Mathon, O

Pascarelli, S

Pettifer, RF

Ruffoni, MP

Trapananti, A

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c S SThermal Differential EXAFSM. P. Ruffoni and R. F. PettiferDepartment of Physics, University of Warwick, Coventry, CV4 7AL, UKS. Pascarelli, A. Trapananti, and O. MathonESRF, 6 Rue Jules Horowitz, BP220, 38043, Grenoble Cedex, Francec S SOutline• An introduction to Differential EXAFS• Thermal modulation of sample materials• Proof of concept – Thermal expansion measurements• Data analysis procedure• Future work – Probing phase transitions with single Kelvin resolutionc S SWhat is Differential EXAFS?A Differential EXAFS spectrum is the difference between two conventional EXAFSspectra, taken with all environmental parameters kept constant except for unitmodulation of some parameter of interest, such as temperature.As a result, the signal contains information relating to structural strain that occurreddue the change in chosen parameter.First used to measure magnetostriction in FeCo (R.F. Pettifer et al., Nature 435, 78)Potential problems:• Energy drift of the beam generating spurious signals• Spatial drift of the beam causing measurement of different parts of sample• Statistical noise preventing resolution of structural changes, typically ~10-5ÅSolutions:• Acquire both spectra in minimal time; of the order of a few seconds or less• Use a high intensity 3rd generation source in conjunction with a sensitive detector• Average signal over many pairs of measurements (O. Mathon et al., J. Synchrotron Rad. 11, 423)c S SID24 for Differential EXAFS• All Differential EXAFS experiments performed to date have been conducted on ID24, the Dispersive XAS beamline of the ESRF.• Mounted on a high-intensity 3rd generation undulator source.• Entire spectrum is obtained simultaneously in around 200ms, minimising drift.• Has no moving parts, which improves beam stability.• Tight focal spot size allows use of samples with tiny thermal mass.c S SThermal modulation apparatus• Thermal modulation apparatus must alternately heat and cool the sample material between XAS measurements at T+ and T-.• The heating/cooling must be quick. Ideally less than 1 second.• Temperature at T+ and T- must be both stable and reproducible.• Solution is to use two jets of heated gas, switched by a fluidic valve.c S SThermal modulation apparatusTemperature• Gas is heated as it traverses the heatsink• Heated jet of gas strikes sample• Gas passing around the rear of the sample provides secondary heatingc S SThermal Differential EXAFS       2 22 ( ), sinjT kj j jjk T A k e s T k kc               22, , ,j jj j js T Tk T k T k TT s T T T Tc c c                            2 2 2 222 2 ( )2,cos 2 sinj jT k T kjj j j j j j jjk Ts kA k e s T k k k A k e s T k kT T c                           2 2 2 222 2 ( )2,cos 2 sinj jT k T kjj j j j j j jjk Ts kA k e s T k k k A k e s T k kT T c           Neglect weak path length dependence of A and , making them T independent.Take a first order Taylor expansion with respect to temperatureKey Features• The Differential signal contains both a Thermal Expansion and Disorder term.• Thermal Disorder contributions are in phase with the original EXAFS signal.• Thermal Expansion contributions are in quadrature with the original EXAFS signal.• Given  <<  , signal will be largely in phase with c, but slightly phase shifted.2 /j T c S STuning the apparatus• Must obtain a flat DiffEXAFS baseline, passing through c = 0, for T = 0K.• Pressure gradients within sample mount generated grey signal.• 4 days of beamtime were needed to produce a flat baseline!c S SThermal Expansion measurements• To prove Thermal DifferentialEXAFS works in practice, thermalexpansion measurements weremade on samples of -Fe andSrF2• Signals are averaged over 600pairs of acquisitions for a range oftemperature differences.• Disorder term dominates givensignals are largely in phase withEXAFS.• DiffEXAFS peaks are phaseshifted, indicating detection of thethermal expansion component.c S SThermal Expansion measurementsTo obtain the thermal expansion coefficient:1. Define a reference from which to measure thermally induced displacements2. Fit the differential fine-structure function to each differential signal to establish and the3.  for Fe is 11.8 x 10-6K-12 /j T T = 1.7K T = 2.4K T = 3.2KSS1 1.13±0.041.08±0.021.08±0.01SS2 0.88±0.080.91±0.050.91±0.04SS3 0±300 2.1±0.1 1.72±0.08SS4 2.6±0.4 3.4±0.3 2.7± 0.2 12±1 12.1±0.8 11.8±0.6Units of                are 10-4 Å2and  is 10-6K-12 /j T 2 /j T c S SFuture Work – Phase TransitionsThermal expansion measurements have shown Thermal Differential EXAFSworks in practice.But the true power of the technique lies in studies of disordered or amorphoussystems or of non-linear phenomena such as phase transitions.With temperature steps of ~1K, it is possible to measure structural changesover many points through the transition region itself rather than just aboveand below it.

Thermal Differential EXAFS

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