9. For a two dimensional lattice with, a1= a az= a/2 (a) what is the area of a primitive cell? (b) show that the lattice is a rectangular lattice? (c) draw the Wigner-Seitz cell of this lattice and show that the area of the Wigner-Seitz cell is the same as in (a).

9. For a two dimensional lattice with, a1= a az= a/2 (a) what is the area of a primitive cell? (b) show that the lattice is a rectangular lattice? (c) draw the Wigner-Seitz cell of this lattice and show that the area of the Wigner-Seitz cell is the same as in (a).

Understanding Motor Controls

4th Edition

ISBN:9781337798686

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter44: Semiconductors

Section: Chapter Questions

Problem 4RQ

See similar textbooks

Related questions

Q: 3. Show that the angle between a lines (bonds) joining a site of a dia its four nearest neighbors is…

Q: When we calculate the reciprocal lattice of "hexagonal" why we multiply 2π

A: To obtain the vectors the equation is written in terms of 2π.

Q: (c) Find drk1 for: (i) A simple cubic lattice (ii) A orthorhombic lattice (a ± b + c, ¤ = B = y=…

A: The interplanar spacing dhkl between two planes can be calculated with the help of direction cosine…

Q: Sketch within a cubic unit cell the following planes: (a) (012), (c) (101),

A: Given data To sketch the following planes. (a) (012) (b) (10 -1)

Q: Consider an fcc lattice with cube side length 2.7 Ă. What are the planar densities of the (110) and…

Q: plane of simple cubic has a lattice constant of (5 A°). find diffraction angle when the

A: The given crystallographic planes are as shown below, lattice constant, a=5 A°Wavelength, λ=1.54 A°

Q: Sketch the (1-1 01) and (11-20) planes in a hexagonal unit cell.

A: The miller indices of planes are given, the intercepts of this points is shown below.

Q: Q2.What is the name of lattice systems, whose sides are not equal, and two of its angles are equal…

Q: Calculate BC, HC and HG Rod forces in the lattice system?

Q: Vanadium has the Body-Centered Cubic (BCC) crystal structure shown in the figure below. The radius…

A: Given bcc vanadium r=0.132nm

Q: What are basic unit cells / Crystal structure systems in materials? Plot crystal planes hkl - 112,…

Q: Calculate the planar density on the (110), and (111) planes in both BCC and FCC structures. a.Which…

Q: Find the total number of equivalent planes i the cubic structure (multiplicity factor) belonging to…

A: To determine the equivalent number of planes for each given family of planes.

Q: 7. Sketch within a cubic unit cell the following planes (a) (077) (e) (TIT) (b) (112) (f) (122) (g)…

A: Given: Sketch within a cubic unit cell the given planes:

Q: Draw the following planes within a simple cubic unit cell: (213), (213), (213), (213), (213), (213),…

A: Simple cubic unit cell is an arrangement in the form of cube where lattice points are located at…

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

Q: 1. Many substances crystallize in a cubic structure. The unit cell for such crystals is a cube…

A: “Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Sketch the following planes within a cubic unit cell (provide the steps followed and mark the…

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

Q: 1. It is often convenient to represent a fcc lattice as simple cubic, with a cubic primitive cell of…

A: (a) In the fcc lattice, the unit cell contains four atoms, located at (0,0,0), (a/2, a/2, 0), (a/2,…

Q: 2. A 2D representation of crystalline structure is shown below. Please indicate the type of defects…

A: a) Vacancy defect: This defect is due to missing of an atom from crystal lattice. Due to this defect…

Q: Lead FCC Structure and Atomic Radius, r = 1.746. Find the Distance between the planes (200), (220)…

Q: Consider an fcc lattice with cube side length 1.2 Å. What are the planar densities of the (110) and…

Q: 4. Figure out the indexes of the following lattice planes. (The arrows are the basic vectors of the…

A: Given: Figure out the indexes of the following lattice planes. (The arrows are the basic vectors of…

Q: Determine the indices for the directions shown for A, B, C and D in the cubic unit cell in Figure…

Q: Q.1. Determine the Miller-Bravais indices for the plane shown with the question mark (?) in the…

A: In hexagonal system, we use (a1,a2, a3, c) coordinate system.First we have calculated intersection…

Q: Q4). Sketch the [112 2 ] plane in the outline of the hexagonal lattice below

A: It is asked to draw plane in hexagonal lattice

Q: For BCC metal X, compute the interplanar spacing for the 212 set of planes. The lattice parameter…

Concept explainers

The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.

Question

9. For a two dimensional lattice with,
a1= a
az= a/2
P- 1/3
(a) what is the area of a primitive cell?
(b) show that the lattice is a rectangular lattice?
(c) draw the Wigner-Seitz cell of this lattice and show that the area of the Wigner-Seitz
cell is the same as in (a).

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Principal Metallic Crystal Structures and Crystal Structure Analysis

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

1. It is often convenient to represent a fcc lattice as simple cubic, with a cubic primitive cell of side a and a four-point basis. (a) Show that the structural factor is then either 4 or 0 at all points of the simple cubic reciprocal lattice. (b) Show that when points with zero structural factor are removed, the remaining points of the reciprocal lattice makes up a bcc cubic lattice with conventional cell of side 4л/a. Why is this expected?
Draw the plane direct and reciprocal lattice for: 3-1) a rectangular centered lattice with parameters a = 10nm, b = 14nm. 3-2) the rectangular lattice in (a) drawn as a primitive lattice.
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)
Draw the following planes within a simple cubic unit cell: (213), (213), (213), (213), (213), (213), (213), and (213).
Consider an fcc lattice with cube side length 2.7 Å. What are the planar densities of the (110) and (100) planes respectively (in units of 1020 atoms/m²): (This question has only one correct answer) a. (100) = 0.19, (110) = 0.27 b. (100) = 0.27, (110) = 0.19 c. (100) = 0.41, (110) = 0.19 d. (100) = 0.27, (110) = 0.24
!
Q4). Sketch the [112 2 ] plane in the outline of the hexagonal lattice below a P
Lead FCC Structure and Atomic Radius, r = 1.746. Find the Distance between the planes (200), (220) and (111), and draw the planes
I need handwritten i warn once again handwritten only otherwise skip
Need help on this
Sketch the following planes within a cubic unit cell (provide the steps followed and mark theselected origin).(0 1̅ 1 )(1 1 2̅ )(0 1 3̅ )
i need the answer quickly