Andrew J. Abraham

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.

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 13 o MK in Sun’s Core Melting Point of Iron = 1783 o K 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

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 thermophysical properties such as: - Heat Conductivity -Thermal Diffusivity -Spectral Emissivity -Heat Capacity -Thermal Expansion Coefficient

Some New Definitions: The Close-Packed, packing fraction in 2-D and 3-D is a well accepted value: 2-D: M = D: M = The Randomly Close-Packed, packing fraction has also been investigated: 2-D: M = 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.

Data Acquisition

Computerized Image Processing Why use a computer? Look at the numbers! An atom diameter ~ 1Å → ~10 15 atoms in 1cm 2. There are 600 beads per image → It will take images to get 0.1% the number of atoms in 1cm 2. This would represent 10 4 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

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

SSSSSLSLL LLL Basic States of Smallest Crystallites A.K.A. “Clusters”

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

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

Data: The Degree of Crystallinity

Data: Crystallite Size Distribution

Data: Final Analysis 1)The distribution changes based on the binary ratio 2)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 20%S Binary Ratio the range of the peak bin is 24.5mm mm 2 S A +3L A =29.53mm 2 2S A +2L A =26.30mm 70%S Binary Ratio the range of the peak bin is 10.98mm mm 2 The 3S A +0L A =14.88mm 2 2S A +L A =18.11mm 2 won’t fit into bin!

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.