Characterization of the Density and Spatial Distribution of Dispersoids in Al-Mg-Si Alloys
Abstract
:1. Introduction
2. Methodology
2.1. Existing Methods for Assessing Spatial Uniformity
2.2. Global Shannon Entropy (GSE)
2.3. Generation of Spatial Point Patterns
- A point is given random x- and y-coordinates.
- Based on the location of the first point, new points are distributed at distances around this location, based on a normal distribution. If a point lands outside the image boundaries, the generation process will continue regardless, and the cluster will contain one less point. The amount of points per cluster will be referred to as nc.
- The generation process is continued until the desired number of points in the image, xi, is fulfilled.
- The intensity of clustering is changed by varying the number of points in each cluster, nc, and the standard deviation in the normal distribution, σ. The standard deviation is set to be a factor multiplied with the maximum dispersoid radius (150 nm), e.g., σ = 5rmax.
2.4. Effect of Point Intensity and Number of Quadrats (q) on the GSE Metric
2.5. Efficiency of the GSE Metric in Detecting Non-Uniformity
2.6. A Modified GSE Metrics
2.7. Differentiating Degrees of Spatial Uniformity
3. Materials and Methods
4. Results
4.1. Number Density and Area Fraction of Dispersoids
4.2. Size and Spatial Distribution of Dispersoids
5. Discussion
5.1. Density and % Area
5.2. Spatial Distribution (GSE)
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Alloy | Si | Mg | Fe | Mn | Cr | Cu |
---|---|---|---|---|---|---|
6063 | 0.52 | 0.47 | 0.22 | 0.05 | - | - |
6005 | 0.59 | 0.55 | 0.19 | 0.14 | - | 0.11 |
6061 | 0.67 | 0.84 | 0.23 | 0.06 | 0.08 | 0.24 |
6082 | 1.03 | 0.66 | 0.21 | 0.51 | - | - |
Alloy | Heating Rate | Density | St.dev. | % Change | % Area | St.dev. | % Change |
---|---|---|---|---|---|---|---|
6063 | Slow | 5.18 × 104 | 2.89 × 104 | - | 0.027 | 0.019 | - |
Normal | 5.21 × 104 | 3.05 × 104 | 0.6 | 0.025 | 0.018 | −7.4 | |
Fast | 3.76 × 104 | 2.73 × 104 | −27.4 | 0.019 | 0.016 | −29.6 | |
6005 | Slow | 1.37 × 105 | 3.63 × 104 | - | 0.108 | 0.034 | - |
Normal | 1.52 × 105 | 5.14 × 104 | 10.9 | 0.1 | 0.038 | −7.4 | |
Fast | 1.61 × 105 | 6.65 × 104 | 17.5 | 0.095 | 0.043 | −12.0 | |
6061 | Slow | 3.31 × 105 | 1.38 × 105 | - | 0.197 | 0.091 | - |
Normal | 3.17 × 105 | 1.54 × 105 | −4.3 | 0.163 | 0.084 | −17.2 | |
Fast | 3.38 × 105 | 1.68 × 105 | 2.1 | 0.160 | 0.075 | −18.4 | |
6082 | Slow | 5.06 × 105 | 7.53 × 104 | - | 0.547 | 0.103 | - |
Normal | 5.72 × 105 | 1.26 × 105 | 13.0 | 0.521 | 0.129 | −4.8 | |
Fast | 6.15 × 105 | 1.04 × 105 | 21.6 | 0.559 | 0.116 | 2.2 |
Alloy | Heating Rate | n | q/q* | GSE | GSE* | |
---|---|---|---|---|---|---|
6063 | Slow | 1879 | 12/99 | 0.90 | 0.56 | 0.80 |
Normal | 1888 | 12/99 | 0.86 | 0.59 | 0.76 | |
Fast | 1362 | 12/99 | 0.79 | 0.73 | 0.71 | |
6005 | Slow | 4979 | 48/180 | 0.97 | 0.26 | 0.92 |
Normal | 5555 | 48/180 | 0.95 | 0.34 | 0.84 | |
Fast | 5818 | 48/180 | 0.93 | 0.41 | 0.80 | |
6061 | Slow | 12010 | 120/224 | 0.96 | 0.42 | 0.81 |
Normal | 11496 | 120/224 | 0.95 | 0.49 | 0.80 | |
Fast | 12257 | 120/224 | 0.95 | 0.5 | 0.78 | |
6082 | Slow | 18347 | 180/288 | 0.99 | 0.15 | 0.91 |
Normal | 20678 | 180/288 | 0.98 | 0.22 | 0.84 | |
Fast | 22304 | 180/288 | 0.99 | 0.17 | 0.87 |
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Remøe, M.S.; Westermann, I.; Marthinsen, K. Characterization of the Density and Spatial Distribution of Dispersoids in Al-Mg-Si Alloys. Metals 2019, 9, 26. https://doi.org/10.3390/met9010026
Remøe MS, Westermann I, Marthinsen K. Characterization of the Density and Spatial Distribution of Dispersoids in Al-Mg-Si Alloys. Metals. 2019; 9(1):26. https://doi.org/10.3390/met9010026
Chicago/Turabian StyleRemøe, Magnus Sætersdal, Ida Westermann, and Knut Marthinsen. 2019. "Characterization of the Density and Spatial Distribution of Dispersoids in Al-Mg-Si Alloys" Metals 9, no. 1: 26. https://doi.org/10.3390/met9010026