Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 4.8, Problem 42AAP
To determine
If there are 250 grains per square inch on a photomicrograph of a ceramic material at 200x, what is the ASTM grain-size number of the material.
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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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- A paper clip has a mass of 10.75 grams and is made of gold. (FCC, R = 0.1442 nm), calculate: a) The number of unit cells in the sample volume. b) The number of atoms contained in the volume of the sample.arrow_forwardDerive the dimension ratio c/a for regular HCP crystal. Please do not use the atomic packing factorarrow_forwardEstimate the ASTM grain size number for a 300-mm (12in) silicon wafer used to produce computer chipsarrow_forward
- Derive the dimension ratio c/a for regular HCP crystal. Note: Please do not use the atomic packing factor in the derivation.arrow_forwardDetermine the ASTM grain size number if 90 grains per square inch are measured at a magnification of 55×. In this problem, you are asked to find the ASTM grain size number given the number of grains per square inch and the magnification. Solve Equation 4.18 (below) for G.arrow_forwardThe density of a sample of HCP beryllium is 1.844 g/cm 3 , and the lattice parameters are a 0 = 0.22858 nm and c 0 = 0.35842 nm. Calculate (a) the fraction of the lattice points that contains vacancies: and (b) the total number of vacancies in a cubic centimetre of Bearrow_forward
- If a single crystal material has a Young's Modulus of 100 MPa in the [100] direction, and a Young's Modulus of 150 MPa in the [010] direction, why is the polycrystalline (i.e., many crystal) form of the material isotropic?arrow_forwardMetallic Crystal Structures1. For the HCP crystal structure, show that the ideal c/a ratio is 1.633. 2. Show that the atomic packing factor for HCP is 0.74.arrow_forwardAssume that 16 grains per square inch are counted in a micrograph taken at 250X.What is the ASTM number for grain size?arrow_forward
- How many atoms constitute one unit cell of a face centered cubic crystal?arrow_forwardIllustrate the difference between crystalline structure and amorphous structure using an examplearrow_forwardSuppose that a particular crystal has a primitive unit cell that can be described by the following primitive lattice vectors: NOTE: i, j and k are unit vectors. a1 = √2ai + √2aja2 = (−3a/√2)i +( 3a/√2)ja3 = −√2ai − √2aj + 2√3ak (a) Determine the crystal system of the crystal. (b) Using the reciprocal lattice, determine an expression for the interplanar spacings of the crystal. (c) Suppose that the constant ? has a value of 0.546 nm and that the interplanar spacing for planes with certain unknown Miller indices was measured to be 0.539 nm. Determine an equation satisfied by the Miller indices of the planes and hence suggest which planes they are.arrow_forward
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