---
title: "Diamond Anvil Cell Interactive Lab | Sandbox Physics"
description: "How can we tell the pressure inside a tiny compressed sample chamber? Ruby fluorescence shifts toward red under pressure."
canonical_url: "https://sandboxphysics.com/labs/diamond-anvil-cell/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/diamond-anvil-cell/"
last_modified: "2026-11-04"
---

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.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

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 counts Blind 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.

Physics tutorial

## Pressure read from a tiny ruby grain

**Background** Opposed transparent diamonds compress a gasket around a small sample chamber. A ruby grain inside the chamber emits a red doublet when illuminated by green light.

**Why it matters** The force on the outside passes through diamonds, seats and a deforming gasket. A local optical gauge helps establish what reached the enclosed sample.

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 misconception** Dividing the applied force by the diamond tip area tells the specimen pressure.

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

#### A redshift can have more than one cause

**Typical misconception** Every redshift means that pressure increased.

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

### Run the experiment

1. 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.

2. 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.

3. 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.

4. 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.

Physical conclusion

A ruby spectrum gives a conditional local pressure. Temperature, nonhydrostatic stress and spatial variation must be checked before assigning one pressure to a sample.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How a diamond anvil cell reads pressure in ruby light**](https://sandboxphysics.com/stories/instruments/diamond-anvil-cell/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)