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3.4.1 Microstructure and Compositional Analysis

A Cameca SX-100 electron microprobe (EM) equipped with X-ray energy dispersive spectrometry (EDS) and wavelength dispersive spectrometry (WDS) was used to analyze the microstructures and chemical compositions of the solution heat treated samples. Back-scattered electron (BSE) imaging mode was used to investigate the present phases. The specimens for electron microprobe study were prepared by mechanical polishing down to a final step of 0.05 µm colloidal silica and investigated with no etching. As an addition to WDS, bulk samples were also analyzed with inductively coupled plasma – atomic emission spectrometry (ICP-AES) to validate the observations.

The samples for TEM/HRTEM studies were first machined as 3 mm in diameter discs and mechanically ground down to 100 µm thickness and finally prepared through double jet electropolishing using a 30% HNO3 and 70% methanol solution at -20 oC and

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a voltage of ~ 12 V. The TEM observations were conducted at room temperature using a Hitachi H600 conventional microscope operated at 100 kV and a JEOL 2011 high resolution transmission electron microscope with an LaB6 filament, equipped with an energy-dispersive X-ray (EDX) sprectrometer and operated at an accelerating voltage of 200 kV.

3.4.2 Crystal Structures

The crystal structures of the transforming phases in the SHT and precipitation heat treated materials were investigated via a Bruker-AXS D8 X-ray diffractometer operated with CuKα radiation (1.5406 Å). Since it was not possible to obtain a fully martensitic phase at room temperature for the alloy systems containing only 15 at.% ternary addition, e.g. Ni50.3Ti34.7Zr15 and Ni50.3Ti34.7Hf15, and since it was not possible to cool down in the present X-ray device, these experiments were only performed for the alloys containing 20 at.% ternary element namely Ni50.3Ti29.7Zr20 and Ni50.3Ti29.7Hf20. The X-ray diffraction (XRD) experiments were carried out between 2θ range of 20-80o for the martensite phase at room temperature and the lattice parameters for the martensite phase were calculated using the obtained diffraction peaks. The d-spacing for the indexed planes was determined using the Bragg Law, λ = 2dsinθ, where the 2θ values of the planes and wavelength (λ) of the CuK_α radiation (1.5406 Å) were used as an input. In order to provide equivalent thermodynamically conditions and study the crystallographic compatibility, e.g. λ2, of the transforming phases, the lattice parameters of the high temperature phase austenite should be extrapolated to room temperature.

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Therefore, for the high temperature austenite phase, the XRD experiments were carried out at 5 different temperatures when the samples were at fully austenitic state such as Ms + 15 oC, Ms + 30 oC, Af, Af + 15 oC and Af + 30 oC. For this purpose, the samples were first heated to a temperature 30 oC above their Af temperature (Af + 30 oC) to transform to fully austenite phase and then cooled to Ms + 15 oC temperature while the sample was still in fully austenitic state and the first XRD experiment was performed. Then the sample heated to next temperature, e.g Ms + 30 oC, and the experiment was repeated. The experimental temperatures were increased incrementally until Af + 30 oC temperature and the experiments were repeated. The XRD measurements in the austenite state were conducted on a Pt heating strip and the samples were heated up through passing current from the strip. The temperature of the samples was controlled using an external K-type thermocouple placed on the surface of the samples. The experiments in the austenite state were restricted to 2θ range of 39-43o

since the highest intensity peak, e.g. from (111) plane, for B2 austenite appears in this range. Finally, the 2θ values for the obtained peaks were plotted as a function of experiment temperature and extrapolated to room temperature. Then the 2θ value for the room temperature was used to calculate the lattice parameters of the austenite phase using Bragg Law.

3.4.3 Maximum Theoretical Strains and the Elastic Constants

It has been formerly shown for several other SMAs such as binary NiTi that the maximum theoretical transformation strains could be calculated using their transformation matrix. The transformation matrix, U, describes the homogeneous

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deformation that occurs during transformation of the austenite matrix to the martensite matrix [112]. Therefore, assuming that all austenite matrix will transform to martansite matrix and vice-versa without any remnant phase, one can calculate the maximum theoretical strain levels using the transformation matrix. Bhattacharya showed that the components of the transformation matrix are a function of lattice parameters of the transforming phases and for different crystal structures of the transforming phases the symmetry of the matrix as well as the number of martensite variants change. Therefore, the transformation matrix changes for the specific crystal structures of the transforming phases. Since the alloys used in the present study has an austenite crystal structure of B2, base centered cubic, and a martensite crystal structure of B19’, monoclinic, the lattice parameters of transforming phases found via the XRD were used to generate the transformation matrix. More information on how to generate the transformation matrix of a B2 to B19’ transformation can be found elsewhere. The generated transformation matrix was embedded in a MATLAB code in order to calculate the maximum theoretical of the alloys in several single crystal orientations. These calculations were performed for the Ni50.3Ti29.7Zr20 and Ni50.3Ti29.7Hf20 and compared with each other.

Furthermore, using the lattice parameters of the transforming phases measured via XRD studies, the elastic constants of the transforming phases were also calculated. The elastic constants were computed through imposing a set of strains, ε = (ε1, ε2, ε3, ε4, ε5, ε6) on the crystal structures of the transforming phases [113]. Then the generated stresses (σi) as a consequence of the change in energy due to deformation were calculated. Using the Hooke’s Law σi = Cijεj, the stiffness tensor namely Cij was

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computed. Using the elements of the stiffness tensor, the bulk modulus (B) is computed as:

𝐵 = 2_{9 (𝐶11 + 𝐶12 + 2𝐶13 +} 𝐶33_{2 )}

Voight approximation was used to calculate the shear modulus as following: 𝐺 = ₁₅ 1 (2𝐶11 + 𝐶33 − 𝐶12 − 2𝐶13) + 1_{5 (2𝐶44 +} 1₂ (𝐶11 − 𝐶12)) The Young’s modulus is calculated as:

𝐸 = _{3𝐵 + 𝐺}9𝐵𝐺

Finally the Poisson’s ratio for the alloys is calculated using the following formula: 𝜈 = 𝐸

2𝐺 − 1

These elastic constants calculated were used to compare the mechanical properties of Ni50.3Ti29.7Zr20 and Ni50.3Ti29.7Hf20 systems.

3.4.4 Microhardness

In order to study the effect of precipitation on the microhardness of Ni50.3Ti29.7Zr20 HTSMA, samples with 1 mm in thickness and 5 mm in diameter were cut from the extruded rod parallel to the extrusion direction using EDM. The extracted samples were SHT and then subjected to precipitation heat treatments at 550 oC and 600 o

C for durations of 1 hour to 48 hour. Furthermore another set of the samples were SHT and subsequently furnace cooled from 700 oC to 100 oC for different durations varying from 3 hours to 72 hours. Vickers microhardness was measured using a Leco LM 300AT

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microhardness tester applying 300 g load for 15 s. At least 10 indentations were made on the samples and averaged to find the microhardness of the samples.