Jawaharlal Nehru Technological University Hyderabad B.Tech IV SCIENCE AND TECHNOLOGY OF CERAMICS Previous Question Paper (October/November - 2020 - R16)

The radius ratio is defined as the ratio of the radius of the cation (r_c) to the radius of the anion (r_a) in an ionic crystal structure, expressed as r_c/r_a. It serves as a geometric criterion to predict the coordination number (CN) and the stability of the crystal lattice, as it determines how many anions can pack around a central cation without causing instability due to cation-anion repulsion.

The stability of an ionic structure is maintained when anions are in contact with the cation. As the radius ratio increases, the coordination number increases to accommodate more anions around the cation.

The following table summarizes the relationship between radius ratio, coordination number, and geometry:

Key crystal structures in ceramics based on these ratios include:

• AX Type Structures: These include the Rock Salt structure (CN=6, ratio 0.414-0.732) where ions occupy octahedral sites, and the Cesium Chloride structure (CN=8, ratio >0.732) where the cation sits in a cubic void.
• AmXp Type Structures: These occur when cation and anion charges are not equal. For example, the Fluorite structure (CaF₂) features a coordination number of 8 for the cation and 4 for the anion, dictated by the stoichiometry and the relative sizes of the ions.
• Silicate Structures: Many ceramics, particularly silicates, are based on the SiO₄^4- tetrahedron, where the Si⁴⁺ cation occupies a tetrahedral site (CN=4) within a network of oxygen anions, consistent with the radius ratio requirements for tetrahedral coordination.

In practice, the actual coordination observed in ceramic materials may deviate from these theoretical limits due to factors like covalent bonding character, polarization effects, and temperature-induced lattice expansion.

The BaO-TiO2 binary system is a critical phase diagram in materials science, particularly for the production of dielectric ceramics. The system exhibits several stable compounds, most notably Barium Titanate (BaTiO3), which is a ferroelectric material widely used in capacitors, transducers, and sensors.

Key features of the BaO-TiO2 phase diagram include:

• Eutectic points: The diagram features several eutectic reactions where liquid phases solidify into two distinct solid phases at specific temperatures, such as the eutectic between Ba2TiO4 and BaTiO3.
• Peritectic reactions: Several compounds, such as BaTi2O5 and BaTi4O9, form through peritectic reactions where a solid phase reacts with a liquid to form a new solid phase upon cooling.
• Liquidus and Solidus lines: The liquidus line represents the temperature above which the entire system is molten, while the solidus line represents the temperature below which the entire system is completely solid.

Important ceramic compounds and their applications include:

• BaTiO3 (Barium Titanate): The most significant compound, characterized by its high dielectric constant and ferroelectric properties. It is the primary material for multilayer ceramic capacitors (MLCCs) and piezoelectric devices.
• BaTi4O9: Known for its excellent microwave dielectric properties, specifically a high quality factor and low temperature coefficient of resonant frequency, making it ideal for microwave resonator applications.
• Ba2TiO4: Often studied for its role in the sintering kinetics of barium titanate-based ceramics and its influence on the dielectric loss profile of the final ceramic body.

In practice, the BaO-TiO2 system is controlled during the firing process to ensure the desired stoichiometry and grain size, which directly dictate the electrical performance of the resulting dielectric components.