Useful Extensions of the statistical theory of sintering

Fang, Te‐Hua; Palmour, Hayne

doi:10.1016/0272-8842(89)90045-x

Cited by 27 publications

(4 citation statements)

References 6 publications

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“…The morphological kinetic equation 25 was used to evaluate the activation energies of the samples. The mixed powders were microwave dried, ground in a mortar, and calcined at 1250°C for 4 h. The calcined powders were wet-ball milled in ethyl alcohol for 24 h and dried.…”

Section: Methodsmentioning

confidence: 99%

The defect structure, sintering behavior, and dielectric responses of Cr2O3-doped Sr0.5Ba0.5Nb2O6

Fang

Chen

2006

Journal of Applied Physics

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Phase structure, dielectric properties, and relaxor behavior of ( K 0.5 Na 0.5 ) NbO 3 -( Ba 0.5 Sr 0.5 ) TiO 3 lead-free solid solution for high temperature applications Effect of sintering temperature on the phase transition and dielectrical response in the relaxor-ferroelectricsystem 0.5PZN-0.5PZT Sr 0.5 Ba 0.5 Nb 2 O 6 ͑SBN50͒ with and without Cr 2 O 3 dopant had been prepared by the solid-state reaction. The structural variations of undoped and Cr 2 O 3 -doped SBN were examined by the x-ray diffractometer. As the Cr 2 O 3 content increases, the lattice parameters remain almost unchanged initially but become greatly changed revealing the increase in a axis and the decrease in c axis when the Cr 2 O 3 content is Ͼ1 mol %, which was mainly influenced by the created oxygen vacancies. Isothermal sintering behavior of undoped and Cr 2 O 3 -doped SBN50 has been investigated. It was found that the creation of the charge-compensated oxygen vacancies and the accompanied structural change had a significant influence on the sintering behavior. The direct jumping path through vacant O sites ͑path 2 in Fig. 9͒ was further considered as the main reason for the enhancement of the densification rate and slight increase of the activation energy when the Cr 2 O 3 content is Ϲ1 mol % and the decrease of the densification rate but great increase of the activation energy when the Cr 2 O 3 content is Ͼ1 mol %. T max ͓temperature at the maximum dielectric constant ͑ max ͔͒ decreased with the increase of Cr doping and is essentially determined by the structural change of the NbO 6 units in SBN. max is suggested to be determined by the competition between the reduction of the polarization due to the substitution of Cr for Nb and the enhancement of the polar moment arising from the weakening of Nb-O bonds due to the creation of the oxygen vacancies.

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Section: Methodsmentioning

confidence: 99%

The defect structure, sintering behavior, and dielectric responses of Cr2O3-doped Sr0.5Ba0.5Nb2O6

Fang

Chen

2006

Journal of Applied Physics

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“…Where

boldκ

is a constant,

{\overset{r}{true}}_{a}

is the mean intra‐aggregate pore radius, and the value of

s = 1 / 2

for intermediate stage and

s = 1

for final stage …”

Section: The Modelmentioning

confidence: 99%

“…Then, by making several averages, expressions for the porosity with various morphological parameters are derived. This theory has been subsequently improved by considering the effect of the fraction of pores that are not located at the grain boundaries, and therefore do not contribute to densification. The statistical theory of sintering considers the effect of grain growth by using the widely known Zener's relation.…”

Section: Introductionmentioning

confidence: 99%

Novel model for the sintering of ceramics with bimodal pore size distributions: Application to the sintering of lime

Maya

Bhatia

2016

AIChE Journal

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A mathematical model for the sintering of ceramics with bimodal pore size distributions at intermediate and final stages is developed. It considers the simultaneous effects of coarsening by surface diffusion, and densification by grain boundary diffusion and lattice diffusion. This model involves population balances for the pores in different zones determined by each porosimetry peak, and is able to predict the evolution of pore size distribution function, surface area, and porosity over time. The model is experimentally validated for the sintering of lime and it is reliable in predicting the so called “initial induction period” in sintering, which is due to a decrease in intra‐aggregate porosity offset by an increase inter‐aggregate porosity. In addition, a novel methodology for determination of mechanisms based on the analysis of the pore size distribution function is proposed, and with this, it was demonstrated that lattice diffusion is the controlling mechanism in the CaO sintering. © 2016 American Institute of Chemical Engineers AIChE J, 63: 893–902, 2017

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“…The morphological kinetic equation 12 has been used to evaluate the activation energy of the single-phase SBN with different Sr:Ba ratios. It can be expressed as…”

Section: (1) Densification Behavior Of Single-phase Sbn With Differenmentioning

confidence: 99%

Effect of the Strontium:Barium Ratio and Atmosphere on the Sintering Behavior of Strontium Barium Niobate

Lee

Fang

1998

Journal of the American Ceramic Society

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The sintering behavior of Sr x Ba 1−x Nb 2 O 6 (SBN) (x = 0.5, 0.6, and 0.7) was studied. The densification rate increased and the evaluated activation energy of SBN decreased as the Sr:Ba molar ratio increased. Also, when SBN50 (SBN where x = 0.5) was sintered at <1300°C, the densification rate decreased as the oxygen partial pressure increased, and, at 1300°C, the oxygen partial pressure had insignificant influence on the densification. The relationship of sintering behavior and structure of SBN has been discussed, and the niobium ion was suggested as being the ratelimiting species when sintering SBN.

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Useful Extensions of the statistical theory of sintering

Cited by 27 publications

References 6 publications

The defect structure, sintering behavior, and dielectric responses of Cr2O3-doped Sr0.5Ba0.5Nb2O6

The defect structure, sintering behavior, and dielectric responses of Cr2O3-doped Sr0.5Ba0.5Nb2O6

Novel model for the sintering of ceramics with bimodal pore size distributions: Application to the sintering of lime

Effect of the Strontium:Barium Ratio and Atmosphere on the Sintering Behavior of Strontium Barium Niobate

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