Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Chapter 1, Problem 45QTP
To determine
Prove that the radius
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1. Many substances crystallize in a cubic structure. The unit cell for such crystals is a cube having an edge
with a length equal to do.
-Face diagonal
a. What is the length, in terms of do, of the face diagonal, which runs diagonally across one face of
the cube? (Hint: Use the Pythagorean theorem.)
b. What is the length, again in terms of do. of the cube diagonal, which runs from one corner, through
the center of the cube, to the opposite corner? (Hint: Make a right triangle having a face diagonal
and an edge of the cube as its sides, with the hypotenuse equal to the cube diagonal, then use the
Pythagorean theorem again.)
2. In an FCC structure, the centers of the atoms are found on the corners of the cubic unit cell and at the
center of each face. The unit cell has an edge whose length is the distance from the center of one corner
atom to the center of another corner atom on the same edge. The atoms on the diagonal of any face are
touching. One of the faces of the unit cell is shown…
Iron(Fe) is unusual in that it transforms from a BCC to an FCC structure at high temperature. Calculate the ratio of the densities of FCC-iron and BCC-iron . find the value of the expression shown
Sketch the planar cross section for the following planes in the FCC structure (label the edge lengths in terms of a and R) and calculate the planar densities for the three planes (do so in terms of both atoms/nm2 AND the dimensionless quantity):
a. (001)b. (011)c. (111)
Chapter 1 Solutions
Manufacturing Engineering & Technology
Ch. 1 - What is the difference between an atom and a...Ch. 1 - Prob. 2RQCh. 1 - Prob. 3RQCh. 1 - Prob. 4RQCh. 1 - Define anisotropy. What is its significance?Ch. 1 - What effects does recrystallization have on the...Ch. 1 - What is strain hardening, and what effects does it...Ch. 1 - Explain what is meant by structure-sensitive and...Ch. 1 - Prob. 9RQCh. 1 - What influence does grain size have on the...
Ch. 1 - What is the relationship between the nucleation...Ch. 1 - What is a slip system, and what is its...Ch. 1 - Explain the difference between recovery and...Ch. 1 - What is hot shortness, and what is its...Ch. 1 - Explain the advantages and limitations of cold,...Ch. 1 - Describe what the orange peel effect is. Explain...Ch. 1 - Some metals, such as lead, do not become stronger...Ch. 1 - Describe the difference between preferred...Ch. 1 - Differentiate between stress relaxation and stress...Ch. 1 - What is twinning? How does it differ from slip?Ch. 1 - Prob. 21QLPCh. 1 - What is the significance of the fact that some...Ch. 1 - Is it possible for two pieces of the same metal to...Ch. 1 - Prob. 24QLPCh. 1 - A cold-worked piece of metal has been...Ch. 1 - What materials and structures can you think of...Ch. 1 - Two parts have been made of the same material, but...Ch. 1 - Do you think it might be important to know whether...Ch. 1 - Explain why the strength of a polycrystalline...Ch. 1 - Describe the technique you would use to reduce the...Ch. 1 - What is the significance of the fact that such...Ch. 1 - Prob. 32QLPCh. 1 - It has been noted that the more a metal has been...Ch. 1 - Is it possible to cold work a metal at...Ch. 1 - Comment on your observations regarding Fig. 1.14.Ch. 1 - Is it possible for a metal to be completely...Ch. 1 - Prob. 37QTPCh. 1 - Prob. 38QTPCh. 1 - Plot the data given in Table 1.1 in terms of...Ch. 1 - A strip of metal is reduced from 30 mm in...Ch. 1 - Prob. 41QTPCh. 1 - How many grains are there on the surface of the...Ch. 1 - Prob. 43QTPCh. 1 - Prob. 44QTPCh. 1 - Prob. 45QTPCh. 1 - A technician determines that the grain size of a...Ch. 1 - If the diameter of the aluminum atom is 0.28 nm,...Ch. 1 - The following data are obtained in tension tests...Ch. 1 - Prob. 50QTPCh. 1 - Prob. 51QTPCh. 1 - Prob. 52QTPCh. 1 - Same as Prob. 1.39, but ASTM no. versus...Ch. 1 - By stretching a thin strip of polished metal, as...Ch. 1 - Draw some analogies to mechanical fiberingfor...Ch. 1 - Draw some analogies to the phenomenon of hot...Ch. 1 - Take a deck of playing cards, place a rubber band...Ch. 1 - Give examples in which anisotropy is scale...Ch. 1 - The movement of an edge dislocation was described...
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- 3. Show that the angle between any two of the lines (bonds) joining a site of a diamond lattice to its four nearest neighbors is cos-¹(-1/3) = 109° 28'. Note, a diamond lattice is a FCC lattice with a two atom basis:arrow_forwardDraw the plane L3-12 me cubic unif Cell.arrow_forwardAnswer the following question with drawing the atom configurations of the plane or direction.What is the planar density for the (110) plane in a FCC structure?arrow_forward
- b. Given that Na = 6.022x1023 atoms/mol. Calculate the theoretical density of nickel. Show your calculations.arrow_forward(c) Determine the indices for the directions shown for A, B, C and D in the cubic unit cell in Figure Q1(c). +z A D +y Figure Q1(c). 1/2arrow_forwardX :) Determine the indices for the planes in the cubic unit cell shown in the figure below. N B 1/3 ½ A →Yarrow_forward
- Draw a sketch of the (111) plane of the FCC unit cell. Are these atoms close packed? Draw a sketch of the close packed plane in hexagonal close packed. It will be simply an atom surrounded by 6 others in the plane.arrow_forwardPolonium is an element with a simple cubic crystal arrangement. Find the radius of the polonium atoms in this structure with a density of 9.4 g / cm3 and a weight of 209 g / atom.arrow_forward(1) Atomic radius of a copper atom is 128nm. Copper has an FCC crystal structure. Find the linear density along (111] direction.arrow_forward
- Rhodium (Rh) has the Face-Centered Cubic (FCC) crystal structure. The atomic radius of Rhodium is r= 0.134 nm at room temperature (20°C). Calculate the edge length "a" of the unit cell Select one: Oa 0.379 Ob.0.428 Oc 0.612 Od0.488 O e. 0.233 The indices for the direction shown in the figure are: 10:13 PM 15-Apr-2021arrow_forwardCalcium has the Face-Centered Cubic (FCC) crystal structure shown in the figure below. The atomic radius of calcium is r = 0.197 nm at room temperature (20°C). Calculate the edge length "a" of the unit cell Select one: a. None of these O b. 0.612 O c. 0.488 O d. 0.333 e. 0.557arrow_forwardNickel has face -centered (FCC) cubic structure and atomic mass is 58.69. The atomic radius of nickel is given by 1.243*10^-10m. Calculate the density of Nickel crystal.arrow_forward
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