Elongation of Fe-Fe atomic pairs in the Invar alloy ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$

In this study, atomic-scale origin of the Invar effect, which is nearly-zero thermal expansion observed in the Invar alloy ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$, was investigated by reverse Monte Carlo analysis using complementary data sets of extended x-ray absorption fine structure and x-ray diffraction. The interatomic distances of the nearest neighboring Fe-Fe atomic pairs were $\sim 0.02$ Å longer than those of the Fe-Ni and Ni-Ni pairs at the minimum pressure in this study (0.6 GPa). The elongation in the Fe-Fe pairs was suppressed with increasing pressure, and the distances of the three pairs were comparable under pressures above the magnetic transition from ferromagnetic to paramagnetic phase at $P_{\text{c}}\approx 7$ GPa. Therefore, the Fe-Fe pairs dominantly contribute to the volume expansion due to the magnetovolume effect. Because a similar magnitude of elongation was observed in the Fe-Fe pairs of a non-Invar Fe-Ni alloy, we conclude that the Invar effect originates from the delicate balance between the number of Fe-Fe pairs and their elongation depending on the magnetization.

Figure 1

Comparison of the experimental profiles with fits by the RMC calculations. Absolute values of Fourier transformed profiles ($\left|\text{FT}\right[k^2\chi \left(k\right)\left]\right|$) of ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ Invar at (a) Fe $K$-edge and (b) Ni $K$-edges together with the data of non-Invar ${\mathrm{Fe}}_{55}{\mathrm{Ni}}_{45}$ alloy. (c) X-ray diffraction patterns under high pressures.

Figure 2

(a) Partial pair distribution functions $g_{ij}\left(R\right)$ of $i$ and $j$ atomic pairs, where $i,j=$ Fe or Ni, in ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ Invar alloy at selected pressures together with the data of ${\mathrm{Fe}}_{55}{\mathrm{Ni}}_{45}$ non-Invar alloy. Each $g_{ij}\left(R\right)$ profile is normalized to approach to unity with increasing $R$. The vertical dashed lines indicate the lengths expected from the lattice constant of fcc structure. (b) Atomic clusters of the Invar alloy obtained by the RMC method. The clusters viewed from the $\left[11\overline{2}\right]$ direction are depicted. The insets display enlarged illustrations of the atomic cluster.

Figure 3

(a) Enlarged plots of pair distribution functions $g_{ij}\left(R\right)$ ($i,j=\mathrm{Fe}$ or Ni) of 1NN Fe-Fe and Fe-Ni and Ni-Ni atomic pairs in ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ Invar alloy and ${\mathrm{Fe}}_{55}{\mathrm{Ni}}_{45}$ non-Invar alloy. The vertical dashed lines indicate the lengths of 1NN pairs expected from the lattice constant of fcc structure. (b) Pressure dependences of the average length within a range of 0.6 Å centered on the 1NN peaks of Fe-Fe, Fe-Ni, and Ni-Ni pairs for ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ Invar alloy. The inset shows comparison of the average length of 1NN atomic pairs between ${\mathrm{Fe}}_{55}{\mathrm{Ni}}_{45}$ non-Invar alloy and ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ Invar alloy determined at the lowest pressures. (c) Ni composition dependence of the lattice constant of Fe-Ni alloys at ambient pressure. For comparison, lattice constants of antiferromagnetic $\gamma$(fcc)-Fe and ferromagnetic $\gamma$-Co are plotted [31].

Figure 4

Top: (a) angle distribution of Fe-Fe-Fe and Ni-Ni-Ni atomic triplets in the Invar alloy at selected pressures. Bottom: atomic clusters composed of 12 Fe/Ni nearest neighboring atoms and the central Fe atom at (b) initial undistorted model, (c) 0.6 GPa, and (d) 16.3 GPa. These clusters are picked up from the same position of the atomic cluster that we used for the RMC calculations.