# Determining the three-dimensional morphology of {gamma}{prime}-particles in {gamma}-{gamma}{prime} superalloys

## Abstract

The authors propose qualitative and quantitative methods for determining the three-dimensional morphology of second-phase particles in Ni-based superalloys in the late stages of coarsening. Qualitatively, they determine a way to identify the three-dimensional shape of a particle from its (111) cross section. Quantitatively, they derive a method that uses stereological analysis on a single (111) section to compute the average shape of a particle in three dimensions. For cases where the average shape does not necessarily reflect the particles' true morphology, they derive another method based on sectioning probability to compute the shape of individual particles. The authors are also able to determine a particle's orientation in three dimensions by examining its (111) cross section. The methods were tested by using computer-generated (111) sections of three-dimensional arrays of rectangular particles. They conclude that (111) sections can be used to provide an accurate calculation of the interfacial area per unit volume (S{sub v}) of the structure. Finally, they illustrate the efficacy of using (111) sections to determine particle morphology by examining (111) transmission electron microscopy (TEM) micrographs of particles undergoing splitting.

- Authors:

- Publication Date:

- Research Org.:
- Northwestern Univ., Saratoga, CA (US)

- OSTI Identifier:
- 20075677

- Alternate Identifier(s):
- OSTI ID: 20075677

- Resource Type:
- Journal Article

- Journal Name:
- Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials Science

- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 1073-5623

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; MICROSTRUCTURE; NICKEL BASE ALLOYS; PARTICLES; MORPHOLOGY; SHAPE; ORIENTATION; TRANSMISSION ELECTRON MICROSCOPY

### Citation Formats

```
McElhaney, K.W., and Voorhees, P.W.
```*Determining the three-dimensional morphology of {gamma}{prime}-particles in {gamma}-{gamma}{prime} superalloys*. United States: N. p., 2000.
Web. doi:10.1007/s11661-000-0252-6.

```
McElhaney, K.W., & Voorhees, P.W.
```*Determining the three-dimensional morphology of {gamma}{prime}-particles in {gamma}-{gamma}{prime} superalloys*. United States. doi:10.1007/s11661-000-0252-6.

```
McElhaney, K.W., and Voorhees, P.W. Mon .
"Determining the three-dimensional morphology of {gamma}{prime}-particles in {gamma}-{gamma}{prime} superalloys". United States. doi:10.1007/s11661-000-0252-6.
```

```
@article{osti_20075677,
```

title = {Determining the three-dimensional morphology of {gamma}{prime}-particles in {gamma}-{gamma}{prime} superalloys},

author = {McElhaney, K.W. and Voorhees, P.W.},

abstractNote = {The authors propose qualitative and quantitative methods for determining the three-dimensional morphology of second-phase particles in Ni-based superalloys in the late stages of coarsening. Qualitatively, they determine a way to identify the three-dimensional shape of a particle from its (111) cross section. Quantitatively, they derive a method that uses stereological analysis on a single (111) section to compute the average shape of a particle in three dimensions. For cases where the average shape does not necessarily reflect the particles' true morphology, they derive another method based on sectioning probability to compute the shape of individual particles. The authors are also able to determine a particle's orientation in three dimensions by examining its (111) cross section. The methods were tested by using computer-generated (111) sections of three-dimensional arrays of rectangular particles. They conclude that (111) sections can be used to provide an accurate calculation of the interfacial area per unit volume (S{sub v}) of the structure. Finally, they illustrate the efficacy of using (111) sections to determine particle morphology by examining (111) transmission electron microscopy (TEM) micrographs of particles undergoing splitting.},

doi = {10.1007/s11661-000-0252-6},

journal = {Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials Science},

issn = {1073-5623},

number = 5,

volume = 31,

place = {United States},

year = {2000},

month = {5}

}