Loose Leaf For Foundations Of Materials Science And Engineering
6th Edition
ISBN: 9781260049169
Author: William Smith, Javad Hashemi, Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4.8, Problem 3KCP
In the solidification of a pure metal, what are the two energies involved in the transformation? Write the equation for the total free-energy change involved in the transformation of liquid to produce a strain-free solid nucleus by homogeneous nucleation. Also, illustrate graphically the energy changes associated with the formation of a nucleus during solidification.
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Q1/ In a homogeneous solidification process, assume molten metal solidifies into a spherical
nucleus with a BCC structure. The given data are; lattice parameter (0.292 nm), the heat of
fusion energy (1.85×10-9 J/m³), latent surface free energy (0.204 J/m²), critical radius (1-35
nm), equilibrium melting temperature (1516 K), and room temperature (27 °C). Calculate the
following for this metal;
(a) supercooling value temperature (b) activation tree energy (c) number of atoms in a
nucleus of critical size.
Question-6. For solidification of a piece of FCC-metal at 860 °C. The melting point of the metal
is 1260 °C. The latent heat of fusion and surface free energy are -2.16 x108 J/m³ and 0.126 J/m²,
respectively. If nucleation is homogeneous, answer the following questions:
(a) Compute the critical radius r* in nm
(b) Compute the activation free energy AG* in J
(c) If the lattice parameter is 0.26 nm at the melting temperature, compute the number of atoms
found in a nucleus of critical size
(d) Compute the critical radius at the supercooling degree of 260 K.
Chapter 4 Solutions
Loose Leaf For Foundations Of Materials Science And Engineering
Ch. 4.8 - Prob. 1KCPCh. 4.8 - Define the homogeneous nucleation process for the...Ch. 4.8 - In the solidification of a pure metal, what are...Ch. 4.8 - In the solidification of a metal, what is the...Ch. 4.8 - During solidification, how does the degree of...Ch. 4.8 - Distinguish between homogeneous and heterogeneous...Ch. 4.8 - Describe the grain structure of a metal ingot that...Ch. 4.8 - Distinguish between equiaxed and columnar grains...Ch. 4.8 - How can the grain size of a cast ingot be refined?...Ch. 4.8 - Prob. 10KCP
Ch. 4.8 - Prob. 11KCPCh. 4.8 - Prob. 12KCPCh. 4.8 - Distinguish between a substitutional solid...Ch. 4.8 - What are the conditions that are favorable for...Ch. 4.8 - Prob. 15KCPCh. 4.8 - Prob. 16KCPCh. 4.8 - Prob. 17KCPCh. 4.8 - Prob. 18KCPCh. 4.8 - Describe the structure of a grain boundary. Why...Ch. 4.8 - Describe and illustrate the following planar...Ch. 4.8 - Prob. 21KCPCh. 4.8 - Describe the optical metallography technique. What...Ch. 4.8 - Prob. 23KCPCh. 4.8 - Prob. 24KCPCh. 4.8 - Prob. 25KCPCh. 4.8 - Prob. 26KCPCh. 4.8 - Prob. 27KCPCh. 4.8 - Prob. 28KCPCh. 4.8 - Prob. 29KCPCh. 4.8 - Prob. 30KCPCh. 4.8 - Prob. 31KCPCh. 4.8 - Calculate the size (radius) of the critically...Ch. 4.8 - Prob. 33AAPCh. 4.8 - Prob. 34AAPCh. 4.8 - Calculate the number of atoms in a critically...Ch. 4.8 - Prob. 36AAPCh. 4.8 - Prob. 37AAPCh. 4.8 - Prob. 38AAPCh. 4.8 - Prob. 39AAPCh. 4.8 - Prob. 40AAPCh. 4.8 - Prob. 41AAPCh. 4.8 - Prob. 42AAPCh. 4.8 - Determine, by counting, the ASTM grain-size number...Ch. 4.8 - Prob. 44AAPCh. 4.8 - For the grain structure in Problem 4.43, estimate...Ch. 4.8 - Prob. 46AAPCh. 4.8 - Prob. 47SEPCh. 4.8 - Prob. 48SEPCh. 4.8 - Prob. 49SEPCh. 4.8 - Prob. 50SEPCh. 4.8 - In Chapter 3 (Example Problem 3.11), we calculated...Ch. 4.8 - Prob. 52SEPCh. 4.8 - Prob. 53SEPCh. 4.8 - Prob. 54SEPCh. 4.8 - Prob. 55SEPCh. 4.8 - Prob. 56SEPCh. 4.8 - Prob. 57SEPCh. 4.8 - Prob. 58SEPCh. 4.8 - Prob. 59SEPCh. 4.8 - Prob. 60SEPCh. 4.8 - Prob. 61SEPCh. 4.8 - Prob. 62SEPCh. 4.8 - Prob. 63SEPCh. 4.8 - Prob. 64SEPCh. 4.8 - Prob. 65SEPCh. 4.8 - Prob. 66SEP
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- Can you explain the kinetics of recovery, recrystallization, and grain growth? (Draw three plots showing the kinetics of each prosess and explain the plot)arrow_forward2. Solidification is one of the most important processing techniques used in the manufacturing of materials. Discuss the solidification process in terms of its atomic arrangements, nucleation formation, and total free energy change. Why is undercooling required for solidification? Derive an equation showing the total free energy change as a function of undercooling when the nucleating solid has the critical nucleus radius r*What do the terms "primary" and "secondary" processing mean? Sketch a graph of the total free energy of the solid-liquid system changes with the size of the solid to improve your discussion.arrow_forwardFor the solidification of nickel, calculate the critical radius r* and the activation energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are -2.53×109 J/m3 and 0.255 J/m2, respectively. The supercooling value ΔT for the homogeneous nucleation of Ni is 319 oC. The melting point for Ni is 1455 oC.arrow_forward
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Explanation of Solidification of Metals & Alloys | Manufacturing Processes; Author: Magic Marks;https://www.youtube.com/watch?v=G5z9KknF_s8;License: Standard Youtube License