Avalanche criticality in externally Avalanche criticality in - PowerPoint PPT Presentation

Avalanche criticality in externally Avalanche criticality in externally driven materials driven materials Antoni Antoni Planes Antoni Antoni Planes Planes Planes (antoniplanes@ub.edu) Departament Departament de de Física Física de la de la Matèria Matèria Condensada Condensada Universitat Universitat de Barcelona de Barcelona Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Collaborators E. Vives, Ll. Mañosa, J. Baró * , D. Soto-Parra ** E. Bonnot *** , P. Castillo-Villa ** Present address: * University of Calgary, Canada; * Queen’s University , Belfast; ** IPICyT , San Luís Potosí, Mexico Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Collaborators E. Vives, Ll. Mañosa, J. Baró * , D. Soto-Parra ** E. Bonnot *** , P. Castillo-Villa ** Present address: * University of Calgary, Canada; * Queen’s University , Belfast; ** IPICyT , San Luís Potosí, Mexico B. Ludwig , U. Klemradt B. Ludwig , U. Klemradt E. K. H. Salje C.Gallardo, J. Romero, J. M. Martín-Olalla Y. Fan, R. S. Edwards, S. Dixon R. Romero, M. Stipcich R. Niemann, S. Fälher F. J. Pérez-Reche T. Kakeshita, T. Fukuda Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Systems of interest • Systems that respond to a slowly driven external field • • • intermittently with discrete events that occur over a broad range of sizes ( avalanches) . • This behaviour typically occur in heterogenous / disordered • • • systems with athermal dynamics. • • • • Examples: - Dislocation dynamics - Plasticity - Fracture - Magnetization processes - Ferroelastic/martensitic transitions .... - Seismicity Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Systems of interest • Systems that respond to a slowly driven external field • • • intermittently with discrete events that occur over a broad range of sizes ( avalanches) . • This behaviour typically occur in heterogenous / disordered • • • systems with athermal dynamics. • • • • Examples: - Dislocation dynamics - Plasticity - Fracture of porous materials under compression - Magnetization processes - Ferroelastic/ martensitic transitions .... - Seismicity Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Acoustic emission AE occurs associated with these externally stimulated processes. The acoustic waves originates from localized processes that occur at length scales ranging from nano to micrometers that give rise to rapid changes of the internal strain field of the system. It is typically detected in the frequency range of MHz. It is typically detected in the frequency range of MHz. Its detection provides a potentially interesting technique to characterize avalanches and avalanche dynamics. Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Detection Acoustic Emission : Elastic waves originate from the source and propagate through the sample. A(V) ( ) U t Electric signal Piezoelectric transducer (PZT) Acoustic source Acoustic source t end ( ) dt t ∫ ∝ E U t 2 Signal, U ( t ) A Treshold Example of AE signal : 0 ∆ t = t end – t 0 Time (ms) Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Data analysis • The AE carries the whole temporal and spatial information of the source mechanism. • Extracting this information is difficult since the signal U ( t ) is severely distorted due to the acoustic coupling of the transducer and its frequency response. Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Data analysis • The AE carries the whole temporal and spatial information on the source mechanism. • Extracting this information is difficult since the signal U ( t ) is severely distorted due to the acoustic coupling of the transducer and its frequency response. • Partial information: • Partial information: • Pulse counting rate: Acoustic Emission activity Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Examples Martensitic transition in Cu-Zn-Al Compression of porous Vycor Calorimetry AE activity AE activity 0 1 2 3 4 T (º C ) AE activity Calorimetry Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Data analysis • The AE carries the whole temporal and spatial information on the source mechanism. • Extracting this information is difficult since the signal U ( t ) is severely distorted due to the acoustic coupling of the transducer and its frequency response. • Partial information: • Partial information: • Pulse counting rate: Acoustic Emission activity • Statistical analysis of the amplitude, energy, duration, waiting- time, ... of the AE signals: provides information related to the collective behaviour of the system Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Criticality • Amplitude, energy and duration of AE signals span over a broad range (decades). • Often the statistical distribution of these quantities is power-law which is a typical feature of criticality , i.e., avalanche dynamics shows scale invariance . ( ) = , , ∆ : • Statistical distribution Y A E t ( ( ) ) exp exp = = − − λ λ Y Y ω Y Y ω − − p(Y) p(Y) C C Y Y λ Y : measures the distance to criticality C Y : normalization factor ω : critical exponent (= α , ε , τ corresponding to A, E, ∆ t )  ∼ z E A   Statistical relation:   ∼ ∆ x A t   • Criticality ( ) ( )  α − = ε − = τ − z x 1 1 1 Scaling relation: Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Martensitic transition • A martensitic transformation (ferroelastic) is a σ diffusionless structural transition from a high symmetry to a lower symmetry crystallographic phase. • Can be induced by changing temperature and/or T stress (conjugated field). • Shows athermal character and proceeds intermittently as a • Shows athermal character and proceeds intermittently as a sequence of jerks (avalanches). • Produce a complex multiscale domain microstructure. Courtesy of Prof. Michel Morin Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Framework • The intermittent (jerky) character of the transformation is a consequence of dynamical constraints imposed by disorder : • Intrinsic disorder: lattice defects, impurities, etc... • Self-generated elastic long-range interaction effects. Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Framework • The intermittent (jerky) character of the transformation is a consequence of dynamical constraints imposed by disorder : • Intrinsic disorder: lattice defects, impurities, etc... • Self-generated: long-range interaction effects. • The jerks or avalanches are associated with discontinuities of the strain ( O.P. ) associated with the jumps from one metastable state to another metastable state. another metastable state. Driving Field O.P F F Driving Field O.P O.P Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

AE signals Martensitic transition of a Cu-Zn-Al alloy Sampling rate: 2 MHz 15 Waiting times ÷ 20 U (mV) 10 5 2 3 1 Times (ms) Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Acoustic and optical activity (2d) Niemann et al., PRB, 89 , 216118 (2014) Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Acoustic and optical activity (2d) Niemann et al., PRB, 89 , 216118 (2014) Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016

Cycling across the transition Cu-Al-Mn, single crystal: Cubic → orthorhombic Annealed at 800 ºC, cooled in air down to RT and cycled 220 240 260 280 300 320 220 240 260 280 300 320 1.0 0 -1000 n = 1 0.5 -2000 -3000 0.0 1.0 600 300 action n = 2 n = 2 J/K) dQ / dT (mJ/K 0.5 0.5 0 0 Transformed frac -300 0.0 300 1.0 0 n = 9 0.5 -300 0.0 -600 200 1.0 n =24 0 0.5 -200 0.0 220 240 260 280 300 320 220 240 260 280 300 320 T (K) T (K) Pérez-Reche et al., PRB, 69 , 064101 (2004) Hysteresis, Avalanches and Interfaces in Solid Phase Transformations, Oxford, UK, 19-21 September 2016