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 5KCP
During solidification, how does the degree of undercooling affect the critical nucleus size? Assume homogeneous nucleation.
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Problems
OF T
1
Lithium at 20°C is BCC and has a lattice constant of 0.35092 nm.
Calculate a value for the atomic radius of a lithium atom in
nanometers.
2
During solidification, how does the degree of undercooling affect
the critical nucleus size? Assume homogeneous nucleation.
3
Describe the grain structure of a metal ingot that was produced by
slow-cooling the metal in a stationary open mold.
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.
(a) For the solidification of iron, calculate the critical radius r* and the activation free energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are –1.85 × 109 J/m3 and 0.204 J/m2, respectively. Use the supercooling value ΔT = 286 K, and the melting point of iron is 1538°C.
(Critical radius, r* in nm and Activation Free Energy ΔG* in J)
(b) Now calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.292 nm for solid iron at its melting temperature.
(Number of Atoms for Critical Size in atoms/critical nuclues)
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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- Please answer all the parts from a -d complelty and clearlyarrow_forward4.a) For the solidification of iron, calculate the critical radius r* and the activation free energy AG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are -1.85 x 10° J/m3 and 0.204 J/m?, respectively. Use the supercooling value of 295°C for iron. 4.b) Calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.292 nm for solid iron at its melting temperature..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
- Describe the cooling of a peritectic alloy with the concentration CO and sketch the microstructure during solidification. T S+α 8 S S+B a+ß В сarrow_forwardQuestion-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.arrow_forwardb) For the solidification of a metal, Tm =1000K with undercooling of 200K, calculate the rate of homogeneous nucleation in nuclei/m³/s. Neglect activation energy. Assume v=1o12/s and s'pd estimated as 1028/m³, AH=-1.26x10° J/m³, yLs= 0.16 J/m².arrow_forward
- The nucleation rate for a phase transformation depends on which factors? Density O Yield Strength O Undercooling (Temperature Energy) O Diffusivity of atoms O Holding time above Temperaturearrow_forward(a) Determine the composition of each phase at 1300C, 1250C, and 1200C temperatures. Indicate wt%Ni of the first solid to form and the last liquid to solidify. Show it on phase diagram below.arrow_forwarda- Calculate the size of the critical nucleus of tin (Sn) after it has been supercooled by 20 °C. Assume that nucleation is uniform. For the solidification of tin (melting point is 232 °C), the enthalpy change is 0.42 GJ/m³. The interfacial energy between liquid and solid is 0.055 J/m². b- Answer the following questions? (Chose only two) 1- What are the advantages of the Hydrothermal growth method? 2- What are the parameters that the perfection of the final crystal is based on by using the growth from the Gel method? 3- What are the types of techniques for growing crystals from the vapor phase?arrow_forward
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