la seguridad vial.
4. Desarrollo del simulador de conducción.
4.1. Flujo de trabajo en Unity.
XRD spectra of GC compressed in the PP-DAC in steps up to a maximum pressure of 47 GPa is shown in Fig. 6.6. As a reminder, in this experiment the incident X-ray beam is parallel to the compression axis of the DAC.
Figure 6.6: XRD spectra measured in the PP-DAC with the incident X-ray beam parallel to the compression axis up to a maximum pressure of 47 GPa. All spectra shown have been scaled to the height of the {100} peak and all peaks have been indexed to graphite. The spectra taken at 28 GPa on decompression has a sharp fea- ture at∼3 ˚A−1 due to the beam tail clipping the rhenium gasket. The ‘uncompressed
Sigradur-G’ and ‘recovered material’ scans were measured outside of the DAC.
There are three main peaks in the XRD spectrum of the precursor, Sigradur-G, that are located at 1.8 ˚A−1, 3.0 ˚A−1, and 5.2 ˚A−1. These peaks have been indexed to graphite, and correspond to the{002}, {100}, and {110} reflections, respectively. There is also a broad and relatively weak peak located at ∼3.6 ˚A−1 which corre-
sponds to the {004}, and there is a very weak shoulder at ∼3.1 ˚A−1 corresponding
to the{101}reflection. The highly disordered and turbostratic stacking of graphene layers that comprise the majority of the GC structure cause the layer separations to be slightly larger than in well-ordered graphite. For this reason the {002} peak is located at 1.8 ˚A−1, rather than at 1.9 ˚A−1 as it is for well-ordered graphite. This
disordered and turbostratic structure also means that there is little registration be- tween stacked graphene sheets, leading to a significant reduction in the intensity of interlayer reflections such as the{101} relative to graphite.
As pressure increases the {002} peak shifts to higher Q, indicating that the graphitic layers are being forced closer together. At the same time the {100} peak shifts only slightly to the right, which indicates that the in-plane spacings within the graphene sheets are compressed by only a small amount. These results are consistent with the XRD data published by Linet al. [61] of an AA1100 GC sample compressed in a DAC. There is also a significant change in the relative intensity of the{002}and
{100} peaks as pressure is increased. This can be explained by the gradual preferred orientation of graphitic layers that was highlighted previously in the pan-DAC data. As the layers orient themselves perpendicular to the incoming X-ray beam the Bragg condition is lessened, and the intensity of the{002} peak drops.
On decompression the {002} peak shifts back toward its original position at 1.8 ˚
A−1. This recovery is sluggish, similar to the recovery of graphite after compression
in a DAC which was published in a recent study conducted by Wang et al. [51]. The original intensity of the {002} (relative to the {100}) doesn’t fully recover after decompression. This is unsurprising, as the results presented in Chapter 5 showed that when GC is compressed to above 35-45 GPa the isotropic structure is lost and the graphitic layers will be permanently aligned perpendicular to the incident X-ray beam, lowering the Bragg condition, and weakening the {002}. It is also clear that the {002} peak is not shifting at a constant rate with respect to pressure, and that this rate decreases with increasing pressure. Also, the change in the relative peak intensities slows as pressure is increases. These trends suggest that the material is approaching some form of phase transformation threshold.
To investigate this further, a compression curve was generated from the XRD data in Fig. 6.6. This compression curve compares the change in the volume with respect to pressure and is plotted in Fig. 6.7. The volume used is that of the hexagonal unit cell, where the a and c parameters were determined from the positions of the
{100} and {002} peaks, respectively. The equation used to calculate the volume is displayed in the bottom left corner of Fig. 6.7. It is important to recognise that this relative change in volume represents the microscopic volume change. (Note: this is different from the compression curve presented by Zhao et al. [64] which includes the compression of voids). There is a discontinuity in the data between 36-39 GPa, which is highlighted by the pink shaded region in Fig. 6.7. This discontinuity can be seen more clearly by the sudden change in slope of the first derivative (with respect
to pressure) which is plotted in the inset. The specific pressure step at which this discontinuity occurs aligns well with the discontinuity observed in the in situ XRD data collected in the pan-DAC and with the permanent breakdown of the isotropic structure of GC between 35-45 GPa that was identified in Chapter 5.
Figure 6.7: This figure shows the relative change in volume of the hexagonal unit cell, where the a and c parameters have been determined from the positions of the
{100}and the{002}peaks from the spectra shown in Fig. 6.6. X error bars indicated the possible uncertainty in the pressure calibration method used which increases with pressure. Y error bars have not been included as the peak locations are easy to accurately determine. This means that the error bars are so small that they are hidden beneath the points on the plot. The hexagonal unit cell volume equation is shown in the bottom left-hand corner. (inset) A plot of the first derivative of the change in unit cell volume with respect to pressure, showing a discontinuity between 36-41 GPa.
To further analyse the compression curve in Fig. 6.7, a third order isothermal Burch-Murnaghan equation of state (BM-EoS) was fitted to the data in a similar method to that used by Boehleret al. [214]. The equation used is
P = 3B0 2 hV V0 −7/3 −V V0 −5/3in 1 + 3(B 0 0−4) 4 hV V0 −2/3 −1io (6.1)
where B0 is the bulk modulus and B0’ is its first derivative with respect to pressure.
The three data points above the discontinuity were not included in the least squares fit as the EoS will not predict the sudden change in slope that occurs at ∼36 GPa which suggests a phase transformation. The BM-EoS fit is shown in Fig. 6.8, and the values determined for B0 and B0’ are 9.6 GPa and 29.1, respectively. The value
determined for B0 is typical of a relatively soft material, however the value of 29.1
determined for B0’ is very high as the compression curves for most materials return a
value of∼4 [64]. In order to explore this value it is possible to force B0’ to equal 4 and
re-fit the data. This provides a very poor fit. Zhao et al. [64] previously determined a value of 7.98 for B0’ from a compression curve of AA1100 GC in a DAC. This value
was determined from a compression curve that included the volumetric compression of voids but excluded the first 2 GPa. Hanflandet al. [96] determined a similar value for graphite, where B0’ was calculated to be 8. However, if B0’ is forced to equal 8
the fit to this data is still poor. In an attempt to provide a more accurate fit, another term was added to the BM-EoS which incorporates the second derivative of the bulk modulus, B0” [215]. The least squares fit using this method yielded a negative value
of -0.9 for B0’, which appears highly irregular. For further details of the EoS fitting
and errors see Appendix 1.
Figure 6.8: A third order BM-EoS fitted to the compression curve data shown in Fig. 6.7 to all points below 36 GPa. This shows the least squares fit obtained by letting both the B0 and B0’ values vary.
In summary, there are two things that require highlighting from this section of the results. The first is that there is a discontinuity observed between 36-39 GPa in the
compression curve that is derived from the in situ PP-DAC data. This discontinuity may be a result of the same change that is noticed in thein situ pan-DAC between 36- 41 GPa, and the permanent breakdown of the isotropic structure observed in the data presented in Chapter 5. The second thing to highlight is that the value determined here for B0’ from the GC compression curve is extremely high, even relative to values
determined from other high pressure studies of GC [64] and graphite [96].
6.4
Discussion
The discussion is separated into two sections. The first section discusses the validity of the values extracted from the BM-EoS fit to the compression curve data, and explains how the values obtained are reasonable for GC. The second section elaborates on a proposed structural model that describes the physical origins behind the discontinuity observed in both sets ofin situ XRD data at ∼36 GPa.
To begin, the EoS fitting procedure and results require discussion. The values determined for B0 and B0’ from the least squares fit of the EoS to the compression
curve data shown in Fig. 6.7 are 9.6 GPa and 29.1, respectively. As mentioned previously, the value of 9.6 GPa for B0is entirely reasonable for an easily compressible
material. The value for B0’ of 29.1 is very large. This determination is in comparison
with graphite where B0 has been shown to be ∼8 [96], or for standard metal and
ceramic materials where it is typically∼4 [64]. So that raises one important question. Is a B0’ of 29.1 a reasonable value to represent GC? This value B0’ describes how much
B0 (which is a measure of the compressibility) changes with increasing pressure. This
means that a very high B0’ is an indicator that the compressibility of GC decreases
rapidly as pressure increases. This is a reasonable assumption for GC, as will now be explained.
Typically a BM-EoS (or any other form of EoS) will be fitted to a region of a compression curve over which the structural phase of the material does not change. However, GC transforms continuously as pressure increases. At ambient the struc- ture of GC can be described relatively well as an isotropic compilation of graphitic nanostructures (defined by a graphite unit cell) with an∼5% sp3 bonding component connecting the graphitic nanostructures, as shown in Chapter 5. This small frac- tion of sp3 bonds both stabilises the disordered isotropic nature of the structure and strongly influences the compressibility. It has been shown by both experiment [61] and simulations [66] that this sp3 bonding component increases gradually as pressure
bonding composition, which in turn will alter the compressibility. It is reasonable to assume that as the % of sp3 bonds present in GC increases (as it effectively trans- forms away from graphite toward diamond) it will become more difficult to compress. If this sp3 bonding fraction increases enough, it is entirely reasonable that the B
0
of the material will increase substantially. This would warrant a high value for B0’.
Whether or not 29.1 is a realistic value is difficult to answer, but a value that is well above the standard of∼4, or even well above∼8 [96] is reasonable. GC does exhibit extreme mechanical properties, such as superelasticity, so it should not be surprising that it may also require extreme values to describe its mechanical behaviour at high pressure.
Adding a second derivative term (B0”) to the BM-EoS is perhaps necessary for
materials that exhibit such a high value for B0’. This method is not standard, which
makes it difficult to compare to other materials. However, GC is a unique and unusual material, so it is possible that standard methods of analysis may only poorly describe its behaviour.
Taking this into account, the question regarding the physical origin of the discon- tinuity observed in both sets ofin situ XRD data at ∼36 GPa is now addressed.
The best place to begin this discussion is with the previously reported gradual increase is sp3 bonding that is known to occur in GC as pressure increases. This
gradual increase was observed in the in situ X-ray Raman spectroscopy experiment of Lin et al. [61], and has been predicted by simulations that are part of a recent publication that includes the results presented in Chapter 5 [66]. A plot of thein situ
sp3 bonding content with respect to pressure from the simulation study is shown in Fig. 6.9. This figure shows that the sp3 bonding increase gradually up to ∼32 GPa,
before there is a sudden increase in the rate of increase at∼32 GPa. What is proposed is that the discontinuity observed in thein situXRD data is not a result of the gradual increase in sp3 bonding, but is related to this sudden increase in the rate of increase
in sp3 bonding observed at ∼32 GPa. This sudden increase is potentially thought to
indicate the onset (or nucleation) of sp3 bonded nanocrystals. This does not mean
that the entire bulk of the material has transformed into sp3 bonded nanocrystals, but that this has occurred only in small localised regions where it is possible for the original sheets to register. From the simulation results in Fig. 6.9 it is clear that the sp3 bonding fraction does not increase to 100%, which supports the fact that the
{002} peak does not completely vanish in thein situ XRD data presented earlier. A physical model to explain these observations will be discussed in Chapter 8.
Figure 6.9: This plot shows the sp3 bonding fraction with respect to pressure for a
simulated carbon structure generated using the LAMMPS molecular dynamics pack- age [216] equipped with EDIP for carbon [217]. It shows that there is a non-zero component of sp3 bonds in the material at ambient and that this percentage gradu-
ally increases with pressure before a sharp jump at∼32 GPa. This figure is adapted from ref [66].
6.5
Concluding remarks
In the study presented in this chapter a GC sample was compressed in a DAC with- out a pressure medium and observed in situ from two orthogonal beam directions. In the PP-DAC experiment, the sample was probed parallel to the DAC compres- sion axis. In the pan-DAC experiment the sample was probed perpendicular to the DAC compression axis, where the results showed the gradual preferred orientation of graphitic layers up to 36 GPa. Both sets of in situ XRD data show a discontinuity at 36 GPa, which is thought to represent the initial nucleation of small localised sp3