3.29 The unit cell for Al₂O3 has hexagonal symme- try with lattice parameters a = 0.4759 nm and c = 1.2989 nm. If the density of this material is 3.99 g/cm³, calculate its atomic packing factor. For this computation, use ionic radii listed in Table 3.4.

3.29 The unit cell for Al₂O3 has hexagonal symme- try with lattice parameters a = 0.4759 nm and c = 1.2989 nm. If the density of this material is 3.99 g/cm³, calculate its atomic packing factor. For this computation, use ionic radii listed in Table 3.4.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: The fraction of lattice points occupied by vacancies in solid magnesium at 660°C is 103. Compute the…

Q: A hypothetical metal has the SC crystal structure, a density of 7.08 g/cm3, and an atomic weight of…

Q: Calculate the number of vacancies per cubic meter in gold (Au) at 900°C. The energy for vacancy…

Q: Calculate the density of NaCl given it has a rock salt crystal structure. Na has an atomic weight of…

A: NaCl crystal structure

Q: Calculate the radius of the atomic structure with a density of 0.541g/cm^3 and an atomic weight of…

A: Given data is

Q: a. b. Figure 2 shows another ball-and-stick model of a very small crystal of a- Polonium, but this…

A: Given: To find: Number of bonds broken to move by slip by one unit of b from left to right

Q: Silver crystallizes as fcc structure. If the density of silver is 10.51g/cm3. Calculate the volume…

Q: Iron (Fe) has an atomic radius of 0.126nm (1.26A°) with B.C.C crystal structure and an atomic weight…

Q: Consider the ReO3 unit cell shown below, with a = 3.74 Å and ∆ Hsub = 626 kj/mol (a) What is the…

A: Solution: Given Data: a=3.74 Ao∆Hsub=626 kJ/mol To Find: (a) What is the Bravais lattice and…

Q: Q 5: In the cubic cell unit find: A- Miller's indices of the directions shown in Figure (4) B-…

A: Miller indices: It is a set of three number which shows the orientation of a set of parallel planes…

Q: Determine the planar density for FCC nickel in the (111) plane with lattice parameters of ao=3.5187.…

Q: (b) Find planar atomic densities by considering the section of a (110) plane within a unit cell for:…

A: For solution refer below images.

Q: Q.2) If that palladium has an FCC crystal structure, a density of 12 gm/cm and an atomic weight of…

A: Unit cell: The unit cell is the most basic and least volume of the solid which repeats itself to…

Q: Solve the linear densities of the direction [100] and [110] on aluminium which has a face centered…

A: Answer: (a) The linear density in the direction of [1 0 0] is 2.4724 nm-1. (b) The linear density in…

Q: . A. The term linear atomic density is derived for FCC [111]. [100] The vectors in terms of radius B…

A: In FCC cell 1/2 part atom is present at each face and 1/8 part atom is present at each corner.…

Q: Lead has FCC crystal structure. If the atomic weight of Pb is 207.2 g/mol and density of 11.36…

A: It is required to determine atomic radius of Pb

Q: Aluminum forms an FCC structure and has an atomic radius of 0.143 nm. Calculate the theoretical…

A: Answer: The theoretical density of aluminum metal in the unit cell is 2.71 g/cm3.

Q: Beryllium with a crystalline structure HCP lattice constant c / a = 1.568 and the radius of the atom…

A: Unit cell: The unit cell is the smallest part of the lattice which repeats multiple times to form a…

Q: Prof that the relation between atomic radius and lattice constant for FCC is a- 4r/V3 ? Question #3/…

Q: Platinum is a metal having a FCC crystal structure with a density p= 21.45 kg/m3. Calculate the…

Q: Question 4: What are the Miller indices for the plane shown in the following cubic unit cell? 3 y…

A: To Find: Miller Indices = ?

Q: 1. Show that the atomic packing factor for HCP is 0.74. 2. Calculate the radius of Palladium atom…

A: given; (1) atomic packing factor for HCP? (2) radius of palladium(r)=?density(ρ)=12g/cm3atomic…

Q: It is the structure of metals wherein atoms are located at each corners and centers of all cube…

A: GIVEN DATA- A MCQ GIVEN OF MATERIAL SCIENCE SUBJECT WE HAVE TO TELL WHICH TYPE OF CUBIC STRUCTURE…

Q: BCC Iron has a lattice parameter of .2866 nm. Calculate its planar density on (111).

A: lattice parameter, R = 0.2866 nmIn a BCC unit cell, there is one atom at each corner (1/8 of each…

Q: •Find the Miller indices for the points in the cubic unit cell below: Note: J is on the left face of…

A: Consider a crystal vector r passing from the origin. The expression for the crystal vector r passing…

Q: Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight of 95.94…

Q: Niobium has a BCC crystal structure, an atomic radius of 0.143 nm and an atomic weight of 92.91…

Q: 4. Platinum (atomic radius = 1.38 Å) crystallizes in a cubic closely packed structure. Calculate the…

Q: Draw the plane direct and reciprocal lattice for: 3-1) a rectangular centered lattice with…

Q: 1) Find the theoretical density of lead (P). which has a face-centered cubic lattice, with a lattice…

Q: Answer the following question with drawing the atom configurations of the plane or direction. What…

A: Solution:

Q: Under what conditions, will the body centered tetragonal lattice become (a) a bcc structure? (b) an…

A: Under what conditions, will the body centered tatragonal lattice become A)bcc structure b)fcc…

Q: Within a different cubic unit cell, sketch the following: [111]. [122], (011), (110), (010).

Q: Sketch the planar cross section for the following planes in the FCC structure (label the edge…

Q: Q2. Compute the density of Zinc, where the atomic radius of Zn=1.453×10* and atomic weight =72.4…

Q: A metal crystallizes in the face‑centered cubic (FCC) lattice. The density of the metal is 12020…

Q: Consider a unit cell with lattice dimensions a, b, and c in the x-, y and z directions. Which of the…

Question

C
3.29 The unit cell for Al₂O3 has hexagonal symme-
try with lattice parameters a = 0.4759 nm and
c = 1.2989 nm. If the density of this material is
3.99 g/cm³, calculate its atomic packing factor.
For this computation, use ionic radii listed in
Table 3.4.

Cation
AP+
Ba²+
Cx+
Fo
Fe³+
K+
Mg²+
Mn2
Na
Ni²+
Sj4
Ti
Jonic
Radius (nm)
0.053
0.136
0.100
0.170
0.077
0.069
0.138
0.072
0.067
0.102
0.069
0.040
0.061
Anion
Br
a
F
I
0²
S²
Jonic
Radius (nm)
0.196
0.181
0.133
0.220
0.140
0.184

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Calculation

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 21 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Types of Phase Diagrams and Its Applications in Metallurgy

Learn more about

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

a. Molybdenum at 20°C has Body Centered Cubic (BCC) crystal structure with an atomic radius, R of 0.140 nm. Draw the BCC crystal, identify the relationship between atomic radius, R and lattice constant, a. Calculate the atomic packing factor (APF) for Molybdenum at 20°C. b. What is grain boundary and state the importance of grain boundaries
In an ideal hexagonal closed packed system, if the atomic radius of the atom was 0.112 nm, write down the three digit value of the lattice parameter c in nm unit
Calculate the density in g / cm3 of a metal with a structure fcc molecular mass of 100g / mol and an atomic radius of 0.145nm
Consider an fcc lattice with cube side length 1.2 Å. What are the planar densities of the (110) and (100) planes respectively (in units of 1020 atoms/m?): (This question has only one correct answer) O a. (100) = 2.08, (110) = 0.98 O b. (100) = 1.39, (110) = 0.98 O c. (100) = 1.39, (110) = 1.20 O d. (100) = 0.98, (110) = 1.39
14. In an ideal hexagonal closed packed system, if the atomic radius of the atom was 0.112 nm, write down the three digit value of the lattice parameter cin nm unit Enter your answer
4. Figure out the indexes of the following lattice planes. (The arrows are the basic vectors of the lattice.) (a) (b) (c)
Consider a unit cell with lattice dimensions a, b, and c in the x-, y and z directions. Which of the following sets of Miller indices can represent a crystallographic plane with intercepts of b and (c/4) along the y- and z-axes respectively? (more than one answer is possible for this question. marks will only be awarded for the question if all the correct options are selected (i.e. 'all or nothing' marking scheme). a. b. C. d. (214) (421) (114) e. (412)
Nickel 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.
Niobium (Nb) and Vanadium (V) have the BCC crystal structure, and Ag forms a substitutional solid solution at room temperature. Calculate the unit cell edge length (nm) for a 25 wt% Nb-75 wt% V alloy
Nickel has the fcc crystal structure and a lattice parameter of a = 0.3517 nm. Using this information, determine the atomic radius of Ni in angstroms.
Calculate the LPF for [101] in a FCC crystal.
Estimate the density of platinum and lead from their lattice parameters at room temperature. Both are FCC. Compare the theoretical density with experimental values. Which is closer? Why? For platinum A=192.09, Avogadro number =6.02x1043, a=3.9239 Angstrom. Experimental density of Pt = 21.47. For lead A=207.2, and a=4.9502Angstrom.