Acoustic emission and energy dissipation during front propagation in a stress-driven martensitic transition Erell Bonnot, Eduard Vives, Lluís Mañosa, and Antoni Planes Departament d’Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia Ricardo Romero IFIMAT, Universidad del Centro de la Província de Buenos Aires and Comisión de Investigaciones Científicas de la Província de Buenos Aires, Pinto 399, 7000 Tandil, Argentina Received 15 April 2008; revised manuscript received 24 June 2008; published 5 September 2008 In the present paper, by using a specially designed experiment, we analyze the relationship between the acoustic emission and the deformation resulting from front propagation during a stress-induced transition from cubic to a single-variant martensite in a Cu-Zn-Al single crystal. The front propagates by nucleation and growing needle domains parallel to the parent martensitic interface. A good correlation between the acoustic emission activity and front velocity is obtained. By using a phenomenological model, we discuss the relation between such acoustic activity and the dissipated energy during the process. Results suggest that the acoustic emission has its origin in the interaction of needle domains and dislocations. DOI: 10.1103/PhysRevB.78.094104 PACS numbers: 81.30.Kf, 64.60.av, 61.72.Hh I. INTRODUCTION Acoustic waves are emitted during many externally stimulated solid-state processes which occur at scales rang- ing from nanometers to micrometers. These acoustic waves propagate through the solid and can be detected by means of suitable sensors giving rise to the so-called acoustic emission AE. 1 AE has been reported in plasticity-related phenomena such as dislocation dynamics, 2,3 microcrack propagation, 4 and first-order phase transitions taking place in multiferroic materials. 5,6 Detection of AE reveals an intermittent and jerky character of the dynamics in all these phenomena. Usu- ally an external field is responsible for the modification of the internal distribution of strains due to induced local micro/nano displacements which are at the origin of the generated acoustic waves. Therefore, it is commonly as- sumed that AE provides basic information related to energy dissipation mechanisms of the studied process. In first-order phase transitions local displacements are di- rectly related to the transition mechanism when strain is the primary order parameter as in the case of ferroelastic or mar- tensitic transitions or, indirectly, when the order parameter is coupled to strain as in ferroelectric and ferromagnetic sys- tems. Shape-memory alloys undergoing a martensitic transi- tion are prototypical systems which display this behavior. In these systems, due to spontaneous symmetry breaking, ener- getically equivalent domains or variants nucleate at the tran- sition. The arrangement of these domains can be understood as arising from the competition between interface energy short-range and long-range interactions arising from com- patibility constraints. 7 In these materials the complexity of the transformation process results in multiscale dynamics characterized by the absence of length and time scales of the transformation events revealed by power-law distributions of the amplitude and duration of AE signals. 8 This interesting approach to the understanding of the dynamics of the system proves that, in spite of the significant first-order character of martensitic transitions in shape-memory alloys, some under- lying criticality occurs, which is essentially a consequence of the inhomogeneous properties of the material and the long- range correlations between transformation events. Neverthe- less, in these AE experiments aimed at statistically analyzing amplitude and duration of AE events, no information regard- ing the relationship between interface dynamics and AE can be extracted. Actually, it should be possible to obtain this kind of information from the study of AE associated with a propagating parent-martensite interface at constant tempera- ture. We have designed an experiment aimed at exploring this situation as far as possible. This was achieved by induc- ing the martensitic transition in a Cu-Zn-Al single crystal by controlling the externally applied stress at constant tempera- ture while the strain and AE are measured. Simultaneously, front propagation was observed by means of optical micros- copy. Since the transition takes place at or very close to the limit of metastability due to its athermal character, 9 once the parent phase becomes unstable a single variant grows until transformation of the full sample is accomplished. This is essentially different from usual mechanical experiments per- formed using standard screw-driven tensile machines where the controlled variable is the strain. In this case the transition is constrained by the externally imposed length of the sample which prevents free motion of interfaces. In contrast, in our experiment shape changes are not constrained and thus the strain is free to fluctuate. The aim of the present work is studying the relationship between AE and dissipated energy during propagation of martensitic front in a stress-induced transition from cubic to a single-variant martensite. II. EXPERIMENTAL DETAILS A single Cu-Zn-Al crystal, obtained by melting metals of 99.999% purity, was grown using a Bridgman technique. Its composition was obtained from energy dispersive x-ray mea- surements EDX to be 68.13 at. % Cu, 15.74 at. % Zn, and PHYSICAL REVIEW B 78, 094104 2008 1098-0121/2008/789/0941045 ©2008 The American Physical Society 094104-1