Solid Solutions - Material Science for Engineers - Lecture Slides, Slides of Material Engineering

Download Solid Solutions - Material Science for Engineers - Lecture Slides and more Slides Material Engineering in PDF only on Docsity!

The Science and Engineering of

Materials, 4

th

ed

Chapter 9 – Solid Solutions and Phase

Equilibrium

Objectives of Chapter 9

• The goal of this chapter is to describe the underlying

physical concepts related to the structure of matter.

• To examine the relationships between structure of

atoms-bonds-properties of engineering materials.

• Learn about different levels of structure i.e. atomic

structure, nanostructure, microstructure, and

macrostructure.

• Phase - Any portion including the whole of a system, which is physically homogeneous within it and bounded by a surface so that it is mechanically separable from any other portions.
• Gibbs phase rule - Describes the number of degrees of freedom, or the number of variables that must be fixed to specify the temperature and composition of a phase (2 + C = F + P, where pressure and temperature can change, 1 + C = F + P, where pressure or temperature is constant).
• P-T diagram - A diagram describing thermodynamic stability of phases under different temperature and pressure conditions (same as a unary phase diagram).

Section 9.1 Phases and the Phase

Diagram

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learningherein under license. ™ is a trademark used

Figure 9.1 Illustration of phases and solubility: (a) The three forms of water – gas, liquid, and solid – are each a phase. (b) Water and alcohol have unlimited solubility. (c) Salt and water have limited solubility. (d) Oil and water have virtually no solubility.

Because magnesium (Mg) is a low-density material ( ρ Mg = 1. g/cm^3 ), it has been suggested for use in an aerospace vehicle intended to enter the outer space environment. Is this a good design?

Example 9.1 SOLUTION

• In space the pressure is very low. Even at relatively low temperatures, solid magnesium can begin to change to a vapor, causing metal loss that could damage a space vehicle.
• A low-density material with a higher boiling point (and, therefore, lower vapor pressure at any given temperature) might be a better choice.
• Other factors to consider: In load-bearing applications, we should not only look for density but also for relative strength. Therefore, the ratio of Young’s modulus to density or yield strength to density could be a better parameter to compare different materials.

Example 9.

Design of an Aerospace Component

Many ceramic materials are made into powders using different oxides and carbonates (Chapter 14). This is because ceramics melt at too high a temperature and tend to exhibit brittle behavior. For example, the synthesis process for YBa 2 Cu 3 O7-x, a ceramic superconductor known as YBCO , involves mixing and reacting powders of yttrium oxide (Y 2 O 3 ), copper oxide (CuO), and barium carbonate (BaCO 3 ). The barium carbonate decomposes to BaO during the high temperature reactions and reacts with yttria and copper oxide to form different phases. Often, this process, known as the ‘‘oxide mix’’ technique, produces ceramic powders that are relatively coarse. Some other undesired phases may also form, and deleterious impurities (from processing or raw materials) may become incorporated in the product.

Example 9. Freeze Drying Synthesis of Ceramic Superconductors

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

is a trademark used herein under license.™

Figure 9.3 (a) Pressure- temperature diagram for H 2 O. The triple point temperature is 273.0098 K and the triple point pressure is 4.6 torr. Notice the solid-liquid line sloping to the left. At normal pressure (1 atm or 760 torr), the melting temperature is 273 K. A possible scheme for freeze drying is shown as starting with point S and following the dashed line to the left. (b) Pressure-temperature diagram for CO2. Many researchers are examining the applications of super-critical CO 2 for use as a solvent for applications related to the processing of plastics and pharmaceuticals. (c) Pressure- temperature diagram for Si0 2 , The dotted line shows the 1 atm pressure.

Example 9.2 SOLUTION

• Prepare a solution of nitrates of yttrium, copper, and barium in proper cation stoichiometry.
• Remove the nitric acid (HNO 3 ) and H 2 O without causing any melting by lowering the pressure to approximately 10-2^ torr (point B).
• Increase the temperature while maintaining the low pressure causing the ice and nitric acid to sublimate (solid  vapor).
• The mixed metal nitrate powder will then be heated carefully and the nitrates can be decomposed to form a ceramic powder.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learninglicense. ™ is a trademark used herein under

Figure 9.4 (a) Liquid copper and liquid nickel are completely soluble in each other. (b) Solid copper-nickel alloys display complete solid solubility, with copper and nickel atoms occupying random lattice sites. (c) In copper-zinc alloys containing more than 30% Zn, a second phase forms because of the limited solubility of zinc in copper.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

is a trademark used herein under license.™

Figure 9.5 The solubility of zinc in copper. The solid line represents the solubility limit; when excess zinc is added, the solubility limit is exceeded and two phases coexist.

 Hume-Rothery rules - The conditions that an alloy or ceramic system must meet if the system is to display unlimited solid solubility. Hume-Rothery’s rules are necessary but are not sufficient for materials to show unlimited solid solubility.

 Hume-Rothery rules:

• Size factor
• Crystal structure
• Valence
• Electronegativity

Section 9.3 Conditions for Unlimited

Solid Solubility

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learningunder license. ™ is a trademark used herein

Figure 9.7 Mg0 and Ni0 have similar crystal structures, ionic radii, and valences; thus the two ceramic materials can form solid solutions.

Example 9.3 SOLUTION (Continued)

The percent difference in ionic radii and the crystal structures are also shown and suggest that the FeO-MgO system will probably display unlimited solid solubility. The CoO and ZnO systems also have appropriate radius ratios and crystal structures.

 Solid-solution strengthening - Increasing the strength of a metallic material via the formation of a solid solution.

 Dispersion strengthening - Strengthening, typically used in metallic materials, by the formation of ultra-fine dispersions of a second phase.

Section 9.4 Solid-Solution

Strengthening