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Liquid helium
Liquid helium
Liquid helium
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Liquid helium
Liquid helium in a transparent bowl, cooled below the Lambda point, where it exhibits properties of superfluidity
Properties
He
Molar mass 4.002602 g·mol−1
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).

Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity.

At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temperature of −269 °C (−452.20 °F; 4.15 K). Its boiling point and critical point depend on the isotope of helium present: the common isotope helium-4 or the rare isotope helium-3. These are the only two stable isotopes of helium. See the table below for the values of these physical quantities. The density of liquid helium-4 at its boiling point and a pressure of one atmosphere (101.3 kilopascals) is about 125 g/L (0.125 g/ml), or about one-eighth the density of liquid water.[1]

Liquefaction

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Helium was first liquefied on July 10, 1908, by the Dutch physicist Heike Kamerlingh Onnes at the University of Leiden in the Netherlands.[2] At that time, helium-3 was unknown because the mass spectrometer had not yet been invented. In more recent decades, liquid helium has been used as a cryogenic refrigerant (which is used in cryocoolers), and liquid helium is produced commercially for use in superconducting magnets such as those used in magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), magnetoencephalography (MEG), and experiments in physics, such as low temperature Mössbauer spectroscopy. The Large Hadron Collider contains superconducting magnets that are cooled with 120 tonnes of liquid helium.[3]

Liquified helium-3

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See also: Fermionic condensate § Helium-3 superfluid

A helium-3 atom is a fermion and at very low temperatures, they form two-atom Cooper pairs which are bosonic and condense into a superfluid. These Cooper pairs are substantially larger than the interatomic separation.

Characteristics

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Phase diagram of helium-4
Liquid helium-3 and -4 isotopes in phase diagram, showing the demixing zone.

The temperature required to produce liquid helium is low because of the weakness of the attractions between the helium atoms. These interatomic forces in helium are weak to begin with because helium is a noble gas, but the interatomic attractions are reduced even more by the effects of quantum mechanics. These are significant in helium because of its low atomic mass of about four daltons. The zero-point energy of liquid helium is less if its atoms are less confined by their neighbors. Hence in liquid helium, its ground state energy can decrease by a naturally occurring increase in its average interatomic distance. However at greater distances, the effects of the interatomic forces in helium are even weaker.[4]

Because of the very weak interatomic forces in helium, the element remains a liquid at atmospheric pressure all the way from its liquefaction point down to absolute zero. At temperatures below their liquefaction points, both helium-4 and helium-3 undergo transitions to superfluids. (See the table below.)[4] Liquid helium can be solidified only under very low temperatures and high pressures.[5]

Liquid helium-4 and the rare helium-3 are not completely miscible.[6] Below 0.9 kelvin at their saturated vapor pressure, a mixture of the two isotopes undergoes a phase separation into a normal fluid (mostly helium-3) that floats on a denser superfluid consisting mostly of helium-4.[7] This phase separation happens because the overall mass of liquid helium can reduce its thermodynamic enthalpy by separating.

At extremely low temperatures, the superfluid phase, rich in helium-4, can contain up to 6% helium-3 in solution. This makes the small-scale use of the dilution refrigerator possible, which is capable of reaching temperatures of a few millikelvins.[6][8]

Superfluid helium-4 has substantially different properties from ordinary liquid helium.

History

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In 1908, Kamerlingh-Onnes succeeded in liquifying a small quantity of helium. In 1923, he provided advice to the Canadian physicist John Cunningham McLennan, who was the first to produce quantities of liquid helium almost on demand.[9]

Important early work on the characteristics of liquid helium was done by the Soviet physicist Lev Landau, later extended by the American physicist Richard Feynman.

In 1961, Vignos and Fairbank reported the existence of a different phase of solid helium-4, designated the gamma-phase. It exists for a narrow range of pressure between 1.45 and 1.78 K.[10]

Data

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Properties of liquid helium Helium-4 Helium-3
Critical temperature[4] 5.2 K (−267.95 °C) 3.3 K (−269.85 °C)
Boiling point at one atmosphere[4] 4.2 K (−268.95 °C) 3.2 K (−269.95 °C)
Minimum melting pressure[11] 25 bar (360 psi) 29 bar (420 psi) at 0.3 K (−272.850 °C)
Superfluid transition temperature at saturated vapor pressure 2.17 K (−270.98 °C)[12] 1 mK in the absence of a magnetic field[13]
[edit]
  • Liquid helium (in a vacuum bottle) at 4.2 K (−268.95 °C) and 1 bar (15 psi) boiling slowly.
    Liquid helium (in a vacuum bottle) at 4.2 K (−268.95 °C) and 1 bar (15 psi) boiling slowly.
  • Lambda point transition: as the liquid is cooled down through 2.17 K (−270.98 °C), the boiling suddenly becomes violent for a moment.
    Lambda point transition: as the liquid is cooled down through 2.17 K (−270.98 °C), the boiling suddenly becomes violent for a moment.
  • Superfluid phase at temperature below 2.17 K (−270.98 °C). In this state, the thermal conductivity is extremely high. This causes heat in the body of the liquid to be transferred to its surface so quickly that vaporization takes place only at the free surface of the liquid. Thus, there are no gas bubbles in the body of the liquid.
    Superfluid phase at temperature below 2.17 K (−270.98 °C). In this state, the thermal conductivity is extremely high. This causes heat in the body of the liquid to be transferred to its surface so quickly that vaporization takes place only at the free surface of the liquid. Thus, there are no gas bubbles in the body of the liquid.
  • The liquid helium is in the superfluid phase. A thin invisible film creeps up the inside wall of the bowl and down on the outside. A drop forms. It will fall off into the liquid helium below. This will repeat until the cup is empty—provided the liquid remains superfluid.
    The liquid helium is in the superfluid phase. A thin invisible film creeps up the inside wall of the bowl and down on the outside. A drop forms. It will fall off into the liquid helium below. This will repeat until the cup is empty—provided the liquid remains superfluid.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Liquid helium

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Liquid helium is the liquid phase of helium, a , achieved by cooling it below its of 4.2 K (−269 °C) at standard , making it the coldest bulk substance known and essential for ultra-low-temperature research. The common isotope, (^4He), has a of 4.2 K, while the rarer (^3He) boils at 3.19 K and exhibits different low-temperature behaviors. Unlike most substances, liquid helium does not solidify under even at (0 K), requiring pressures above 25 atmospheres to form a solid, due to its weak interatomic forces and quantum mechanical . First liquefied in 1908 by Dutch Heike Kamerlingh Onnes at the University of , this breakthrough enabled the exploration of phenomena near and earned Onnes the 1913 . Liquid helium-4 exists in two distinct phases: helium I (He I), a normal viscous fluid above the of 2.1768 K, and helium II (He II), a phase below this exhibiting zero , extraordinary thermal conductivity, and the ability to flow without friction through narrow channels. The lambda transition at 2.1768 K marks a second-order phase change driven by quantum effects, where He II behaves as a mixture of normal and superfluid components according to the two-fluid model proposed by . in helium II was independently discovered in 1937–1938 by Pyotr Kapitza, John F. Allen, and Don Misener, revealing properties like the fountain effect and persistent currents that defy classical . Due to its extreme low temperature and inertness, liquid helium is indispensable in cryogenic applications, primarily as a coolant for superconducting materials and devices. It maintains the superconducting state in magnets used for (MRI) scanners, (NMR) spectroscopy, particle accelerators like the , and experiments. Additionally, its superfluid properties facilitate precise low- physics studies, including investigations of Bose-Einstein condensates and neutron scattering. Global demand for liquid helium, produced via cryogenic of , continues to rise with advancements in these fields, though supply constraints pose challenges for research infrastructure.

Fundamental Properties

Phase Behavior and Diagram

Liquid helium-4 exhibits a distinctive characterized by the absence of a solid-liquid-gas , a feature unique among quantum fluids due to helium's weak interatomic forces and significant . At , helium-4 does not solidify even at ; instead, it remains in the liquid state down to 0 K under its saturated , with solidification requiring external pressures exceeding approximately 25 bar. This behavior arises because the zero-point motion of helium atoms dominates, preventing the lattice formation necessary for a solid phase at low pressures. The thus features a liquid region extending from the critical point to along the curve, without the typical intersection found in classical substances. The liquid-vapor critical point of occurs at a of 5.2 and a of 2.27 , marking the end of the liquid-vapor coexistence curve. Below the normal boiling point of 4.2 at 1 , the phase splits into two distinct regions separated by the lambda line: the normal liquid phase, denoted He I, exists above this line, while below it lies the superfluid phase, He II. The lambda transition, a second-order phase change, takes place at 2.17 under saturated vapor , where He I transforms into He II, accompanied by the onset of superfluid ρ_s > 0 in the lower phase. The lambda line traces a steep path in the pressure- (P-T) diagram at low pressures with a positive slope of approximately 30 bar/ near the lambda point, extending to higher pressures and lower s up to about 1.8 and 29 bar before terminating at the tricritical point with the phase. The phase boundaries in the helium-4 diagram, including the vapor pressure curve and melting curve, follow the Clausius-Clapeyron relation, dPdT=ΔHTΔV,\frac{dP}{dT} = \frac{\Delta H}{T \Delta V}, which describes the slope of first-order transition lines based on the enthalpy change ΔH and volume change ΔV across the boundary. For the lambda transition, as a second-order process with ΔH = 0 and ΔV ≈ 0, the relation adapts through Ehrenfest equations to yield the observed slope via differences in specific heat and thermal expansion: dPdT=ΔCpTVmΔα\frac{dP}{dT} = \frac{\Delta C_p}{T V_m \Delta \alpha}, where VmV_m is the molar volume. At higher pressures, the solid phases (body-centered cubic and hexagonal close-packed) emerge along the melting curve, which exhibits a minimum pressure of about 25 bar at (0 K).

Thermodynamic Characteristics

Liquid displays distinctive thermodynamic properties influenced by quantum effects, particularly below the lambda transition temperature of approximately 2.17 at saturated . The exhibits a pronounced lambda-shaped anomaly at this transition, with a sharp peak in the helium-I phase just above the lambda point, followed by a rapid decrease in the superfluid helium-II phase. This behavior arises from the onset of long-range order in the superfluid state, where excitations such as phonons and rotons contribute less to compared to the disordered helium-I phase. Measurements confirm that the specific heat drops by nearly a factor of two immediately below the lambda point, deviating from classical expectations for a simple fluid. In the superfluid helium-II phase, thermal conductivity reaches extraordinarily high values, often exceeding that of high-purity by factors of up to 10510^5 at temperatures around 1 , due to efficient via counterflow of the normal and superfluid components involving phonons and rotons. This quantum-enhanced conduction allows superfluid to maintain near-uniform temperatures over macroscopic distances without significant gradients, contrasting sharply with the relatively low thermal conductivity of helium-I, which is about 10410^4 times poorer than . The mechanism relies on the collisionless propagation of excitations in the dilute normal fluid, enabling effective rates on the order of watts per square centimeter in confined geometries. Viscosity in superfluid helium-II is described by the two-fluid model, which posits the liquid as a of a viscous normal fluid component with ρn\rho_n and a frictionless superfluid component with ρs\rho_s, such that the total ρ=ρn+ρs\rho = \rho_n + \rho_s. The superfluid component exhibits zero shear , allowing dissipationless flow, while the normal component carries finite akin to a classical and is responsible for transport. Above the , ρs=0\rho_s = 0 and ρn=ρ\rho_n = \rho, recovering normal liquid behavior; below it, ρs\rho_s increases with decreasing temperature, reaching nearly the full at millikelvin temperatures. This model, originally formulated by Landau, quantitatively accounts for observed flow and dissipation phenomena in helium-II. For liquid helium-3, which remains normal down to much lower temperatures due to its fermionic nature, the specific heat at very low temperatures (below ~0.1 K) follows a linear dependence C=γTC = \gamma T, characteristic of a degenerate Fermi liquid, where γ\gamma is the Sommerfeld coefficient enhanced by strong interactions compared to the free value. This linear term dominates over a weaker phonon contribution proportional to T3T^3, reflecting the excitation of quasiparticles near the .

Superfluidity and Quantum Phenomena

Transition to Superfluid State

Liquid helium-4, composed of bosonic atoms with zero spin due to the helium-4 nucleus having zero spin, obeys Bose-Einstein statistics. Below the critical temperature of approximately 2.17 K, known as the lambda point, a macroscopic fraction of these atoms occupies the ground state, forming a Bose-Einstein condensate that underlies the superfluid transition. This condensation arises because, for non-interacting bosons, the occupation of the lowest energy state becomes macroscopic when the thermal de Broglie wavelength exceeds the interparticle spacing, a condition met in liquid helium-4 at low temperatures. Landau developed the two-fluid model to describe the superfluid state, positing that liquid helium-II consists of two interpenetrating components: a normal fluid with density ρn\rho_n that carries viscosity and entropy, and a superfluid component with density ρs\rho_s that flows without friction. The normal fluid arises from thermal excitations in the system, specifically phonons at low energies and rotons at higher energies near the minimum of the excitation spectrum, while the superfluid component represents the condensate. The total density is ρ=ρn+ρs\rho = \rho_n + \rho_s, and the model's derivation relies on the Galilean invariance of the excitation spectrum, ensuring no entropy in the superfluid part. This framework explains the thermodynamic anomalies at the lambda transition, such as the divergence in specific heat. In the Ginzburg-Landau phenomenological theory, the superfluid transition is characterized by an order parameter ψ\psi, a complex scalar field representing the macroscopic wavefunction of the condensate. Near the , the free energy expansion in powers of ψ\psi and its gradient captures the second-order phase transition, with the coefficient of ∣ψ∣2|\psi|^2 changing sign at 2.17 K. The phase ϕ\phi of ψ=∣ψ∣eiϕ\psi = |\psi| e^{i\phi} determines the superfluid velocity through the relation vs=ℏm∇ϕ,\mathbf{v}_s = \frac{\hbar}{m} \nabla \phi, where mm is the mass of a helium-4 atom and ℏ\hbar is the reduced Planck's constant; this expression follows from the hydrodynamic form of the Schrödinger equation for the condensate. The irrotational nature of vs\mathbf{v}_s (except at singularities like vortices) ensures quantized circulation in multiples of h/mh/m, with hh as Planck's constant.

Behaviors in Superfluid Helium-II

Superfluid helium-II exhibits remarkable macroscopic quantum behaviors, including the formation of thin films that enable frictionless flow over surfaces. The , a layer approximately 30 nm thick, forms on solid surfaces in contact with helium-II and creeps along them due to zero , allowing the superfluid to transfer without resistance even against . This creeping motion is observed as the film climbs container walls and flows over edges, with transfer rates reaching up to several centimeters per second near the , decreasing at lower temperatures. The facilitates the thermomechanical , commonly known as the fountain effect, where a across a narrow channel causes superfluid to flow from the colder to the warmer side, building that can eject as a fountain. This counterintuitive flow arises because the difference drives the superfluid component, with no carried by the flow, leading to a rise proportional to the difference. Experiments demonstrate this in setups with fine capillaries, where heating one reservoir results in squirting from the other, highlighting the irreversible nature of in helium-II. Another key behavior is the quantization of circulation in superfluid flow, where vortices form with discrete circulation values predicted by Onsager and elaborated by Feynman. The circulation κ around a closed path enclosing a vortex core is quantized as κ = n (h / m), where n is an , h is Planck's constant, and m is the of a helium-4 atom. In rotating helium-II, these quantized vortices arrange into tangles or lattices to mimic solid-body rotation, with vortex density proportional to the rotation rate, enabling the superfluid to achieve without classical . The core radius of these vortices is on the order of angstroms, comparable to interatomic spacing, underscoring the atomic-scale quantum coherence. Superfluid flow remains dissipationless only below a critical , typically around 1 cm/s, beyond which quantized vortices are created, leading to energy dissipation through vortex motion and reconnection. This critical velocity marks the onset of quantum turbulence, where vortex creation at obstacles or boundaries causes a sudden drop in superflow conductivity, with the value depending on and but generally scaling inversely with channel size. In ion-trapping experiments, positive ions accelerate to this threshold before nucleating vortex rings, confirming the mechanism involves quantum tunneling or thermal activation for vortex formation. Superfluidity persists in confined geometries, such as the porous Vycor glass with pore diameters around 4 nm, where helium fills the nanopores and exhibits a shifted superfluid transition. In these restrictions, the superfluid fraction emerges below approximately 1.95 K, lower than the bulk of 2.17 K, due to dimensional crossover effects, yet the helium maintains coherent flow with reduced but finite superfluid density. Path-integral simulations reveal that superfluidity localizes in adsorbed layers near pore walls, with the response robust even at high pressures up to 62 bar.

Production Methods

Liquefaction Processes for Helium-4

Gaseous , primarily extracted from deposits via cryogenic distillation or processes, is purified to high purity before . is produced by cooling gaseous helium through a series of thermodynamic processes that exploit its unique properties, primarily using the Collins cycle, a modified Claude cycle developed in the mid-20th century. This cycle involves compressing helium gas to moderate pressures (typically around 15-20 bar), followed by precooling with to approximately 80 , and then employing multiple heat exchangers and expansion stages to progressively lower the temperature to the liquefaction point. The key innovation lies in the use of expansion turbines—either reciprocating pistons or centrifugal turbines—for isentropic expansion, which provides more efficient cooling than purely isenthalpic processes, allowing the system to reach temperatures below 4.2 K from ambient gaseous helium. The normal boiling point of helium-4 is 4.222 at 1 , where it condenses into a under saturated vapor pressure conditions. To achieve , the Collins cycle incorporates counterflow exchangers that transfer from the high-pressure incoming stream to the low-pressure returning vapor, maximizing thermal efficiency. The final stage employs a Joule-Thomson (JT) valve for isenthalpic expansion, where the gas cools upon throttling due to the positive JT for helium below its inversion of approximately 40 . The JT is defined as μJT=(∂T∂P)H\mu_{JT} = \left( \frac{\partial T}{\partial P} \right)_H, which quantifies the temperature change with at constant and enables the necessary cooling for when pre-cooled sufficiently. Achieving the superfluid transition at the (2.17 K at saturated ) requires additional cooling beyond simple , typically via evaporative pumping under reduced pressure, which lowers the by decreasing the over the liquid. While dilution refrigeration using mixtures can extend cooling further, for pure , evaporation suffices to cross the line. This process demands precise control to avoid excessive boil-off and maintain system integrity. Liquefaction efficiency is inherently limited by the low critical temperature of (5.2 ), resulting in a small Carnot (COP) of about 0.014 for cooling from 300 to 4.2 , calculated as COPCarnot=TcTh−Tc\text{COP}_\text{Carnot} = \frac{T_c}{T_h - T_c}. Actual systems achieve a (FOM) of 0.25–0.32 relative to Carnot, translating to a specific liquefaction work of approximately 200 kJ/mol, far exceeding the thermodynamic ideal of around 27 kJ/mol due to irreversibilities in compression, , and expansion. These metrics highlight the energy-intensive nature of helium-4 production, with modern Collins-based plants requiring roughly 2–5 kW of electrical input per liter of produced per hour.

Handling Liquid Helium-3

Liquid (³He) consists of fermionic atoms with nuclear , subjecting it to Fermi-Dirac statistics that inhibit Bose-Einstein and thus prevent through bosonic mechanisms observed in helium-4. Instead, in ³He emerges only at ultralow temperatures below approximately 2.6 mK, facilitated by p-wave spin-triplet pairing of Cooper pairs, as first observed in the A and B phases. This fermionic behavior dominates its thermodynamic properties, with the liquid remaining in a normal Fermi-liquid state down to the superfluid transition. The of liquid ³He at standard is 3.19 , significantly lower than that of helium-4 due to its lighter mass and weaker interatomic interactions. Its scarcity contributes to high production costs; ³He constitutes only about 1 in 10⁶ atoms in natural deposits, primarily extracted as a from tritium decay in nuclear facilities. Handling ³He requires specialized cryogenic infrastructure to maintain it in the liquid phase, often involving mixtures with helium-4 to leverage for cooling. To achieve the millikelvin temperatures essential for studying ³He's quantum properties, the exploits the in ³He/⁴He mixtures. In this device, ³He dissolves into the ⁴He superfluid at higher temperatures but separates into a concentrated ³He-rich phase and a dilute phase below ~0.8 ; continuous circulation of ³He from the concentrated to the dilute phase absorbs via the endothermic mixing enthalpy, providing cooling power on the order of 1 μW at 15 mK. This method enables sustained temperatures down to ~10 mK without solidification, critical for probing ³He's Fermi-liquid regime. In the normal liquid state above the superfluid transition, ³He exhibits degenerate Fermi behavior characterized by the Fermi temperature TF≈0.3T_F \approx 0.3 K, below which quantum effects like Pauli exclusion become prominent and Pauli blocking suppresses scattering. The low-temperature specific heat follows the linear form C=γTC = \gamma T, where the Sommerfeld coefficient γ=8.4\gamma = 8.4 mJ/mol·K² reflects the enhanced effective mass of quasiparticles due to strong interactions in this dilute Fermi liquid. These properties underscore ³He's role as a model system for correlated fermionic matter, distinct from the bosonic helium-4.

Historical Development

Initial Discovery and Early Studies

The liquefaction of was first achieved by Dutch on July 10, 1908, at the University of Leiden, marking a pivotal advancement in low-temperature physics. employed a closed-cycle process inspired by Carl von Linde's method for , involving the compression of helium gas, its pre-cooling to approximately 20 using , and subsequent expansion through a throttle valve in a vacuum-insulated vessel. This apparatus also utilized for initial cooling stages, yielding about 60 milliliters of liquid helium on the first successful run, with a measured of 4.25 at and a critical slightly above 5 . The achievement, detailed in Onnes' contemporaneous communications from the Leiden laboratory, enabled systematic exploration of phenomena below 4.2 , previously inaccessible. Early investigations revealed striking anomalies in liquid helium's behavior. Onnes noted the absence of a solid phase under even at temperatures as low as 1.15 , achieved through rapid in vessels equipped with high-capacity pumps; no intermediate liquid-to-solid transition was observed, unlike other substances. measurements, conducted via dilatometry shortly after , showed an unusual density maximum around 2.2 , implying negative expansion coefficients below this point—a deviation from classical expectations governed by the , which typically predicts positive expansion for most materials. These findings, reported in Onnes' 1909-1910 publications, highlighted helium's non-classical liquid properties and spurred theoretical interest in quantum effects at low temperatures. In 1911, Onnes' access to liquid facilitated the serendipitous discovery of during resistance measurements on pure mercury wires immersed in the cryogen. At 4.2 , the electrical resistance dropped abruptly to nearly zero, a initially attributed to the extreme low temperatures enabled by helium but later recognized as distinct from helium's own quantum behaviors. This observation, replicated in tin and lead, underscored helium's role in probing metallic properties but was not immediately connected to liquid helium's intrinsic anomalies. By the early 1920s, foundational thermodynamic studies further illuminated liquid helium's peculiarities. In 1922, Onnes and visiting researcher L.I. Dana conducted preliminary specific heat measurements using calorimetric techniques on samples at saturated , revealing a that did not conform to the classical Dulong-Petit limit of approximately 3R per mole expected for monatomic systems at higher temperatures; instead, it exhibited a marked increase toward the without saturating classically at low temperatures. These results, published in communications, indicated quantum deviations in helium's properties, setting the stage for deeper investigations into its low-temperature phase behavior up to the mid-1920s.

Key Milestones in Superfluidity Research

In 1938, the phenomenon of superfluidity in liquid was independently discovered by Pyotr Kapitza at the Institute of Physical Problems in and by John F. Allen and Donald Misener at the Royal Society Mond Laboratory in . Kapitza's experiments demonstrated that below the transition temperature of approximately 2.17 K, liquid exhibited an extraordinarily low , effectively flowing without resistance through narrow capillaries, which he termed "." Concurrently, Allen and Misener observed similar frictionless flow in helium passed through fine glass tubes, confirming the absence of viscous drag in this phase. These findings marked the onset of intensive research into the quantum mechanical nature of helium's low-temperature behavior. The at 2.17 was first indicated by a characteristic lambda-shaped anomaly in the specific heat curve, observed in calorimetric studies by W. H. Keesom and K. Clusius in 1932, well before the discovery of . This anomaly, observed years before the discovery, was later explained in part by London's 1938 proposal linking to Bose-Einstein in atoms. In 1938, proposed the initial conceptual framework for understanding via a two-fluid model, suggesting that liquid helium-II consists of an inviscid superfluid component and a viscous normal fluid component, with their relative proportions varying with temperature. This idea was further developed in 1941 by , who provided a rigorous theoretical foundation, incorporating and excitations to explain the model's hydrodynamics and predict phenomena like . Landau's formulation reconciled experimental observations of thermal transport and flow properties, establishing the two-fluid model as a cornerstone of theory. During the 1950s, experimental investigations into rotational motion in superfluid revealed the quantized nature of . H.E. Hall and W.F. Vinen conducted pioneering studies on rotating helium-II, demonstrating that circulation around closed paths is quantized in units of h/mh/m, where hh is Planck's constant and mm is the mass, arising from the formation of discrete vortex lines. Their work on mutual between the superfluid vortices and the normal fluid component quantified interactions that dissipate in rotating systems, providing direct evidence for the microscopic quantum structure underlying macroscopic superfluid flow. Advancing into the , research on ultracold superfluid nanodroplets has enabled precise quantum simulations of nanoscale effects, such as vortex dynamics and molecular in confined quantum environments. These droplets, maintained at temperatures below 0.4 , serve as isolated nanolaboratories where persists down to sizes of a few hundred atoms, allowing studies of finite-size quantum phase transitions and ultrafast relaxation processes triggered by extreme-ultraviolet pulses. Recent experiments up to have explored temporary capture and quantum tunneling of light atoms within these droplets, revealing universal laws in vortex reconnection and dissipation at the nanoscale, which inform broader simulations.

Practical Applications

Cryogenic Cooling Systems

Liquid helium plays a critical role in cryogenic cooling systems by providing the low temperatures necessary for in magnets used in and high-energy physics. In (MRI) machines, liquid helium cools the superconducting coils to approximately 4 , enabling the generation of strong, stable magnetic fields without electrical resistance. Conventional MRI scanners typically require over 1,000 liters of liquid helium to maintain this state. Similarly, in particle accelerators like the (LHC) at , liquid helium circulates in a to cool superconducting magnets to 1.9 , with an inventory of approximately 140 tons required for operation. Dewar flasks and cryostats designed for liquid helium storage and transport feature jackets and to minimize heat ingress and reduce boil-off rates at 4.2 . The jacket creates a thermal barrier, while —consisting of alternating layers of reflective foil and spacers—further suppresses radiative , enabling storage durations of weeks with losses below 1% per day in optimized systems. These designs are essential for maintaining the cryogenic conditions in both and industrial settings. Helium recovery systems employ closed-loop to capture and reliquefy boil-off gas, addressing supply constraints in cryogenic infrastructures. These systems purify evaporated helium through compression, cooling, and re-liquefaction, achieving recovery efficiencies up to 90% and converting open-cycle operations to zero-boil-off configurations. Global consumption of liquid helium for cryogenic applications is approximately 100,000 m³ per year, underscoring the importance of such to sustain availability. Helium scarcity intensified in the 2010s due to production disruptions and rising demand, driving prices up by as much as 400% between 2010 and 2013. As of 2025, renewed shortages following the U.S. Federal Helium Reserve shutdown have further increased prices and supply constraints, emphasizing the need for conservation. To mitigate these challenges, alternatives such as (LN₂) pre-cooling are integrated into helium systems, reducing the energy and helium volume needed for initial cooldown by lowering temperatures to around 80 K before final helium refrigeration. Recent innovations, including zero-boil-off cryostats and helium-efficient MRI systems using pulse-tube refrigerators, reduce helium use by up to 90% and are increasingly adopted as of 2025.

Use in Scientific Experiments

Liquid helium plays a pivotal role in low-temperature physics experiments, particularly through its superfluid phase (helium II), which enables the study of quantum excitations via neutron scattering techniques. In superfluid helium-4 (He II), neutron scattering has been instrumental in probing roton excitations, which are quantized quasiparticles representing local density fluctuations with a characteristic energy minimum around 8.65 K and momentum near 1.92 Å⁻¹. These studies reveal that rotons behave as interstitial helium atoms, providing evidence for their atomic-scale structure through inelastic neutron scattering measurements that map the excitation spectrum. Such experiments, conducted at facilities like the Institut Laue-Langevin, have confirmed the Landau dispersion relation for excitations in He II, offering insights into the microscopic origins of superfluidity. Dilution refrigerators, which exploit the phase separation of liquid helium-3 (³He) and helium-4 (⁴He) mixtures, achieve millikelvin temperatures essential for experiments with superconducting qubits. These devices cool samples to below 10 mK by leveraging the entropy-driven dilution , where ³He atoms dissolve into ⁴He at low temperatures, enabling efficient heat extraction. In setups, such as those at , dilution refrigerators maintain the coherence of superconducting qubits by minimizing thermal noise, allowing for the operation of multi-qubit processors with gate fidelities exceeding 99%. Immersion in liquid ³He further suppresses qubit decoherence from environmental phonons, demonstrating prolonged coherence times exceeding 100 μs in qubit arrays. Superfluid helium serves as a medium for experiments that explore analogs to Bose-Einstein condensates (BECs) by trapping nanoparticles and observing quantum hydrodynamic effects. In these setups, a focused beam (optical tweezer) confines nanoparticles, such as particles of ~50–80 nm diameter, within superfluid He II at 1.4 K, where the superfluid's vanishing allows for frictionless motion and minimal damping. This enables the study of quantized vortex dynamics and phonon-roton interactions as BEC-like analogs, with trapped particles exhibiting ballistic trajectories over microns before interacting with excitations. Such techniques, pioneered in cryogenic optical systems, provide a platform for visualizing superfluid flow at the single-particle level, bridging atomic BECs and macroscopic quantum fluids. In the 2020s, superfluid helium has emerged as a sensitive medium in quantum sensors for detection, particularly through bolometric configurations that detect sub-GeV particle interactions. Superfluid ⁴He targets, operated as calorimeters, convert -induced nuclear recoils into excitations, with energy thresholds around 150 eV due to the material's low (~1.5 mJ/mol·K at 0.1 ). The QUEST-DMC experiment employs superfluid ³He bolometers with nanomechanical resonators to amplify signals from scattering, achieving background rejection via dynamics in the B-phase. These detectors target weakly interacting massive particles (WIMPs) and axions in the 10 MeV to 1 GeV mass range, with prototypes projecting sub-eV energy resolution at millikelvin temperatures.

Quantitative Data

Physical Constants and Tables

Liquid helium's physical properties are characterized by its low atomic mass and quantum effects, leading to unique constants that differ markedly from classical liquids. For the predominant isotope, helium-4 (^4He), the standard atomic mass is 4.002602 u. The density of liquid ^4He at absolute zero under saturated vapor pressure is 0.1453 g/cm³, increasing slightly with temperature to 0.125 g/cm³ at the normal boiling point. In the normal fluid phase (He I), the speed of first sound is approximately 230 m/s near 3 K. These values highlight the material's low density and high compressibility compared to other substances. The phase behavior of liquid ^4He is summarized in the following table, including key transition points under saturated vapor pressure unless otherwise noted:
Phase TransitionTemperature (K)Pressure (bar)Density (g/cm³)Notes
Normal boiling point4.2221.013250.125Equilibrium with vapor at 1 atm.
Lambda point (He I to He II)2.17680.05 (saturated)0.146Superfluid transition at low pressure.
Critical point5.19532.27460.06964End of liquid-vapor coexistence.
Liquid isotopes ^3He and ^4He exhibit contrasting quantum behaviors due to their fermionic (^3He) and bosonic (^4He) nature. The following table compares selected properties relevant to their superfluidity and electronic structure:
Property^3He^4He
Superfluid transition temperature (maximum)0.002491 K (at ~3 bar)2.1768 K (at saturated vapor pressure)
Fermi energy (non-interacting gas model, E_F / k_B)~2.8 KN/A (bosonic)
Recent refinements to the equation of state for , published by NIST in 2023, provide updated thermophysical data, including coefficients derived for the liquid phase. For liquid ^4He under saturated , the isobaric coefficient α_p near the (e.g., at 2.18 ) is approximately 0.35 ⁻¹, reflecting anomalous expansion in the superfluid phase; values decrease to ~0.05 ⁻¹ approaching the critical point at 5 . These updates incorporate high-precision measurements and improve accuracy for cryogenic modeling by up to 0.1% in derived properties compared to prior formulations.

Measurement Techniques

Measuring the properties of liquid helium presents unique challenges due to its extremely low temperatures, quantum mechanical , and the need for minimal thermal disturbances during experiments. Techniques must operate below 4.2 K for helium-4 and even lower for helium-3, often requiring superconducting or dilution refrigerators to maintain cryogenic conditions while ensuring high precision and low noise. These methods focus on probing viscosity, heat capacity, excitation spectra, and structural features like vortices, with instruments designed to isolate quantum effects from classical thermal noise. Viscometry in superfluid helium-II (He II) relies on torsional oscillators to confirm its zero , a hallmark of . In these setups, a solid or disk filled with liquid helium is suspended by a thin torsion and oscillates at low ; the remains unchanged below the (≈2.17 K), indicating no viscous drag from the superfluid component, as the normal fluid fraction alone contributes to dissipation. This technique, pioneered in , achieves sensitivities to viscosity changes on the order of 10^{-9} poise by measuring frequency shifts and . Complementary measurements use fountain effect pressure transducers, which exploit the thermomechanical effect in He II: a across a superleak (e.g., packed ) generates a difference without mass flow, allowing indirect viscosity assessment through flow resistance in narrow channels. These methods have verified the two-fluid model's predictions for superfluid flow. Calorimetry for liquid helium employs AC techniques to measure specific heat near the lambda transition, circumventing self-heating issues inherent in DC methods at millikelvin scales. A small heater applies sinusoidal power at frequencies around 10-100 Hz to a thin film or droplet sample thermally linked to a (e.g., ruthenium oxide resistor), while the phase shift and amplitude of the temperature response yield the without significant steady-state warming. This approach resolves the sharp specific heat peak at the , where classical methods fail due to divergent thermal relaxation times, enabling studies of in the superfluid transition. AC calorimetry has been refined for pressures up to several bars, providing data on helium's thermodynamic anomalies. Spectroscopy techniques, particularly neutron inelastic scattering, probe the elementary excitations in liquid helium, such as rotons, which underpin its superfluid properties. Cold neutrons from reactors or spallation sources are scattered off a liquid helium target at ≈1.5 K, with energy transfers measured via time-of-flight or triple-axis spectrometers to map the dispersion relation. This method has determined the roton energy gap as Δ/k_B = 8.65 K in He II at saturated vapor pressure, revealing a parabolic minimum in the excitation spectrum around momentum ħk ≈ 1.93 Å^{-1}. The technique's momentum and energy resolution (≈0.1 meV) allows distinction between phonon, maxon, and roton contributions, confirming Landau's quasiparticle model. Modern measurement methods include cryogenic for visualizing quantized vortices in He II, addressing the need for non-invasive at atomic scales. Optical , often using at 532 nm, illuminate a cell with a phase grating induced by density variations from vortex cores, producing interference patterns that map vortex lattice structures with sub-micrometer resolution. This technique captures dynamical behaviors like vortex reconnection in real time, using high-speed cameras cooled to avoid helium boiling. While scanning tunneling microscopy (STM) has been explored for surface studies, its application to bulk liquid helium remains limited due to evaporation and charging issues, highlighting ongoing challenges in atomic-scale probing. These methods quantify superfluid behaviors such as persistent currents and vortex dynamics, as explored in research.

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