High-pressure physics — the study of matter at static or dynamic pressures orders of magnitude above atmospheric (≳ 1 GPa, with laboratory diamond-anvil cells reaching multi-Mbar, and dynamic shock or laser experiments exceeding 10¹² Pa). …
high-pressure-physics
Isothermal compressibility: κ_T = -(1/V)·(∂V/∂P)_T; ideal gas κ_T = 1/P
The isothermal compressibility κ_T = -(1/V)·(∂V/∂P)_T is the fractional volume change per unit pressure change at fixed temperature — the…
Adiabatic compression: T·V^(γ-1) = const; γ=5/3 monatomic
An adiabatic (reversible, no heat flow) compression of an ideal gas follows the Poisson adiabat P·V^γ = const, equivalently T·V^(γ-1) =…
Isothermal work: W = −n·R·T·log(V_f/V_i)
For an ideal-gas isothermal process (T fixed, heat exchanged with reservoir), the work done ON the gas is W = −∫(V_i→V_f) P dV =…
Ideal-gas compressibility pins: κ_T=1/P; κ_T(2P)/κ_T(P)=1/2
Sympy-exact witness of the ideal-gas isothermal compressibility. Setup: κ_T = 1/P (derived from PV = nRT). Identity 1 (symbolic): κ_T =…
Adiabatic halving: T_f/T_i = 2^(2/3) for γ=5/3 monatomic
Sympy-exact witness of the monatomic adiabatic halving temperature ratio. Setup: T_f/T_i = (V_i/V_f)^(γ-1) (rearranged Poisson adiabat). …
Isothermal work halving: W(V_f=V_i/2) = n·R·T·log(2)
Sympy-exact witness of the isothermal halving-compression work. Setup: W = −n·R·T·log(V_f/V_i). Identity: at V_f = V_i/2, W =…
Murnaghan EOS p(V) = (K_0/K_0')[(V_0/V)^K_0' - 1]; polynomial expansion
Murnaghan equation of state framework (Murnaghan 1944 Proc Natl Acad Sci 30, 244). Setup: assuming the bulk modulus varies linearly with…
Birch-Murnaghan 3rd-order EOS p = (3K_0/2)[f^7/3 - f^5/3][1 + (3/4)(K'-4) f^2/3]; jet expansion
Birch-Murnaghan equation of state framework (Birch 1947 Phys Rev 71, 809; 1952 J Geophys Res 57, 227). Setup: Eulerian finite-strain f =…
Bridgman bulk-modulus derivative dK/dp = K_0' (constant); root-finding via bisection
Bridgman bulk-modulus framework (Bridgman 1949 Rev Mod Phys 21, 7; The Physics of High Pressure 1931). Setup: Bridgman established by…
Theorem: p(V = V_0) = 0 (Murnaghan EOS zero-pressure reference state)
Theorem (Murnaghan-zero-pressure canonical): substituting V = V_0 into p(V) = (K_0/K_0')[(V_0/V)^{K_0'} - 1] gives p = (K_0/K_0')[1 - 1] =…
Theorem: BM3 correction factor (K_0' - 4) at K_0' = 4 vanishes (BM3 -> BM2 reduction)
Theorem (BM3-correction-vanishing canonical): the Birch-Murnaghan 3rd-order correction factor (3/4)(K_0' - 4)((V_0/V)^{2/3} - 1) vanishes…
Theorem: dK/dp - K_0' = 0 for K(p) = K_0 + K_0' p (Bridgman bulk-modulus linearity)
Theorem (Bridgman-linear-K-derivative canonical): for the Bridgman/Murnaghan linear bulk-modulus law K(p) = K_0 + K_0' p, dK/dp = K_0'…
Diamond anvil cell (Mao-Bell 1976)
H K Mao-P Bell 1976 DAC reaches >1 Mbar; modern toroidal-DAC ~700 GPa; ruby-fluorescence pressure calibration; foundation of static high-P…
Metallic H (Wigner-Huntington 1935)
Wigner-Huntington 1935 predicted; Dias-Silvera 2017 claim ~495 GPa contested; modern interest for room-T superconductivity.
H-rich superconductors (Drozdov 2015)
Drozdov-Eremets 2015 H3S Tc=203K; LaH10 Tc=260K Hemley 2019; modern high-pressure-superconductor revolution; theoretical Ashcroft 2004.
Iron phase diagram
Bridgman 1930s + Mao 1990 Earth's-core epsilon-Fe HCP > 13 GPa + 600 K; foundation of mineral-physics + Earth-core composition.
Vinet EOS (1986)
P Vinet 1986 universal-equation-of-state; modern Birch-Murnaghan competitor; routine fitting for high-P measurements.
Synchrotron-XRD high-P
APS-HPCAT + ESRF-ID27 + SPring-8 BL10XU high-P diamond-anvil-cell stations; routine kelvin-bar in-situ structure determination.
Bridgman (1946)
P Bridgman 1946 (Nobel 1946) high-pressure 100 kbar; modern diamond-anvil-cell Mao-Bell 1978 + 1 Mbar+ static-pressure modern record.
DAC (Mao-Bell 1978)
H K Mao-P Bell 1978 diamond-anvil-cell 1 Mbar; modern Dubrovinsky 600+ GPa + nano-DAC + double-stage DAC 700 GPa 2024.
Metallic H (Wigner-Huntington 1935)
E Wigner-H Huntington 1935 prediction; modern Dias-Silvera 2017 + Eremets-Drozdov 2019 superconducting-H3S 203 K disputed.
EOS (Vinet 1989)
P Vinet 1989 universal EOS; modern modern P-V-T equation-of-state DFT-fitting + planetary-interior + giant-planet-interior models.
Birch-Murnaghan (1947)
F Birch 1947 + F Murnaghan 1944 BM-EOS; modern foundational text equation-of-state mineral-physics + planetary-interior structure.
Hugoniot (Rankine 1870)
W Rankine 1870 + Hugoniot 1887 + Bethe 1942 + Walsh 1955 shock-Hugoniot; modern modern WCG NIF + Z-machine + dynamic-compression.