^{1,2,a)}, Boris Kiefer

^{1}and Kanani K. M. Lee

^{1,3,b)}

### Abstract

Long-duration, high-pressureresistance measurements on highly-ordered pyrolytic graphite in a diamond-anvil cell show a sluggish phase transition occurring at ∼19 GPa, as evidenced by the time-dependent behavior of the sample resistance. The instantaneous resistance response to pressure adjustment shows a ∼10 GPa hysteresis that has been observed previously, rendering the conjectured direct relationship between resistance and phase-transition tentative. In contrast, the evolution of the resistance with time after the instantaneous response shows a systematic, reproducible, and distinct behavior, which allows reducing the uncertainty in transition pressure to ∼2 GPa. This largely reduced hysteresis shows explicitly that the phase transition is directly related to changes in electronic structure and resistance and establishes consistency with other commonly used experimental techniques to explore phase transitions at high pressures. We augment our experiments with first-principle density-functional theory computations to evaluate the pressure dependence of the electronic density of states of proposed candidate structures for the post-graphite phase.

We thank Stefanie Japel and Heinz Nakotte for experimental help, Yuejian Wang for discussions, and RV Electronikka for technical assistance.

I. INTRODUCTION

II. EXPERIMENTAL METHODS

III. THEORETICAL METHODS

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- High pressure
- 22.0
- Graphite
- 19.0
- Electrical resistivity
- 15.0
- Phase transitions
- 15.0
- Diamond
- 9.0

## Figures

Photomicrographs of the sample at various pressures during Run 1. The sample began as a 70 μm square of HOPG remained nearly rectangular at all pressures. For reference, the diameter of the culet is 300 μm.

Photomicrographs of the sample at various pressures during Run 1. The sample began as a 70 μm square of HOPG remained nearly rectangular at all pressures. For reference, the diameter of the culet is 300 μm.

Resistance versus pressure data for Run 1. Upon initial compression, the pressure was increased rapidly (gray circles), with little time (∼15 min) between pressure increases. The phase change was observed, indicated by the steep increase in resistance at ∼19 GPa (point A). Near the maximum pressure of 28 GPa (point B), the resistance began to increase noticeably with time, and each change in pressure (black circles) was subsequently followed by a long observation period to detect these changes. Although the curve shows a large hysteresis in the resistance on decreasing pressure, with the return transition occurring at ∼10 GPa (point D), it can be seen from the time-dependence of the resistance [Figs. 2 and 3] that the transition begins to reverse direction at point C, when the pressure was decreased back to ∼19 GPa.

Resistance versus pressure data for Run 1. Upon initial compression, the pressure was increased rapidly (gray circles), with little time (∼15 min) between pressure increases. The phase change was observed, indicated by the steep increase in resistance at ∼19 GPa (point A). Near the maximum pressure of 28 GPa (point B), the resistance began to increase noticeably with time, and each change in pressure (black circles) was subsequently followed by a long observation period to detect these changes. Although the curve shows a large hysteresis in the resistance on decreasing pressure, with the return transition occurring at ∼10 GPa (point D), it can be seen from the time-dependence of the resistance [Figs. 2 and 3] that the transition begins to reverse direction at point C, when the pressure was decreased back to ∼19 GPa.

Resistance versus time data for Run 1 during compression and decompression surrounding the highest compression point (point B) in Fig. 2. The open circles represent measurements made during the observation periods, while the black circles represent the measurements where the pressure was changed. Note the positive slope of the resistance versus time at high pressures on both compression (left of dashed line) and decompression (right of dashed line). Corresponding pressures are listed for reference.

Resistance versus time data for Run 1 during compression and decompression surrounding the highest compression point (point B) in Fig. 2. The open circles represent measurements made during the observation periods, while the black circles represent the measurements where the pressure was changed. Note the positive slope of the resistance versus time at high pressures on both compression (left of dashed line) and decompression (right of dashed line). Corresponding pressures are listed for reference.

Resistance versus time data for Run 1 during decompression near points C and D in Fig. 2. The open circles represent measurements made during the long observation periods, while the black circles represent the points where the pressure was changed. At point C, corresponding to the 19 GPa transition, the slope of the resistance versus time curve changes from zero to negative. At point D (∼10 GPa), it can be seen that the decrease in resistance over time is larger than the increase seen at each adjustment, leading to an overall decrease in the resistance versus pressure behavior. Corresponding pressures are listed for reference.

Resistance versus time data for Run 1 during decompression near points C and D in Fig. 2. The open circles represent measurements made during the long observation periods, while the black circles represent the points where the pressure was changed. At point C, corresponding to the 19 GPa transition, the slope of the resistance versus time curve changes from zero to negative. At point D (∼10 GPa), it can be seen that the decrease in resistance over time is larger than the increase seen at each adjustment, leading to an overall decrease in the resistance versus pressure behavior. Corresponding pressures are listed for reference.

Resistance versus pressure data for Run 2. Symbol notation is the same as in Fig. 2. The overall behavior was similar to that during Run 1, but several long observation periods were recorded during compression as well as decompression. Again, we observe a large resistance increase near 18-19 GPa on compression (point E), and a large hysteresis to this curve, with resistance beginning to decrease at ∼9 GPa on decompression (point H). However, we observe the change in the slope of the resistance versus time curve at points E and G [Figs. 6 and 7].

Resistance versus pressure data for Run 2. Symbol notation is the same as in Fig. 2. The overall behavior was similar to that during Run 1, but several long observation periods were recorded during compression as well as decompression. Again, we observe a large resistance increase near 18-19 GPa on compression (point E), and a large hysteresis to this curve, with resistance beginning to decrease at ∼9 GPa on decompression (point H). However, we observe the change in the slope of the resistance versus time curve at points E and G [Figs. 6 and 7].

Resistance versus time data for Run 2 during compression up to point F in Fig. 5. Gray and black circles represent resistance measurements taken during pressure adjustment and correspond to the respective points in Fig. 5. Open circles represent measurements taken during the long observation periods. During the loading phase of Run 2, the resistance decreased with pressure but remained constant with time up until the transition pressure (point E, 18-19 GPa) when the slope of the resistance versus time began to increase, at first slowly, and then quickly after each pressure adjustment. Corresponding pressures are listed for reference.

Resistance versus time data for Run 2 during compression up to point F in Fig. 5. Gray and black circles represent resistance measurements taken during pressure adjustment and correspond to the respective points in Fig. 5. Open circles represent measurements taken during the long observation periods. During the loading phase of Run 2, the resistance decreased with pressure but remained constant with time up until the transition pressure (point E, 18-19 GPa) when the slope of the resistance versus time began to increase, at first slowly, and then quickly after each pressure adjustment. Corresponding pressures are listed for reference.

Resistance versus time data for Run 2 during decompression near points G and H in Fig. 5. Symbol notation is the same as in Fig. 6. During the unloading phase of Run 2, the sample resistance exhibited nearly identical behavior to that in Fig. 4. As the transition pressure (point G, 18-16 GPa) was reached, the slope of the resistance versus pressure curve again became negative. It is possible that this transition began ∼1-2 GPa earlier, where the slope becomes flat. At point H, these resistance drops became larger than the increase seen at each adjustment, and thus the resistance drops become apparent in the overall resistance versus pressure behavior. Corresponding pressures are listed for reference.

Resistance versus time data for Run 2 during decompression near points G and H in Fig. 5. Symbol notation is the same as in Fig. 6. During the unloading phase of Run 2, the sample resistance exhibited nearly identical behavior to that in Fig. 4. As the transition pressure (point G, 18-16 GPa) was reached, the slope of the resistance versus pressure curve again became negative. It is possible that this transition began ∼1-2 GPa earlier, where the slope becomes flat. At point H, these resistance drops became larger than the increase seen at each adjustment, and thus the resistance drops become apparent in the overall resistance versus pressure behavior. Corresponding pressures are listed for reference.

Two models of gasket thickness used for resistivity calculations for measurements taken during the initial compression (Run 1). Gray symbols correspond to a model where gasket thickness changes linearly with pressure, while black symbols correspond to a model where gasket material is allowed to flow out between the culet edges and to compress with applied pressure.

Two models of gasket thickness used for resistivity calculations for measurements taken during the initial compression (Run 1). Gray symbols correspond to a model where gasket thickness changes linearly with pressure, while black symbols correspond to a model where gasket material is allowed to flow out between the culet edges and to compress with applied pressure.

Geometric factor *wt*/*l* in the resistivity calculation as calculated from the gasket-flow model for Run 1 (black symbols) and Run 2 (gray symbols). Filled symbols represent compression, while open symbols represent decompression. It can be seen that this factor is approximately the same at all pressures for both Run 1 and Run 2 and thus cannot be a factor in the overall change in resistance.

Geometric factor *wt*/*l* in the resistivity calculation as calculated from the gasket-flow model for Run 1 (black symbols) and Run 2 (gray symbols). Filled symbols represent compression, while open symbols represent decompression. It can be seen that this factor is approximately the same at all pressures for both Run 1 and Run 2 and thus cannot be a factor in the overall change in resistance.

The total eDOS as computed by GGA for graphite, lonsdaleite, diamond, bct-C_{4}, and M-carbon at 0 GPa (light gray), 15 GPa (dark gray), and 25 GPa (black). All phases of carbon except for graphite show a large band gap, yielding insulating behavior as compared to semimetallic graphite. The eDOS of all phases show little variation with pressure at least up to 25 GPa.

The total eDOS as computed by GGA for graphite, lonsdaleite, diamond, bct-C_{4}, and M-carbon at 0 GPa (light gray), 15 GPa (dark gray), and 25 GPa (black). All phases of carbon except for graphite show a large band gap, yielding insulating behavior as compared to semimetallic graphite. The eDOS of all phases show little variation with pressure at least up to 25 GPa.

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