### Abstract

We propose that a weak compatibility condition predicts the elongated directions for Widmanstätten type precipitates. The distribution of the elongated directions of precipitates lies on a family of crystallographically equivalent cones in 3D determined by a certain transformation stretch matrix obtained independently. A 3D visualization and digitization method is developed to show how the cone variants control the preferred growth directions during precipitation of Sb_{2}Te_{3} in a (5 μm)^{3} PbTe matrix. A series of two-dimensional secondary electron images are acquired along the direction perpendicular to the imaging plane. By pixelating all the images and calculating the position vectors on the surface of each precipitate, the elongation directions are calculated using a 3-dimensional ellipsoidal fitting for 182 precipitates. The 3D plot of the elongation directions shows that their spacial orientations are close to four predicted cones with a standard deviation of 5.6°. The length along the elongation directions reveals an asymmetric distribution with a mean value of about 240 nm. The total volume fraction of the precipitates is 8.3%. The average area of the precipitates per volume is 0.68 μm^{-1} by one point statistical calculation. These results build on our study presented in [1] by analyzing a significantly bigger data set and by including the length distribution and 1-point statistics.

Original language | English (US) |
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Title of host publication | 1st International Conference on 3D Materials Science 2012, 3DMS 2012 |

Pages | 125-130 |

Number of pages | 6 |

State | Published - Dec 1 2012 |

Event | 1st International Conference on 3D Materials Science 2012, 3DMS 2012 - Seven Springs, PA, United States Duration: Jul 8 2012 → Jul 12 2012 |

### Publication series

Name | 1st International Conference on 3D Materials Science 2012, 3DMS 2012 |
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### Other

Other | 1st International Conference on 3D Materials Science 2012, 3DMS 2012 |
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Country | United States |

City | Seven Springs, PA |

Period | 7/8/12 → 7/12/12 |

### Fingerprint

### Keywords

- Compatibility
- Focused-ion-beam
- Precipitates
- Slice-and-view
- Widmanstätten

### Cite this

_{2}Te

_{3}precipitates in PbTe matrix with prediction by a weak compatibility condition. In

*1st International Conference on 3D Materials Science 2012, 3DMS 2012*(pp. 125-130). (1st International Conference on 3D Materials Science 2012, 3DMS 2012).

**3D microstructures of Sb _{2}Te_{3} precipitates in PbTe matrix with prediction by a weak compatibility condition.** / Chen, Xian; Cao, Shanshan; Ikeda, Teruyuki; Srivastava, Vijay; Snyder, G. Jeffrey; Schryvers, Dominique; James, Richard D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

_{2}Te

_{3}precipitates in PbTe matrix with prediction by a weak compatibility condition. in

*1st International Conference on 3D Materials Science 2012, 3DMS 2012.*1st International Conference on 3D Materials Science 2012, 3DMS 2012, pp. 125-130, 1st International Conference on 3D Materials Science 2012, 3DMS 2012, Seven Springs, PA, United States, 7/8/12.

_{2}Te

_{3}precipitates in PbTe matrix with prediction by a weak compatibility condition. In 1st International Conference on 3D Materials Science 2012, 3DMS 2012. 2012. p. 125-130. (1st International Conference on 3D Materials Science 2012, 3DMS 2012).

}

TY - GEN

T1 - 3D microstructures of Sb2Te3 precipitates in PbTe matrix with prediction by a weak compatibility condition

AU - Chen, Xian

AU - Cao, Shanshan

AU - Ikeda, Teruyuki

AU - Srivastava, Vijay

AU - Snyder, G. Jeffrey

AU - Schryvers, Dominique

AU - James, Richard D

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We propose that a weak compatibility condition predicts the elongated directions for Widmanstätten type precipitates. The distribution of the elongated directions of precipitates lies on a family of crystallographically equivalent cones in 3D determined by a certain transformation stretch matrix obtained independently. A 3D visualization and digitization method is developed to show how the cone variants control the preferred growth directions during precipitation of Sb2Te3 in a (5 μm)3 PbTe matrix. A series of two-dimensional secondary electron images are acquired along the direction perpendicular to the imaging plane. By pixelating all the images and calculating the position vectors on the surface of each precipitate, the elongation directions are calculated using a 3-dimensional ellipsoidal fitting for 182 precipitates. The 3D plot of the elongation directions shows that their spacial orientations are close to four predicted cones with a standard deviation of 5.6°. The length along the elongation directions reveals an asymmetric distribution with a mean value of about 240 nm. The total volume fraction of the precipitates is 8.3%. The average area of the precipitates per volume is 0.68 μm-1 by one point statistical calculation. These results build on our study presented in [1] by analyzing a significantly bigger data set and by including the length distribution and 1-point statistics.

AB - We propose that a weak compatibility condition predicts the elongated directions for Widmanstätten type precipitates. The distribution of the elongated directions of precipitates lies on a family of crystallographically equivalent cones in 3D determined by a certain transformation stretch matrix obtained independently. A 3D visualization and digitization method is developed to show how the cone variants control the preferred growth directions during precipitation of Sb2Te3 in a (5 μm)3 PbTe matrix. A series of two-dimensional secondary electron images are acquired along the direction perpendicular to the imaging plane. By pixelating all the images and calculating the position vectors on the surface of each precipitate, the elongation directions are calculated using a 3-dimensional ellipsoidal fitting for 182 precipitates. The 3D plot of the elongation directions shows that their spacial orientations are close to four predicted cones with a standard deviation of 5.6°. The length along the elongation directions reveals an asymmetric distribution with a mean value of about 240 nm. The total volume fraction of the precipitates is 8.3%. The average area of the precipitates per volume is 0.68 μm-1 by one point statistical calculation. These results build on our study presented in [1] by analyzing a significantly bigger data set and by including the length distribution and 1-point statistics.

KW - Compatibility

KW - Focused-ion-beam

KW - Precipitates

KW - Slice-and-view

KW - Widmanstätten

UR - http://www.scopus.com/inward/record.url?scp=84889781403&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889781403&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84889781403

SN - 9781627489331

T3 - 1st International Conference on 3D Materials Science 2012, 3DMS 2012

SP - 125

EP - 130

BT - 1st International Conference on 3D Materials Science 2012, 3DMS 2012

ER -