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Kinetic Modeling of Solid-state Reaction Synthesis of Single Crystals /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Kinetic Modeling of Solid-state Reaction Synthesis of Single Crystals // Connor McNamara.
Author:	McNamara, Connor,
Description:	1 electronic resource (96 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-07, Section: B.
Contained By:	Dissertations Abstracts International85-07B.
Subject:	Materials science. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30813320
ISBN:	9798381377712

Kinetic Modeling of Solid-state Reaction Synthesis of Single Crystals /
McNamara, Connor,

Kinetic Modeling of Solid-state Reaction Synthesis of Single Crystals /Connor McNamara. - 1 electronic resource (96 pages)

Source: Dissertations Abstracts International, Volume: 85-07, Section: B.

Single crystal materials are sought after for their uniform ordered structure and lack of grain boundaries which imparts unique properties to the materials, including mechanical, optical, and electrical. The conventional methods to grow single crystal materials include growth from melt, growth from solution, and growth from vapor, but recently more research has been done on solid-state growth techniques. Solid-state growth is of interest because it presents a more cost effective method to grow smaller scale single crystal materials. One novel method is the formation of pseudo single crystals of compounds with pseudobrookite crystal structures via solid-state reaction from a duplex grain mixture. The pseudo single crystal can be formed from unseeded or seeded powder mixtures. This a more efficient solid-state method and observed growth regimes of some compounds indicate that the final structure can be tuned via templating the powders.The potential use of templates to control the final microstructure can be capitalized upon by creating a simulation to aid in predicting the outcome. A variety of modeling techniques have been used to model the kinetics of solid-state reactions, such as the shrinking core model, cellular automata, and Monte Carlo simulation. These three methods all have drawbacks for their application to predicting the microstructure in a solid-state system. The shrinking core model is limited in its scope due to being based on specific geometry and cellular automata is a robust, but computationally intensive method. Kinetic Monte Carlo is the most common technique used for modeling grain growth, but there have been refinements to this model over time. One notable iteration is the Gillespie algorithm, or stochastic simulation algorithm, developed by Daniel T. Gillespie. This was developed for the stochastic solution to coupled chemical reactions, and has been widely used in chemical and biological modeling.Further refinement of the Gillespie algorithm produced τ -leaping, which speeds up the relatively slow method by incrementing simulation time by a variable τ . This method has not been previously applied to a solid-state system and showed promise that it would be an efficient method that gave control over the starting structures and was not as computationally intensive as previous methods. As such initial testing was focused on ensuring that the model was able to accurately simulate the reaction-diffusion process A + B → C. A single interface case was simulated where the starting geometry consisted of two regions consisting of purely A and B. The simulation results were evaluated based on the work of Galfi and Racz who determined the local rate of production, R (z, t) of C as a function of z and t at late times. The calculated concentration of C at the interface at late times aligns with the results of the simulation results. Similar agreement for the early time were achieved based on the work of Taitelbaum et al..The microstructure was expanded to a checkerboard pattern to explore the effects of certain variables in the system. This included diffusivity rates, product stoichiometry, and different diffusivity rates for the A and B atoms. The results give insight into how one can tune the system, such as speeding up or slowing down the product growth and controlling the location of the product phase.Further geometry was tested by setting the initial microstructure to a top seeded model with alternating vertical strips of A and B atoms. Additionally, this model focused on the condition that the product phase can only grow adjacent to existing product. The time-dependence of the propagating reaction in terms of reactant interdiffusion was studied. Mathematically it was determined that CC ∝ t5/2 . The proportionality was found in the simulation data plot of the concentration of C vs scaled time. The model was determined to be a good representation of the physical system. Additionally, insight was gained into how the growth rate of the system changes with time.The microstructure was adjusted further for the final series of simulations which added grain boundaries between the solid A and B regions. This was influenced by discontinuous dissolution reactions in which a migrating front tracks the evolution of a system from a two-phase structure to a single-phase structure. These grain boundaries allowed for a faster diffusion rate when compared to the bulk. The system was run with two initial settings for the grain boundary: with no atoms and with atoms. For the case of no atoms, the relative concentration of C increased approximately as t 3 , which was the results of the mathematical analysis. This setting resulted in a lower product production at the seed when compared to the full channel.

English

ISBN: 9798381377712Subjects--Topical Terms:

543314
Materials science.
Subjects--Index Terms:

Pseudo single crystal

Kinetic Modeling of Solid-state Reaction Synthesis of Single Crystals /
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520 $a Single crystal materials are sought after for their uniform ordered structure and lack of grain boundaries which imparts unique properties to the materials, including mechanical, optical, and electrical. The conventional methods to grow single crystal materials include growth from melt, growth from solution, and growth from vapor, but recently more research has been done on solid-state growth techniques. Solid-state growth is of interest because it presents a more cost effective method to grow smaller scale single crystal materials. One novel method is the formation of pseudo single crystals of compounds with pseudobrookite crystal structures via solid-state reaction from a duplex grain mixture. The pseudo single crystal can be formed from unseeded or seeded powder mixtures. This a more efficient solid-state method and observed growth regimes of some compounds indicate that the final structure can be tuned via templating the powders.The potential use of templates to control the final microstructure can be capitalized upon by creating a simulation to aid in predicting the outcome. A variety of modeling techniques have been used to model the kinetics of solid-state reactions, such as the shrinking core model, cellular automata, and Monte Carlo simulation. These three methods all have drawbacks for their application to predicting the microstructure in a solid-state system. The shrinking core model is limited in its scope due to being based on specific geometry and cellular automata is a robust, but computationally intensive method. Kinetic Monte Carlo is the most common technique used for modeling grain growth, but there have been refinements to this model over time. One notable iteration is the Gillespie algorithm, or stochastic simulation algorithm, developed by Daniel T. Gillespie. This was developed for the stochastic solution to coupled chemical reactions, and has been widely used in chemical and biological modeling.Further refinement of the Gillespie algorithm produced τ -leaping, which speeds up the relatively slow method by incrementing simulation time by a variable τ . This method has not been previously applied to a solid-state system and showed promise that it would be an efficient method that gave control over the starting structures and was not as computationally intensive as previous methods. As such initial testing was focused on ensuring that the model was able to accurately simulate the reaction-diffusion process A + B → C. A single interface case was simulated where the starting geometry consisted of two regions consisting of purely A and B. The simulation results were evaluated based on the work of Galfi and Racz who determined the local rate of production, R (z, t) of C as a function of z and t at late times. The calculated concentration of C at the interface at late times aligns with the results of the simulation results. Similar agreement for the early time were achieved based on the work of Taitelbaum et al..The microstructure was expanded to a checkerboard pattern to explore the effects of certain variables in the system. This included diffusivity rates, product stoichiometry, and different diffusivity rates for the A and B atoms. The results give insight into how one can tune the system, such as speeding up or slowing down the product growth and controlling the location of the product phase.Further geometry was tested by setting the initial microstructure to a top seeded model with alternating vertical strips of A and B atoms. Additionally, this model focused on the condition that the product phase can only grow adjacent to existing product. The time-dependence of the propagating reaction in terms of reactant interdiffusion was studied. Mathematically it was determined that CC ∝ t5/2 . The proportionality was found in the simulation data plot of the concentration of C vs scaled time. The model was determined to be a good representation of the physical system. Additionally, insight was gained into how the growth rate of the system changes with time.The microstructure was adjusted further for the final series of simulations which added grain boundaries between the solid A and B regions. This was influenced by discontinuous dissolution reactions in which a migrating front tracks the evolution of a system from a two-phase structure to a single-phase structure. These grain boundaries allowed for a faster diffusion rate when compared to the bulk. The system was run with two initial settings for the grain boundary: with no atoms and with atoms. For the case of no atoms, the relative concentration of C increased approximately as t 3 , which was the results of the mathematical analysis. This setting resulted in a lower product production at the seed when compared to the full channel.
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650 4 $a Condensed matter physics. $3 3173567
650 4 $a Applied mathematics. $3 2122814
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653 $a Pseudo single crystal
653 $a Grain boundaries
653 $a Mathematical analysis
653 $a Solid-state reactions
653 $a Monte Carlo simulation
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710 2 $a Lehigh University. $b Materials Science and Engineering. $e degree granting institution. $3 3765641
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