---
title: "Quartz Crystal Microbalance Interactive Lab | Sandbox Physics"
description: "When does a crystal frequency drop really measure added mass? A thin rigid coating moves with the quartz and adds inertia, lowering its shear resonance."
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  zh-CN: "https://sandboxphysics.com/zh/labs/quartz-crystal-microbalance/"
last_modified: "2026-11-03"
---

IN16 · A thin film slows a shear wave

# Quartz Crystal Microbalance

**When does a crystal frequency drop really measure added mass?** A thin rigid coating moves with the quartz and adds inertia, lowering its shear resonance. A compatible blank removes baseline drift before converting that shift to mass per area. Liquid drag and compliant attachment also change frequency and loss, so frequency alone cannot identify dry mass.

Coat a quartz crystal and compare dry, liquid and compliant loads. Fit saved current sweeps before converting a compatible frequency shift to areal mass.

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

Drag the gold drive dial to preview ideal crystal motion and current. Save a sweep to compare calibrated ADC observations with clean temperature blanks.

Surface medium Uniform film areal mass$2$ Equilibrated temperature$20$ Drive offset from 5 MHz$-110$

Three dry blanks and a coated sweep are loaded.

Liquid, attachment, receiver and sweep

Film attachment model Liquid density / kg per cubic metre$998.2$ Liquid viscosity / mPa s$1.002$ Net parallel capacitance / pF$20$ Sweep half span / Hz$2500$ Current noise / microamp RMS per component$0.02$ Bipolar ADC current range / mA$1$ Random seed$189$

Blank acquisition prepares a clean dry crystal at 15, 25 and 35 degrees Celsius, then restores the sample setup. It assumes repeatable cleaning and unchanged electrodes. No thermal transient or deposition kinetics is simulated.

Model assumptions

Fundamental-only 5 MHz thickness-shear teaching resonator. Complex-current ADC sweeps use a BVD circuit with a prescribed motional capacitance; fitted frequency, half-width and shunt capacitance come from raw samples. Independent current, frequency and temperature standards and three dry temperature blanks are saved. Uniform thin rigid gas-phase films use the small-load Sauerbrey relation. One-face semi-infinite Newtonian liquid loading and a passive lumped compliant attachment are counterexamples; this dry-mass estimator withholds mass in those conditions. Suitable liquid QCM experiments can still measure mass with additional assumptions and matched references. No multimode, finite-thickness viscoelastic inversion, distributed sensitivity, thermal transients or commercial accuracy is claimed. Shear displacement, quartz thickness and film thickness are explicitly enlarged; plots remain outside the apparatus.

Simulated complex-current ADC observations

## Fit the peak before assigning a mass

Saved sweep

Shift from dry temperature blank $-113\,\mathrm{Hz}$

Fitted half-width $25.9\,\mathrm{Hz}$

Dissipation factor $1.04\times10^{-5}$

Conditional dry areal mass $2.00\,\mathrm{\mu g/cm^2}$

Blank, receiver calibration and fit quality

The ADC stores two RMS-current components at each indicated frequency. Independent current standards set the complex scale and offset; known frequency and temperature references set their scales. Three clean dry sweeps remove the assumed quadratic temperature drift only between their measured temperatures. New controls or standards do not replace those inside an earlier scan. The active uniform-weight area is 0.20 square centimetres; total mass additionally uses this assumed area. No statistical confidence interval or commercial uncertainty is claimed.

$$
Y(\omega)=i\omega C_0+\frac{1}{R_m+i(\omega L_m-1/(\omega C_m))}
$$

Mechanical model, visual scales and limits

Fundamental-only small loading of a 5 MHz AT-cut thickness-shear plate. A uniform rigid gas-phase coating uses Sauerbrey; a one-face Newtonian liquid adds frequency shift and damping. This dry-mass estimator withholds a mass for liquid or compliant loading. Other liquid-QCM protocols can measure rigid increments with a matched liquid reference and additional assumptions. The compliant case is a passive lumped mass connected by a spring and dashpot, not a finite-thickness viscoelastic-film inversion. No film modulus or liquid density and viscosity pair is uniquely inferred.

Shear displacement is enlarged one million times, quartz thickness 12 times and film thickness 50,000 times. Motion is replayed at 0.65 cycles/s. Fluid tracer height is enlarged 5,000 times to reveal the model Stokes penetration; the bulk liquid dome is schematic. Gold electrode thickness and mounting hardware are schematic. Actual thin-film and seal deformations, spatial sensitivity weighting, nonlinear piezoelectric response, liquid conductivity, surface roughness and thermal transients are omitted. Temperature affects the chosen quartz baseline only; liquid viscosity and density are independent inputs at that temperature.

$$
\Delta f=-\frac{2f_0^2m_A}{\sqrt{\rho_q\mu_q}},\qquad \Gamma=\frac{R_m}{4\pi L_m}
$$

[SRS QCM200 manual Rev. 2.5 (6/2018), pp. 15–16, 27–30, 35–37, 42, 49–55](https://www.thinksrs.com/downloads/pdfs/manuals/QCM200m.pdf)

Physics tutorial

## The surface drags its load sideways

**Background** Voltage across the electrodes drives opposite sideways motion at the two quartz faces. A rigid film follows the surface; liquid also draws energy from that motion.

**Why it matters** A frequency counter is very sensitive, but a downward shift can have several physical causes.

Start with the essentials

- **Focus question**: When does a crystal frequency drop really measure added mass?
- **One-sentence intuition**: A mass estimate needs a suitable load model, a compatible blank and a resonance fitted from observations.

### Core mathematical model

#### Thin rigid film at the fundamental

$$
\Delta f=-\frac{2f_0^2}{\sqrt{\rho_q\mu_q}}m_A
$$

A uniform, acoustically thin and rigidly coupled gas-phase coating gives a frequency shift proportional to mass per area. Quartz density and shear modulus set the sensitivity.

#### The electrical resonance has two paths

$$
Y(\omega)=i\omega C_0+\frac{1}{R_m+i(\omega L_m-1/(\omega C_m))}
$$

Current can charge the parallel capacitance or drive the motional branch. Fitting both complex components separates the shunt from the series resonance.

#### Half-width and dissipation convention

$$
\Gamma=\frac{R_m}{4\pi L_m},\qquad D=\frac{2\Gamma}{f_s}
$$

Gamma is half the full conductance half-power bandwidth. Dissipation is the inverse resonant quality factor in this underdamped BVD model.

### Common difficulties

#### A lower frequency means more mass

**Typical misconception** Any downward frequency shift can be converted with the same sensitivity.

**Better mental model** Liquid drag, compliant motion and temperature also shift resonance. The sample model and blank must support a mass conversion.

#### The highest total current locates the mechanical resonance

**Typical misconception** Pick the maximum magnitude of total admittance.

**Better mental model** Parallel capacitance changes that magnitude. Fit complex current with its shunt path to locate the series resonance.

### Run the experiment

1. 01

   #### Drag the actual frequency dial

   Drag the source knob across the resonance.

   **What to observe:** The drive frequency changes immediately. Shear amplitude and current respond to the same BVD circuit.

2. 02

   #### Save a coated scan

   Compare Rigid film and More rigid film.

   **What to observe:** A stronger uniform inertial load shifts the fitted center downward while keeping the small-loss width nearly unchanged.

3. 03

   #### Add liquid without adding a film

   Choose Bare water, then More viscous liquid.

   **What to observe:** Both center and linewidth change. This dry-mass estimator retains those observations and withholds a mass value.

4. 04

   #### Check a compliant connection

   Choose A slipping attachment.

   **What to observe:** A spring-dashpot attachment changes how much of the film follows the quartz and dissipates energy. One frequency/width pair does not determine all film properties.

5. 05

   #### Keep the temperature reference

   Acquire a known-standard set and clean dry temperature blanks, then save the sample.

   **What to observe:** Each scan retains its original standards. The three blank temperatures remove the declared quadratic drift within their covered interval.

Physical conclusion

Read frequency and loss together before deciding what the surface acquired.

## 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 **When a slower quartz crystal can measure added mass**](https://sandboxphysics.com/stories/instruments/quartz-microbalance/)

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)