygen is primarily bonded to 2 aluminum atoms and 1 silicon atom.
Q n Species
From Figure 2-8 it is clear that a majority of the non-bridging oxygen in the structure is associated with silicon, rather than aluminium. Note the relatively constant value of aluminum Q4 species in the glass with changing composition, compared to the increasing number of silicon Q4 units.
Bond-lengths
A clear difference can be seen in the bond length of the bridging oxygen versus the non-bridging oxygen. The compositional trends in bond length of aluminosilicate glasses are less clear than in sodium silicates.
Bond-angles
The sodium-oxygen distance was found to increase slightly due to an increase in the number of BO and TBO in the system with increasing aluminum content. The tense bond angles seen in aluminum tetrahedrons for glasses containing small amounts of sodium are related to small bi- and tri-membered rings in the structure.
System Size Comparison for Sodium Silicate Glasses
The presence of five-coordinate silicon in the system is a little more troubling, but perhaps more easily explained. Five-coordinated silicon atoms are seen in the smaller simulations, but in much smaller amounts.
Conclusions
Similar to the shifts seen in the Qn species population, the presence of five-coordinate silicon atoms indicates an increased fictitious temperature. Fibers were formed with different system sizes and cross-sectional geometries, and the surface structures of these fibers were investigated.
Sample Formation
At least 20Å of extra space was added on either side of the box, in the x and y directions, leaving the z direction as continuously periodic. Images of the separation of two hexagonal periodic boxes in the y direction by adding extra box space, and the final fiber, are shown in Figure 3-1.
Annealing
The percentages of different species found in the fiber at different stages of the forming process are shown for the square fiber in Table III-II. It is clear from Table III-II that a lot of disorder is added to the system, especially at the cutting edges of the fiber, when it is separated from the bulk.
Defining Surfaces
Although a large number of these unusual species are favorably recombined into the structure by the end of the annealing process, a small amount of disorder remains in the final sample. Trioni et al.64 found that a peak in the bond angle distribution around 120° was found for the sample within 5 Å of the surface.
Fiber Surfaces, examined as a function of system size
Using the number of unusual species in each half Å slice of the fibers, the surface layers of these three fibers are shown in Figures 3-7. The number of unusual species that form the surface of the three differently sized square cross-section fibers is shown here.
Fiber Surfaces, Examined as a Function of Cross-Sectional Shape
The apparently thinner surface layer in the circular fiber is again likely due to the slight rotation of the hexagonal fiber before analysis. The number of special species that form the surface of the three differently shaped fibers is shown here.
Conclusions
This may also indicate that the smaller surface thickness of the circle is not only due to the smaller number of atoms, but also to the interactions between neighboring atoms on the surface. Small voids were found in the crack path, up to 20 nm before the crack tip.
Straining Process
Since the specimen box contains void space in the x and y directions, as explained in Chapter Three, the specimen may contract naturally in the unstressed directions in response to the load applied in the z direction. Fracture of the sample typically occurred within 300,000 time steps, and the runs were allowed to continue to 600,000 time steps, which corresponds to 1.2 nanoseconds in real time.
Choice of System Size
Although this strain rate is fast relative to experimental strain rates, it is one of the slowest that has been used in computational simulation of fracture of silicate glasses.103 The use of a fast strain rate is required by computational resource limitations. The real time between recalculating the forces, a single time step, is 2 femptoseconds, and so to perform these calculations for a single second of real time would require 5 x 1014 iterations of the calculations and is very expensive in terms of computationally to be feasible using current. technologies.
Elastic Properties
The values of failure stress and failure stress found in this work are compared with the results of simulations of bulk glass and experimental study in Table IV-II. Failure stress, failure stress and the elastic modulus for the fibers, previous bulk silica work and experimental study.
Fracture Surface Structure
An example of this increased population of defective species is shown in Tables IV-III. Pre- and post-failure defect species population for the square fiber sample NBO Q3 units 3-coordinated silica Q2 units.
Distortion of Structure Under Strain
An illustration of the Si-O-Si bond angles found with a triple-bridged oxygen is shown here. These small, strained bond angles in the two- and three-membered rings shift the average bond angle of the system to lower values.
Failure Process
This crack continues to travel along the surface while also moving through the bulk of the fiber. Formation of voids on the fiber surface, C) Failure completely through the center of the fiber, D) Parts of the fiber surface are still intact as B is observed.
Bond Breaking and Reforming
The movement of the three-coordinated silicon as it bonds with surrounding bridging oxygen atoms is an attempt to achieve a fully coordinated tetrahedron. During the tensioning process, fracture without reformation was noted at several locations on the surface of the fiber.
Crack Formation in the Square Fiber
The four-coordinate silicon is pulled away from one of the bridging oxygens to become a three-coordinate silicon, in yellow. What was a four-coordinated silicon is pulled away from one of the bridging oxygens to become a three-coordinated silicon, in yellow.
Breaking the Cylindrical Fiber
The first connection to be broken within the area of void A's formation is shown here. The second connection broken within the area of void A's formation is shown here in the black oval.
Conclusions
Voids A and B opened progressively through the deformation process, visible on the surface, and their progress through the bulk of the sample was slowed by the network of bonds below the surface. When crack C opened, it quickly traveled through the less dense region behind it and into the bulk of the fiber at a higher speed than voids A and B.
Straining Method
In Chapter Two, a series of sodium silicate and sodium aluminosilicate glasses were formed, and their structures were evaluated and compared with theory, experiments, and other simulations. These samples were therefore judged to be suitable candidates for study under tensile stress, in a manner similar to that used for bulk silica36 and the silica fibers presented in Chapter Four.
Distortion of the Structure Under Strain
Si-O-Si average bond Si-O. The bond angles and lengths were compressed and elongated under tension, respectively, but no relaxation was observed, despite the fact that glass failure was expected at a strain of about 16%. Some of the deformation was recovered elastically, but the remaining distortion of the sample also indicated plastic deformation.
Thermostatting in MD
The configuration temperature is calculated using Equation 4-2 and the position, velocity, and acceleration of the atoms in the system at a given time step. This apparent correspondence between the kinetic and configurational temperatures of the system fails to explain the elevated structural temperature of the glass and does not suggest the cause of the viscous stretching behavior under tension.
Forced Failure
Conclusions
Conclusions and Future Work
A computer simulation study," J. Du, "Molecular dynamics simulations of the structure and properties of low-silica yttrium aluminosilicate glasses," J. Price, "Molecular dynamics simulations of temperature-induced structural changes in cristobalite, coesite, and amorphous silica," J. Cormack , “Medium-scale structure of sodium silicate glass:. Horbach, "Molecular dynamics computer simulation of amorphous silica under high pressure," J. Price, "Molecular dynamics simulations of glassy silicon structures," J. Atake, "A new description of structural disorder in silica glass," J. 34;Molecular Dynamics Studies stress -deformation behavior of silica glass under tensile loading," Chem.
