---
title: "Atomic Stick-Slip: How an AFM Tip Feels Friction Interactive Lab | Sandbox Physics"
description: "Why does a tip dragged across a crystal move in jumps? Because the spring holding the tip is too soft to stop it catching in the hollows between atoms."
canonical_url: "https://sandboxphysics.com/labs/afm-stick-slip-friction/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/afm-stick-slip-friction/"
last_modified: "2026-10-31"
---

FR40 · Prandtl–Tomlinson model

# Atomic Stick-Slip: How an AFM Tip Feels Friction

**Why does a tip dragged across a crystal move in jumps?** Because the spring holding the tip is too soft to stop it catching in the hollows between atoms. The tip waits in one hollow while the spring stretches, then the hollow vanishes and it falls into the next. The energy released in each fall becomes heat, and that heat per atom spacing is the friction. With the parameters fitted to salt, the slow, cold tip slips at about 0.68 nN and averages 0.53 nN.

Drag a spring-held tip across a salt crystal and watch it stick, then jump one atom ahead. The sawtooth force and the heat each jump leaves are the friction.

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

Model assumptions

The tip is the one-dimensional Prandtl–Tomlinson model: a point mass on a spring above a sinusoidal substrate potential, with Langevin damping and thermal noise. The default parameters are those Sang, Dubé and Grant (2001) chose to match NaCl measurements: lattice period 0.4 nm, corrugation 0.27 eV, spring 0.93 N/m, mass 8.7e-12 kg and damping 8.9e5 1/s. Wear, contact-area changes, the second lateral direction and the elasticity of the cantilever beyond one spring are left out. The motion on screen is slowed by about eight orders of magnitude.

Energy the tip feels now

Lateral force: the sawtooth

Where the work goes

Physics tutorial

## Friction one atom at a time

**Background** An atomic force microscope drags a sharp tip across a surface while a soft cantilever holds it. On a clean crystal the measured lateral force is not steady. It rises slowly, drops suddenly, and repeats with the spacing of the surface atoms. That sawtooth is friction seen at its smallest scale.

**Why it matters** The Prandtl–Tomlinson model explains the sawtooth with only a spring and a wavy potential. It says when a tip sticks, how much force it needs before it jumps, and where the work done by the scanner goes. It is the starting point for almost every later model of atomic friction.

Start with the essentials

- **Focus question**: Why does a tip dragged across a crystal move in jumps?
- **One-sentence intuition**: While the spring is soft compared with the curvature of the substrate potential, the tip has more than one place to rest. It stays in its well while the spring stretches, until that well disappears and the tip falls into the next one. The energy released in the fall turns into heat, and that heat per period, divided by the lattice period, is the friction force.

### Core mathematical model

#### Energy of the tip

$$
E(x;X)=-U_0\cos\frac{2\pi x}{a}+\frac{k}{2}(x-X)^{2}
$$

The tip at $x$ feels the substrate with amplitude $U_0$ and period $a$, and a spring of stiffness $k$ ties it to the scanner at $X$. This is Eq. 1 of Sang, Dubé and Grant (2001).

#### When the tip can stick

$$
\eta=\frac{4\pi^{2}U_0}{k a^{2}}>1
$$

With $U_0=0.27\,\mathrm{eV}$, $k=0.93\,\mathrm{N\,m^{-1}}$ and $a=0.4\,\mathrm{nm}$ the value is $\eta=11.5$. Below 1 the energy has a single minimum for every scanner position, so the tip follows smoothly and the zero-temperature friction vanishes.

#### Friction from the energy ledger

$$
\langle F\rangle=\frac{Q_{\text{period}}}{a}
$$

Over many periods the spring and the tip return to the same state, so all work done by the scanner leaves as heat $Q_{\text{period}}$. At room temperature and $100\,\mathrm{nm\,s^{-1}}$ the simulated tip gives $0.324\,\mathrm{nN}$, so each period leaves about $0.81\,\mathrm{eV}$.

### Common difficulties

#### The jump is the friction

**Typical misconception** Friction is the force the tip feels while it rubs against each atom.

**Better mental model** The substrate force averages to zero over a period. What remains is the energy that the slip releases and the damping removes; without slips, a slowly dragged tip returns all the work it receives.

#### Heat makes friction larger

**Typical misconception** A warmer tip should rub harder.

**Better mental model** Thermal kicks let the tip hop over the barrier before the well vanishes, so it slips at a smaller force. In this model room temperature lowers the friction from 0.53 nN to about 0.32 nN at 100 nm/s.

### Run the experiment

1. 01

   #### Watch one slip

   Choose Cold tip slips at the fold and watch the force chart and the energy chart together.

   **What to observe:** The force climbs to about 0.68 nN, the barrier ahead shrinks to zero, and the tip falls one lattice period. The mean force is about 0.53 nN, on the $T=0$ reference.

2. 02

   #### Predict, then soften the substrate

   Guess what happens when $\eta$ drops below 1, then choose Smooth sliding.

   **What to observe:** At 0.02 eV, $\eta=0.85$: the sawtooth disappears, the tip follows the scanner and the mean friction falls to almost nothing.

3. 03

   #### Explain longer jumps

   Choose Long slips, where the damping is ten times lighter, and read the slip length.

   **What to observe:** The tip overshoots and lands two wells ahead. Because it releases less energy per period, the mean friction drops to about 0.37 nN.

Physical conclusion

Atomic friction appears when the spring is soft enough for the tip to stick. The work stored in the spring is released in a sudden slip and lost as heat, and the mean force is that heat divided by the lattice period.

## Related experiments and articles

Nanofriction · Reading path

### From one sticking tip to a twisted flake that glides

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

1. [Article **How large friction is at a single atomic contact**](https://sandboxphysics.com/stories/nanofriction/friction-at-a-single-contact/)
2. [Article **How the Tomlinson model explains stick-slip**](https://sandboxphysics.com/stories/nanofriction/stick-slip-and-the-tomlinson-model/)
3. [Article **Friction as the energy lost in each slip**](https://sandboxphysics.com/stories/nanofriction/where-the-work-goes/)
4. [Article **Thermolubricity and the limits of rate theory**](https://sandboxphysics.com/stories/nanofriction/thermolubricity-and-the-limits-of-rate-theory/)
5. [Lab **Thermal Friction: Why Faster Scans Rub Harder** Raise the damping and see when rate theory is accurate](https://sandboxphysics.com/labs/thermal-friction-velocity-scan/)
6. [Article **Reading the 2013 friction-modelling review by Vanossi and co-workers, section by section**](https://sandboxphysics.com/stories/nanofriction/reading-vanossi-2013/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

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