Topological Modelling of the B2-B19' Martensite Transformation Crystallography in NiTi Alloy

doi:10.11900/0412.1961.2018.00078

Acta Metall Sin

2018, Vol. 54

Issue (10): 1461-1470 DOI: 10.11900/0412.1961.2018.00078

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Topological Modelling of the B2-B19' Martensite Transformation Crystallography in NiTi Alloy

Zhaozhao WEI^1,², Xiao MA²(

), Xinping ZHANG²

1 School of Mechanical and Electrical Engineering, Wuyi University, Jiangmen 529020, China
2 School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China

Cite this article:

Zhaozhao WEI, Xiao MA, Xinping ZHANG. Topological Modelling of the B2-B19' Martensite Transformation Crystallography in NiTi Alloy. Acta Metall Sin, 2018, 54(10): 1461-1470.

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Abstract

Some NiTi alloys, generally known as shape memory alloys or smart materials, exhibit larger negative thermal expansion (NTE) strain than that of traditional nonmetallic NTE materials. Furthermore, high strength and better ductility of NiTi alloy make it more advantageous compared to nonmetallic materials. The NTE response of NiTi alloy may be attributed to the transformation strain that originates from the volume change accompanying the B2-B19' martensitic transformation in the alloy. Therefore, it is of great importance and interests to study the martensitic transformation crystallography in NiTi alloy. In this work, the martensitic transformation crystallography in an equiatomic NiTi alloy was investigated by using the topological model, as well as the optimum twist criterion developed lately. The optimum twist angle, ω_o, in NiTi alloy was determined to be -0.969°, and the so-obtained transformation crystallography results, including the habit plane index and parent-martensite orientation relationship, agree well with the corresponding experimental data and theoretical calculations in the literature. Furthermore, the martensitic transformation strain of NiTi alloy was calculated based on the analysis of interfacial dislocation movement, and the total transformation strain can be resolved into an in-habit-plane shear strain and an axial strain perpendicular to the habit plane. In particular, the value of the axial strain that represents the volume change due to the B19' to B2 transformation was found to be negative, indicating that the NiTi alloy shrinks during the reverse martensitic phase transformation when heated, which might shed some light on the relationship between the NTE mechanism and martensitic transformation in NiTi alloy. The measured NTE strain is much smaller than the theoretical calculated phase transformation strain in NiTi alloy, due to the self-accommodation effect of martensite variants and the compensation of transformation strains in polycrystalline materials.

Key words: topological model NiTi alloy martensitic transformation crystallography transformation strain negative thermal expansion

Received: 05 March 2018

ZTFLH:	TG131
	TG139

Fund: Supported by National Natural Science Foundation of China (No.51571092), Natural Science Foundation of Guangdong Province (No.2017A030310657), Young and Creative Talents Project of University Innovation Program of Guangdong Province (No.2016KQNCX170) and Start-Up Research Grant of Wuyi University (No.2015BS16)

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https://www.ams.org.cn/EN/10.11900/0412.1961.2018.00078 OR https://www.ams.org.cn/EN/Y2018/V54/I10/1461

Fig.1 Schematic of the step-terrace interface structure between parent and martensite phases in the topological model (The habit plane is reticulated by arrays of disconnection (b^D, h) and lattice invatiant deformation (LID) dislocation (b^L, 0) with spacings of d^D and d^L, and line directions of ξ^D and ξ^L respectively; h is the step height of disconnections, and the macroscopic habit plane is incline to the terrace plane by an angle ψ)

Fig.2 Crystal structures of the B2 parent phase (a) and the B19′ martensite phase (b) in NiTi alloy (β—monoclinic angle)

Fig.3 Schematics of natural dichromatic pattern (a) and commensurate dichromatic pattern (b), where lattice sites of the parent and the martensite crystals are depicted by black and white circles respectively (TP—terrace plane, CTP—commensurate terrace plane)

Fig.4 Schematics of the crystallographic orientation relationship between the (100)_P plane in B2 parent phase and the (100)_M plane in B19′ martensite of NiTi alloy (a), and twist of +ω/2 in the parent and -ω/2 in the martensite with respect to the normal of the terrace plane (b) (ω—twist angle)

Fig.5 Schematics of the commensurate dichromatic pattern formed by projecting the parent and martensite lattices onto the terrace plane (a) and the disconnection

b + 1 / + 1 D

viewed along x^TP direction (b)

Type	b_x / nm	b_y / nm	b_z / nm	h / nm	Burgers vector
Disconnection	0	0.03785	0.01344	0.30175	$b + 1 / + 1 D$ =[100]_P-[100]_M
LID dislocation	0.06972	0.07413	0	0	$b L = 2 s d K 1 b M 2 + c M 2 [011] M$

Table 1 Topological parameters of the disconnection

b + 1 / + 1 D

and the LID dislocation b^L expressed in the terrace plane coordinate

Parameter	TM		Experiment^[25]
	ω=ω_o=-0.969°	ω=-1.000°
Habit plane	(-0.8951, 0.3940, 0.2084)_P	(-0.8969, 0.3899, 0.2087)_P	(-0.8684, 0.4138, 0.2688)_P
d^D / nm	0.662	0.667	?
d^L / nm	1.840	1.831	?
Orientation	(100)_P ^ (100)_M : 1.300°	(100)_P ^ (100)_M : 1.287°	See Table 4 in Ref.[25]
relationship	$[0 1 ? 1] P$ ^ $[010] M$ : 0.969°	$[0 1 ? 1] P$ ^ $[010] M$ : 1.000°

Table 2 Comparison between the calculated transformation crystallography data obtained by the topological model (TM) and experimental results in NiTi alloy

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