Determination of the Pressure Dependence of Raman Mode for an Alumina–Glass Pair in Hertzian Contact
Abstract
:1. Introduction
- The materials are homogeneous and elastic. They are considered semi-infinite;
- Their surfaces are continuous;
- Their geometries do not conform;
- The dimensions of the materials are large compared to the dimensions of the contact;
- There is no friction and no adhesive force.
- The boson peak is between 10 and 250 cm;
- The low-frequency region is between 250 and 700 cm;
- The intermediate region is between 700 and 850 cm;
- The high-frequency region is between 850 and 1300 cm.
2. Materials and Methods
- The spectra were truncated from 300 to 1300 cm;
- The cosmic peaks were eliminated;
- The signal-to-noise ratio was reduced by filtering;
- The spectra were normalised using the strongest alumina peak at 417 cm.
3. Results
3.1. Optical Measurements
3.2. Raman Measurements
3.3. Contact Radii and Pressures
3.4. Relationship between Contact Pressure and Raman Shift
4. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Band | FWHM | Intensity | Symmetry |
---|---|---|---|
(cm) | (cm) | (norm.) | or Assignment |
378 | 5.2 | 0.28 | E |
417 | 5.3 | 1 | A |
430 | 7.1 | 0.11 | E |
450 | 4.7 | 0.03 | E |
577 | 12.0 | 0.10 | E |
645 | 14.2 | 0.27 | A |
751 | 13.8 | 0.13 | E |
Band | FWHM | Intensity | Symmetry |
---|---|---|---|
(cm) | (cm) | (norm.) | or Assignment |
458 | 27.5 | 0.05 | Q - Sym. strech. |
554 | 34.5 | 0.17 | Q - Sym. strech |
600 | 82.2 | 0.20 | Q - Sym. strech |
789 | 48.0 | 0.06 | Si oscillations |
939 | 35.5 | 0.06 | Q - Si-O strech. |
991 | 68.1 | 0.15 | Q - Si-O strech. |
1096 | 97.9 | 0.70 | Q - Si-O strech. |
Contact | Radius | Max. Pressure |
---|---|---|
Number | in µm | in GPa |
1 | 47 | 0.37 ± 0.05 |
2 | 53 | 0.41 ± 0.05 |
3 | 73 | 0.57 ± 0.07 |
4 | 88 | 0.69 ± 0.08 |
5 | 97 | 0.75 ± 0.09 |
6 | 103 | 0.80 ± 0.09 |
7 | 108 | 0.84 ± 0.10 |
8 | 115 | 0.90 ± 0.10 |
9 | 122 | 0.95 ± 0.11 |
10 | 126 | 0.98 ± 0.11 |
11 | 138 | 1.07 ± 0.12 |
12 | 143 | 1.12 ± 0.12 |
13 | 151 | 1.17 ± 0.13 |
Polycrystalline Alumina | Soda–Lime Glass | |||||
---|---|---|---|---|---|---|
Contact | ||||||
Number | in cm | in µm | in GPa | in cm | in µm | in GPa |
1 | 0.31 ± 0.02 | 68.0 ± 0.5 | 0.53 ± 0.06 | - | - | - |
2 | 0.51 ± 0.02 | 77.3 ± 0.6 | 0.60 ± 0.07 | 1.20 ± 0.02 | 76.8 ± 0.9 | 0.60 ± 0.06 |
3 | 0.82 ± 0.02 | 93.5 ± 0.5 | 0.73 ± 0.08 | 2.23 ± 0.03 | 88.8 ± 0.5 | 0.69 ± 0.07 |
4 | 1.18 ± 0.02 | 116.6 ± 0.7 | 0.91 ± 0.10 | 3.03 ± 0.04 | 114.4 ± 0.7 | 0.89 ± 0.09 |
5 | 1.26 ± 0.02 | 123.4 ± 0.6 | 0.96 ± 0.10 | 3.25 ± 0.02 | 123.6 ± 0.8 | 0.96 ± 0.10 |
6 | 1.27 ± 0.02 | 125.0 ± 0.9 | 0.98 ± 0.10 | 3.17 ± 0.05 | 124.3 ± 0.9 | 0.97 ± 0.10 |
7 | 1.45 ± 0.02 | 133.5 ± 0.7 | 1.04 ± 0.11 | 3.54 ± 0.04 | 132.0 ± 0.7 | 1.03 ± 0.11 |
8 | 1.51 ± 0.02 | 142.6 ± 0.9 | 1.11 ± 0.12 | 3.46 ± 0.12 | 142.0 ± 2.0 | 1.11 ± 0.13 |
9 | 1.64 ± 0.02 | 149.4 ± 0.7 | 1.17 ± 0.12 | 3.85 ± 0.06 | 155.0 ± 0.8 | 1.21 ± 0.13 |
10 | 1.74 ± 0.03 | 157.1 ± 0.7 | 1.23 ± 0.13 | 4.27 ± 0.05 | 163.8 ± 0.7 | 1.28 ± 0.13 |
11 | 1.89 ± 0.03 | 164.4 ± 0.9 | 1.28 ± 0.14 | 4.91 ± 0.05 | 175.2 ± 0.7 | 1.37 ± 0.14 |
12 | 2.02 ± 0.03 | 173.3 ± 0.8 | 1.35 ± 0.14 | 4.97 ± 0.06 | 184.2 ± 0.8 | 1.44 ± 0.15 |
13 | 2.17 ± 0.03 | 181.0 ± 0.7 | 1.41 ± 0.15 | 4.91 ± 0.06 | 186.9 ± 0.8 | 1.46 ± 0.15 |
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Delbé, K.; De Sousa, C.; Grizet, F.; Paris, J.-Y.; Yahiaoui, M. Determination of the Pressure Dependence of Raman Mode for an Alumina–Glass Pair in Hertzian Contact. Materials 2022, 15, 8645. https://doi.org/10.3390/ma15238645
Delbé K, De Sousa C, Grizet F, Paris J-Y, Yahiaoui M. Determination of the Pressure Dependence of Raman Mode for an Alumina–Glass Pair in Hertzian Contact. Materials. 2022; 15(23):8645. https://doi.org/10.3390/ma15238645
Chicago/Turabian StyleDelbé, Karl, Cyril De Sousa, François Grizet, Jean-Yves Paris, and Malik Yahiaoui. 2022. "Determination of the Pressure Dependence of Raman Mode for an Alumina–Glass Pair in Hertzian Contact" Materials 15, no. 23: 8645. https://doi.org/10.3390/ma15238645