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Deformation-induced structural transition in body-centred cubic molybdenum.

Wang SJ, Wang H, Du K, Zhang W, Sui ML, Mao SX - Nat Commun (2014)

Bottom Line: The face-centred cubic domains then revert into <111>-oriented body-centred cubic domains, equivalent to a lattice rotation of 54.7°, and ~15.4% tensile strain is reached.The face-centred cubic structure appears to be a well-defined metastable state, as evidenced by scanning transmission electron microscopy and nanodiffraction, the Nishiyama-Wassermann and Kurdjumov-Sachs relationships between the face-centred cubic and body-centred cubic structures and molecular dynamics simulations.Our findings reveal a deformation mechanism for elemental metals under high-stress deformation conditions.

View Article: PubMed Central - PubMed

Affiliation: 1] Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China [2] Beijing National Center for Electron Microscopy, Tsinghua University, Beijing 100084, China.

ABSTRACT
Molybdenum is a refractory metal that is stable in a body-centred cubic structure at all temperatures before melting. Plastic deformation via structural transitions has never been reported for pure molybdenum, while transformation coupled with plasticity is well known for many alloys and ceramics. Here we demonstrate a structural transformation accompanied by shear deformation from an original <001>-oriented body-centred cubic structure to a <110>-oriented face-centred cubic lattice, captured at crack tips during the straining of molybdenum inside a transmission electron microscope at room temperature. The face-centred cubic domains then revert into <111>-oriented body-centred cubic domains, equivalent to a lattice rotation of 54.7°, and ~15.4% tensile strain is reached. The face-centred cubic structure appears to be a well-defined metastable state, as evidenced by scanning transmission electron microscopy and nanodiffraction, the Nishiyama-Wassermann and Kurdjumov-Sachs relationships between the face-centred cubic and body-centred cubic structures and molecular dynamics simulations. Our findings reveal a deformation mechanism for elemental metals under high-stress deformation conditions.

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Strain analysis by MD simulation.(a) A snapshot showing the bcc1 and fcc phases during tensile loading. The atoms are coloured according to their coordination number, white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9. (b–d) The normal strain mapping along [001], [100] and [010], respectively. The atoms are coloured according to the strain scale: colours for positive values represent tensile strain, and colours for negative values represent compressive strain. The scale bar is shown in the right colour column.
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f6: Strain analysis by MD simulation.(a) A snapshot showing the bcc1 and fcc phases during tensile loading. The atoms are coloured according to their coordination number, white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9. (b–d) The normal strain mapping along [001], [100] and [010], respectively. The atoms are coloured according to the strain scale: colours for positive values represent tensile strain, and colours for negative values represent compressive strain. The scale bar is shown in the right colour column.

Mentions: The next question concerns the stress states of the bcc Mo crystal when the deformation-induced structural changes occur. To demonstrate that the sample region of interest indeed experiences enhanced stress concentration, quantitative strain analysis was performed using the lattice distortion analysis (LADIA) package2021 on time-resolved HRTEM images. An angle-θ is used to describe the lattice shear strain in the bcc1 crystal at the crack tip (see details in the Methods section). The angle-θ is defined as the included angle between two basic vectors u (1/2[110]) and v (1/2[1-10]) in the (001) plane (Fig. 5). Figure 5a was extracted from Supplementary Movie 1 (t=1.5 s). The lattice distortion of the red-boxed area in Fig. 5a is shown in Fig. 5b. The shear strains shown in Fig. 5b using different colours suggest that the local Mo matrix is under a shear stress (indicated by black arrows) that originated from the external tensile stress. Figure 5c displays the quantitative lattice distortion profile for the black-boxed region (used as a lattice strain gage) in Fig. 5b, indicating that the mean value of shear strain is 0.051±0.013 (all the error bars here represent the s.d.). The resolution here represents an estimated value for the static observations that correspond to individual HRTEM images2223. Alternatively, using a FFT (the inset in Fig. 5c) from the HRTEM image area corresponding to the black-boxed region in Fig. 5b, the average angle between the (110) and (1-10) planes was measured24 to be 93.6±0.6°, corresponding to a shear strain of 0.063±0.010. This shear strain is consistent with, within the margin of error, that given by the LADIA analysis. Therefore, the local elastic shear stress is ~8 GPa, based on the shear modulus of 126 GPa25. Furthermore, the local normal strains in the viewing plane were also analysed. The normal strain distributions of the red-boxed area in Fig. 5a along [100] and [010] are shown in Fig. 5d,f, respectively, in which the atoms are coloured according to the strain scale: colours for positive values represent tensile strain and those for negative values represent compressive strain. These figures reveal that the local normal stresses along the two directions in front of the crack tip are all tensile stresses. The corresponding quantitative strain profiles presented in Fig. 5e,g indicate that the mean elastic tensile strains are 0.063±0.008 and 0.017±0.007, respectively. Accordingly, the tensile stresses along [100] and [010] are estimated to be ~20.7±2.6 GPa and ~5.6±2.3 GPa, respectively, given that the Young’s modulus is 329 GPa (ref. 25). These normal stresses would correspond to a shear stress of ~7.6 GPa, roughly estimated using the equation (G[010]-G[100])/2, which is consistent with the measured shear stress along [1-10] of ~8 GPa. Owing to the projection view of the HRTEM image, the normal stress perpendicular to the viewing plane is not available by LADIA analysis. Thus, an MD simulation was used for the analysis of the three-dimensional normal stresses. The strain results for the [001], [100] and [010] directions are presented in Fig. 6b–d, respectively. Figure 6a shows the structural features in different regions at the same moment with the three strain maps during the MD simulation. In Fig. 6a, the atoms are coloured according to their coordination number (white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9). In Fig. 6b–d, the atoms are coloured according to the strain scale: colours for positive values represent tensile strain and colours for negative values represent compressive strain. It is apparent that tensile stresses are also present along the [100] and [010] directions in front of the crack tip, which agrees with the LADIA analysis results. For the [001] direction, no significant tensile stress is observed. Therefore, such a three-dimensional stress state in front of the crack tips is more complicated than the hydrostatic stress and uniaxial stress states, which likely explains the occurrence of the bcc1→fcc phase transition.


Deformation-induced structural transition in body-centred cubic molybdenum.

Wang SJ, Wang H, Du K, Zhang W, Sui ML, Mao SX - Nat Commun (2014)

Strain analysis by MD simulation.(a) A snapshot showing the bcc1 and fcc phases during tensile loading. The atoms are coloured according to their coordination number, white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9. (b–d) The normal strain mapping along [001], [100] and [010], respectively. The atoms are coloured according to the strain scale: colours for positive values represent tensile strain, and colours for negative values represent compressive strain. The scale bar is shown in the right colour column.
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Related In: Results  -  Collection

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f6: Strain analysis by MD simulation.(a) A snapshot showing the bcc1 and fcc phases during tensile loading. The atoms are coloured according to their coordination number, white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9. (b–d) The normal strain mapping along [001], [100] and [010], respectively. The atoms are coloured according to the strain scale: colours for positive values represent tensile strain, and colours for negative values represent compressive strain. The scale bar is shown in the right colour column.
Mentions: The next question concerns the stress states of the bcc Mo crystal when the deformation-induced structural changes occur. To demonstrate that the sample region of interest indeed experiences enhanced stress concentration, quantitative strain analysis was performed using the lattice distortion analysis (LADIA) package2021 on time-resolved HRTEM images. An angle-θ is used to describe the lattice shear strain in the bcc1 crystal at the crack tip (see details in the Methods section). The angle-θ is defined as the included angle between two basic vectors u (1/2[110]) and v (1/2[1-10]) in the (001) plane (Fig. 5). Figure 5a was extracted from Supplementary Movie 1 (t=1.5 s). The lattice distortion of the red-boxed area in Fig. 5a is shown in Fig. 5b. The shear strains shown in Fig. 5b using different colours suggest that the local Mo matrix is under a shear stress (indicated by black arrows) that originated from the external tensile stress. Figure 5c displays the quantitative lattice distortion profile for the black-boxed region (used as a lattice strain gage) in Fig. 5b, indicating that the mean value of shear strain is 0.051±0.013 (all the error bars here represent the s.d.). The resolution here represents an estimated value for the static observations that correspond to individual HRTEM images2223. Alternatively, using a FFT (the inset in Fig. 5c) from the HRTEM image area corresponding to the black-boxed region in Fig. 5b, the average angle between the (110) and (1-10) planes was measured24 to be 93.6±0.6°, corresponding to a shear strain of 0.063±0.010. This shear strain is consistent with, within the margin of error, that given by the LADIA analysis. Therefore, the local elastic shear stress is ~8 GPa, based on the shear modulus of 126 GPa25. Furthermore, the local normal strains in the viewing plane were also analysed. The normal strain distributions of the red-boxed area in Fig. 5a along [100] and [010] are shown in Fig. 5d,f, respectively, in which the atoms are coloured according to the strain scale: colours for positive values represent tensile strain and those for negative values represent compressive strain. These figures reveal that the local normal stresses along the two directions in front of the crack tip are all tensile stresses. The corresponding quantitative strain profiles presented in Fig. 5e,g indicate that the mean elastic tensile strains are 0.063±0.008 and 0.017±0.007, respectively. Accordingly, the tensile stresses along [100] and [010] are estimated to be ~20.7±2.6 GPa and ~5.6±2.3 GPa, respectively, given that the Young’s modulus is 329 GPa (ref. 25). These normal stresses would correspond to a shear stress of ~7.6 GPa, roughly estimated using the equation (G[010]-G[100])/2, which is consistent with the measured shear stress along [1-10] of ~8 GPa. Owing to the projection view of the HRTEM image, the normal stress perpendicular to the viewing plane is not available by LADIA analysis. Thus, an MD simulation was used for the analysis of the three-dimensional normal stresses. The strain results for the [001], [100] and [010] directions are presented in Fig. 6b–d, respectively. Figure 6a shows the structural features in different regions at the same moment with the three strain maps during the MD simulation. In Fig. 6a, the atoms are coloured according to their coordination number (white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9). In Fig. 6b–d, the atoms are coloured according to the strain scale: colours for positive values represent tensile strain and colours for negative values represent compressive strain. It is apparent that tensile stresses are also present along the [100] and [010] directions in front of the crack tip, which agrees with the LADIA analysis results. For the [001] direction, no significant tensile stress is observed. Therefore, such a three-dimensional stress state in front of the crack tips is more complicated than the hydrostatic stress and uniaxial stress states, which likely explains the occurrence of the bcc1→fcc phase transition.

Bottom Line: The face-centred cubic domains then revert into <111>-oriented body-centred cubic domains, equivalent to a lattice rotation of 54.7°, and ~15.4% tensile strain is reached.The face-centred cubic structure appears to be a well-defined metastable state, as evidenced by scanning transmission electron microscopy and nanodiffraction, the Nishiyama-Wassermann and Kurdjumov-Sachs relationships between the face-centred cubic and body-centred cubic structures and molecular dynamics simulations.Our findings reveal a deformation mechanism for elemental metals under high-stress deformation conditions.

View Article: PubMed Central - PubMed

Affiliation: 1] Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China [2] Beijing National Center for Electron Microscopy, Tsinghua University, Beijing 100084, China.

ABSTRACT
Molybdenum is a refractory metal that is stable in a body-centred cubic structure at all temperatures before melting. Plastic deformation via structural transitions has never been reported for pure molybdenum, while transformation coupled with plasticity is well known for many alloys and ceramics. Here we demonstrate a structural transformation accompanied by shear deformation from an original <001>-oriented body-centred cubic structure to a <110>-oriented face-centred cubic lattice, captured at crack tips during the straining of molybdenum inside a transmission electron microscope at room temperature. The face-centred cubic domains then revert into <111>-oriented body-centred cubic domains, equivalent to a lattice rotation of 54.7°, and ~15.4% tensile strain is reached. The face-centred cubic structure appears to be a well-defined metastable state, as evidenced by scanning transmission electron microscopy and nanodiffraction, the Nishiyama-Wassermann and Kurdjumov-Sachs relationships between the face-centred cubic and body-centred cubic structures and molecular dynamics simulations. Our findings reveal a deformation mechanism for elemental metals under high-stress deformation conditions.

Show MeSH
Related in: MedlinePlus