Acoustic emissions from spin crossover complexes

Abstract

Acoustic emission from the compounds [Fe(HB(tz)₃)₂] and [Fe(Htrz)(trz)₂]BF₄ was detected during the thermally induced spin transition and is correlated with simultaneously recorded calorimetric signals. We ascribe this phenomenon to elastic waves produced by microstructural and volume changes accompanying the spin transition. Despite the perfect reversibility of the spin state switching (seen by the calorimeter), the acoustic emission activity decreases for successive thermal cycles, revealing thus irreversible microstructural evolution of the samples. The acoustic emission signal amplitude and energy probability distribution functions followed power-law behavior and the characteristic exponents were found to be similar for the two samples both on heating and cooling, indicating the universal character, which is further substantiated by the well scaled average temporal shapes of the avalanches.

Fig. 1. Schematics of the setup (1: microphone housing, 2: pressing spring, 3: microphone, 4: steel waveguide, 5: plexiglas, 6: silicon wafer, 7: sample, and 8: DSC furnace) and a typical temporal shape of the acoustic emission signal with the definition of the measured parameters. The duration time is the time at which the signal falls below the threshold (and is equal to t_f–t_s). The threshold was determined far from the spin transition event, i.e. when no AE due to structural changes was present (see also the text).

Fig. 2. Hysteresis loop (a) calculated from the DSC curves (b) for compound 1.

Fig. 3. DSC curves (red lines) and the cumulative number of AE events (N_t = ∑N_i, blue lines) for the first, second and sixth heating/cooling runs in compound 1. Dots indicate the amplitude of individual AE hits (the numbers on the right hand vertical axis show the values of N_t. The heat flow in mW is given by the same numbers after multiplying by the factor indicated in the brackets).

Fig. 4. Cumulative number of AE events (red and blue dots) and the relative value of the transformation heat (compared to the first cycle) as a function of the number of cycles.

Fig. 5. Examples of probability distribution density functions of (a) energy, (b) amplitude and (c) area as well as illustrations of (d) energy–amplitude, (e) area–amplitude and (f) area–duration power relations for compound 1. The fitted straight lines are the results of fits according to eqn (1) (see also the text and ESI†) as well as of fits according to the power relations between E and A as well as S and A.

Fig. 6. Schematic representation of the composition of an avalanche signal in acoustic emission experiments (reprinted with permission from ref. 55). During local switching, an avalanche with V(t) emits a strain signal (i.e. the source function) which propagates through the sample and is eventually measured by the detector. During the propagation and attenuation, the signal also generates the ringing of the sample. The profile of a source delta function would generate T(t), the so-called transfer function. The distortion is manifested on the time scale in a long exponential decay tail at the end of the avalanche. Thus, the duration of the avalanche is heavily distorted, while the amplitude and rising time are less influenced.

Fig. 7. Scaled temporal avalanche shapes for different bins of area.