Ruby pressure scale

The ruby fluorescence pressure scale is an optical method to measure pressure within a sample chamber of a diamond anvil cell apparatus.^[1] Since it is an optical method, which fully make use of the transparency of diamond anvils and only requires an access to a small scale laser generator, it has become the most prevalent pressure gauge method in high pressure sciences.

Principles

Ruby is chromium-doped corundum (Al₂O₃). The Cr³⁺ in corundum's lattice forms an octahedra with surrounding oxygen ions. The octahedral crystal field together with spin-orbital interaction results in different energy levels. Once 3d electrons in Cr³⁺ are energized by lasers, the excited electrons would go to ⁴T₂ and ²T₂ levels. Later they return to ²E levels and the R₁, R₂ lines come from luminescence from ²E levels to ⁴A₂ ground level.^[2] The energy difference of ²E levels are 29 cm⁻¹, corresponding to the splitting of R₁, R₂ lines at 1.39 nm.^[2]

Development

Ruby fluorescence spectra has two strong sharp lines, R₁ and R_2. R₁ refers to the stronger intensity and lower energy (longer wavelength) excitation and is used to gauge pressure.

Pressure is calculated as: $P(Mbar)={\frac {a}{b}}[\left({\frac {\lambda }{\lambda _{0}}}\right)^{b}-1]$ , where λ₀ is the R₁ wavelength measured at 1atm, a and b are constants. (e.g. a = 19.04, b = 5^[3])

Since first demonstrated by Forman and colleagues in 1972,^[4]^[5] many scientists have contributed to the establishment of accurate ruby pressure scale in various experimental conditions.

A likely incomplete summary of is given below:


Year	First Author	a	b	Primary pressure standard used	Temperature	Pressure range	Pressure transmitting medium	References
1972	R. A. Forman	-	-, linear	Transitions of CCl₄, H₂O, C₂H₅Br, n-C₇H₁₆	Room temperature	2.2 GPa	See standards used	^[4]
1978	H. K. Mao	1904	5	Ag, Cu, Mo, Pd	Room temperature	6 - 100 GPa	M-E, H₂O	^[3]
1986	H. K. Mao	1904	7.665	Cu, Ag, Ar	Room temperature	80 GPa	Ar	^[6]
2004	A. Dewaele	1904	9.5	Al, Cu, W	Room temperature	153 GPa	Helium	^[7]
2005	A. D. Chijioke	1876(6.7)	10.71(0.14)	Au, Pt	Room temperature	150 GPa	Helium, Hydrogen, Ar	^[8]
2008	S.D Jacobsen	1904	10.32(7)	MgO	Room temperature	118 GPa	Helium	^[9]
2012	H. Yamaoka	1762*ln(λ/λ₀)		Ruby R₁	Low temperature to 16K	26 GPa	M-E, Silicone oil	^[10]
2020	G. Shen	1870	5.63(3)	MgO, Mo, Cu, Diamond	Room temperature	150 GPa	Helium	^[11]

References

^ Bassett, William A. (2009-05-21). "Diamond anvil cell, 50th birthday". High Pressure Research. 29 (2): 163–186. doi:10.1080/08957950802597239. ISSN 0895-7959. S2CID 15204168.
^ ^a ^b Syassen, K. (June 2008). "Ruby under pressure". High Pressure Research. 28 (2): 75–126. doi:10.1080/08957950802235640. ISSN 0895-7959. S2CID 95275637.
^ ^a ^b Mao, H. K.; Bell, P. M.; Shaner, J. W.; Steinberg, D. J. (June 1978). "Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby "R₁" fluorescence pressure gauge from 0.06 to 1 Mbar". Journal of Applied Physics. 49 (6): 3276–3283. doi:10.1063/1.325277. ISSN 0021-8979.
^ ^a ^b Forman, Richard A.; Piermarini, Gasper J.; Barnett, J. Dean; Block, Stanley (1972-04-21). "Pressure Measurement Made by the Utilization of Ruby Sharp-Line Luminescence". Science. 176 (4032): 284–285. doi:10.1126/science.176.4032.284. ISSN 0036-8075. PMID 17791916. S2CID 8845394.
^ Piermarini, G.J. (Nov 2011). "High pressure X-ray crystallography with the diamond cell at NIST/NBS". Journal of Research of the National Institute of Standards and Technology. 106 (6): 910–912. doi:10.6028/jres.106.045. ISSN 1044-677X. PMC 4865304. PMID 27500054. S2CID 18150811.
^ Mao, H. K.; Xu, J.; Bell, P. M. (1986). "Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions". Journal of Geophysical Research. 91 (B5): 4673. doi:10.1029/jb091ib05p04673. ISSN 0148-0227.
^ Dewaele, Agnès; Loubeyre, Paul; Mezouar, Mohamed (2004-09-22). "Equations of state of six metals above94GPa". Physical Review B. 70 (9). doi:10.1103/physrevb.70.094112. ISSN 1098-0121.
^ Chijioke, Akobuije D.; Nellis, W. J.; Soldatov, A.; Silvera, Isaac F. (Dec 2005). "The ruby pressure standard to 150GPa". Journal of Applied Physics. 98 (11): 114905. doi:10.1063/1.2135877. ISSN 0021-8979.
^ Jacobsen, S. D.; Holl, C. M.; Adams, K. A.; Fischer, R. A.; Martin, E. S.; Bina, C. R.; Lin, J.-F.; Prakapenka, V. B.; Kubo, A.; Dera, P. (2008-11-01). "Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for helium pressure media". American Mineralogist. 93 (11–12): 1823–1828. doi:10.2138/am.2008.2988. ISSN 0003-004X. S2CID 21661728.
^ Yamaoka, Hitoshi; Zekko, Yumiko; Jarrige, Ignace; Lin, Jung-Fu; Hiraoka, Nozomu; Ishii, Hirofumi; Tsuei, Ku-Ding; Mizuki, Jun'ichiro (2012-12-15). "Ruby pressure scale in a low-temperature diamond anvil cell". Journal of Applied Physics. 112 (12): 124503. doi:10.1063/1.4769305. ISSN 0021-8979.
^ Shen, Guoyin; Wang, Yanbin; Dewaele, Agnes; Wu, Christine; Fratanduono, Dayne E.; Eggert, Jon; Klotz, Stefan; Dziubek, Kamil F.; Loubeyre, Paul; Fat’yanov, Oleg V.; Asimow, Paul D. (2020-07-02). "Toward an international practical pressure scale: A proposal for an IPPS ruby gauge (IPPS-Ruby2020)". High Pressure Research. 40 (3): 299–314. doi:10.1080/08957959.2020.1791107. ISSN 0895-7959. S2CID 225460396.

[1] Bassett, William A. (2009-05-21). "Diamond anvil cell, 50th birthday". High Pressure Research. 29 (2): 163–186. doi:10.1080/08957950802597239. ISSN 0895-7959. S2CID 15204168.

[:2-2] Syassen, K. (June 2008). "Ruby under pressure". High Pressure Research. 28 (2): 75–126. doi:10.1080/08957950802235640. ISSN 0895-7959. S2CID 95275637.

[:0-3] Mao, H. K.; Bell, P. M.; Shaner, J. W.; Steinberg, D. J. (June 1978). "Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby "R₁" fluorescence pressure gauge from 0.06 to 1 Mbar". Journal of Applied Physics. 49 (6): 3276–3283. doi:10.1063/1.325277. ISSN 0021-8979.

[:1-4] Forman, Richard A.; Piermarini, Gasper J.; Barnett, J. Dean; Block, Stanley (1972-04-21). "Pressure Measurement Made by the Utilization of Ruby Sharp-Line Luminescence". Science. 176 (4032): 284–285. doi:10.1126/science.176.4032.284. ISSN 0036-8075. PMID 17791916. S2CID 8845394.

[5] Piermarini, G.J. (Nov 2011). "High pressure X-ray crystallography with the diamond cell at NIST/NBS". Journal of Research of the National Institute of Standards and Technology. 106 (6): 910–912. doi:10.6028/jres.106.045. ISSN 1044-677X. PMC 4865304. PMID 27500054. S2CID 18150811.

[6] Mao, H. K.; Xu, J.; Bell, P. M. (1986). "Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions". Journal of Geophysical Research. 91 (B5): 4673. doi:10.1029/jb091ib05p04673. ISSN 0148-0227.

[7] Dewaele, Agnès; Loubeyre, Paul; Mezouar, Mohamed (2004-09-22). "Equations of state of six metals above94GPa". Physical Review B. 70 (9). doi:10.1103/physrevb.70.094112. ISSN 1098-0121.

[8] Chijioke, Akobuije D.; Nellis, W. J.; Soldatov, A.; Silvera, Isaac F. (Dec 2005). "The ruby pressure standard to 150GPa". Journal of Applied Physics. 98 (11): 114905. doi:10.1063/1.2135877. ISSN 0021-8979.

[9] Jacobsen, S. D.; Holl, C. M.; Adams, K. A.; Fischer, R. A.; Martin, E. S.; Bina, C. R.; Lin, J.-F.; Prakapenka, V. B.; Kubo, A.; Dera, P. (2008-11-01). "Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for helium pressure media". American Mineralogist. 93 (11–12): 1823–1828. doi:10.2138/am.2008.2988. ISSN 0003-004X. S2CID 21661728.

[10] Yamaoka, Hitoshi; Zekko, Yumiko; Jarrige, Ignace; Lin, Jung-Fu; Hiraoka, Nozomu; Ishii, Hirofumi; Tsuei, Ku-Ding; Mizuki, Jun'ichiro (2012-12-15). "Ruby pressure scale in a low-temperature diamond anvil cell". Journal of Applied Physics. 112 (12): 124503. doi:10.1063/1.4769305. ISSN 0021-8979.

[11] Shen, Guoyin; Wang, Yanbin; Dewaele, Agnes; Wu, Christine; Fratanduono, Dayne E.; Eggert, Jon; Klotz, Stefan; Dziubek, Kamil F.; Loubeyre, Paul; Fat’yanov, Oleg V.; Asimow, Paul D. (2020-07-02). "Toward an international practical pressure scale: A proposal for an IPPS ruby gauge (IPPS-Ruby2020)". High Pressure Research. 40 (3): 299–314. doi:10.1080/08957959.2020.1791107. ISSN 0895-7959. S2CID 225460396.

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