Andrew J. Abraham

THE CRYSTALLITE SIZE DISTRIBUTION IN 2-D BEDS OF RANDOMLY CLOSE-PACKED, BINARY BEADS

DefinitionsCrystalline 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 SpheresAssumptions:

1) Atoms may be treated as if they were hard (impenetrable) spheres

Justification: Coulomb repulsive force of atom’s electron cloudsFusion @ 13oMK in Sun’s CoreMelting 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

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 = 0.90693-D: M = 0.7405

The Randomly Close-Packed, packing fraction has also been investigated:2-D: M = 0.82-0.893-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.

AreaTotal

OccupyBeadsAreaMFraction Packing

Number of Grains in Crystallites1) Degree of Crystallinity =Total Number of Grains

Data Acquisition

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

Image Recognition Program

Goal: To create a program to determine the coordinates (x,y) of the center of each bead.

Raw Image

Program workswell under

right conditions→

Success! A Moderate Failure A Severe Failure

but... or...

Problems…?!

Rough Processing ID 1st Species ID 2nd Species

SSS SSL SLL LLL

Basic States of Smallest Crystallites

A.K.A. “Clusters”

Crystallite Identification Algorithm

Step 1: Identify Clusters

A

B

C

AB=AC=BC = r1+r2 ± Δ

Step 2: Match Clusters

Step 3: Done Iterating

Repeat the process until the crystallite is fully grown

A

B

C

D

E

FCluster ABC and BCD both share B&C

A

B

D

C

A

B

CE

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

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 10.98mm2-17.98mm2 The

3SA+0LA=14.88mm2

2SA+LA=18.11mm2 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.