---
title: "Neutron Triple-Axis Spectrometer Interactive Lab | Sandbox Physics"
description: "What does a neutron’s final energy tell us about motion inside a sample? A neutron that leaves with less energy has excited motion in the sample. Scanning its energy loss reveals excitation peaks, and the energy-gain partner shows how thermal motion populates those excitations."
canonical_url: "https://sandboxphysics.com/labs/neutron-triple-axis-spectrometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/neutron-triple-axis-spectrometer/"
last_modified: "2026-10-23"
---

B-X4 · Measure energy exchange

# Neutron Triple-Axis Spectrometer

**What does a neutron’s final energy tell us about motion inside a sample?** A neutron that leaves with less energy has excited motion in the sample. Scanning its energy loss reveals excitation peaks, and the energy-gain partner shows how thermal motion populates those excitations.

Select the incident and outgoing neutron energies with two crystals. Scan energy transfer at fixed momentum transfer, record counts and fit an excitation with its thermal partner.

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

A nonrelativistic neutron beam scatters from an illustrative thermal harmonic excitation. Final energy is fixed at 14.7 millielectronvolts. Every scan point solves the momentum triangle and the Bragg angles of a schematic 3.355-angstrom monochromator and analyzer. The sample spectrum contains an elastic Gaussian and one pair of excitation lines with a fixed intrinsic standard deviation of 0.18 millielectronvolts. Gaussian energy response, the outgoing-to-incoming wavevector factor, a flat background and Poisson counts are included. The fit uses those counts and known response widths. It searches excitation energies from one to 5.5 millielectronvolts. This is an energy-only response, not a full TAS resolution volume, a material identification or a reproduction of historical measurements. Magnetic scattering, absorption, multiple scattering, phonon eigenvectors and structure refinement are omitted. Hardware lengths are schematic and increase near backscattering to keep the two crystal mounts and open apertures apart. Particle motion is a slowed illustration; the spectra come from the recorded count model.

Turn the energy-transfer probe$\varepsilon/\mathrm{meV}$ $3$

Drag the gold analyzer handle or move the transfer below. Both energy selectors stay connected to the sample.

Neutron energies

$\begin{aligned}E_i&=17.7\,\mathrm{meV}\\E_f&=14.7\,\mathrm{meV}\\Q&=2.00\,\mathring{\mathrm A}^{-1}\end{aligned}$

Crystal and sample angles

$\begin{aligned}\alpha&=41.6^\circ\\\theta_M&=18.7^\circ\\\theta_A&=20.6^\circ\end{aligned}$

Arm lengths are schematic; rotation angles follow the scattering geometry.

Apparatus scale and particle motion

Arm directions and crystal planes follow the solved Bragg geometry. Hardware lengths and moving particles are schematic. The spectrum stays in the data row below.

Measurement sequence

## Scan the energy. Find the excitation.

One hundred sixty-one energy settings follow the same fixed momentum transfer. Each count keeps its own solved scattering geometry.

1. 01 Set the instrument
2. 02 Record the scan
3. 03 Infer from counts

Ready. Choose a setup, then start the scan.

Start a scan to record counts. The spectrum will appear here as measurements arrive.

Recorded counts

### Neutron energy transfer

No acquisition yet

$\varepsilon/\mathrm{meV},\quad N_{\rm bin}$

Click to move the instrument probe. Teal dots: counts. Purple: fit. Gold dashed: separate generating mean.

Estimated from the stored scan

### The sample’s excitation

Fitted energy and local counting error

$\text{—}$

Thermal gain/loss area ratio

$\text{—}$

Fit residual RMS

$\text{—}$

A result appears after acquisition and analysis.

Test the measurement model

### What remains after fitting?

$\varepsilon/\mathrm{meV},\quad N-\widehat N$

Residuals use the same retained counts. The fit assumes a known Gaussian energy response.

Known instrument response

### Peak width needs a resolution scale

$\delta E/\mathrm{meV},\quad R/R_{\max}$

Purple: fixed intrinsic profile. Gold: instrument-broadened profile. These are known response shapes, not acquired counts.

$\sigma_{\rm int}=0.18\,\mathrm{meV}$

The response width and the fixed intrinsic width combine before counts are generated. A broad, overlapping thermal pair can still give a visible peak while leaving temperature unresolved.

The thermal comparison uses integrated peak areas with the wavevector factor removed. No calibration or model uncertainty is included in the local counting errors.

Read the original experiment

[Historical evidence and the limits of this model](https://sandboxphysics.com/stories/probe-evidence/neutrons-structure-and-motion/) [Brockhouse’s Nobel lecture](https://www.nobelprize.org/uploads/2018/06/brockhouse-lecture.pdf)

## Read the experimental evidence

The simulation uses the assumptions stated above. Read how the historical apparatus measured the effect, what its records supported, and where the interpretation was limited.

[Neutrons reveal structure and motion](https://sandboxphysics.com/stories/probe-evidence/neutrons-structure-and-motion/) [All six reading paths](https://sandboxphysics.com/stories/probe-evidence/)

Physics tutorial

## Neutron Triple-Axis Spectrometer

**Background** Select the incident and outgoing neutron energies with two crystals. Scan energy transfer at fixed momentum transfer, record counts and fit an excitation with its thermal partner.

**Why it matters** Diffraction tells us about spatial order. Selecting the outgoing energy also reveals excitations that carry energy inside the sample.

Start with the essentials

- **Focus question**: What does a neutron’s final energy tell us about motion inside a sample?
- **One-sentence intuition**: The energy the neutron loses is the energy the sample gains.

### Core mathematical model

#### Energy and momentum given to the sample

$$
\mathbf Q=\mathbf k_i-\mathbf k_f,\qquad\varepsilon=E_i-E_f,\qquad E=\frac{\hbar^2k^2}{2m_n}
$$

Positive energy transfer excites the sample. Wavevectors use radians per angstrom, so the wavelength is a full turn divided by the wavevector magnitude.

#### The scattering triangle must close

$$
\cos\alpha=\frac{k_i^2+k_f^2-Q^2}{2k_i k_f},\qquad2d\sin\theta_B=\lambda
$$

The sample scattering angle is the full angle between the two beams. Each crystal uses its own Bragg half-angle to select energy.

#### Thermal occupation sets the two integrated areas

$$
\frac{A_{\rm gain}}{A_{\rm loss}}=e^{-\varepsilon_0/(k_B T)}
$$

The fitted amplitudes correct the final-to-incident wavevector factor. This relation uses integrated lines, not the two raw peak heights.

### Common difficulties

#### A reconstructed result depends on the measurement model

**Typical misconception** The width of the measured peak is the sample’s intrinsic width.

**Better mental model** The instrument response also broadens the spectrum. The fit here uses a known Gaussian energy response and a fixed intrinsic width.

### Run the experiment

1. 01

   #### Follow both energy selectors

   Move the energy-transfer probe and inspect the source and collector views.

   **What to observe:** The monochromator changes incident energy; the analyzer keeps final energy fixed. The sample arm moves to keep momentum transfer fixed.

2. 02

   #### Measure the thermal pair

   Acquire and analyze Resolved excitation. Then compare Cool the sample.

   **What to observe:** Cooling suppresses the energy-gain line because fewer excitations are already present.

3. 03

   #### Test the geometry

   Choose Unreachable transfer and try to acquire.

   **What to observe:** The scan stops when part of the chosen momentum and energy transfer cannot form a scattering triangle.

Physical conclusion

A nonrelativistic neutron beam scatters from an illustrative thermal harmonic excitation. Final energy is fixed at 14.7 millielectronvolts. Every scan point solves the momentum triangle and the Bragg angles of a schematic 3.355-angstrom monochromator and analyzer. The sample spectrum contains an elastic Gaussian and one pair of excitation lines with a fixed intrinsic standard deviation of 0.18 millielectronvolts. Gaussian energy response, the outgoing-to-incoming wavevector factor, a flat background and Poisson counts are included. The fit uses those counts and known response widths. It searches excitation energies from one to 5.5 millielectronvolts. This is an energy-only response, not a full TAS resolution volume, a material identification or a reproduction of historical measurements. Magnetic scattering, absorption, multiple scattering, phonon eigenvectors and structure refinement are omitted. Hardware lengths are schematic and increase near backscattering to keep the two crystal mounts and open apertures apart. Particle motion is a slowed illustration; the spectra come from the recorded count model.

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)