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Transition Zone Theory: A New Way to Describe Crystal Growth

Dr James Martin has established a crystallization model that describes melt crystal growth rate using variables such as line enthalpy of activation, the entropy of activation, and cooperativity—variables many chemists have yet to combine when examining melt crystal growth. This theory is the first of its kind to provide a platform to compare diverse crystal systems' physical and chemical properties. To briefly describe these variables, enthalpy is an energy term that describes the energy as heat in a system; entropy is a distribution of energy in a system; cooperativity is how molecules are working together to grow the crystal.

Multiple variables need to be considered to assess whether a molecule will bind to form a crystal. Most standard crystallization models provide a general examination of crystal growth rate concerning over-extrapolated assumptions like equilibrium concepts and bond energy. Not one of these models has been able to closely predict diverse crystal growth, like the unique growth of the NaPO3 network, like Dr Martin's Transitional Zone Theory (TZT) of crystallization.

The cover photo of this article depicts the accuracy of Dr Martin's theory. Dr James Martin's Transition Zone Theory (solid black line) more closely fits experimental crystal growth rate data (open circles) than standard models of crystal growth (red dashed line). Photo courtesy of James Martin, NC State University.

The problem with standard crystallization models is not that they cannot describe crystal growth, but that there are far too many theories that cannot apply to a wide range of crystals, albeit all crystals. Similar crystalline compounds, for example, Li2O 3SiO2, Na2O 2SiO2, and Na2O 3SiO2 needed different classical models to describe their growth, and they weren't entirely accurate either. This makes understanding chemistry extremely inefficient. Because TZT accurately describes melt crystal growth rates of all crystals, Dr Martin's single theory aids in understanding solid-state chemistry much more efficiently.

Dr Martin's theory wasn't established without the help of other scientists' theories. TZT is an analogue of chemist Walter Kauzmann's concept of configurational entropy, or the organizational energy of the particles, and Adam and Gibbs' idea of cooperativity, or how the particles work together to form and grow the crystal.  

Below is the equation that Dr Martin has derived from Eyring's Transition State Theory and Adam Gibbs' cooperativity that describes diverse crystal growth.

These variables may seem foreign to the average person. Even Dr Martin admits that he was intimidated by complex mathematical equations before he created his own.

"You show me these mathematical equations, and I'm going to turn around and run!" "I would have feared my papers," Dr Martin said about being math-phobic himself. He's much more of a visual learner and would rather see the trend in the data for himself. He's been accused of "scribbling shit down" (Dr Martins' words), which refers to writing down scrap calculations to see if he can match patterns in data. He'll then go dig into his calculus books and find pictures of functions that match the data he's accumulated. From there, he ensures that every parameter (enthalpy and entropy of activation, cooperativity, etc.) in any function he finds has a physical or chemical significance.

The diagram below shows the crystal growth rate of standard crystallization models compared to Dr Martin's TZT; a diagram Dr Martin is extremely proud of. Dr Martin notes how different standard models (colored dashed lines) are used to describe the similar crystalline compounds of Li2O 3SiO2, Na2O 2SiO2, and Na2O 3SiO2, whereas his TZT model (solid line) can accurately describe the crystal growth of all three structures. Photo courtesy of James Martin, NC State University.


Growing up in a working-class family, with his father being a high school science teacher and his mother being a stay-at-home mom, Dr Martin found himself to be a scrappy and academically curious kid looking up to his father with a science background.

"Everybody taught me that when scientists discover something new, they push to disprove the old and prove the new, so I just had in my mind that's how science worked." "If I just did good work, people would accept it," says Dr Martin, addressing his early misconceptions about challenging the scientific community.

Of course, it hasn't come without controversy. When scientists choose to challenge other scientists, there are going to be some disagreements and skepticism. Dr Martin is challenging theories that have been accepted for more than 75 years because he truly believes there are far too many cracks and assumptions in standard theories that don't accurately depict a wide enough range of crystals. His paper on TZT was submitted to seven different journals before he was finally able to get it published, solving what was known widely to be one of the greatest outstanding challenges in condensed matter science. His paper is still a topic of controversy for many scientists, despite its compelling evidence.

While Dr Martin hasn't found any exceptional crystals that don't fit his model yet, he still has research topics worth exploring. His study in polymers, for example, involves examining the cooperativity variable of the crystal since this parameter has been seen to be slightly different due to different structures when being observed through TZT. Polymers are more of a two-dimensional crystalline structure, and Dr Martin has found that this structure, as opposed to three-dimensional structures, possesses different cooperativity data.

Another one of Dr Martin's projects involves tweaking what's known as "classical nucleation theory." He's been comparing nucleation to crystal growth, which is the process by which droplets of liquid condense from vapor. He believes that nucleation is the catalyst for crystal growth. Dr Martin also questions how crystals grow out of solution because, again, classical models do not accurately depict how crystals grow out of solution.


These topics are of major interest to Dr Martin, and he's very excited that his research team is getting close to answering these questions.

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