Measuring strain at the atomic-scale with Differential X-ray Absorption Spectroscopy

Strain-inducing phenomena, such as magnetostriction, lie at the heart of transducer technologies. Knowledge of their origin and mechanics, and how they manifest themselves in different materials, underpins the development and optimisation of sensor and actuator devices. DiffXAS has been developed to permit strain measurements at an atomic-scale, and thus verify theoretical models for transducer behaviour.Submitted versio

Thermal Differential EXAFS

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EXPERIMENTALLY MEASURED RADIATIVE LIFETIMES AND OSCILLATOR STRENGTHS IN NEUTRAL VANADIUM

We report a new study of the V i atom using a combination of time-resolved laser-induced fluorescence and Fourier transform spectroscopy that contains newly measured radiative lifetimes for 25 levels between 24,648 cm−1 and 37,518 cm−1 and oscillator strengths for 208 lines between 3040 and 20000 Å from 39 upper energy levels. Thirteen of these oscillator strengths have not been reported previously. This work was conducted independently of the recent studies of neutral vanadium lifetimes and oscillator strengths carried out by Den Hartog et al. and Lawler et al., and thus serves as a means to verify those measurements. Where our data overlap with their data, we generally find extremely good agreement in both level lifetimes and oscillator strengths. However, we also find evidence that Lawler et al. have systematically underestimated oscillator strengths for lines in the region of 9000 ± 100 Å. We suggest a correction of 0.18 ± 0.03 dex for these values to bring them into agreement with our results and those of Whaling et al. We also report new measurements of hyperfine structure splitting factors for three odd levels of V i lying between 24,700 and 28,400 cm−1

Fe I Oscillator Strengths for Transitions from High-lying Odd-parity Levels

We report new experimental Fe I oscillator strengths obtained by combining measurements of branching fractions measured with a Fourier Transform spectrometer and time-resolved, laser-induced fluorescence lifetimes. This study covers the spectral region ranging from 213 to 1033 nm. A total of 120 experimental log( ) gf -values coming from 15 odd-parity energy levels are provided, 22 of which have not been reported previously and 63 of which have values with lower uncertainty than the existing data. The radiative lifetimes for 60 upper energy levels are presented, 39 of which have no previous measurements

The Local Atomic-scale Joule Magnetostriction of FePt

Commonly, the magnetostriction of a material is ascertained from macroscopic measurements on bulk samples. However, to truly understand their intrinsic microscopic behaviour, and allow direct comparison with theoretical models, it is necessary to measure structural strain at the atomic level. Commonly employed local probes, such as X-ray Absorption Spectroscopy (XAS), may obtain the absolute structural parameters on a scale of picometres, but lack the resolution to observe magnetostrictive strain, which is typically two or three orders of magnitude smaller. However, such measurements have recently become possible with the development of Differential XAS (DiffXAS) at the European Synchrotron Radiation Facility [1][2]. Here, we present the results of XAS and DiffXAS measurements obtained from the technologically important FePt system. Sputtered thin films of stoichiometric FePt were prepared in the disordered state and then annealed at temperatures in the range 400°C-600°C to produce the ordered high anisotropy L10 phase. Data analysis indicates that the magnetostriction coefficients of the as-deposited films are of the order of 100ppm in the cubic 100 direction and 250ppm in the 111 direction, and decrease systematically to approximately one fifth of those values as the annealing temperature is increased up to 600°C. Furthermore, the chemical selectivity of DiffXAS has permitted the magnetostrictive strain to be quantified from both the perspective of the local structure surrounding the Fe site, and from that surrounding the Pt site. This has allowed the contributions from different bond types (Fe-Fe, Fe-Pt, Pt-Fe, and Pt-Pt) to be deconvolved from the bulk magnetostriction and assessed individually within the first two coordination shells around the absorbing atom. References [1] Pettifer, R. F. and Mathon, O. and Pascarelli, S. and Cooke, M. D. and Gibbs, M. R. J., Nature 435 78-81 (2005) [2] Pascarelli, S. and Ruffoni, M. P. and Trapananti, A. and Mathon, O. and Aquilanti, G. and Ostanin, S. and Staunton, J. B. and Pettifer, R. F., Phys. Rev. Letters 99 237204 (2007)Submitted versio

The Local Atomic Joule Magnetostriction of Fe81Ga19

Using X-ray Absorption Spectroscopy (XAS) in differential mode (DiffXAS), the magnetostriction of a Fe81Ga19 splat cooled ribbon has been measured and the strain coefficients quantified. Due to the local atomic nature of XAS, this represents the first microscopic analysis of such a system, and was made possible only by recent advances in synchrotron radiation based techniques, capable of detecting atomic strains on the scale of femtometres [1]. Previously, magnetostriction measurements have relied on macroscopic techniques, commonly via strain gauges. However, such measurements on thin films and ribbons, which tend to be of the greatest importance from a technical perspective, are notoriously difficult. This is in part due to the measured strains being extremely small over a sample thickness of a few tens of microns, but also due to the practicalities of coupling such a sample to a sensor. Consequently, published magnetostriction coefficients vary immensely. In some cases, giant magnetostrictions have been reported for Fe(1-x)Gax ribbons [2][3] although doubt has recently been cast upon their validity [4]. This serves to assert a need for a more fundamental approach to measuring magnetostrictive strains. A need which is satisfied by DiffXAS. Being based upon XAS, DiffXAS probes changes in local atomic structures and is just dependent upon the short-range order of the first one or two atomic shells surrounding an absorbing atom. However, whilst even giant magnetostrictive strains exhibited by a number of rare-earth based Fe alloys are on the very limits of detection by conventional XAS techniques, DiffXAS offers an increase in sensitivity of two orders of magnitude and so makes such strains easily measurable. Direct detection of strains on the scale of tens or hundreds of ppm then becomes possible. Furthermore, in principle, this is true for any type of strain that is reproducible upon the modulation of some external sample property [5]. Additionally, since x-ray absorption is chemically selective, these structural changes may be viewed from different positions within the crystal lattice, and so the underlying significance of different atomic species in the overall process elucidated. Contributions from different types of bonds within the structure may then be decoupled and analysed. Such information has immense value when trying to obtain fundamental knowledge of atomic strains, and particularly when attempting to verify theoretical models. Concerning Fe(1-x)Gax, a theory for the observed strain enhancement was first put forward by Wu [6] in 2002, which has more recently been developed by Cullen et al [7] after modelled the behaviour of the material’s magnetocrystalline anisotropy. Experimental verification of these proposals has yet to be presented, but is something that DiffXAS has the potential to provide. Using this technique, we have focused on the problem of enhanced magnetostriction observed in the Fe(1-x)Gax system. Such systems have attracted significant interest from a technological and device applications perspective since, although they do not possess truly giant magnetostrictions, they are both absent of expensive rare-earth components and have desirable mechanical properties. They also show appreciable low-field magnetostriction, saturating at fields of only several hundred Oersteds. Working within these saturation conditions, DiffXAS detects the changes in photoelectron scattering path length induced by structural distortions that occur when the sample’s magnetisation vector is modulated between two states – parallel and perpendicular to the x-ray polarisation vector. Subsequent data analysis uses a framework of Cartesian tensors to model the structural properties of the sample, and ab initio XAS theory to model the observed perturbations. From this, the atomic strain tensor may be derived and related to the sample magnetisation vector in order to find the coefficients of the Joule magnetostriction tensor [8]. These coefficients may then be reduced to the more familiar macroscopic 100 and 111 coefficients by exploiting the crystal symmetry elements [8]. Working on a splat cooled foil of Fe81Ga19, preliminary analyses performed with this technique have yielded a magnetostriction coefficient of (3/2)100 = 250±20ppm (111 coefficient is approximately zero for this composition), based upon a disordered A2 structure, determined from analysis of the sample’s conventional XAS signal. This analysis failed to detect the D03 structure reported by some authors for this composition. Further experiments are planned to examine the full range of compositions over which magnetostriction enhancement is observed in this system. [1] R.F. Pettifer, O. Mathon, S. Pascarelli, M.D. Cooke, M.R. J. Gibbs, Nature 435, 79 (2005) [2] M.C. Zhang, H.L. Jiang, X.X. Gao, J. Zhu, and S.Z. Zhou, J. Appl. Phys. 99, 023903 (2006) [3] G.D. Liu, L.B. Liu, Z.H. Liu, M. Zhang, J.L. Chen, J.Q. Li, G.H. Wu, Y.X. Li, J.P. Qu, T.S. Chin, J. Appl. Phys. 84, 2124 (2004) [4] R. Grössinger, R. Sato Turtelli, N. Mehmood, S. Heiss, H. Müller, C. Bormio-Nunes, J. Mag. Mag. Mater., in press [5] M. P. Ruffoni, R.F. Pettifer, S. Pascarelli, A. Trapananti, O. Mathon in X-Ray Absorption Fine Structure XAFS13, edited by B. Hedman and P. Pianetta, AIP Conf. Proc. No. 882 (AIP, 2007), p. 838. [6] R. Wu, J. Appl. Phys. 91, 7358 (2002) [7] J. Cullen, P. Zhao, M. Wuttig, J. Appl. Phys. 101, 123922 (2007) [8] E du T, de Lacheisserie in Magnetostriction: Theory and Applications of Magnetoelasticity (CRC Press, 1993), p133 and 161-162Submitted versio

Measurement of Individual Bond Magnetostrictive Strain in α-TbFe2

The structural changes exhibited by materials in response to their surroundings is of fundamental importance across countless disciplines in science and engineering. In the field of transducer technologies, strain-inducing phenomena (such as magnetostriction) are utilised in their own right, and form the physical foundation for sensor and actuator devices. Knowledge of their origin, and how they manifest themselves in different materials, underpins the development of new transducers and the optimisation of existing technologies. Yet in spite of this, direct measurement of a material’s intrinsic magnetostriction – the strain induced between individual atoms at a microscopic level – has proven elusive. This has essentially been due to the difficulty in measuring atomic motion with sufficient precision. In most materials, magnetostrictive atomic displacements saturate at just a few femtometres. Here, even sensitive atomic probes, such as x-ray absorption spectroscopy (XAS), lack the resolution to observe this motion by some two orders of magnitude. As a result, common experiments employ strain gauges on macroscopic samples, where the strain is easier to detect, but where atomic information is lost. However, with the recent development of differential XAS (DiffXAS) at the European Synchrotron Radiation Facility (ESRF), such atomic-scale measurements have become possible [1,2]. Initial studies into the magnetostriction of FeCo thin films demonstrated a sensitivity to femtometre scale motion [1]. Subsequent work extended this study to investigate the magnetoelastic coupling of FeCo under applied hydrostatic pressure [3], and new experiments looked into the behaviour of FePt, and rare-earth iron alloys such as Fe2Tb. But the most significant study conducted to date has been that of the Fe-Ga system [4,5]. In recent years, binary metal alloys such as Fe-Al or Fe-Ga, have attracted considerable interest [6]. It is well known that pure Fe exhibits only an extremely small magnetostriction, but when alloyed with certain nonmagnetic metallic elements, it can be enhanced by over an order of magnitude. Compositions of Fe-Ga with around 19at% Ga have reported strains of up to 400 ppm [7]. Although this doesn’t constitute a truly ‘giant’ magnetostriction, it is of interest for device applications since Fe-Ga is devoid of expensive rare-earth components, saturates in fields of only several hundred Oersteds, and possesses more desirable mechanical properties than, say, the much studied Terfenol-D alloy. In order to identify the origin of this enhancement, we took a splat-cooled foil of Fe81Ga19 and measured its Joule saturation magnetostriction with DiffXAS [4]. Unlike conventional macroscopic measurements that describe the sample as a whole, magnetostriction coefficients provided by DiffXAS describe the strain of just the first two or three atomic coordination shells surrounding a photo-excited atom. Furthermore, since it is possible to tune the x-ray energy, and so select which atom in the material is excited, it is possible to look at the strain in the local environment of each atomic species separately. Contributions from different types of bond within the structure may then be decoupled and analysed. Such fundamental information has immense value when attempting to verify theoretical models. In 2002, Wu [8] proposed a model for the magnetostriction of FexGa(1-x) that suggested a tetragonal “B2-like” structure in the vicinity of the Ga atoms was responsible for the observed enhancement. More recently, Cullen et al. [9] reached a similar conclusion, and stated that such a structure could be formed by Ga pairs randomly arranged throughout the material. Conventional XAS studies have confirmed the presence of these Ga pairs [5], but it is DiffXAS that describes how they influence the magnetostriction. From our DiffXAS spectra, we extracted the strain present in different types of bond, and with a subsequent analysis, solved the magnetostriction tensor for the material. This provided two sets of magnetostriction coefficients. In the environment around Fe, (3/2)100 = 40ppm and (3/2)111 = -32ppm, and in the environment around Ga, (3/2)100 = 390ppm and (3/2)111 ~0ppm. This demonstrates that the observed enhancement is dominated by strain in the vicinity of the Ga atoms. Furthermore, our analysis revealed that the strain in the Ga pairs was negligible, indicating that they do not contribute directly to the enhanced magnetostriction, but rather mediate the enhancement in the surrounding Ga-Fe bonds. Further experiments are planned to examine the full range of compositions over which magnetostriction enhancement is observed in this system, and, with the use of single crystal samples, investigate how the microscopic magnetostriction scales up to that seen macroscopically. [1] R.F. Pettifer, O. Mathon, S. Pascarelli, M.D. Cooke, M.R. J. Gibbs, Nature 435, 79 (2005) [2] M. P. Ruffoni, R.F. Pettifer, S. Pascarelli et al., AIP Conf. Proc. No. 882, 838 (2007) [3] S. Pascarelli, M. P. Ruffoni, A. Trapananti et al., Phys. Rev. Lett. 99, 237204 (2007) [4] M. P. Ruffoni, S. Pascarelli, R. Grössinger et al., Phys. Rev. Lett. 101, 147202 (2008) [5] S. Pascarelli, M. P. Ruffoni, R. Sato-Turtelli et al., Phys. Rev. B 77, 184406 (2008) [6] E. M. Summers, T. A. Lograsso, M. Wun-Fogle, J. Mater. Sci. 42, 9582 (2007) [7] A. E. Clark, A. B. Hathaway, M. Wun-Fogle et al., J. Appl. Phys. 93, 8621 (2003) [8] R. Wu, J. Appl. Phys. 91, 7358 (2002) [9] J. Cullen, P. Zhao, M. Wuttig, J. Appl. Phys. 101, 123922 (2007)Submitted versio

Measuring strain at the atomic-scale with Differential X-ray Absorption Spectroscopy

The development of smart materials for use in transducer devices has driven considerable research in recent decades. In this field, phenomena such as magnetostriction underpin the operation of sensors and actuators, and energy harvesting devices. Thus, knowledge of their origin and mechanics, and how they manifest themselves in different materials, enables the development of new devices and optimisation of existing technologies. Yet this research is not without its limitations. Theoretical studies naturally describe material properties at a fundamental, atomic-scale. But experimental work struggles to verify such models at a similarly microscopic scale. Saturation strains from typical magnetostrictive materials induce displacements between neighbouring atoms of only a few femtometres. On such a scale, even commonly employed local probes, such as x-ray absorption spectroscopy (XAS), lack the resolution to observe this motion by some two orders of magnitude. As a result, experiments typically employ strain gauges on large, macroscopic samples, where the strain is easier to detect, but where atomic information is lost. However, the recent development of differential XAS (DiffXAS) at the ESRF presents a unique opportunity to bridge this gap between macro-scale experimental work, and fundamental theoretical models [1]. This talk will study the development of DiffXAS via the most significant results obtained to date. These include studies of the important Fe-Ga and Fe-Pt systems, where DiffXAS analysis procedures have allowed chemically-selective, atomic magnetostriction coefficients to be quantified [2][3]; and an investigation of the magneto-elastic coupling of FeCo through measurements under applied hydrostatic pressure [4]. [1] R.F. Pettifer et al., Nature 435, 79 (2005) [2] M. P. Ruffoni et al., Phys. Rev. Lett. 101, 147202 (2008) [3] S. Pascarelli et al., Phys. Rev. B 77, 184406 (2008) [4] S. Pascarelli et al., Phys. Rev. Lett. 99, 237204 (2007)Submitted versio