Calibration of a Gold-coated Quartz Crystal


This Application Note concerns the eQCM 10M™ and assumes that you have read and understand the material covered in the Application Note Basics of a Quartz Crystal Microbalance.

The purpose of this Application Note is to demonstrate a simple experiment to reduce Cu2+ onto a gold electrode and then oxidize Cu back off. We then use the result to calculate a calibration factor for the crystal. Conversely, we show you how to calculate the molar mass of the species deposited using a calibration factor.

Each crystal has a theoretical calibration factor; however, under typical experimental conditions, these calibration factors vary slightly. We use Cu2+ to calculate a calibration factor which could then be used in subsequent experiments on the same crystal.

Cu2+ is reduced in a two-electron reaction:

CuSO 4 (aq) + 2 e-   qcm pic1Cu (s) + SO 4 2- (aq)

Our goal is to reduce Cu2+ onto an gold electrode, then use the decrease in frequency and the charge passed to calculate a calibration factor.


Experiment Setup

A solution of CuSO4 (5–10 mM) in 1 M H2SO4 was prepared and placed into the PTFE cell containing a 10 MHz Au-coated quartz crystal. No air/solution interface was present in the cell. The crystal’s electroactive area was 0.209 cm2 and the area of overlap was 0.205 cm2.

The eQCM 10M™ was connected to the cell using the supplied cell cable. A Gamry Instruments Reference 600+™ potentiostat was connected to the working face of the crystal using a stacking banana plug-to-stacking pin cable. Cell setup was completed with a Pt counter electrode and an Ag|AgCl reference electrode.

Upon starting Gamry Instruments Resonator™ software, the nominal frequency of the crystal, 10 MHz, was entered in the Center Freq. field along with a Freq. Width of 50 kHz and a Freq. Step of 0.2 Hz. Clicking the Single Scan button resulted in the spectrum shown in Figure 1. Next, the green cursors that appeared on the spectrum were moved closer to the resonant frequencies and the Start button was clicked to trigger continuous data acquisition.

qcm fig1

Figure 1. Resonator screenshot after entering initial parameters and clicking Single Scan button.

The potentiostat was set up by selecting Cyclic Voltammetry from the Technique drop-down menu and clicking the Setup button. A setup screen for cyclic voltammetry appeared and parameters were entered as shown below: 

Initial E (V): 0.050
Scan Limit 1 (V): -0.250
Scan Limit 2 (V): 0.300
Final E (V): 0.050
Scan Rate (mV/s): 50
Step Size (mV): 2
Cycles (#): 5
I/E Range Mode: Fixed
Max Current (mA): 30
Sampling Mode: Surface 

After the potentiostat was set up, the OK button was clicked (which closed the setup window), followed by the Run button.

A screenshot of the potentiostat panel in Resonator during acquisition is shown in Figure 2. Note that the top plot shows both resonant frequencies for the entire time that the QCM has been acquiring data, while the bottom plot shows current and voltage data. It is also possible to show current and voltage versus time by selecting Time in the Display Graph drop-down menu.


qcm fig2

Figure 2. Screenshot of Resonator during acquisition

Data Analysis

The first plot in Echem Analyst is a plot of the change in current and frequency versus voltage (Fig. 3), and the second plot is change in frequency versus charge (Fig. 4).

qcm fig3

Figure 3. Echem Analyst showing change in current and frequency versus voltage for the five cycles.

qcm fig4

Figure 4. Echem Analyst showing change in frequency versus charge for the five cycles.

Use the Curve Selector qcm curve selector to plot data a variety of ways and also to show or hide specific curves. The deposition portion of the curve was selected by clicking on the Select Portion of the Curve using the Mouse tool button qcm mouse tool  A linear fit was then calculated by choosing the Linear Fit option under the Common Tools menu. The Quick View pane at the bottom of the window in Figure 5 gives the slope of the linear fit as 376 kHz/C.

qcm fig5

Figure 5. Echem Analyst showing the linear fit of change in frequency 
versus charge in the Quick Viewpane at the bottom of the window.

The calibration factor for the crystal is then calculated according to the equation

Calibration factor for the crystal is then calculated according to the equation


where F is the Faraday Constant, EA is the electroactive area, MMCu is the molar mass of Cu, and n is the number of electrons. The 106 is used to convert from grams to micrograms. Cis calculated to be 232 Hz cm2/µg. This is approximately 3% different than the theoretical value of 226 Hz cm2/µg.

If you already know your calibration factor accurately you can determine the molar mass of the mobile species (deposited, in this instance) during your experiment:

Use the Curve Selector to plot change in mass (∆M) versus charge as shown in Figure 6.

qcm fig6

Figure 6. Echem Analyst showing the linear fit for change in mass versus charge in the Quick View pane at the bottom of the window.

Echem Analyst uses the calibration factor entered into Resonator software, along with the electroactive area, to calculate the mass. The slope of the line, after performing a second linear fit, for the deposition is –‍347.6 µg/C. The molar mass of the Cu2+ can be calculated using the equation

The molar mass of the Cu2+ can be calculated using the equation



where F and n are as described previously. In this instance the molar mass was calculated to be 67.1 g/mol.

The purpose of this application note was to show how a calibration factor can be calculated for any given crystal. This application note also showed how to calculate the molar mass of a mobile species if the calibration factor of the crystal is known.

System Information

The eQCM 10M is shipped with the Gamry Instruments Resonator software, Gamry Echem Analyst software, a Quick Start Guide, a Hardware Operator’s Manual (CD), a Software Operator’s Manual (CD), one EQCM cell, one AC Power Adapter, one USB interface cable, one BNC cable, one potentiostat interface cable, and 5 Au-coated quartz crystals (5 MHz).

The eQCM 10M is protected by a two-year factory service warranty.

The eQCM 10M must be connected to a computer with a Gamry Instruments potentiostat and a Physical Electrochemistry software license for incorporation and combination of QCM and potentiostat data into Echem Analyst. Microsoft® Windows® 7 or higher is required.

eQCM 10M

Gamry eQCM 10M with Cables



Frequency range 1–10 MHz
Frequency resolution 0.02 Hz
Connection USB
Operating temperature range 0–45°C
Relative humidity maximum 90% non-condensing
Storage and shipping temperature –25 to 75 ° C
Weight 1 kg
Dimensions 175 × 115 × 80 mm
AC power adapter 100–264 VAC, 47–63 Hz
Quartz-crystal microbalance 12 VDC, 25 W