Phase Field Modelling of nanoparticle sintering

Introduction

My project involved simulating, visualizing and obtaining parameters used to study nanoparticle sintering using the phase field model. Sintering is a process of compacting two or more particle powder into single solid at high temperatures, but below the particles’ melting points. This process is used in powder metallurgy to produce high strength and durable materials. To gain understand into how this process takes place in a nanoscale, a phase field modeling approach is used to study the evolution of the microstructures during sintering. Phase field is a set of values of a single variable called order parameter that represent the entire state of the microstructure during sintering[1]. Phase field has proven to be a good model in modelling sintering because it enables the computational simulation of microstructure evolution without making restrictive assumptions[2]. This feature of the phase field model makes it an attractive approach to study nanoscale sintering. Computational simulation of nanoscale sintering is presented.

Goal

• The motivation of this project is to understand the temporal evolution of nanoscale sintering.
• The project objective is to successfully perform a 3D simulation and visualization of nanoscale particle sintering using the Phase Field Model.

Approach

Mass Transport Phenomena

• Grain boundary diffusion
• Surface diffusion
• Volume diffusion

Methods

• Phase field model
• Finite difference method

Result

Figure 1: Temporal evolution of nanoparticle sintering

Summary

Accomplishment & Observation

1. Temporal growth of nanoparticle sintering was successfully simulated yielding insights into how particle microstructures evolve during sintering.
2. Most important observation is change in density of individual particles as it sinters while the overall density of the system remains relatively constant as it evolves.

Acknowledgement

• Institute for Computational Engineering and Sciences, UT Austin.
• Department of Mechanical Engineering, UT Austin.
• Dr M. Cullinan
• Georgina Obehi Dibua

References

[1] Qin, R. S., and H. K. Bhadeshia. "Phase Field Method." Review. n.d.: n. pag. Web. 20 May 2017.

[2] Wang, Yu U. “Computer Modeling and Simulation of Solid-State Sintering: A Phase Field Approach.” Acta Materialia, vol. 54, no. 4, 9 Dec. 2005, pp. 953–961. ELSEVIER, Science Direct, doi:10.1016/j.actamat.2005.10.032.

Code Blocks

Simulation & Parameter Estimation

The simulation program was written by Georgina Obehi Dibua in C++. I added some routines to make it work for the purpose of parameter value Estimation. The following table has information about the added routines I developed to achieve my goal.

Modifier	Method and Description
double	inRange(double low, double high, double seed) Returns a random number between low and high inclusive
void	resetParams() Sets parameters' values to default
void	resetRho(double* rho,double* newrho, double** eta, int Size) Sets the density and order parameter values
void	reassign(constants* cons, int count, ...) Sets parameter values to new values
bool	modify(const double* sumrho, double* param, double* lowerbound, double* upperbound, const double* maximum, double* t, const int master = 0) Searches for the maximum parameter value

Visualization

Visualization involved reading the data and plotting it. It was written in Python using Matplotlib(Could have used VTK). The following table has information about the functions I wrote to get the job done.

Modifier	Method and Description
def	getnumzeros(vector) Returns the number of zeroes in the vector
def	readRow(filename) Reads a single line
def	getProduct(row) Returns an array of the products of first element and the rest of the elements in row
def	parseData(filename) Return a tuple of a m by n matrix of data from a text file and number of lines read
def	unpack(matrix) Unpacks the matrix so that each column represent a single particle. Returns the new matrix
def	genColor(n = 1, manager = None) Generates n hexadecimal color codes.
def	readBinary(fname,fmt,bsize) Reads data from a data file.
def	getcoords(data, xsize, ysize, zsize) Generates the x,y,z coordinate for data
def	plot(coords, fig, ax, start = 0, count = 10,fcolor = None, multijob = (False,"filename")) Plots the coords
def	readsingle(file, offset = 0, ndata = 44, dtype='d') Reads ndata of type dtype from file using offset as the byte offset to control read location.
def	process(rho, eta) Returns the element by element product of two vectors.
def	writable(filename, writtable) Writes writtable data to file with name filename.
def	readable(filename) Reads data from file with name filename
def	multijob(fname) Multiple process job. fname is a single job
def	buildCmd(args) uses args to build a command