On the mathematical theory of zone-melting

Braun, I; Marshall, Stephen P.

doi:10.1088/0508-3443/8/4/307

Cited by 14 publications

(5 citation statements)

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“…Examples include the work of Braun et al, who have offered a comprehensive solution toward mapping the redistribution of solutes in the zone refining process as well as solved the ultimate distribution of different impurities by taking into account the final effect due to the typical freezing in the last zone. [160,161] Reiss et al solved the differential-difference equation of solute concentration distribution in a finite ingot, zone refined for a particular number of passes. [162,163] Through the use of a mathematical model, Jackson et al demonstrated a linear gradient of solute concentration by altering the molten zone's volume.…”

Section: Numerical Modeling and Simulation On Zone Refiningmentioning

confidence: 99%

A Review on the Zone Refining Process Technology toward Ultra‐Purification of Gallium for GaAs/GaN‐based Optoelectronic Device Applications

Ghosh,

Mani

2024

Cryst. Res. Technol.

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Ultrapure gallium up to 99.9999%/ 99.99999% (6N/7N) purity level is a highly demanding material needed for the growth of gallium‐based group III–V semiconductor compounds and optoelectronic devices. However, general extraction of gallium from Bayer liquor contains high impurity content and ultra‐purification of the same cannot be accomplished by a single step. Thus, the purpose of this review is to assess various purification processes for the production of ultra‐pure gallium and to critically examine its applications in the optoelectronics industry. Through this research survey, it is found that zone refining of the zone melting process stands tall over other methods in purifying materials even up to 13N. Hence, scientists are adopting detailed mathematical models and simulation tools for designing unique zone refining systems for material purification. Current‐day technology even adopts intelligence methods such as machine learning, which sheds light on the importance of different zone refining parameters that influence the purification process. Here, the practical aspects of zone refining and how the feedback from the theoretical models or performance prediction through intelligence methods can be effectively incorporated into practice have also been emphasized

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Section: Numerical Modeling and Simulation On Zone Refiningmentioning

confidence: 99%

A Review on the Zone Refining Process Technology toward Ultra‐Purification of Gallium for GaAs/GaN‐based Optoelectronic Device Applications

Ghosh,

Mani

2024

Cryst. Res. Technol.

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“…As the molten zone advances distance d x , it freezes out an amount of impurity C n i and takes in an amount C n –1 i +1 . Thus, eq , used in all numerical methods for representing zone melting, − was then derived by taking the mass balance over impurity: 1 k eff nobreak0em0.25em⁡ normald C n i = ( C n − 1 i + 1 − C n i ) nobreak0em0.25em⁡ normald x …”

Section: Numerical Model and Simulationmentioning

confidence: 99%

Numerical and Experimental Investigation of Arsenic Removal Process from Phosphoric Acid by Vertical Zone Melting Technique

Ren

Duan

Wang

et al. 2012

Ind. Eng. Chem. Res.

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A combined numerical and experimental approach was undertaken to investigate the arsenic removal process from phosphoric acid by vertical zone melting technique. The numerical model, which predicts the arsenic re-distribution at any point of the single zone pass, multiple molten zone passes, or ultimate distribution, is described for providing simulations. Experimental work on arsenic removal by vertical zone melting process was carried out with prepared phosphoric acid samples as the starting material. The experimentally obtained axial concentration profiles were compared with the theoretical predictions, which proved the efficiency of the proposed model in removing the arsenic concentration significantly. Following the model and as evidenced from the theoretical predictions, the arsenic concentration reduced to <50 ng•g −1 and a 99.8% removal rate were obtained under the conditions of molten zone length of 0.1L, molten zone velocity of 3 mm•h −1 , and nine molten zone passes. Also, the experimental and simulated results were undertaken to find out the influence of the crucial zone melting parameters including the number of passes, the molten zone length, and the molten zone velocity on the efficiency of arsenic removal from phosphoric acid by vertical zone melting technique.

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“…[5][6][7] A relatively large body of theoretical work has been done in the metallurgical field focusing on the segregation of impurities during ZA of semiconductors. [8][9][10][11] This phenomenon, which is driven by the distribution coefficient for the impurity between the crystal and the liquid, can lead to ultrapure materials with relevance to electronics.…”

Section: Introductionmentioning

confidence: 99%