The Science and Engineering of Materials, 4th ed Donald R ...

The Science and Engineering of Materials, 4th ed Donald R ...

1 Section 5.2 Stability of Atoms and Ions Arrhenius equation Activation energy -The energy required to cause a particular reaction to occur. 2 2 3

3 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.8 The Arrhenius plot of in (rate) versus 1/T can be used to determine the activation energy required for a reaction 4

4 Section 5.3 Mechanisms for Diffusion Self-diffusion - The random movement of atoms within an essentially pure material. Vacancy diffusion - Diffusion of atoms when an atom leaves a regular lattice position to fill a vacancy in the crystal. Interstitial diffusion - Diffusion of small atoms from one interstitial position to another in the crystal structure.

5 5 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.10 Diffusion of copper atoms into nickel. Eventually, the copper atoms are randomly distributed throughout the nickel

6 6 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.11 Diffusion mechanisms in material: (a) vacancy or substitutional atom diffusion and (b) interstitial diffusion 7 7

Section 5.4 Activation Energy for Diffusion 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Diffusion couple - A combination of elements involved in diffusion studies Figure 5.12 A high energy is required to squeeze atoms past one another

during diffusion. This energy is the activation energy Q. Generally more energy is required for a substitutional atom than for an interstitial atom 8 8

Section 5.5 Rate of Diffusion (Ficks First Law) Ficks first law - The equation relating the flux of atoms by diffusion to the diffusion coefficient and the concentration gradient. Diffusion coefficient (D) - A temperature-dependent coefficient related to the rate at which atoms, ions, or other species diffuse. Concentration gradient - The rate of change of composition with distance in a nonuniform material, typically expressed as atoms/cm3.cm or at%/cm. 9

9 Section 5.6 Factors Affecting Diffusion Temperature and the Diffusion Coefficient (D) Types of Diffusion - volume diffusion, grain boundary diffusion, Surface diffusion Time Dependence on Bonding and Crystal Structure Dependence on Concentration of Diffusing Species and Composition of Matrix

10 10 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.18 The diffusion coefficient D as a function of reciprocal temperature for some metals and ceramics. In the Arrhenius plot,

D represents the rate of the diffusion process. A steep slope denotes a high activation energy 11 11 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.20 Diffusion in ionic compounds. Anions can only

enter other anion sites. Smaller cations tend to diffuse faster 12 12 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.15 Illustration of the concentration gradient

13 13 Section 5.9 Diffusion and Materials Processing Sintering - A high-temperature treatment used to join small particles. Powder metallurgy - A method for producing monolithic metallic parts. Dielectric resonators -Hockey puck-like pieces of ceramics such as barium magnesium tantalate

(BMT) or barium zinc tantalate (BZN). Grain growth - Movement of grain boundaries by diffusion in order to reduce the amount of grain boundary area. Diffusion bonding - A joining technique in which two surfaces are pressed together at high pressures and temperatures. 14 14 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.

Figure 5.28 Diffusion processes during sintering and powder metallurgy. Atoms diffuse to points of contact, creating bridges and reducing the pore size 15 15 Figure 5.30 The microstructure of BMT ceramics obtained by compaction and sintering of BMT powders. (Courtesy of

H. Shirey.) Figure 5.29 Particles of barium magnesium tantalate (BMT) (Ba(Mg1/3 Ta2/3)O3) powder are shown. This ceramic material is useful in making electronic components known as dielectric resonators that are used for wireless communications. (Courtesy of H. Shirey.) 16

16 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.31 Grain growth occurs as atoms diffuse across the grain boundary from one grain to another 17 17 Figure 5.32 Grain growth in alumina ceramics can be seen from the SEM micrographs of alumina ceramics. (a)

The left micrograph shows the microstructure of an alumina ceramic sintered at 1350oC for 150 hours. (b) The right micrograph shows a sample sintered at 1350oC for 30 hours. (Courtesy of I. Nettleship and R. McAfee.) 18 18 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure 5.33 The steps in diffusion bonding: (a) Initially the

contact area is small; (b) application of pressure deforms the surface, increasing the bonded area; (c) grain boundary diffusion permits voids to shrink; and (d) final elimination of the voids requires volume diffusion 19 19 Example 5.9 SOLUTION First, since the bottles are to be used for storing carbonated beverages, a plastic material with a small diffusivity for carbon dioxide gas should be chosen.

The bottles should have enough strength so that they can survive a fall of about six feet. This is often tested using a drop test. The surface of the polymer should also be amenable to printing of labels or other product information. The effect of processing on the resultant microstructure of polymers must also be considered. 20 20 Example 5.9

Design of Carbonated Beverage Bottles You want to select a polymer for making plastic bottles that can be used for storing carbonated beverages. What factors would you consider in choosing a polymer for this application? 21 21

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