・ How the well-known "invar effect" -- near-zero thermal expansion -- plays out separately in each element of complex, cobalt-containing stainless invar alloys (iron, cobalt, chromium, nickel) has been unclear, particularly how it responds to small shifts in the iron-to-cobalt ratio.
・ Researchers combined synchrotron element-specific X-ray absorption spectroscopy with dilatometry and atomic-scale Monte Carlo simulation on several face-centered-cubic (fcc) alloy samples with slightly different iron-to-cobalt ratios, finding that both iron and cobalt locally suppress thermal expansion but iron's contribution is larger, and that this balance shifts measurably even with small compositional changes; a non-annealed, body-centered-cubic version of the same alloy instead showed ordinary, positive thermal expansion, confirming the invar behavior is specific to the annealed fcc structure.
・ These findings refine understanding of element-specific magnetovolume behavior in stainless invar alloys, distinguishing them from classic iron-nickel invar and the related Kovar alloy where iron dominates more strongly, though the authors caution that the iron-to-cobalt ratio alone does not fully explain the observed trends across all samples tested, and the conclusions rest on a small set of compositions examined only between 30 and 400 K.
Invar alloys resist expanding or contracting with temperature, a property valuable for precision instruments, but it has been unclear how this "invar effect" plays out separately in each element of complex, multi-metal stainless invar alloys. By combining synchrotron X-ray absorption spectroscopy with atomic-scale computer simulation, researchers measured how iron and cobalt atoms individually respond to temperature change in cobalt-containing stainless invar alloys, finding that both elements contribute to the effect but iron's contribution is more pronounced, and that its strength shifts with small changes in the iron-to-cobalt ratio.
Iron-nickel invar alloys have long been known to show almost no thermal expansion near room temperature, an effect attributed to magnetovolume coupling, in which the local magnetic spin state of iron atoms changes with temperature and offsets normal lattice-vibration-driven expansion. How this effect operates at the level of individual elements in more complex, multi-element stainless invar alloys containing iron, cobalt, chromium, and nickel has been less well understood. Prior work by the same research group had shown that in one cobalt-containing face-centered-cubic (fcc) stainless invar composition (roughly Fe39Co50Cr9Ni2), both iron and cobalt contribute to the invar effect, unlike the related Kovar alloy (Fe53Co17Ni29), where iron dominates and cobalt contributes much less. It remained unknown how this element-specific behavior changes when the iron-to-cobalt ratio is varied only slightly within the stainless invar family, and how the non-invar, body-centered-cubic (bcc) phase of the same base alloy -- obtained before the final heat-treatment step -- compares to the annealed, invar-exhibiting fcc phase.
The researchers prepared four fcc-phase stainless invar alloy samples with slightly different iron-to-cobalt ratios (grouped by distinct thermal expansion behavior into "sample A," averaging Fe39.0Co49.9Cr9.2Ni1.9 from three alloys, and "sample B," Fe37.8Co51.3Cr9.0Ni1.9 from one alloy), plus a non-annealed bcc-phase version of one composition and a Kovar alloy for comparison. They measured overall thermal expansion by dilatometry (100-400 K) and element-specific local atomic structure by chromium, iron, and cobalt K-edge extended X-ray absorption fine structure (EXAFS) spectroscopy (30-300 K) at a synchrotron facility, then compared the results with path-integral effective classical potential Monte Carlo (PIECP MC) simulations that model each element's spin-state behavior and resulting lattice vibrations.
Dilatometry, which tracks how a sample's length changes with temperature, showed that sample A's overall lattice barely expanded between 100 and 200 K (expansion coefficient 0.393 ± 0.006 ×10⁻⁶ per kelvin at 125 K) while sample B expanded roughly five times more (2.152 ± 0.005 ×10⁻⁶ per kelvin) -- a difference larger than the measurement uncertainty. Element-specific EXAFS, which measures the distance between a chosen atom type and its nearest neighbors, traced this difference to iron and cobalt behaving differently in each sample: at 125 K, sample A's iron neighborhood contracted slightly on warming (-1.3 ± 0.2 ×10⁻⁶ per kelvin) while its cobalt neighborhood expanded only modestly (0.82 ± 0.14 ×10⁻⁶ per kelvin), whereas in sample B iron stayed close to flat (0.77 ± 0.42 ×10⁻⁶ per kelvin) while cobalt expanded considerably more (5.7 ± 0.4 ×10⁻⁶ per kelvin) -- indicating both elements help suppress expansion, but iron's contribution is larger. Computer simulations that track each atom's magnetic "spin state" -- a high-spin state associated with a larger local volume versus a low-spin state associated with a smaller one -- suggest this pattern arises because iron already carries a substantial low-spin fraction (over 30%) even at the lowest simulated temperatures, shifting further toward low-spin on warming, whereas cobalt starts almost entirely high-spin and loses that state only gradually; the simulations reproduced the same element-level ordering as experiment, though the simulated overall lattice coefficient for model A came out negative (-1.433 ×10⁻⁶ per kelvin at 125 K) rather than matching the small positive value measured, so agreement is only qualitative. By contrast, the non-annealed bcc version of the same alloy, obtained before the final heat treatment, showed ordinary, positive expansion throughout -- 8.608 ± 0.013 ×10⁻⁶ per kelvin at 200 K by dilatometry -- in both the lattice and every element examined, confirming that the invar effect appears only after annealing into the fcc structure. In this bcc phase, EXAFS also showed the interatomic distance around chromium atoms was consistently longer than around iron or cobalt -- suggesting, but not proving, that lattice strain concentrates near the comparatively scarce chromium atoms -- whereas these distances converged closely after annealing into the fcc phase.
These results show that within this fcc stainless invar family, both iron and cobalt locally help suppress thermal expansion, with iron's contribution somewhat larger than cobalt's -- a pattern distinct both from classic iron-nickel invar, where iron alone drives the effect, and from the related Kovar alloy, where iron dominates and cobalt contributes much less. The magnitude of this effect shifted measurably with only a small change in the iron-to-cobalt ratio between the two sample groups, but the authors caution that this ratio alone does not fully explain their data, since thermal expansion did not vary monotonically with it across all four alloys tested, pointing to other unresolved factors such as chromium content. Several methodological caveats limit how far the findings can be generalized: the "constant atomic radius model" used to split average EXAFS distances into individual atom-pair distances, and the theoretical EXAFS standards, which assumed atoms sit at ideal, undistorted lattice positions despite expected real lattice strain, are both approximations intended only to reveal qualitative trends; the chromium EXAFS signal was also disturbed by trace manganese contamination, and nickel's local behavior could not be measured directly because its EXAFS signal was too weak. The PIECP simulations used simplified model compositions and interatomic potentials that only approximate the real alloys, reproducing the same qualitative trends between samples but not exact quantitative agreement, including an opposite-signed lattice coefficient for one composition. These conclusions rest on a limited set of four fcc alloys (grouped into two samples), one bcc composition, and one Kovar comparison alloy, all examined only between 30 and 400 K, so they should not yet be extended to other iron-to-cobalt ratios, alloy systems, or the higher temperatures and mechanical loads relevant to practical use.
Authors: Toshihiko Yokoyama, Hiromichi T. Fujii, Shingo Matsumura, Naoki Sakaguchi
Journal Name: Journal of Alloys and Compounds
Journal Title: "Element specific local thermal expansion of Co-containing stainless invar alloys"
DOI: 10.1016/j.jallcom.2026.189030
Journal of Alloys and Compounds
Experimental study
Not applicable
Element specific local thermal expansion of Co-containing stainless invar alloys
25-Jun-2026