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Electron gun
Higher voltage means faster electrons and a shorter wavelength.
Detector
Swing the Faraday cup around the crystal.
Crystal material
Each metal has its own row spacing.
Crystal and conditions
More rows give sharper peaks; heat blurs them.
Voltage scan
Repeat the 1927 measurement: sweep the voltage at a fixed detector angle.
Layers
Model checks
The science
Electrons behave as waves
De Broglie (1924) proposed that a particle of momentum p has the wavelength λ = h / p. For electrons accelerated through a potential difference V the kinetic energy is e V, so
At 54 V this is 0.167 nm, about the spacing between atoms in a crystal, which is why a crystal can act as a diffraction grating for electrons. In 1927 Davisson and Germer saw a strong peak in the electrons scattered from a nickel crystal at 54 V and a detector angle of 50 degrees, which matched the wave prediction.
Surface rows as a grating
Low-energy electrons penetrate only a few atomic layers, so the (111) face of the crystal acts as a reflection grating made of parallel atomic rows a distance D apart. For a beam hitting the face at normal incidence, neighbouring rows scatter in phase when the path difference is a whole number of wavelengths:
With N rows contributing the pattern is the N-slit function [sin(Nδ/2) / (N sin(δ/2))]² with δ = 2π D sinθ / λ, so more rows give sharper peaks. The simulation multiplies it by a Debye-Waller factor exp(-K² <u²>) (thermal motion of the atoms, K = 4π sin(θ/2)/λ), an angular factor (1 + cos²θ)/2 and a flat inelastic background.
A hexagonal surface net produces six first-order spots around the beam; the fcc stacking below makes alternate spots weaker, which gives the three-fold symmetry the experiment found when the crystal was turned.
Honest simplifications
This is a kinematic model: single scattering from one layer, no multiple scattering, no inner-potential refraction, no electron spin and no layer-to-layer interference. The real 1927 peak sat at 54 V and 50 degrees; the model gives 55.4 V for exactly 50 degrees with D = 0.215 nm. The collector signal is in relative units, not amperes. The incoming and outgoing wave fronts in the pictures are drawn to scale in wavelength but not in size of the apparatus.
What to try
- Press Run the voltage scan at 50 degrees and watch a single peak build up near 55 V, as in the famous 1927 curve.
- Raise the voltage to 120 V and follow the diffraction ring to a smaller angle; at a fixed angle the peak voltage follows
V = (1.2264 n / D sinθ)². - Change the number of rows N and see the lobes narrow; heat the crystal to 900 K and see the peak fade.
- Turn the detector azimuth: strong and weak spots alternate every 60 degrees.
- Choose a larger spacing (aluminium or gold) and see the first order move to a smaller angle.