Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 4.8, Problem 34AAP
To determine
The size (radius) of the critical nucleus for pure iron when nucleation takes place homogeneously.
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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.
Define eutectic, eutectoid and peritectic reactions with the examples
Q3/ A- What are the important reactions in( Fe- C) system?
B- Calculate the activation energy for vacancy formation in aluminum ,given that the
equilibrium number of vacancies at 500°C is 7.57 x10 m.The atomic weight and density for
aluminum are respectively, 26.98g /mol and 2.62 g/em.,Avogadros number ( 6.022x10 atoms/mol
), and Boltzmanns constant (8.62x10 ev /atom.K).?
Chapter 4 Solutions
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- For 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_forwardCalculate the number of vacancies per m 3 for gold at 900 C. The energy for vacancyformation is 0.86 eV/atom.arrow_forwardDefine annealing. (a) What effects does it have on the microstructure? (b) How does this affect dislocation movement? (c) Why/how does this affect the properties?arrow_forward
- Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084degC. assume an energy vacancy formation of 0.90eVlatom. * 6.56 x 10^-5 O 0.9992 O 4.56 x 10^-4 O 2.19 X 10^-4arrow_forward10-Calculate the number of vacancies per m3 for gold at 900 C. the energy for vacancy formation is 0.86 eV/atom.arrow_forwardCalculate the approximate total dislocation line length(or range of lengths) expected in a cubic cm of a very highlycold-worked metal.arrow_forward
- Calculate the invariant reactions for Cu-Zn Reaction (eutectic eutectoid peritectic peritectoide) Temperature Transformationarrow_forwardQl: For homogeneous nucleation of iron, calculate the activation free energy, critical radius and number of atoms found in a critical size nucleus. If the Iron melting temperature 1538°C, super cooling 295°C, surface free energy 0.204J/m?, latent heat of fusion -1.85x10° and lattice parameter 0.292 nm.arrow_forwardA metal has a certain fraction f = 105 of vacancies at the atomic level at finite temperatures. If the activation energy for vacancy formation was increased by 50%, what would be the new vacancy concentration? Select one: a. 7.43E-10 b. 6.22 E-5 C. 1.24E-6 O d. 3.16E-8 e. 5.48E-4arrow_forward
- 4.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_forwardCalculate the number of vacancies per m3 for gold at 900 C. the energy for vacancy formation is 0.86 eV/atom.arrow_forwardHow do dislocationjunctions contributeto strengthening?arrow_forward
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