Counterfeit Detection Physics: XRF Spectrometry, Ultrasonic Density, and Metallurgy

Authenticating rare historical coinage and precious metal bullion requires non-destructive scientific instrumentation capable of probing alloy stoichiometry, subsurface metallurgy, and crystal structures without damaging coin surfaces. Modern sophisticated counterfeits (using tungsten cores, transfer dies, and electroplated silver) can visually deceive expert numismatists but fail against rigorous physical diagnostic testing.

This guide details the physical principles of X-ray Fluorescence (XRF) spectrometry, Archimedes hydrostatic density testing, ultrasonic propagation velocity, and magnetic eddy current balance testing.

1. Quick-Reference: Non-Destructive Testing Methods

+-----------------------------------------------------------------------------------------+
|                               METALLURGICAL AUTHENTICATION MATRIX                       |
+-----------------------------------------------------------------------------------------+
| Diagnostic Method      | Physical Principle Tested         | Detection Specialty        |
+------------------------+-----------------------------------+----------------------------+
| XRF Spectrometry       | Characteristic X-ray emission     | Surface alloy composition  |
| Hydrostatic Density    | Archimedes buoyant force balance  | Core metal bulk density    |
| Ultrasonic Testing     | Acoustic wave velocity in solids  | Tungsten / lead sub-layers |
| Eddy Current / Sigma   | Electromagnetic electrical cond.  | Plated fake detection      |
| Precision Die Analysis | High-mag confocal laser microscopy| Cast vs struck die tooling |
+-----------------------------------------------------------------------------------------+

2. X-Ray Fluorescence (XRF) Mechanics

When a coin is irradiated with primary high-energy X-rays, inner-shell electrons are ejected. As outer-shell electrons drop into the vacancies, they emit secondary fluorescent X-rays with discrete energy peaks characteristic of specific elements (e.g., Gold $K_lpha = 68.8\, ext{keV}$ , Silver $K_lpha = 22.1\, ext{keV}$ ).

Limitation: XRF penetration depth is limited to $\sim 10 - 20\,\mu ext{m}$ , requiring complementary core-penetrating tests (ultrasonic or density) to detect gold-plated tungsten bars.

3. Ultrasonic Velocity Discrimination

Acoustic wave propagation speed $v = \sqrt{rac{E}{ ho}}$ varies drastically across precious metals and counterfeit substitutes:

Pure Gold ( $Au$ ): $v = 3,240\, ext{m/s}$
Tungsten ( $W$ ): $v = 5,220\, ext{m/s}$ (Nearly $60\%$ faster!)
Pure Silver ( $Ag$ ): $v = 3,650\, ext{m/s}$

Transmitting a $5\, ext{MHz}$ ultrasonic pulse through a bullion coin precisely measures transit time, immediately exposing core material disparities.