IN32 · Read pressure in ruby light

Diamond Anvil Cell

How can we tell the pressure inside a tiny compressed sample chamber? Ruby fluorescence shifts toward red under pressure. Comparing a grain with its own ambient spectrum gives a local pressure when temperature and stress conditions match the pressure scale. Several grains reveal spatial differences that the applied load alone cannot tell us.

Illuminate five ruby grains between opposed diamonds, retain their photon spectra and infer local pressures from independently checked wavelength references.

What pressure reached the sample?

Conditional mean pressure $8.71\,\mathrm{GPa}$

Observed pressure span $0.245\,\mathrm{GPa}$

Photons in the selected spectrum $10^5\,\mathrm{count}$

Recorded grain temperature $298\,\mathrm K$

Applied load

F/\mathrm N

1400

Illuminated grain position

x/\mathrm{\mu m}

0

Drag the upper diamond to load the cell. The load–gasket relation is schematic; pressure comes from the saved spectra.

Optics, sampling and model inputs

Pressure mediumSynthetic pressure gradient amplitude

\Delta P_{\mathrm{in}}/\mathrm{GPa}

Specimen temperature input

T_{\mathrm{in}}/\mathrm K

Collection numerical aperture

\mathrm{NA}

Exposure per spectrum

\tau/\mathrm s

Synthetic gasket response

c_{\mathrm{gasket}}

Hidden generating wavelength gain

a_{\mathrm{gen}}

Hidden generating wavelength offset

b_{\mathrm{gen}}/\mathrm{nm}

Count seed

s

Independent count noise

Changing optical or wavelength hardware acquires fresh references. The inverse never reads the generating gain, offset or load–pressure relation.

Model assumptions

This is a simulated room-temperature ruby pressure measurement. The explicitly adopted Mao–Xu–Bell 1986 quasi-hydrostatic scale uses each grain’s measured ambient reference and is restricted here to zero through twenty gigapascals. Neon wavelength references and an independent argon check calibrate the spectrometer; separately acquired known-pressure observations test the pressure transfer. A synthetic load/gasket response generates the specimen interaction and never supplies pressure to the inverse. Five local ruby observations estimate spatial variation, without reconstructing an arbitrary pressure field or sample structure. The companion doublet, intrinsic Lorentzian linewidth, optical throughput and stress broadening are bounded teaching assumptions; no quantitative stress tensor or R2 pressure scale is inferred. Quantitative pressure requires a qualified quasi-hydrostatic condition and temperature matched within one kelvin of the ambient references. The temperature preset demonstrates spectral confusion and withholds pressure; a universal high-pressure thermal correction is not applied. Finite-NA refraction, Fresnel transmission, an ideal thin objective and a real dichroic/collector geometry determine the detected photon fraction. Refractive indices are assumed constant, and diffraction, polarization selection, absorption by diamond, internal spectrometer optics and laser heat transport are omitted. Local fit precision conditions on the observed wavelength calibration and line shape; it omits scale, grain, temperature, optical/model and full covariance uncertainties. A separate temperature-matching allowance is shown. Counts use Poisson or high-count rounded-Gaussian sampling with independent acquisition seeds. Complete standards, temperatures, positions, clocks, counts and settings are retained in immutable records and CSV/JSON. The gasket sector is removed only for viewing; geometry uses millimetres and photon size/speed are schematic.

Simulated photon counts · room-temperature ruby scale

Five grains test whether the pressure agrees

Inspect acquired observations

Selected grain: actual binned counts and fitted doublet

$N/\mathrm{count}$

$\lambda_{\mathrm{air}}/\mathrm{nm}$

Recorded countsBlind doublet fit

Separate local pressure estimates

$P/\mathrm{GPa}$

$x/\mathrm{\mu m}$

Counting errors only; five separate sampled positions.

Reference checks, every grain and raw channels

Bars show conditional counting standard errors. They omit pressure-scale, grain, temperature and model systematics; the five points do not reconstruct an arbitrary pressure field.

Local fits from the selected observations
$x/\mathrm{\mu m}$	$\lambda_1/\mathrm{nm}$	$P/\mathrm{GPa}$	$u_{\mathrm{count}}/\mathrm{GPa}$	$b_T/\mathrm{GPa}$

The temperature allowance is separate from counting precision. Ambient spectra belong to these same grains; independent wavelength and pressure checks remain excluded from the fitted references.

All raw channels of the selected grain
Channel	Photons	Clipped

Separate synthetic source reference

The load and gasket response generate this teaching specimen. They never enter the spectral pressure inverse. A saved JSON keeps this source description separately; the raw CSV replays without it.

Start with the essentials

Focus question: How can we tell the pressure inside a tiny compressed sample chamber?
One-sentence intuition: Use the same grain’s ambient spectrum and independent wavelength references, then compare several local readings under qualified temperature and stress conditions.

Core mathematical model

The adopted room-temperature pressure scale

P=\frac{A}{B}\left[\left(\frac{\lambda_{R_1}}{\lambda_{R_1,0}}\right)^B-1\right]

The Mao–Xu–Bell 1986 quasi-hydrostatic scale uses $A=1904,mathrm{GPa}$ and $B=7.665$ . The ambient wavelength $\lambda_{R_1,0}$ is measured for the same grain. This teaching model supports zero through twenty gigapascals and temperature matched to the reference.

A counted channel integrates part of a spectral line

\mathbb E[C_j]=b+\sum_i\frac{N_i}{\pi}\left[\tan^{-1}\!\frac{2(\lambda_{j,+}-\lambda_i)}{\Gamma_i}-\tan^{-1}\!\frac{2(\lambda_{j,-}-\lambda_i)}{\Gamma_i}\right]

Each detector channel has finite wavelength edges. Total line photons $N_i$ , center $\lambda_i$ and Lorentzian width $\Gamma_i$ are fitted to the observed counts with a baseline. Line centers are found before any pressure is assigned.

Only a finite cone reaches the receiver

n_m\sin\theta_m=\sin\theta_a,\qquad \eta_{\rm col}=\frac12\int_0^{\theta_{m,\max}}T_{md}T_{da}\sin\theta_m\,d\theta_m

Refraction through the medium and diamond sets the accepted cone. Fresnel transmission factors enter the photon fraction. The objective collimates that cone, and the dichroic redirects it onto the actual spectrometer face.

Compare the individually measured sites

\Delta P_{\rm sites}=\max_i P_i-\min_i P_i

The pressure span is computed from the five acquired spectra. A small span at those grains does not prove every part of the specimen has the same stress.

Common difficulties

External force does not determine the local pressure by itself

Typical misconceptionDividing the applied force by the diamond tip area tells the specimen pressure.

Better mental modelThe gasket supports and redistributes force. A calibrated local marker measures the enclosed conditions separately.

A redshift can have more than one cause

Typical misconceptionEvery redshift means that pressure increased.

Better mental modelTemperature and nonhydrostatic stress also change ruby spectra. A matched zero, temperature measurement and qualified pressure scale are part of the inference.

Run the experiment

01
Follow the light through the cell
Switch between the cell, ruby chamber, laser and collector views.
What to observe: The green beam crosses the upper diamond; red fluorescence returns through the same opening and reaches the spectrometer.
02
Increase the applied load
Drag the upper diamond while holding the pointer, then keep the spectra.
What to observe: The gasket gap changes and the measured doublet shifts. The local pressure is fitted from light, rather than supplied by the load control.
03
Compare five ruby grains
Choose the spatial-gradient demonstration and inspect the local-pressure plot.
What to observe: The fitted pressures differ across the chamber even though one external load is applied.
04
Test the pressure conditions
Try the rigid-medium and warm demonstrations, then open reference checks.
What to observe: Broadened lines or unmatched temperature withhold a pressure conclusion while the counted spectra remain visible.

Diamond Anvil Cell

Five grains test whether the pressure agrees

Pressure read from a tiny ruby grain

Core mathematical model

The adopted room-temperature pressure scale

A counted channel integrates part of a spectral line

Only a finite cone reaches the receiver

Compare the individually measured sites

Common difficulties

External force does not determine the local pressure by itself

A redshift can have more than one cause

Run the experiment

Follow the light through the cell

Increase the applied load

Compare five ruby grains

Test the pressure conditions

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