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Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103 m/sec. The debye frequency, wD is (provide a numerical value in sec-1)
- a)1.1 x 1013
- b)2.2 x 1015
- c)0.6 x 1013
- d)1016
Correct answer is option 'A'. Can you explain this answer?
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Consider a two dimensional hexagonal lattice if lattice spacing a = 3 ...
The debye wave-number. kD is defined such that the total number of states within a radius of kD equals the total number of states in the Biillion zone.
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Most Upvoted Answer
Consider a two dimensional hexagonal lattice if lattice spacing a = 3 ...
To fully specify a hexagonal lattice, we need to know both the lattice spacing and the orientation of the lattice. So let's assume that the hexagonal lattice is oriented such that one of the hexagonal sides is horizontal, and the other two are at 60 degree angles to the horizontal.
In this case, each hexagon has six nearest neighbors, which are the hexagons sharing an edge with it. The distance between neighboring hexagons is simply the lattice spacing a, which is given as 3 in the problem statement.
To illustrate this, we can draw a simple unit cell for the hexagonal lattice, which is the smallest repeating unit of the lattice. In this case, the unit cell is a hexagon with side length a = 3, and we can label the vertices of the hexagon with numbers as shown below:
2-----3
/ \
1 4
\ /
6-----5
We can see that vertex 1 is connected to vertices 2 and 6, which are its two nearest neighbors. Similarly, vertex 2 is connected to vertices 1 and 3, and so on.
If we want to describe the position of a particular hexagon in the lattice, we can use two integers (m,n) to specify its location relative to the origin, which we can take to be the center of our unit cell. For example, the hexagon with vertices labeled 1-6 in the diagram above has coordinates (0,0) since it is centered at the origin. The hexagon to the right of it has coordinates (1,0), and the hexagon above it has coordinates (0,1). We can continue in this way to label all the hexagons in the lattice.
Note that because of the hexagonal symmetry of the lattice, there are different ways to label the hexagons depending on which hexagon we choose as the origin. However, the relative positions of the hexagons will be the same regardless of the origin chosen.
In this case, each hexagon has six nearest neighbors, which are the hexagons sharing an edge with it. The distance between neighboring hexagons is simply the lattice spacing a, which is given as 3 in the problem statement.
To illustrate this, we can draw a simple unit cell for the hexagonal lattice, which is the smallest repeating unit of the lattice. In this case, the unit cell is a hexagon with side length a = 3, and we can label the vertices of the hexagon with numbers as shown below:
2-----3
/ \
1 4
\ /
6-----5
We can see that vertex 1 is connected to vertices 2 and 6, which are its two nearest neighbors. Similarly, vertex 2 is connected to vertices 1 and 3, and so on.
If we want to describe the position of a particular hexagon in the lattice, we can use two integers (m,n) to specify its location relative to the origin, which we can take to be the center of our unit cell. For example, the hexagon with vertices labeled 1-6 in the diagram above has coordinates (0,0) since it is centered at the origin. The hexagon to the right of it has coordinates (1,0), and the hexagon above it has coordinates (0,1). We can continue in this way to label all the hexagons in the lattice.
Note that because of the hexagonal symmetry of the lattice, there are different ways to label the hexagons depending on which hexagon we choose as the origin. However, the relative positions of the hexagons will be the same regardless of the origin chosen.
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Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer?
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Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer?.
Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 103m/sec. The debye frequency, wD is (provide a numerical value in sec-1)a)1.1 x 1013b)2.2 x 1015c)0.6 x 1013d)1016Correct answer is option 'A'. Can you explain this answer?.
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