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Andrew J. Abraham

The Crystallite Size Distribution in 2-D Beds of Randomly Close-Packed, Binary Beads. Andrew J. Abraham. Definitions. Crystalline Solid: A solid which exhibits an orderly, repeating, and l ong- range pattern to the locations of the atoms within that solid.

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Andrew J. Abraham

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  1. The Crystallite Size Distribution in 2-D Beds of Randomly Close-Packed, Binary Beads Andrew J. Abraham

  2. Definitions Crystalline Solid: A solid which exhibits an orderly, repeating, and long- range pattern to the locations of the atoms within that solid. Amorphous Solid: A solid which exhibits no long-range order to the locations of atoms within that solid. Crystallite: A region, within a solid, which exhibits an orderly, repeating, but short-range pattern to the locations of the atoms within that region. Close-Packing: The ordering of granular material such that the material consumes the greatest possible fraction of volume (1-D, 2-D, or 3-D). Random Close-Packing: Close-Packing but with (at least partially) randomized positions of grains. Binary Grains: A collection of granular material such that a particular trait distinguishes exactly two types of granular species.

  3. Modeling Alloys Using Hard Spheres Assumptions: 1) Atoms may be treated as if they were hard (impenetrable) spheres Justification:Coulomb repulsive force of atom’s electron clouds Fusion @ 13oMK in Sun’s Core Melting Point of Iron = 1783oK 2) Earth’s gravity shall simulate the inter-atomic attractive forces found in metallic solids 3) The atomic structure of the solid can be molded using concepts of granular physics, since atoms can essentially be treated as grains* 4) Metallic alloys consist of two or more atomic species, hence the binary investigation *Note energy & entropy changes

  4. Non-Crystalline, Metallic Solids Crystalline Solid Non-Crystalline Solid Close-Packed Randomly Close-Packed Understanding the significance of RCP, Non-Crystalline Solids will lead to a better understanding of thermophysicalproperties such as: - Heat Conductivity -Thermal Diffusivity -Spectral Emissivity -Heat Capacity -Thermal Expansion Coefficient

  5. Some New Definitions: The Close-Packed, packing fraction in 2-D and 3-D is a well accepted value: 2-D: M = 0.9069 3-D: M = 0.7405 The Randomly Close-Packed, packing fraction has also been investigated: 2-D: M = 0.82-0.89 3-D: M = 0.64 My goal: To investigate less understood physical quantities such as… 2) Crystallite Size Distribution To date, there have been no measurements taken, nor theories developed, to determine an estimate of these two quantities, in the binary case.

  6. Data Acquisition

  7. Computerized Image Processing Why use a computer? Look at the numbers! An atom diameter ~ 1Å → ~1015 atoms in 1cm2 . There are 600 beads per image → It will take 1010 images to get 0.1% the number of atoms in 1cm2. This would represent 104 TB of graphical information. We approximate this system by choosing large enough a sample… but small enough to be manageable. How do you use the computer to help you? I wrote 2 programs using C and Python programming languages: -- An image recognition program -- A program to identify crystallites

  8. Image Recognition Program Goal: To create a program to determine the coordinates (x,y) of the center of each bead. Program works well under right conditions→ but... or... Raw Image ID 1st Species Rough Processing ID 2nd Species Success! A Severe Failure A Moderate Failure Problems…?!

  9. Basic States of Smallest Crystallites A.K.A. “Clusters” SSS SSL SLL LLL

  10. Crystallite Identification Algorithm Step 2: Match Clusters Step 1: Identify Clusters A Step 3: Done Iterating A C E C B D A B A C AB=AC=BC = r1+r2 ± Δ B E C D B D F Cluster ABC and BCD both share B&C Repeat the process until the crystallite is fully grown

  11. Processed Data 30%S-70%L Binary Ratio 50%S-50%L Binary Ratio 70%S-30%L Binary Ratio

  12. Data: The Degree of Crystallinity

  13. Data: Crystallite Size Distribution

  14. Data: Final Analysis The distribution changes based on the binary ratio The most common crystallite size consists of 4 spherical grains in low and medium binary concentrations, and 3 spherical grains in the high binary concentrations, as well as the monodisperse cases Justification: @ 20%S Binary Ratio the range of the peak bin is 24.5mm2-31.5mm2 SA+3LA=29.53mm2 2SA+2LA=26.30mm2 @ 70%S Binary Ratio the range of the peak bin is 10.98mm2-17.98mm2The 3SA+0LA=14.88mm2 2SA+LA=18.11mm2 won’t fit into bin!

  15. Conclusions A Computerized Method of determining the degree of crystallinity of Randomly Close-Packed, binary granular systems is more desirable than measurement by hand, due to the large numbers involved. Image recognition programming can be challenging, but it pays off through speed and efficiency. Allowing a program to identify crystallites saves time, energy, and produces more consistent data. The shape of the crystallite size distribution significantly changes as the percentage of the small granular species is varied. There is current work on a theory which exploits the changes in the dynamics of crystallites at increased temperatures in metallic alloys.

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