Matter usually expands when heated because the atoms vibrate more strongly; the amount is described by the coefficient of linear thermal expansion. For high-precision length measurements this expansion creates serious errors. Guillaume found that an iron–nickel alloy containing about 36% nickel shows almost zero expansion near room temperature. He named it Invar, derived from the Latin word invariabilis meaning unchanging. Measuring rods and geodetic wires made of Invar keep their length almost constant, greatly improving the accuracy of long-distance baseline surveys. In watches, balance wheels made of Invar reduce time gain or loss caused by daily temperature variations. Such applications supported unified timekeeping for railways and international telegraphy as well as reliable map making. In short, his research increased the dependability of many technologies we use every day.

Until the late 19th century, precision length standards were made of brass or Pt-Ir alloys whose thermal expansion coefficient α was around 10×10⁻⁶ K⁻¹—far from negligible. Working at the International Bureau of Weights and Measures, Guillaume systematically studied Fe-Ni alloys and discovered that near 36 wt% Ni the coefficient drops dramatically to about 0.5×10⁻⁶ K⁻¹. The low-expansion behavior, later explained by compensating entropy changes between magnetic states and lattice vibrations, was at first an empirical observation. Adoption of Invar enabled sub-micrometer accuracy in international meter comparisons, triangulation baselines and interferometer optical path stabilization. In addition, Guillaume developed sister alloys such as Elinvar with near-zero modulus drift and bimetal strips for temperature compensation in precision thermometers and fuses. His data were incorporated into ASTM and ISO standards; today Invar remains indispensable for aircraft instruments, LNG storage tanks and laser cavity spacers. The Invar effect continues to serve as a model system in solid-state physics for studying spin–lattice coupling. During post-World-War-I geodetic projects, Invar tapes were critical for measuring the Earth’s ellipsoid. These achievements culminated in the 1920 Nobel Prize in Physics. Modern technologies such as LIGO mirror suspensions and semiconductor lithography stages still rely directly on Guillaume’s concept of ultra-low-expansion metals.

The near-room-temperature minimum of the linear expansion coefficient in Fe64Ni36—the Invar effect—has been treated quantitatively with magneto-volume models such as the Inoue-Lawson mechanism and Matsui’s two-state theory. Around 36 wt% Ni, cancellation between enthalpy and lattice-parameter differences of high- and low-spin electronic states flattens the Gibbs free-energy gradient, driving dL/dT toward zero. Guillaume’s original micrometer measurements reported α≈1×10⁻⁶ K⁻¹; later X-ray diffraction and dilatometry refined this to roughly 0.6×10⁻⁶ K⁻¹ with long-term drift below 10⁻⁸ year⁻¹. Although Invar’s Young’s modulus (~140 GPa) is not especially high, its small magneto-elastic constant suppresses thermal hysteresis, leading to its use in gravitational-wave detector springs and telescope mirror cells. At temperatures below 100 K, noticeable negative expansion appears, enabling thermal displacement compensation in laser reference cavities and cryogenic AFM scanners. Guillaume subsequently synthesized Fe-Ni-Cr alloys (Elinvar) whose temperature coefficient of elastic modulus approaches zero, facilitating temperature-independent tuning-fork frequency standards. In international comparisons with BIPM meter prototype No.23, switching transfer standards to Invar reduced uncertainty to 3×10⁻⁸. Recent neutron diffraction and first-principles studies suggest that longitudinal fluctuations of local magnetic moments modulate the Grüneisen parameter, providing a microscopic origin of the Invar effect now being verified by inelastic scattering. Thus, Guillaume’s discovery forged a new interface between phase-transition physics and metrology, remaining indispensable in the practical length-measurement network even after the quantum redefinition of the meter.