An interactive R Shiny application for modeling the kinetics of rapid alumina sintering, based on the 1974 doctoral thesis of Dennis H. Taylor.
Sintering is the process of forming a solid mass from ceramic powder by heating it below the melting point — atoms diffuse and fuse particles together without liquefaction. This app modernizes Dennis Taylor's original research on rapid sintering of alumina (Al₂O₃), examining how trace dopants (Y₂O₃, SnO₂) affect sintering kinetics across three alumina particle morphologies (Linde A/B, Cera, and Fused).
The project was rebuilt by Sean Taylor (2017–2021) to translate his father's Fortran-based dynamic programming algorithm into interactive R code and to make the original research accessible as a living, exploratory tool.
- Qualitative Comparisons — side-by-side plots of sintering curves across dopant types and alumina morphologies
- Kinetics Modeling — interactive curve fitting using a two-phase composite model:
- Non-isothermal phase: exponential growth
Y = A·eᴷᵗ - Isothermal phase: Johnson's equation
Y = 1 − B·e^(−Jt^n)
- Non-isothermal phase: exponential growth
- Dynamic Programming Optimization — automatically finds the inflection point that minimizes combined sum of squared residuals across both fitted curves
- Manual Parameter Tuning — adjust A, K, B, J coefficients interactively and observe the effect in real time
- Vignettes — embedded mathematical derivations, historical context, and the original 1974 Fortran code
Experimental measurements were digitized manually from figures in Dennis Taylor's published thesis. Measurements are normalized to dimensionless ratios:
y = ΔL / ΔL_m(normalized shrinkage)t = (t − t₀) / t₀(normalized time)
The dataset covers multiple alumina samples across dopant concentrations and particle morphologies.
# Install dependencies
install.packages(c("shiny", "dplyr", "ggplot2", "knitr", "rmarkdown"))
# Clone the repo and open in RStudio, then run:
shiny::runApp("app.R")Launch the app and navigate the four tabs:
| Tab | Contents |
|---|---|
| Introduction | Background on alumina, sintering physics, and the original thesis |
| Qualitative Comparisons | Plots comparing sintering rates across dopants and alumina types |
| Modeling | Interactive curve fitting with parameter controls and R² display |
| More | Appendices, Fortran source code, R equivalents, gallery, and background story |
- R / Shiny — application framework
- ggplot2 — scientific visualization
- dplyr — data manipulation
- knitr / R Markdown — embedded vignettes and mathematical notation
- nls / lm — nonlinear and linear least-squares fitting
- Fortran (historical) — original 1974 algorithm, preserved in the appendix
- Sean Taylor — R implementation and application design (seanvig@gmail.com)
- Dennis H. Taylor — original research and 1974 doctoral thesis
MIT