§1 — The two ruby lines R1 and R2
Ruby (Cr³⁺:Al₂O₃) emits two sharp fluorescence lines from the same ²E → ⁴A₂ transition of Cr³⁺: R1 (694.25 nm at 300 K, P = 0) and R2 (692.86 nm). They correspond to two sub-levels of the ²E state, split by the trigonal crystal field of corundum. At ambient conditions the separation is: R1 − R2 = 1.39 nm = 29 cm⁻¹ (300 K, P = 0) Under purely hydrostatic compression this splitting stays close to its ambient value; an excess splitting is the signature of deviatoric (non-hydrostatic) stress.

§2 — Deviatoric (non-hydrostatic) stress
In an ideal DAC experiment, pressure is hydrostatic — equal in all directions. Once the pressure-transmitting medium (PTM) solidifies it can no longer flow and redistribute stresses, and the sample experiences an asymmetric stress tensor. The uniaxial (deviatoric) component is defined as: t = σ₃ − σ₁ where σ₃ is the maximum (axial) stress along the compression axis and σ₁ the minimum (radial) stress. This non-hydrostatic component is the central problem in all precision high-pressure measurements.

§3 — Why it biases EOS measurements (Dewaele & Loubeyre 2007)
In conventional X-ray diffraction geometry the Bragg planes probed lie roughly perpendicular to the compression axis — i.e. under the minimum stress σ₁ — so the measured d-spacing corresponds to an overestimated cell volume, and the pressure deduced from an equation of state is systematically underestimated when deviatoric stress is present. Dewaele & Loubeyre (2007, HPR 27:419) quantified this in helium, the best available PTM: the macroscopic non-hydrostatic stress reaches 0.3–0.5 GPa at 150 GPa while the sample stays embedded in the medium — negligible for most samples, but enough to bias sensitive EOS parameters such as K′₀ of gold.

§4 — How R1 and R2 diagnose it (Chai & Brown 1996)
Chai & Brown (1996, GRL 23:3539) studied ruby single crystals under controlled deviatoric stress at high confining pressure in a DAC. Two key results:
· The R2 line is nearly insensitive to deviatoric stress and represents the local mean stress (pressure) — so P(R2) is the most reliable pressure once the PTM has solidified, while R1 shifts significantly.
· For loading along the c-axis, the R1−R2 splitting varies linearly with deviatoric stress at a rate of −0.241 Å/GPa (= 0.0241 nm/GPa), independent of the confining pressure (it increases non-linearly for a-axis loading).
This is the coefficient BETSA Wave Fit uses to convert excess splitting into an order-of-magnitude deviatoric stress (§7).

§5 — The splitting as an indicator, and its limits (Klotz et al. 2009)
Klotz et al. (2009, J. Phys. D 42:075413) measured R1 linewidth and R1−R2 splitting for 11 PTMs using multiple ruby beads:
· For alcohol mixtures and Daphne oils, linewidth and splitting are reliable indicators of solidification.
· For noble gases (Ar, N₂, Ne, He) they can be misleading: in argon the splitting minimum sits near 12 GPa, yet pressure gradients are already detectable at ~2 GPa; in nitrogen the R1 width suggests hydrostaticity to ~10 GPa while single-crystal diffraction sees gradients at 2.4 GPa (Angel et al. 2007).
· The most sensitive, PTM-independent indicator is the standard deviation σ of pressure across several ruby beads: σ = 0 under perfectly hydrostatic conditions and rises sharply at solidification. With 5–10 BETSA beads, gradients of ±0.015 GPa (150 bar) are resolvable. For a single ruby, the R1 linewidth is a more reliable indicator than the splitting (Bell & Mao 1986).

§6 — Bridging
A splitting much larger than 1.39 nm signals either onset of deviatoric stress (PTM solidified), or — more seriously — bridging: the ruby bead being squeezed directly between the two anvil culets, which completely invalidates the pressure reading. Bridging typically appears above ~80–100 GPa as the anvil gap narrows to a few micrometres (Dewaele & Loubeyre 2007). The most sensitive warning remains σ across multiple beads.

§7 — Practical use in BETSA Wave Fit
Enter λ R1 and λ R2 for each bead. The tool computes:
· P(R1) and P(R2) (Dewaele 2008 calibration) — P(R2) is the recommended pressure under non-hydrostatic conditions.
· Splitting R1−R2 and ΔSplitting = measured − 1.39 nm (excess over the ambient value).
· σ deviatoric (c-axis estimate) = |ΔSplitting| / 0.0241 nm/GPa (Chai & Brown). This single-crystal c-axis coefficient gives an order-of-magnitude value; for randomly-oriented powder beads the σ across multiple beads (P Map tab) is the more robust measure.

Key references
Piermarini, Block & Barnett (1973) J. Appl. Phys. 44:5377 — Hydrostatic limits of liquids and solids to 100 kbar
Chai & Brown (1996) GRL 23:3539 — R2 insensitive to deviatoric stress; R1−R2 splitting = 0.241 Å/GPa (c-axis)
Dewaele & Loubeyre (2007) HPR 27:419 — Non-hydrostatic stress in helium (0.3–0.5 GPa at 150 GPa); bridging
Klotz, Chervin, Munsch & Le Marchand (2009) J. Phys. D 42:075413 — Hydrostatic limits of 11 PTMs; σ across beads the most sensitive indicator
Hilberer, Loubeyre et al. (2026) Nat. Commun. 17 — Spectroscopic limits of diamond anvils to 520 GPa; deviatoric ratio measured by NV / optical spectroscopy