Research ArticleCHEMICAL PHYSICS

Crystal nucleation in metallic alloys using x-ray radiography and machine learning

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Science Advances  13 Apr 2018:
Vol. 4, no. 4, eaar4004
DOI: 10.1126/sciadv.aar4004
  • Fig. 1 Crystal density.

    (A) Normalized crystal density measured by the computer vision algorithm as a function of time for grained refined Al-Cu alloys with 10, 15, 20, and 25 wt % Cu, subdivided into three cooling rates of 0.3, 0.7, and 1.5 K s−1 (time t = 0 s was set when a crystal first appeared in the field of view). The solid lines are the best-fit Avrami equation to the data. (B to D) Typical radiographic images at the three cooling rates obtained toward the end of solidification and showing the equiaxed dendritic Al-rich primary crystals in an Al–25 wt % Cu.

  • Fig. 2 Crystal formation rate.

    (A) Crystal formation rate as a function of time at cooling rates of 0.3, 0.7, and 1.5 K s−1, and (B) as a function of solute content and (C) cooling rate.

  • Fig. 3 Nucleation undercooling measurement method.

    A sequence of images of 1.5 s from the crystallization of an Al–25 wt % Cu alloy: Previously identified crystals are boxed in green, and crystals identified for the first time in each frame are boxed in blue. A cluster of five crystals are boxed in yellow and shown at higher magnification in the second sequence, which is in reverse time. The five grains are tracked with reverse time back through the sequence at higher temporal resolution (0.15 s) until each disappears, which is then assumed to be the instant and location of nucleation from which an estimate of undercooling is made according to the local Cu composition.

  • Fig. 4 Nucleation undercooling distributions.

    The undercooling probability density function (pdf) distributions for each of the 12 experimental conditions. Each one comprises several repeat experiments, together with a best-fit log-normal distribution (dotted line) and a box-plot insert showing the position of the median undercooling (red line), the second and third quartiles (blue box), and the 5 to 95 percentiles. The bin width is 0.01 wt % Cu. The data set includes 6200 validated measurements.

  • Fig. 5 Nucleation bursts.

    (A to C) Solidification of an Al–25 wt % Cu grain-refined with 0.1 wt % Ti using Al-5Ti-1B and cooled at a constant rate of 0.3 K s−1; image frames at time t = 16, 29, and 38 s showing, respectively, three successive nucleation waves (time t = 0 s was set to the first frame in which a crystal appeared; the colormap is an inverted gray scale to enhance crystal visibility). (D) The crystal formation rate as a function of time of the experiment shown in (A) to (C) (yellow line) showing more pronounced bursts of nucleation as the alloy composition increased (at 0.3 K s−1). (E) The frequency spectrum of the crystal formation rate as a function of time for the four Al-Cu alloys at 1.5 K s−1. a.u., arbitrary units; FFT, fast Fourier transform.

  • Fig. 6 Solute-suppressed nucleation.

    (A) Fraction of the solute-enriched liquid (fE, in blue) at fraction solid fS of 0.02 and 0.03 during the solidification of Al–10 wt % Cu and Al–25 wt % Cu. (B) Schematic representation of the size distribution of the nucleant particles and corresponding measured nucleation undercooling without (top) and with (bottom) solute suppression of nucleation.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaar4004/DC1

    section S1. Synchrotron experiments

    section S2. Automatic analysis of radiographic sequences

    section S3. Supplementary results

    fig. S1. Sample preparation steps.

    fig. S2. Experimental setup.

    fig. S3. Image processing steps to obtain an intensity image and solute map.

    fig. S4. Density map overview.

    fig. S5. Variation in crystal size and density for three different sequences.

    fig. S6. Localizing crystals through the density map.

    fig. S7. Counting accuracy.

    fig. S8. Undercooling measurement.

    fig. S9. Nucleant particle diameters.

    fig. S10. Nucleation burst frequencies analysis.

    fig. S11. Solute suppression mechanism.

    table S1. Sample summary.

    table S2. Nucleation burst frequencies.

    movie S1. Comparison between manual and automatic crystal counting.

    movie S2. Crystal detection and tracking.

    movie S3. Crystal formation rate and nucleation bursts.

    References (5671)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Synchrotron experiments
    • section S2. Automatic analysis of radiographic sequences
    • section S3. Supplementary results
    • fig. S1. Sample preparation steps.
    • fig. S2. Experimental setup.
    • fig. S3. Image processing steps to obtain an intensity image and solute map.
    • fig. S4. Density map overview.
    • fig. S5. Variation in crystal size and density for three different sequences.
    • fig. S6. Localizing crystals through the density map.
    • fig. S7. Counting accuracy.
    • fig. S8. Undercooling measurement.
    • fig. S9. Nucleant particle diameters.
    • fig. S10. Nucleation burst frequencies analysis.
    • fig. S11. Solute suppression mechanism.
    • table S1. Sample summary.
    • table S2. Nucleation burst frequencies.
    • References (56–71)

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.avi format). Comparison between manual and automatic crystal counting.
    • movie S2 (.avi format). Crystal detection and tracking.
    • movie S3 (.avi format). Crystal formation rate and nucleation bursts.

    Files in this Data Supplement: