Martensitic transformation in constrained films

doi:10.1016/S1359-6454(98)00165-7

Acta Materialia

Volume 46, Issue 14, 1 September 1998, Pages 5095-5107

https://doi.org/10.1016/S1359-6454(98)00165-7 Get rights and content

Abstract

A thermodynamic analysis is presented for the martensitic transformation in a constrained film upon cooling and heating. It is shown that this transformation proceeds with a variable self-strain corresponding to a variable polydomain structure of the martensite phase. Even the equilibrium microstructure develops irreversibly with changing temperature, i.e. the microstructure evolution paths for the direct and the reverse transformations are different. During the reverse transformation the stressed austenite, incompatible to martensite, is formed. The theory predicts a considerable shift of the temperature interval of transformation and its broadening due to the constraint. Experimental studies of the stress evolution with changing temperature in NiTi polycrystalline films on Si substrates support the principal thermodynamic conclusions.

Introduction

Phase transformations under constraint take place in all multiphase materials where a transforming phase is in contact with nontransforming phases. Interest in the problem of constrained transformations has increased recently due to growing applications of artificial materials and composites with transforming components, in bulk as well as in thin-film form.

The martensitic transformation in constrained particles embedded in a nontransformed matrix has been widely studied and used as an effective mechanism of toughening of ceramics. Another area of applications of constrained martensitic transformations is smart composites with shape memory alloys as the active components1, 2, 3. Layer composites containing transforming shape memory material are particularly interesting for studies of constrained martensitic transformations and for applications as well. There are two typical configurations of composites with transforming constrained films: symmetrical and asymmetrical. The first configuration consists of two identical films on both sides of a substrate (“trimorph”) [Fig. 1(a)]; the second one is a film on a substrate (“bimorph”) [Fig. 1(b)]. The trimorph can be considered as an elementary cell of multilayer composites or heterostructures. Bimorphs are often used as actuators or sensors, because the transformation in the film results in considerable bending. For the same reason the bimorphs are usually used for studies of martensitic transformation itself.

Several studies of the martensitic transformation in NiTi films on Si substrates have been performed recently4, 5. In this paper we present experimental results on the stress evolution in bimorphs and trimorphs consisting of NiTi polycrystalline films on Si substrates with SiO₂ buffer layers. We discuss the principal results of experimental studies from the point of view of the thermodynamics of a martensitic transformation in a constrained film. The high level of stress in a film due to its misfit with a substrate suggests that they can compete with internal stresses in the martensite or martensite–austenite microstructure and considerably change the self-accommodation of the martensitic transformation in shape memory alloys. Therefore, thermodynamic effects in constrained films should be much more pronounced than in bulk materials.

In Section 2of this paper the mechanics of a constrained film is considered. The different physical factors which determine the film–substrate misfit are discussed and formulas for the calculation of the average stress in anisotropic and isotropic films are presented. The thermodynamics of the transformation in a single-crystalline constrained film is discussed in Section 3. The analysis of a cubic–tetragonal model transformation predicts special effects of the constraint, namely:

1.
a structural irreversibility of the evolution of the equilibrium microstructure; and
2.
the appearance of an elastic incompatibility between the austenite and the martensite because the interfaces between these phases are not necessarily invariant planes.

Experimental results on the preparation of polycrystalline constrained NiTi films and their transformation upon cooling and heating are presented in Section 3. These results, together with other published data, are discussed in Section 4where it will be seen that they support the thermodynamical concepts presented in Section 3of this paper.

Section snippets

Mechanics of constrained transformations

A phase transformation in a constrained film is a self-regulated process. The transformation changes the state of stress of the film and the changing stress, in turn, affects the transformation. We consider both sides of the process from the point of view of the observed stress evolution in the film as a function of temperature.

A typical temperature dependence of the average stress in a constrained SMA film is presented in Fig. 2. The two sections of the almost linearly increasing stress with

Thermodynamics of the martensitic transformation in a constrained film

In this section the thermodynamics of the martensitic transformation in a constrained film will be considered to determine the evolution of the equilibrium austenite–martensite microstructure as the temperature changes. The section will first recall the basic features of martensitic transformation. After that, the accommodation of the austenite–martensite mixture to the film constraint during cooling will be considered. Here, the situation is different depending on whether the transformation

Experimental procedure

Well adhering 1 μm thick NiTi films were sputter deposited onto thermally oxidized (100 nm SiO₂) Si cantilevers of different thicknesses utilizing the previously published technique[19]. Periodic post-deposition X-ray, TEM, SEM and RBS characterization served to assure the desired film properties.

The film stresses were determined by measuring the cantilever deflection[20]. To study the stress evolution in the Ni₅₀Ti₅₀/SiO₂/Si film composites as a function of temperature, a cantilever beam

Discussion

A typical experimentally determined σ(T) curve for a NiTi/(SiO₂)/Si bimorph is presented in Fig. 7 together with the equilibrium line corresponding to , , . The film is highly textured[25], and each grain has a (110) plane parallel to the surface of the film. Therefore, the specific self-strain for the B2–B19′ martensitic transformation, $ε ̂_{0}$ , should be calculated as an average expansion in the (110) plane of the B2 phase. The analysis of preferable variants of monoclinic martensite in tensioned

Summary

This paper represents a first attempt to understand the martensitic transformation in constrained films. A cubic to tetragonal transformation of single crystalline material has been used as a model system to simplify the analysis. The analysis leads to the conclusion that the constrained martensitic transformation in stressed films in general should be structural and thermodynamically irreversible even if it develops as the evolution of an equilibrium microstructure. This irreversibility is the

Acknowledgements

This study was supported by the National Science Foundation, Grant No. DMR-97-06815. It also benefited from support by the Office of Naval Research, contract No. N00014-93-10506.

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Martensitic transformation in constrained films

Abstract

Introduction

Section snippets

Mechanics of constrained transformations

Thermodynamics of the martensitic transformation in a constrained film

Experimental procedure

Discussion

Summary

Acknowledgements

Thin Solid Films

Mater. Sci. Engng

Mater. Sci. Eng. A

Acta mater.

Trans. Mater. Res. Soc. Japan.

J. Physique

Physica status solidi (a)

J. appl. Phys.