Ceramic Technology and Processing, King

2 Ceramic Technology and Processing

measurements and calculations. This current book supplements part two and broadens part one to include laboratory equipment and processing. A book by James Reed entitled Introduction to the Principles of Ceramic Processing2 is more theoretical in content than the current book. With these three books, the subject of processing and procedures will be appropriately addressed.

Scope

The scope of this book covers a broad range of ceramic technical crafts, with some notable exclusions. Since comprehensive literature on ceramic lab crafts is unavailable, I had to largely deduce this knowledge from my own experience. While knowledge of these crafts is also applicable to electronic ceramics, this discussion does not directly address electronic ceramics, glass, or composites. Addressing these aforementioned materials is beyond the scope of this book.

Dealing with ceramic crafts in a manufacturing plant can be quite different than in a laboratory. Processing techniques in a manufacturing plant are different principally because of the volume of material involved and the urgency in getting an order out the door. However, there is an overlap, especially in analytical techniques and in instrumentation. In regards to processing, this book addresses laboratory procedures.

The scope includes information on preparing the material, forming the material, and firing the material. Also discussed are laboratory analytical procedures, testing procedures, and the properties of the ceramic that results from this processing procedure.

Various types of instruments and processing equipment are referred to in this book. To avoid any type of endorsement, it is not common practice to specify equipment by their brand name. As such, technical literature quite properly avoids identifying equipment by brand name. However, this book is not considered technical literature in the normal sense; it is about engineering crafts in a ceramics laboratory. Since equipment is a central part of this book, the author would be remiss if he did not include equipment brand names. Mentioning the brand name can implicate two problems. First, with progress being so rapid it is inevitable that some information will be out-of-date, and second, my experience will

Introduction 3

not be all inclusive. As a result, I decided to draw from my limited and sometimes outdated experience regarding the choices of the instruments and process equipment in this book. Please consider these limitations and do not be hesitant to take a fresh look when considering a new instrument or process equipment.

The general objective is to present in the technical literature an assembly of information on the crafts that a ceramic engineer or technician can use in the laboratory. This information will be helpful since it is not found any where else.

3.0 MANAGING DATA

The number of independent variables and anticipated interactions in a system has a lot to do with how an experiment is designed. We will discuss three such contingencies.

Models

Models are mathematical expressions derived from scientific or engineering principles. The expressions predict how the system is expected to function. The next step is to do the experiments to see if the model fits the data, or vice-versa. This is of course the scientific method. Provided one conducts the experiment scientifically, the model is confirmed when there is coincidence between the expected and the predicted results. The beauty of science is that it is self correcting. Anyone with the appropriate skills can run the same experiment and get the same results. Another beauty of science is that it is a discipline simplifying our concept of the physical world. Reducing a system to a working, mathematical expression imparts fundamental understanding and this is beautiful.

In important cases, the model becomes a theory when one experimentally verifies a mathematically derived concept. With very important fundamental cases, the model becomes a law when the experimental results always work. Results in the ceramics lab are usually of a more humble

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stature such as a relationship and correlation between a cause and an effect in a particular system. One can work with this correlation as it describes how the system behaves, and this is often just what one seeks.

Statistical Experiment Design

When the independent variables are mostly known, or can be anticipated, statistical experimental design is sometimes the preferred method. Factorial designs are particularly powerful. For example, consider a small sintering experiment shown in Table 1.1.

Table 1.1: Sintering Experiment

			Sintering Temperature
		Low		Medium		High
Molding	Low	2		2		2
	Medium	2		2		2
Pressure
	High	2		2		2

Table 1.1 depicts two independent variables: sintering temperature and molding pressure. One can expect to observe curvature as each of the independent variables is at three levels. Remember, two points define a straight line. To observe a curvature, there has to be as a minimum of three points: low, medium, and high.

Let us postulate that the dependent variable is sintered density. There are two samples in each condition; enabling us to find an error variance. The total number of samples in the experiment is 18. One can compare the effects of temperature and pressure on density to the error variance with an F ratio. One can find the latter value in a book to determine the probability that the effects are real or just due to chance. This

Introduction 5

provides a much more secure basis for making decisions.

Factorial design also produces an interaction variance that indicates whether the two independent variables have an effect on each other. This is called the curvature. In this example, one would expect an interaction. Often, an interaction is the most important result from the experiment and this is the way to obtain it.

Factorial designs are fine when there are only a few independent, known variables. When there are four or five such variables, the experimentation becomes lengthy. Partial factorials can help to reduce the bulk, but some interactions are lost.

There are many factorial experimental designs; some of these designs are multidimensional. Selecting the best design for an experiment requires some expertise. To achieve this end, one can either consult an experimental statistician or be further trained in this area.

Another method of statistical design is Self Determining Optimization (SDO). This is a method that leads one in a stepwise fashion to the best solution. In SDO, one performs a sequence of experiments that lead in the direction of the desired result. SDO is analogous to the game called Blind Man`s Bluff that also leads you in the right direction. Both these methods provide the person with the right answer rather than an understanding of the system. Since the right answer is important, one benefits from applying these methods. SDO is especially useful when there are a lot of independent variables that render factorial methods impractical.

Other useful statistical measures are standard deviation, coefficient of variation, and the correlation coefficient. When two variables plot as a line, these statistics indicate how good a fit there is in the data.

Table 1.2 and Figure 1.1 depict three sets of data in a decreasing certainty of correlation; this is measured by the correlation coefficient.

Table 1.2: Curve and Correlation Coefficient

Curve	Correlation Coefficient
Good Fit	0.997
Poor Fit	0.938
Bad Fit	0.58

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Figure 1.1: Linear Curve Fitting

Figure 1.1 represents some nonsense data to make a point. It depicts a visual comparison between good, poor, and bad data in correlation to a straight line. In this example, the visual insecurity in the data is compared with the statistic, Correlation Coefficient. The author's preference is to accept a good fit as a mathematical relationship and the poor fit as a trend, but would balk at data scattered widely as in the bad fit. It is not difficult to calculate the linear equation for the good fit line from the slope and intercept. For the above data the equation is:

A = -0.01 + 0.986B

(1.1)

Equation 1.1 can be used to calculate other values of A and B and to extrapolate accordingly, provided one does not go too far.

Standard deviation (SD) is a statistic that measures the scatter in a

Introduction 7

set of data. Coefficient of variation (CV) is the standard deviation divided by the mean (average). Coefficient of variation is used to compare two standard deviations when the mean is different between the two sets of data. Consider the nonsense data in Table 1.3.

Table 1.3: Data with Standard Deviation and Coefficient of Variation

	Set A	Set B
	50	42
	48	58
	54	42
	47	58
	48	56
	57	54
	46	56
	54	50
Average (mean)	50.5	50.75
Standard Deviation	4	7.17
Coefficient of Variation	0.079	0.141

The mean values are almost identical, but the standard deviations and coefficients of variation are different. Set B has more scatter than set A, as seen in Figure 1.2.

8 Ceramic Technology and Processing

Figure 1.2: Scattering in Data

Figure 1.2 is a visual comparison between two sets of data with one having more scatter than the other.

It is always a good idea to look directly at the raw data to help to obtain a feel for the statistical significance. In Figure 1.2, the scatter from off the mean is shown, with set B having more scatter than set A. Visually the scatter in the figure imparts meaning to the statistics. There is another reason for looking at the data. An inconsistent value is obvious and will need an explanation. For instance, a set of identical numbers from the modulus of rupture (MOR) test does not mean that the strengths were perfectly identical; this is very close to impossible. Rather it means that

Introduction 9

there is an instrumental error. It is more common to have one or two numbers that do not fit with the others. For example, if set B had a value of 85, it would be suspect and most statisticians would eliminate it from the set. One can assume that something went wrong and the value is not representative.

Are the results reasonable? Often the experimenter will have a good idea of just what to expect from a test. When the result is good compared with expectations, then either a discovery or a mistake was made. One would have to verify this.

Let us now address the coefficient of variation. Let us assume that we have a third Set C (set not shown) with data that is numerically the same as set A, except that the SD and mean is smaller by a factor of 10. This produces the following statistical result:

	Set A	Set C
Standard deviation	4.0	0.4
Mean	50.5	5.05
Coefficient of Variation	0.079	0.079

The two sets of numbers have different standard deviations and means, by a factor of 10. However, the coefficients of variation are identical, meaning that sets A and C have the same scatter in proportion to their mean values. It is not useful to compare standard deviations between two sets of numbers when the mean values are greatly different. In such a case, use the coefficient of variation instead.

Another way to present data in a meaningful way is to draw contour maps. Contours are drawn through the data points to delineate the locus of equal values. Take for example the data in Figure 1.3. This figure is hypothetical and does not represent a real system. Obviously, there is a wealth of information in a contour map of this sort. There is a maximum, a slowly sloping plateau off to the left, a ridge-like bulge, and then a precipitous drop off on the far left of the map. Parameters A and B are interacting in an active way. An especially important advantage is the almost instantaneous recognition of the system's behavior. This may not occur by merely looking at a page full of numbers.

When drawing the contours over a field of numbers, inconsistencies are to be expected as data has random variability. Surfaces

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usually behave in a consistent pattern. Contours are not independent of each other but are interactive, with the shape of the surface evolving as it is drawn. When a few numbers are not in the right place, it is of little consequence. For example, the figure "93" is on the wrong side of the "95" contour. To make an abrupt change in the contour would compromise the consistency of the pattern and would probably be a false description of the surface shape.

Figure 1.3: Contour Maps

As some computations are lengthy, computers are especially useful for statistical analysis. ECHIP is user-friendly software; it also has a userfriendly manual. STATISTICA is more powerful software, but it is complex to learn and is expensive. CORELDRAW, a graphics software, is one of several good programs for graphics application.

There is a cautionary word about time spent on graphics software application. Data reduction and presentation should not be time consuming and should not be a substitute for experimental time in the laboratory. Simple sketches are often good enough. Some of the most descriptive

Introduction 11

figures I have seen were those drawn by professor Newnham at Penn State; these were simple drawings. Anatomists frequently use drawings to selectively emphasize particular features. As such, a class in drawing techniques can be a substitute for a class in computer graphics. Attaining such drawing skills could be time well spent.

A computer is not a surrogate brain. Similarly, a copy machine is not a surrogate pen. There isn't always a need for long convoluted reports with gorgeous graphics when one only needs a contour map. A contour map can be sketched in a fraction of the time it takes to produce it with a graphics program; moreover, it conveys the same amount of information.

Intuitive Experiments

It is axiomatic that if nothing new is tried that any new discovery is precluded. Creativity in the physical sciences seems to involve inductive processes. A creative individual tries new things with the process often being intuitive. A memorized fact, an observation, or information from a different field can often spark an intuitive experiment.

Despite the fact that the subject of creativity has been extensively addressed, this topic still leaves the author without an understanding of the creative process. However, the following factors contribute toward the art of creativity:

•latitude in time and resources for individual research,

•an environment appreciative of invention,

•an environment where invention is required,

•resources for commercialization particularly in an industrial lab,

•an inquisitive mind, and

•stimulating colleagues.

Another impetus for intuitive creativity is the recognition of a problem with subsequent probing for an answer. The key factor involves understanding the problem. For example, consider the problem with forming recrystallized silicon carbide: the ceramic has little or no firing shrinkage; however, making the green density can be the key to obtaining a high-fired density. Then, start thinking about what processes might increase packing density. Some of these processes include gap sizing, mulling the grain to round the corners, vibrating the mix as it is slip cast, jolting the mix as it is