Equation Of State And Strength Properties Of Selected -

Deep beneath the surface of the Earth, or in the heart of a distant gas giant, the rules of everyday physics start to bend. To understand how materials behave when they are squeezed by millions of atmospheres of pressure, scientists rely on two main pillars: the Equation of State (EOS) Strength Properties The Squeeze: Equation of State

Findings: Copper exhibits quasi-linear ( U_s-u_p ) relation up to ~200 GPa. Above 100 GPa, electronic contributions alter γ. Strength increases modestly with pressure; thermal softening dominates above 800 K.

where ( \gamma(V) = V \left(\frac\partial P\partial E\right)_V ) is the Grüneisen parameter, often assumed ( \gamma(V) = \gamma_0 (V/V_0)^q ). For metals, ( q \approx 1 ) (Slater model). Limitations: fails near melt or phase transitions. equation of state and strength properties of selected

3.3 Alumina (Al₂O₃, Sapphire) – Ceramic Armor & Window Material

• EOS: ( K_0 = 252 \text GPa ), ( K_0' = 4.0 ), ( \rho_0 = 3.98 \text g/cm^3 )
• Strength: Extremely high HEL (~15–20 GPa) but rapid loss of strength post-yield due to microcracking. Spall strength ~5–8 GPa.
• Key finding: The EOS is well-behaved under hydrostatic loading, but deviatoric response shows strong anisotropy due to hexagonal crystal structure.

4.2 Diamond Anvil Cells (DAC) with Synchrotron X‑ray

• Static compression to >300 GPa + laser heating
• Radial X‑ray diffraction – Measures lattice strains → differential stress (strength).
• Result for Fe: EOS from volume; strength from peak broadening. Allows geodynamic modeling of Earth’s inner core.

Example: Tantalum under shock loading (30 GPa peak pressure)

• EOS predicts density increase of ~8% and temperature rise of ~250 K.
• Strength model predicts deviatoric stress of ~0.8 GPa at peak, decaying post-shock due to thermal softening.