Physic Labs

Frontier physics

Materials physics

Observe a three-dimensional crystal lattice with a vacancy, then measure linear elastic response to connect microscopic structure to a mechanical property. Verify the proportionality σ≈Eε\sigma \approx E\varepsilon by varying strain and relative modulus.

Research

Equipment

  • Rotatable 3D crystal-lattice canvas (drag or arrow keys)
  • Sliders for lattice constant and defect position
  • Virtual tensile tester: strain ε and relative-modulus E sliders
  • Stress–strain plot and σ≈Eε readout

Procedure

  1. Rotate the lattice and vary the lattice constant

    Drag the section-1 canvas to rotate the 3×3×3 lattice; use the “Lattice constant” slider to widen or tighten node spacing and watch atomic density change. Read the value beside the slider.

  2. Insert a vacancy into the lattice

    Move the “Defect position” slider through values 0–26 to choose the missing node; a dashed ring marks the vacant site. Note that a single vacancy breaks the lattice's perfect translational symmetry — the basis for defect scattering of electrons or phonons in real materials.

  3. Measure the linear elastic response

    In section 2, hold the “Relative modulus E” slider fixed, raise “Strain ε” through several values, and read the relative stress in the readout under the plot. Check that the point on the line satisfies σ≈Eε\sigma \approx E\varepsilon: multiply ε by E and compare with the σ reading.

  4. Change the modulus and conclude

    Hold ε fixed, switch E between two values, and watch the slope of the σ–ε line and the readout. Conclude: for the same strain, a stiffer material (larger E) bears more stress via σ≈Eε\sigma \approx E\varepsilon; the model holds only in the linear elastic regime, while real materials also depend on the defects and microstructure seen in section 1.

Simulation

Experiment history

In 1807 Thomas Young introduced the elastic modulus linking stress and strain in the linear regime, the basis of the proportional form σ=Eε\sigma = E\varepsilon. In the mid-19th century Auguste Bravais classified the 14 crystal lattices in three dimensions, tying crystal symmetry to geometry. In 1912 Max von Laue showed that crystals diffract X-rays, and William Henry Bragg with his son William Lawrence Bragg quickly turned the effect into a tool for measuring atomic structure; they shared the 1915 Nobel Prize. From then on, materials physics became quantitative: diffraction to determine structure, mechanical–thermal–electrical tests for response, and microscopic models such as band theory and lattice vibrations to connect the two.

Related physicists

Marie CurieWilliam Thomson (Lord Kelvin)Thomas YoungWilliam Henry BraggWilliam Lawrence Bragg

Related library topics

Materials physics