Ceramic powders size distribution

When two samples are veiy similar, t approaches zero when they are different, t approaches infinity. The value of f is used to calculate the P value using Student s f-test tables, given in the appendix of this book. The P value is tte probability that the two distribution means are the same that is, Aj = Ag. When the P value is greater than a critical accepted value (typically 5% [21] or the experimental error due to both sampling and size determination if it is lai ger) then the null hypothesis (Ho Aj = A2) is accepted (i.e., the two populations are considered to be the same). Ceramic powder size distributions are often represented by log-normal distributions and not by normal distributions. For this reason the t statistic must be augmented for use with lognormal distributions. Equation (2.59) can be modified for this purpose to... 

Schematic representation of the effects of powder size distribution on the sintered microstructure. For eJtample, in (a-1), a narrow size distribution and ooturol of the grain-boundary pore interaction result in a dense sintered ceramic with a grain size slightly larger than the original particle size. From Barringer el at. [166). A distribution of particle sizes may result in better sintering, however. See Fig, 39 in Chapter II.

Binder selection depends on the ceramic powder, the size of the part, how it is formed, and the green density and strength requited. Binder concentration is deterrnined by these variables and the particle size, size distribution, and surface area of the ceramic powder. Three percent binder, based on dry weight, generally works for dry pressing and extmsion. 

Characterization. Ceramic bodies are characterized by density, mass, and physical dimensions. Other common techniques employed in characterizing include x-ray diffraction (XRD) and electron or petrographic microscopy to determine crystal species, stmcture, and size (100). Microscopy (qv) can be used to determine chemical constitution, crystal morphology, and pore size and morphology as well. Mercury porosknetry and gas adsorption are used to characterize pore size, pore size distribution, and surface area (100). A variety of techniques can be employed to characterize bulk chemical composition and the physical characteristics of a powder (100,101). 

Formation of spherical, micron-sized ceramic particles was investigated in an RF thermal plasma reactor. It has been concluded that a wide size distribution of feedstock powders gives rise to either excessive evaporation of smaller grains or insufficient melting of bigger ones. Ceramic spheres with more or less voids inside can also be prepared starting from powders pretreated in special ways. 

Taruta, S., Itou, Y., Takusagawa, N., Okada K. and Otsuka, N. Influence of aluminum titanate formation on sintering of bimodal size-distributed alumina powder mixtures , J. Am. Ceram. Soc. 80 (1987) 551-556. 

Mixing is usually carried out in a ceramic ball mill with steel balls. The inevitable attrition of the mill balls leads to an addition of 0.5-1 wt% to the iron content for which allowance must be made. Care must be taken to maintain the quantity and size distribution of the mill balls and to remove those that have become so small that they cannot be separated from the slip or powder on sieving. 

In this figure one sees all the steps that go into making ceramics, starting with grinding the ceramic powders to develop a very fine particle-size distribution (the grinding circuits contain classification and recycle loops). This is... 

Ceramic powder processing technology is discussed in the Tao Shuo [9]. This text describes how kaolin raw materials had to be foimd and ground to the desirable size distribution. After grinding, the earth was washed and purified. This was done by mixing it with water in a large... 

To characterize a ceramic powder, a representative sample must be taken. Methods of sampling and their errors therefore are discussed. Powder characteristics, including shape, size, size distribution, pore size distribution, density, and specific surface area, are discussed. Emphasis is placed on particle size distribution, using log-normal distributions, because of its importance in ceramic powder processing. A quantitative method for the comparison of two particle size distributions is presented, in addition to equations describing the blending of several powders to reach a particular size distribution. 

Porosity can be an advantage or a disadvantage in ceramic powders, depending upon the processing and final application. Tailoring of the pore size distribution is very important for catalytic substrates, because access to the catalytic sites depends on these diflusional pathways. 

The log-normal distribution is frequently observed in ceramic powder processing. The log-normal distribution is skewed to larger sizes compared to the normal distribution and has no finite probability for sizes less than zero as seen with the normal distribution. It is obtained by replacing x with z = In d in the normal distribution, which gives the following distribution function [18] ... 

The particle size distributions of each of these two sanq)les was determined by sieve analysis using five sieves. The cumulative size distribution is plotted on log probability paper in Figure 2.12. Compare the two ceramic powders, 1 and 2. 

This chapter has described the various techniques of ceramic powder characterization. These characteristics include particle shape, surface area, pore size distribution, powder density and size distribution. Statistical methods to evaluate sampling and analysis error were presented as well as statistical methods to compare particle size distributions. Chemical analytical characterization although veiy important was not discussed. Surface chemical characterization is discussed separately in a later chapter. With these powder characterization techniques discussed, we can now move to methods of powder preparation, each of which 3uelds different powder characteristics. 

Chapter 5 will be devoted to solid phase synthesis of ceramic powders Chapter 6, to liquid phase synfiiesis and Chapter 7, to gas phase synthesis. Other miscellaneous methods of ceramic powder synthesis are discussed in Chapter 8. All of these ceramic powder synthesis methods have one thing in common, the generation of particles with a particular particle sized distribution. To predict the particle size distribution a population balance is used. The concept of population balances on both the micro and... 

The first six reactions form mixed oxide ceramic powders. The last three reactions are carbothermal reductions to produce different metal carbides. The most famous is the Atcheson process for synthesis of SiC from Si02 and carbon, where the carbon in the mixture of reactant powders is used as a resistive electrical conductor to heat the mixture to the reaction temperature. This reaction is performed industrially in a 10-20 m long bunker fixed with two end caps that contain the source and sink for the cLc current. The reactant mixture is piled to a height of 2 m in the bunker and a current is applied. The temperature rises to the reaction temperatures, and some of the excess C reacts to CO, providing further heat. The 10-20 m bunker is covered with a blue flame for most of the reaction period. The resulting SiC is loaded into grinding mills to produce the ceramic powders and abrasives of desired size distributions. 

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