Transformation Volume Effects on Shape Memory Alloys
Abstract
:1. Introduction
2. Quantitative Theory of Thermoelastic Behavior of SMAs
2.1. Symmetry Conforming Approach to the Problem
2.2. Cubic-Tetragonal MT
2.3. Cubic-Rhombohedral MT
2.4. Summary of Basic Points and Preview of Applications of the Theory
3. Martensite Stabilization/Destabilization under Hydrostatic Pressure
3.1. Interrelation between the Volume Change during MT and Pressure Effects
- a)
- b)
- an increase/decrease of the soft elastic modulus of martensite.
3.2. Landau Expansion Coefficients Estimated from the Shear Modulus of Ti-Ni Alloy
- (i)
- a theoretical evaluation of the shear modulus from the experimental temperature dependencies of lattice parameters in the martensitic phase;
- (ii)
- a restoring of the temperature dependence of MT strain from the temperature dependence of the shear modulus.
3.3. The Influence of Pressure on the MT Strain and MT Temperature
3.4. The Influence of Pressure on the Shear Elastic Modulus
4. Stabilization of Martensitic Phase by Its Aging
4.1. Isotropic Mechanism of Martensite Stabilization
- (i)
- (ii)
- a gradual change of the lattice parameters during martensite aging [54];
- (iii)
4.2. Martensite Stabilization in Au-Cd Alloys
- (i)
- The time evolution of the crystal defects subsystem leads to a gradual volume change of the SMA aged in the martensitic state.
- (ii)
- According to the general principles of thermodynamics, the time-dependent internal pressure can be defined as the thermodynamic value, which is conjugated to the volume change.
- (iii)
- The internal pressure contributes to the martensite stabilization effect but does not change the symmetry of the crystal lattice; therefore, the gradual volume change of the alloy, held in the martensitic phase, provides the isotropic mechanism of martensite stabilization, which is extrinsic to the commonly known SC-SRO principle formulated in [44,53].
- (iv)
5. Destabilization of Martensitic Phase by Thermomechanical Cycling
5.1. Introductory Statement
5.2. Experiment
5.3. Qualitative Explanation of Experimental Results
5.4. Quantitative Description of the Martensite Destabilization Effects
5.5. Summary of Destabilization Effects
6. Quasi-Second-Order Martensitic Transformations
6.1. General Considerations
6.2. Application to the Ni-Mn-Ga and Au-Cd Alloys
7. Volume Changes Contributing to the Entropy in Magnetic Shape Memory Alloys
7.1. Elastic and Magnetic Components of the Entropy Change during MT
- I)
- The entropy change during MT is inversely proportional to the width of the temperature interval of mixed (austenitic-martensitic) state.
- II)
- The magnetoelastic energy of a deformable magnetic solid, such as FSMA, is the difference between the magnetic energies of its deformed and undeformed states.
- III)
- The magnetic contribution to the total entropy change caused by the deformation of magnetic solid is the partial temperature derivative of magnetoelastic energy taken with the opposite sign.
- IV)
- The ordinary magnetostriction of FSMA is substantially smaller than the MT strain vMT, and the axial magnetostriction is much smaller than the spontaneous volume magnetostriction v(me) in the case if the Curie temperature is of the order of room temperature. In this case the magnetic entropy change is directly proportional to the product vMTv(me)(TMF).
- V)
7.2. Magnetic Entropy Change during MT of Ni-Mn-Ga Alloy
7.3. Magnetic Entropy Change during MT of a Quasi-Stoichiometric Ni-Fe-Ga Alloy
7.4. Summary on the Entropy Change
- (i)
- The total entropy change during MT is inversely proportional to the width of the temperature interval of mixed two-phase state.
- (ii)
- The elastic part of the entropy change is proportional to the value of temperature derivative of the shear elastic modulus. This feature illustrates that the cubic-tetragonal MT is caused by the instability of crystal lattice with respect to the vibrations corresponding to the TA2 [110] phonon mode and to the softening of this phonon mode which leads to a decrease of C′ value in the vicinity of MT. In practice, the evaluation of ΔSel from the temperature dependencies of shear modules of SMAs is hampered by an uncertainty in the experimental values of these modules.
- (iii)
- The elastic part of the entropy change is proportional to the squared tetragonal distortion of the unit cell, (1−c/a)2), which is about of 4 × 10−2 for the Ni-Mn-Ga alloys with c/a > 1, TMS > TC and 3 × 10−3 for the alloys withc/a < 1, TMS < TC. This feature is in line with the fact that the observed in [91] entropy change is noticeably larger for the Ni-Mn-Ga alloys with TMS > TC than for those with TMS < TC.
- (iv)
- In the case of FSMAs with TMS < TC, the Landau theory confirms a crucial role of the interaction between the magnetic and elastic subsystems in the formation of thermodynamic characteristics of the MT. The magnetic part of the entropy change estimated from M(T) curves for Ni-Mn-Ga alloy (Alloy 1) appeared to be close in value to the experimentally observed total entropy change. In this connection, the entropy change demonstrates a sharp decrease when the MT temperature of the alloy moves away from the Curie temperature. The experiments show that this is a common feature of the Ni-Mn-Ga, Ni-Mn-In and Ni-Mn-In-Co alloy systems [32]. Recently, a pronounced dependence of ΔS on TC−TMF has been observed also in Ni-Mn-Ga-Co alloys [95].
- (v)
- The computations illustrate that the evaluation of the magnetic entropy change from the temperature dependence of magnetization is very sensitive to the character of this dependence (see Figure 14). Moreover, it occurs that the standard equations corresponding to the Bragg–Williams approximation do not describe the magnetization of Ni-Fe-Ga alloys. It can be concluded, therefore, that the careful study of the magnetic structure and magnetization of every alloy system must be carried out for the correct evaluation of magnetic entropy change.
- (vi)
- Equation 71 shows that the magnetic entropy change is proportional to the volume magnetostriction. Therefore, a careful theoretical analysis of the effect of spontaneous and forced magnetostriction on the characteristic MT temperatures will be very important.
8. Discussion
Acknowledgments
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Chernenko, V.A.; L'vov, V.A.; Cesari, E.; Kosogor, A.; Barandiaran, J.M. Transformation Volume Effects on Shape Memory Alloys. Metals 2013, 3, 237-282. https://doi.org/10.3390/met3030237
Chernenko VA, L'vov VA, Cesari E, Kosogor A, Barandiaran JM. Transformation Volume Effects on Shape Memory Alloys. Metals. 2013; 3(3):237-282. https://doi.org/10.3390/met3030237
Chicago/Turabian StyleChernenko, Volodymyr A., Victor A. L'vov, Eduard Cesari, Anna Kosogor, and Jose M. Barandiaran. 2013. "Transformation Volume Effects on Shape Memory Alloys" Metals 3, no. 3: 237-282. https://doi.org/10.3390/met3030237