Stress-induced large Curie temperature enhancement in Fe 64 Ni 36 Invar alloy

We have succeeded in increasing up to 150 K the Curie temperature in the Fe64Ni36 invar alloy by means of a severe mechanical treatment followed by a heating up to 1073 K. The invar behavior is still present as revealed by the combination of magnetic measurements with neutron and x-ray techniques under extreme conditions, such as high temperature and high pressure. The proposed explanation is based in a selective induced microstrain around the Fe atoms, which causes a slight increase in the Fe-Fe interatomic distances, thus reinforcing ferromagnetic interactions due to the strong magnetoelastic coupling in these invar compounds.


I. INTRODUCTION
It has been widely recognized that magnetism and structure are strongly interconnected. 1 In fact, it is well known that upon a marginal increase of the crystalline lattice parameter the magnetic exchange coupling is enhanced and probably the ferromagnetism is stabilized. 2,30][11][12][13][14][15] A microscopic explanation of the Invar effect in iron-nickel alloys has been given considering that the magnetic structure is characterized by a continuous transition from the ferromagnetic state at high volumes to a disordered noncollinear arrangement at low volumes. 10n simple words, there must be a negative contribution to the thermal expansion, which is related to the magnetic ordering, and which cancels out the ever-present positive contribution coming from the anharmonicity of the lattice vibrations. 3,16Therefore, this effective temperature invariant thermal expansion can be exploited in a number of technological applications such as precision measurements for standards, large size cryogenic liquid containers, etc. 15,17 Furthermore, the Invar effect is not limited to being a property of only Fe-Ni alloys, but it is also found in many other crystalline three dimensional ͑3D͒ systems such as Fe-Pt, Pd 3 Fe, Fe 3 C, or Fe-Cu, [18][19][20][21][22] amorphous Fe alloys, [23][24][25] as well as intermetallic systems such as R-Fe ͑R = Rare Earth͒. 26,27ence, these alloys can be structurally ordered or disordered, ferromagnetic or antiferromagnetic.0][31][32] It has been observed the interdependence of the latter two variables in Ni-rich Fe-Ni compositions, where LS noncollinear magnetic ordering can be induced under pressure, giving rise to invar behavior. 33n a previous work, we shown that the magnitude of the Curie temperature, T C , of an standard commercial Fe 64 Ni 36 powder sample can be increased in ⌬T C ϳ70 K, by means of a severe mechanical processing, using a high-energy ball mill, followed by a heating up to 1073 K, while the invar character is maintained and its temperature range enlarged as well. 34Previously, Dumpich et al. 35 already observed in "asprepared" Fe 65 Ni 35 evaporated thin films an increase in the T C value of ca 200 K, accompanied by an enhancement of 20% in the saturation magnetization, M s .However, both T C and M s drop down to the corresponding bulk values after annealing of the thin films.In spite of this, we will show that ⌬T C can be increased up to ϳ150 K in Fe 64 Ni 36 invar material through the adequate variation of the milling conditions, being such enlarged value of T C stable under subsequent heating-cooling procedures between RT and 1073 K.
We report here on a detailed study of the temperature and pressure dependencies of the crystalline lattice parameter, the magnetization and the x-ray magnetic circular dichroism in two Fe 64 Ni 36 powders, the starting commercial ͑Standard Fe 64 Ni 36 ͒ and the mechanical stressed ͑MS Fe 64 Ni 36 ͒ ones, showing such outstanding finding.The stress-induced microstructural changes must play a definite role on the magnetic properties of these alloys.Thus, Invar FeNi materials show the extraordinary feature of enhancing the ordering temperature when they are mechanically stressed via high-energy ball milling.These LTE materials have the potential to reduce ͑or even eliminate͒ the effects of strain on material components in systems subjected to large temperature variations.

II. EXPERIMENTAL DETAILS
The starting Fe 64 Ni 36 powder material was milled for 30 h in a high-energy planetary ball mill ͑Retsch PM/400͒ under controlled Ar atmosphere.The chemical composition of both standard and MS samples, Fe 63.8͑3͒ Ni 36.2͑3͒ and Fe 63.4͑2͒ Ni 36.6͑2͒ , respectively, was estimated by means of inductively coupled plasma mass spectroscopy using isotope analysis.This information is very important to rule out a change of stoichiometry in the MS sample.The magnetic measurements were carried out using Faraday, SQUID, and PPMS ͑with VSM option͒ magnetometers.The magnetization vs. temperature curves, M͑T͒, were measured under two different values for the applied magnetic field, H = 300 Oe and 6 kOe, in the temperature range between 4 K and 750 K.The magnetic field dependence of the magnetization, M͑H͒ curves, were measured at 5 K and 300 K under applied magnetic fields up to H = 90 kOe.Neutron powder diffraction patterns were collected every 60 s from the two samples, in two successive controlled heating-cooling cycles from RT to 1073 K and back to RT again at 5 K/min, on the POLARIS time-of-flight diffractometer ͑ISIS facility, U.K.͒.Data collected over the time-of-flight range ϳ2000-19600 s in the backscattering detector bank, ͗2͘ = 145°, ͑corresponding to a d-spacing range of ϳ0.3 to 3.2 Å, which allowed more than 30 reflections from the fcc phase to be monitored͒ were analyzed by full-profile Rietveld refinement 36 using the FULLPROF suite package. 37The wide d-spacing range allowed us to determine lattice parameters of both samples with accuracy better than 0.001 Å. Neutron powder diffraction experiments under high pressure were performed on PEARL ͑Rutherford Appleton Laboratory, U.K.͒ and HIPPO ͑Lujan Center for Neutron Scattering, LANL, USA͒ time-offlight neutron diffractometers, in addition, x-ray diffraction ͑XRD͒ patterns under high pressure were collected on the beam line ID27 ͑ESRF, France͒.The x-ray magnetic circular dichroism ͑XMCD͒ experiments were separately performed in transmission geometry under high-pressure on the beam line 4ID-D-XOR at the Advanced Photon Source ͑ANL, USA͒.

III. RESULTS AND DISCUSSION
The diffraction patterns of both samples show the presence of reflections attributed, via a Rietveld refinement, to a single phase with a face-centered cubic ͑fcc͒ crystal structure ͑see Fig. 1͒.It is worthwhile to note that the lattice parameters, a, of the MS powders are systematically larger ͑0.1%͒ than those of the standard powders at room temperature ͑RT͒.9][40] For the case reported here, it will be shown below that this increment of the lattice parameter at room temperature is due to the increase of the Curie temperature in an Invar material.Generally, in itinerant systems, expansion of the lattice parameter causes a decrease in the bandwidth, i.e., an increase in the density of states at the Fermi surface.As the result ferromagnetism becomes stable.
In Fig. 2, the M͑T͒ curve for the standard Fe 64 Ni 36 alloy ͑red curve͒, measured under an applied magnetic field of H = 6 kOe, is depicted showing a ferromagnetic ͑FM͒ behavior.The estimated Curie temperature is around 500Ϯ 10 K, in good agreement with earlier results in the literature. 41The M͑T͒ curve for the MS Fe 64 Ni 36 sample exhibits a large enhancement in the value of T C , ͑up to 650Ϯ 10 K͒.These findings can be understood on the basis of the magnetic coupling after milling between the MS crystals and the grain boundaries that can induce variations in the intrinsic properties such as Curie temperature and/or magnetic anisotropy. 42,43Further heating-cooling cycles overlap the M͑T͒ curve of the treated sample even when the sample is measured again with time intervals of several years, indicating that the magnetic behavior of the milled powders is maintained and is reversible after a first heating up to 1073 K is done.Moreover, a Curie-Weiss behavior has been found, for both alloys, in the temperature dependence of the reciprocal magnetic susceptibility near T C .The paramagnetic Curie temperatures, are p ϳ490 K and ϳ620 K, for standard and MS samples, respectively.
It is worth noting that M͑T͒ curves under low magnetic fields ͑H Ϸ 300 Oe͒ are quite different as it can be observed in Fig. 3, where the magnetization normalized to its value at T = 5 K vs the reduced temperature, T / T C , is shown in order to better appreciate the different behaviors for both samples.Both curves exhibit almost overlapping trends for temperatures T Ͻ 0.4 T C and T Ͼ T C .However, the slope of the M͑T͒ curve is much higher ͑more negative͒ for the MS sample in the immediacy of the Curie point, suggesting a sharper transition into the paramagnetic state.Moreover, we show the M͑H͒ curves measured at T = 5 K and 300 K ͑see inset in Fig. 3͒, where a slightly lower magnetization ͑less than 10%͒ is observed in the MS sample at low temperature ͑see also Fig. 2͒ probably due to frustration of Fe magnetic moments at the disordered grain boundaries. 42,43he results plotted in Fig. 2 obviously suggest the need to carry out a detailed study of possible correlations between the crystal structures, the large increase in T C , and the role played by magnetovolume effects.Specifically, it is of fundamental importance to determine whether this large enhancement of the Curie temperature also affects the thermal dependence of the expansion coefficient, ␣ T .If the material is found to exhibit Invar behavior with low values for ␣ T up to temperatures close to T C , the temperature range for controlled thermal expansion will have been enlarged by more than 100 K, which would be of great interest for technological applications.It is a remarkable observation that for a non-Invar Fe 50 Ni 50 alloy ͑the magnetovolume coupling in this material is much less important than in the standard Invar Fe 64 Ni 36 one͒ the same physical treatment quoted above leads to a ⌬T C of less than 20 K instead of the 150 K found for the Invar composition.
From the analysis of the neutron diffraction patterns, the fcc lattice parameters at 340 K are a = 3.592͑1͒ Å and 3.596͑1͒ Å respectively, in good agreement with x-ray diffraction results ͑3.59187͑1͒ Å and 3.59498͑3͒ Å, respectively͒, indicating a relative volume increase of ⌬V / V Ϸ 0.3%.It is important to note that the fcc structure remains unchanged over the whole temperature range of measurements for both samples, 44 although the lattice parameter value has increased ͑see above͒ and a slight peak broadening ͓see inset in Fig. 1, where the most intense reflection ͑111͒ is shown͔ is observed in the MS sample, 34 thus suggesting that internal microstrain is retained in the sample 36 after the mechanical and heat treatments.
The temperature dependence of the lattice parameters ͑see Fig. 4͒ for the two Fe 64 Ni 36 materials ͑the standard and the MS samples͒ clearly shows the Invar character of both materials: above T C the variation of the lattice parameter against temperature becomes linear, leading to a value for the thermal expansion coefficient, ␣ T Ϸ͑17Ϯ 1͒ ϫ 10 −6 K −1 , typically expected for a normal metal.However, a drastic change of slope takes place below T C , leading to a decrease in the value of ␣ T below ͑3 Ϯ 1͒ ϫ 10 −6 K −1 .The 450-550 K region where the changes in slope are observed due to the occurrence of magnetic ordering, is much higher than D / 2 ͑in these FeNi materials the Debye temperature is D ϳ370 K͒; i.e., the samples are well in the high temperature limit and zero point motion effects in thermal expansion coefficient are not important.
Two important differences between as received and treated samples can be immediately distinguished in Fig. 4: ͑i͒ the change of slope takes place, for the treated sample, at a temperature more than 100 K above that of the as received sample, thus confirming the correlation between the increase in the LTE temperature range and the raising of T C ; and ͑ii͒ the lattice parameter grows 0.1% after milling and annealing, but only for temperatures below T C .As can be observed the lattice parameters are practically identical for temperatures corresponding to the paramagnetic phase.This fact confirms that the increase in a observed below T C after milling and heat treatment is a consequence of the enhancement of T C .
In order to complete the characterization of the Invar behavior of these standard and MS samples, we, therefore, ex-amine the pressure dependence of the cell parameter and the Curie temperature.In particular, studies of magnetization under high pressure are far from common.It is well known that there are obvious difficulties in combining the requirements of high-pressure technology and classical magnetometry. 30,32,45n Fig. 5, we compare the pressure dependence of the cell parameter for fcc standard and MS samples at RT, showing a change of slope around 3.9 GPa ͑in good agreement with other recent works 33,46,47 ͒ and 7.6 GPa, respectively.The fcc lattice remains stable without any crystalline structural transformation over the whole pressure range up to 10 GPa.The dependencies of the cell parameter of both samples converge around 8 GPa and exhibit a similar pressure dependence above this pressure, while they clearly diverge below 8 GPa indicating that the standard and the MS samples have a different HS+ LS ground state.In fact, these dependencies have been well fitted to a first-order Murnaghan equation of state 48 considering the values of the Bulk modulus, B, as a fitting parameter and that of dB dP has been set to the value of 1.42 and 3.6 for the HS+ LS and LS states, respectively, obtained from ultrasonic measurements. 29The best refinement leads to the values of B around 113 GPa and 127 GPa for standard and MS samples, respectively, at RT and atmospheric pressure, i.e., the compressibility of the standard sample is larger than that of the MS one.This fact could be understood taking into account that ͑i͒ the mechanically stressed sample is probably filled with dislocations and defects after milling that interfere so strongly with each other that the compressibility is found to drop significantly; and ͑ii͒ the HS+ LS states of both materials could be different by the effects of irreversible strain induced during the milling process performed at room temperature, which is below the Curie temperature of the Fe 64 Ni 36 standard Invar alloy.
Figure 6 displays the pressure dependence of the peak-topeak XMCD magnitude for standard and MS samples measured at the Fe K-edge and collected at RT.The XMCD spectra of the standard sample are similar to those measured in the FeNi alloys. 49The lower XMCD signal for the stan- dard sample at ambient pressure agrees with the magnetization results in Figs. 2 and 3 ͑T = 300 K͒.Increasing pressure both XMCD signals start to decrease with a moderate rate at the pressures where the respective cell parameters of these materials showed a change of slope ͑see Fig. 5͒.At high pressure we observe a tendency to collapse, in a similar way to that reported for cementite ͑Fe 3 C͒. 21It is important to determine whether this XMCD collapse is due to the expected transition from a LS state to a nonmagnetic one or due to a concomitant decrease in Curie temperature.Assuming that the M͑T͒ dependence of Fig. 2 is universal under pressure, we have been able to estimate the dependence of T C with pressure using the XMCD values for each pressure.The inset of Fig. 6 shows that these dependencies are fairly linear ͑− dT C dP Ϸ 35 K / GPa for both materials͒ and similar to that of the Invar Fe 68.1 Ni 31.9 ͑− dT C dP =33 K/ GPa͒. 44In the same way, an estimation of − dT C dP can be also obtained from both the neutron diffraction under pressure and magnetization results ͑see Figs. 2 and 5͒.From these it seems that 3.7 GPa corresponds to 150 K; so − dT C dP Ϸ 40 K / GPa, which is quite close to the value determined above from XMCD.Extrapolating the XMCD magnitude to zero value at room temperature ͑measured at around 300 K͒, which makes that the transition temperature to a nonmagnetic sate drops to 300 K in both materials, we obtain critical pressures of ϳ7.0 GPa and ϳ10.7 GPa, for Fe 64 Ni 36 standard and MS samples, respectively.The difference 3.7 GPa in the values of these critical pressures is in quite good agreement with the difference found in the values of pressure where the change of slope in the cell parameters takes place ͑see Fig. 5͒.Furthermore, extrapolating to zero the value of T C from the T C ͑P͒ variation ͑see the inset of Fig. 6͒ leads to the values of ϳ13 GPa and ϳ17 GPa for the pressures needed in order to stabilize the NM state in standard and MS Fe 64 Ni 36 samples, respectively.These critical pressures correspond to the val-ues of the magnetic phase transition from the LS to the nonmagnetic state obtained by inelastic x-ray scattering. 50s a consequence, it seems that in addition to the fact that the treated Fe-Ni Invar alloy become harder to squeeze under pressure, we need to add the feature that owing to the important magnetoelastic coupling in these materials, when they are mechanically stressed below T C , these systems increase notoriously their Curie temperature, leading to an enhancement of the Invar properties, where an almost zero thermal expansion is observed.Up to now the usual way to attempt to increase T C in this FeNi system is through increasing the Ni content, however, in doing so the magnetovolume effects lose importance because Ni atoms stabilize much more the HS state.Ball milling followed by high temperature annealing overcomes these shortcomings.Moreover, x-ray absorption experiments in both Fe-K and Ni-K edges revealed a more disordered local environment around the Fe atoms, 34 suggesting that mechanical stressing of the invar powders mostly affects the Fe-Fe interatomic distances because a slight increase of such distances favors ferromagnetism.

IV. CONCLUSIONS
In summary, the mechanically stressed and thermally treated Fe 64 Ni 36 alloy exhibits an outstanding enhancement of an intrinsic physical property such as the Curie temperature, being the LTE range extended as well.Up to now, the research effort in Invar materials with larger LTE temperature ranges has been mainly focused on the search for new compositions instead of changing the microstructure with the aim of varying the magnetovolume coupling.Furthermore, this work opens new horizons and directions significantly different from those currently being pursued in the so-called Invar problem, which during the last century was mostly oriented in understanding the mechanism leading to LTE.In particular, other deeply mysterious issues about which we have very little comprehension is the enhancement of an intrinsic property, such as the Curie magnetic ordering temperature, in this new modified Invar Fe 64 Ni 36 alloy, will also deserve much more interest and effort within the scientific community.

FIG. 1 .
FIG. 1. ͑Color online͒ Fitted powder neutron diffraction patterns for standard ͑upper panel͒ and MS ͑lower panel͒ Fe 64 Ni 36 samples.Observed ͑+͒ and calculated ͑solid line͒ patterns; positions of the Bragg reflections are represented by vertical bars.The observedcalculated difference is displayed at the bottom of each panel.The inset is a magnification of the ͑111͒ reflection.

FIG. 4 .
FIG. 4. ͑Color online͒ Temperature dependence of the fcc cubic lattice parameter, a, derived from time-of-flight powder neutron diffraction measurements, for standard ͑red solid circles͒ and MS ͑blue solid circles͒ Fe 64 Ni 36 samples.The inset shows the high temperature dependence of the lattice parameter for both samples.