phenomenon

pressure induced phase transition

Pressure causes materials to change their ordered states, such as superconductivity or magnetic patterns.
43 related articles · 6 formulas

Description

Pressure-induced phase transitions occur when applying high pressure rearranges a material's atomic or electronic structure, leading to new states of matter. This can turn insulators into metals, alter magnetic ordering, or even induce superconductivity at higher temperatures than at ambient pressure. The phenomenon is central to condensed matter physics, revealing how the same chemical composition can host radically different properties depending on the lattice spacing and electronic interactions.

History

The systematic study of pressure-induced transitions dates back to the early 20th century, with Percy Bridgman pioneering high-pressure techniques and earning a Nobel Prize in 1946. The discovery of pressure-induced superconductivity in various elements and compounds followed in subsequent decades.

How it works

Pressure compresses the crystal lattice, reducing interatomic distances. This increases orbital overlap and changes the balance between kinetic energy and Coulomb interactions. Electrons that were previously localized may become itinerant, or magnetic moments may align differently. In some cases, the compressed lattice enhances the coupling between electrons and lattice vibrations (phonons), which is the mechanism behind conventional superconductivity.

In practice

High-pressure synthesis is used to create novel materials like superhard ceramics and to study the interiors of planets, where extreme pressures dictate the state of matter. It also guides the search for room-temperature superconductors.

Fun fact

Hydrogen, normally an insulating gas, is predicted to become a metallic superconductor at pressures above 400 gigapascals — a state that may exist in the cores of gas giants like Jupiter.

Concept graph →

Formulas

$$p_1 p_2 = \frac{\gamma}{1+\gamma}$$
Product of pre- and post-shock pressures depends on adiabatic index.
What is in the formula
p_1variablePre-shock pressure — pressure pascal
p_2variablePost-shock pressure — pressure pascal
\gammavariableAdiabatic index (ratio of specific heats) — adiabatic index
p_{\rmpre}p_{\rmpost}=\frac{γ}{1+γ} · 2606.29607
$$\Delta T = -\frac{T}{C_p} \left( \frac{\partial S}{\partial P} \right)_T \Delta P$$
Temperature change under adiabatic pressure variation.
What is in the formula
ΔTvariabletemperature change — temperature kelvin
Tvariableabsolute temperature — temperature kelvin
C_pvariableheat capacity at constant pressure — heat capacity joule per kelvin
Svariableentropy — entropy joule per kelvin
ΔPvariablepressure change — pressure pascal
∂/∂Poperatorpartial derivative with respect to pressure at constant temperature — partial derivative
δt_{ad}=-\frac{t}{c_p}(\frac{\partials}{\partialp})_tδp · 2606.25742
$$F(\psi) = a \psi^2 + b \psi^4 + c \psi^6 - f_{\text{ext}} \psi$$
Describes phase transitions with order parameter.
What is in the formula
FvariableLandau free energy density — free energy density joule per cubic metre
ψvariableorder parameter — order parameter
avariablecoefficient of quadratic term, temperature-dependent — landau coefficient a joule per cubic metre
bvariablecoefficient of quartic term — landau coefficient b joule per cubic metre
cvariablecoefficient of sixth-order term — landau coefficient c joule per cubic metre
f_extvariableexternal field coupled to the order parameter — external field joule per cubic metre
f(ψ)=\frac{a}{2}ψ^2+\frac{b}{4}ψ^4+\frac{c}{6}ψ^6-f_{{ext}}ψ · 2606.29055
v(u)=\frac{a}{2}u^2+\frac{b}{4}u^4+\frac{c}{6}u^6 · 2606.29765
$$\dot{E} \propto \rho v^3 R^2$$
Power from ram pressure scales with density and velocity cubed.
What is in the formula
ρvariablemass density of the medium — mass density kilogram per cubic metre
vvariablevelocity of the object relative to the medium — velocity metre per second
Rvariablecharacteristic radius of the object — radius metre
E_dotvariablepower (energy per unit time) from ram pressure — power watt
\dot{e}_{{in}}=πr_{\star}^2ρv_{\star}δu\approx5.6*10^{42}{эрг/с}(\frac{v_{\star}}{0.1c})^3(\frac{ρ}{3.6*10^{-8}{г/см}^3})(\frac{r_{\star}}{r_{\odot}})^2 · 2607.05508v1
$$\Delta\phi = \frac{2\pi}{\lambda} \Delta n L$$
Phase change due to refractive index variation in medium.
What is in the formula
ΔφvariablePhase shift — phase shift radian
λvariableWavelength of light — wavelength metre
ΔnvariableChange in refractive index — refractive index change
LvariablePath length through medium — length metre
δφ=\frac{2π}{λ}\frac{dn}{dt}δtl · 2505.01609v2
$$\kappa'(\theta) = \lambda\kappa(\theta) + (1-\lambda)$$
Convergence transforms linearly with a constant mass sheet addition.
What is in the formula
\kappa'(\theta)variabletransformed convergence — convergence
\kappa(\theta)variableoriginal convergence — convergence
\lambdavariabletransformation parameter — dimensionless parameter
\kappa_λ(θ)=λ\kappa(θ)+(1-λ) · 2606.03634v1

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