Phase Rule, ceramic

The number of course programmes is directly proportional to the demand made by trade and industry. Many factors have been of influence on this instruction, among others the Gibbs phase rule (see the chapter on Phase rule), X-ray diffraction to clarify the structure of solids and the development of synthetic barium titanate and other ceramic materials whose properties could be influenced by controlling composition and process conditions. As early as 1900 it became clear that the study of ceramics required much knowledge of other subjects, as appears from the Ohio State University s course programme of that year. 

Phase rule studies and describes the occurence of modifications and states of aggregation of pure substances or in mixtures in closed systems as well as the changes which occur in those systems when the pressure, temperature and composition of these substances in the system change. The behaviour of many pure substances and mixtures has thus been studied and recorded in diagrams. These diagrams constitute a vital aid for any scientist studying the development of materials, e.g. ceramics. 

In Russia, besides the Radium Institute, research on the synthesis of crystal ceramics is carried out mainly for the immobilization of actinide-containing wastes at the RPA Radon , the Bochvar VNIINM, and some other organizations. The research activities are at the stage of laboratory experiments with a use of simulators of actinides. As a rule, ceramics of the titanate composition of the SYNROC type are synthesized, or some other phases (for example, monazite). Two methods of synthesis used are the cold crucible or hot pressing. 

In this chapter, the phase relations of those oxide components will be discussed that most commonly occur in ceramics, namely silica, alumina, calcia, magnesia, potassia, and iron oxide. The chapter is introduced by a cursory analysis of the anatomy and construction of phase diagrams based on Gibbs phase rule, progressing from one component to two components, and from three components to multicomponent systems. The thermodynamics of these phase assemblies will be described, some important phase diagrams discussed, and conclusions drawn. 

Phase equilibria in ceramic and refractory systems can be studied with the help of phase diagrams. Phase diagrams are based on Gibb s phase rule, which can be mathematically represented by the following equation ... 

The specific heat of Si3N4 ceramics is in the temperature range 293 up to 1200 K [Cp (293 K) = 0.67 KJ (K kg)-1] nearly independent of the composition of the additives. The isobaric specific heat values agree well with the isochoric specific heat calculated by Debye s theory. Also the Dulong Petit s rule can applied as an approximation of the Cv values [25 J(K mol)-1] at temperatures >1100 K [371]. From the Cp values at around 100 K the amount of the amorphous grain boundary phase can be calculated [371]. 

The coefficient of thermal expansion (CTE) of composite materials usually follows the simple rule of mixtures (or more complex models), based on the CTE of the respective components, their volume fraction and the volume fraction of interfacial phases. Based on these models, a Si3N4-Si3N4(w) composite should possess a similar CTE to monolithic Si3N4 ceramic (3.2 x 10 6/°C). obviously, the chemical composition of the sintering additive will have a certain influence but should remain within the variations observed for monolithic Si3N4. 

In practice ceramics are usually multiphase, consisting of crystalline phases, glasses and porosity. The overall behaviour depends on the distribution as well as the properties of these constituents. A minor phase that forms a layer round each crystallite of the major phases, and therefore results in a 3-0 connectivity system (see Section 2.7.4), can have a major effect. If the minor phase is conductive it can greatly reduce the resistivity of the composite or, if insulating, it can reduce its conductivity. Also, an abrupt change in the mode of conduction at the main phase-intercrystalline phase boundary may introduce barriers to conduction that dominate the overall electrical behaviour. In contrast, minor phases present as small discrete particles, or porosity present as empty cavities, can only modify properties to a minor extent as indicated by one of the mixture relations such as Lichtenecker s rule (see Section 2.7.4). 

In extrusion the existence of a homogenous tribosystem caimot be assumed. As a rule, distinct variations in material and of an energetic nature have to be considered in processing ceramic materials. Even if there are no phase changes, the material parameters vary considerably in respect to their mechanical, thermal, rheological, tribological and chemical characteristics as a result of the effects created by temperature, pressure and speed. It is thus impossible to analyse an extruder as a comprehensive tribosystem in its entirety. 

To understand why ceramics have particular structures and why certain defects form in these structures, it is really important to understand Pauling s rules. These rules require you to visualize a tetrahedron and an octahedron and to see how they fit together. To understand properties such as piezoelectricity or the mechanisms of phase transformations, you must be able to visualize the crystal structure of the material. This is particularly important when we want to predict the properties of single crystals. We summarize the features of crystallography that we use throughout the text and give references to more specialized resources for rigorous proof of theorems and more detailed discussion. 

The densification of single-phase and pure ceramics of transition metal diborides is complicated by two characteristics of these compounds, the high melting point and the comparatively high vapor pressure of the constituents. As a rule, sintering temperatures exceeding 70% of the absolute melting temperature have to be applied. 

Very little further progress in instrumentation was made until the 1950s. A brief summary of the classical DTA and DSC operating system, instrumentation, rules of data treatment, and the differences between DSC and DTA are given in Appendix 9. The first milestone was reached by 1952 when about 1,000 research reports on DTA had been published. At that time, DT A was mainly used to determine phase diagrams, transition temperatures, and chemical reactions. Qualitative analysis (fingerprinting) was developed for metals, oxides, salts, ceramics, glasses, minerals, soils, and foods. 

As mentioned above, a composite in general is a heterostructural materuJ whose properties are determined by the contents, the number of different phases of which the material is composed, their properties, and the ways in which different phases are interconnected (73.67]. The latter is the most important feature of composites, since the mixiiig rules of a given property are controlled by the self-connectiveneas of individual phases. Piezoelectric polymer-ceramic composites, for example, have a number of appUcatioas. since their properties can be tailored to the requirements of various devices by combining the superior properties of a polymer and those of ceramics [67]. 

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