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Consider a plane hkl in a crystal lattice. (A) Prove that the reciprocal lattice vector -h+kb+,...
2. Planes and the reciprocal lattice. In the lectures I claimed that the reciprocal lattice vector...
2. Planes and the reciprocal lattice. In the lectures I claimed that the reciprocal lattice vector Gnın2n3 = nībı + n2b2 + n3b3 = is perpendicular to the plane (nın2n3). This is always true, and does not require the assumption that the primitive lattice vectors are orthogonal. Here you will prove this claim. (a) First prove this statement for the case where two of the integers (n1n2n3) are vanishing, e.g. n2 = П3 0. Hint: the plane is spanned by...
Consider a free electron, empty lattice model with effective mass m* in a simple cubic crystal...
Consider a free electron, empty lattice model with effective mass m* in a simple cubic crystal with direct lattice distance a, and reciprocal lattice vectors of length a. Find the energies at the high symmetry points Г, X, M and R and indicate the zone boundary rsion along TX, TR, Г b. Find the expression for the lowest energy band in the XM direction. Sketch the Energy band diagram along RIXM「 c.
Q1- The atoms in a crystal are modelled as hard spheres in contact. Calculate the Atomic radius i...
Q1- The atoms in a crystal are modelled as hard spheres in contact. Calculate the Atomic radius in a fcc lattice with lattice constant 3.6 A Q2- (a) The atomic in a crystal are modelled as hard spheres in constant. Calculate the atomic radius in a fcc lattice with lattice constant 3.6 A. (b) Consider three-dimensional simple cubic lattice with lattice constant a. What is the distance from the center to a corner of the first Brillouin Zone in the...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
7. A crystalline solid consists of atoms stacked up in a repeat- ing lattice structure. Consider...
7. A crystalline solid consists of atoms stacked up in a repeat- ing lattice structure. Consider a crystal as shown in Fig. ure P1.7a. The atoms reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Sup- pose this crystal cleaves along a face diagonal as shown in Figure P1.7b. Calculate the...
EENG 245 Physical electronics HW 1 1) The NaCl crystal is cubic, and can be described...
EENG 245 Physical electronics HW 1 1) The NaCl crystal is cubic, and can be described as follows. Na atoms sit at the corners and faces of a cube, and Cl atoms sit in between two Na atoms. This means that a Clatom is found half-way along each of the cube edges, and there is a Cl in the center of the cube. (We could also have described the lattice by interchanging Na and Cl in the description above.) Another...
I got parts a-c, but not d A crystal is a periodic lattice of positively and...
I got parts a-c, but not d
A crystal is a periodic lattice of positively and negatively charged one. The goal of the problem is to show that the potential energy person is negative. This is one condition for a crystal to be a stable configuration; otherwise, would be energetically favorable for the fons to be infinitely for aport thich would definitegrate the crystal. Although in general a crystal can have a completed 3D crangement of fone, here we will...
Consider a plane electromagnetic wave propagating in KDP crystal (uniaxial) with its axis k lying in...
Consider a plane electromagnetic wave propagating in KDP crystal (uniaxial) with its axis k lying in the y-z plane and making angle 45° with the optic (or z) axis. Assuming no 1.507 and ne 1.467, obtain phase velocities of the ordinary and extraordinary waves. What is the angle between E and D vectors for the two waves?
3.12 An infinite, thin, plane sheet of conducting material has a circular hole of radius a...
3.12 An infinite, thin, plane sheet of conducting material has a circular hole of radius a cut in it. A thin, flat disc of the same material and slightly smaller radius lies in the plane, filling the hole, but separated from the sheet by a very narrow insulating ring. The disc is maintained at a fixed potential V, while the infinite sheet is kept at zero potential. (a) Using appropriate cylindrical coordinates, find an integral expression involv- ing Bessei functions...
Question 4-9 1. What are the four types of bonding observed in solids? c ndeCavalent bonang...
Question 4-9
1. What are the four types of bonding observed in solids? c ndeCavalent bonang 2. Rank the four types of bonding from strongest to weakest. io<>coaletxalic>H-ro İ 3.1 Derive an algebraic expression for the equilibrium spacing, re of an ionic bond that follows the equation E, in terms of A, B, n, and E. 4. 5. What is the force between the two atoms at the equilibrium spacing? atonic force What is the number of atoms per unit...
2. Planes and the reciprocal lattice. In the lectures I claimed that the reciprocal lattice vector Gnın2n3 = nībı + n2b2 + n3b3 = is perpendicular to the plane (nın2n3). This is always true, and does not require the assumption that the primitive lattice vectors are orthogonal. Here you will prove this claim. (a) First prove this statement for the case where two of the integers (n1n2n3) are vanishing, e.g. n2 = П3 0. Hint: the plane is spanned by...
Consider a free electron, empty lattice model with effective mass m* in a simple cubic crystal with direct lattice distance a, and reciprocal lattice vectors of length a. Find the energies at the high symmetry points Г, X, M and R and indicate the zone boundary rsion along TX, TR, Г b. Find the expression for the lowest energy band in the XM direction. Sketch the Energy band diagram along RIXM「 c.
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
7. A crystalline solid consists of atoms stacked up in a repeat- ing lattice structure. Consider a crystal as shown in Fig. ure P1.7a. The atoms reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Sup- pose this crystal cleaves along a face diagonal as shown in Figure P1.7b. Calculate the...
EENG 245 Physical electronics HW 1 1) The NaCl crystal is cubic, and can be described as follows. Na atoms sit at the corners and faces of a cube, and Cl atoms sit in between two Na atoms. This means that a Clatom is found half-way along each of the cube edges, and there is a Cl in the center of the cube. (We could also have described the lattice by interchanging Na and Cl in the description above.) Another...
I got parts a-c, but not d
A crystal is a periodic lattice of positively and negatively charged one. The goal of the problem is to show that the potential energy person is negative. This is one condition for a crystal to be a stable configuration; otherwise, would be energetically favorable for the fons to be infinitely for aport thich would definitegrate the crystal. Although in general a crystal can have a completed 3D crangement of fone, here we will...
Consider a plane electromagnetic wave propagating in KDP crystal (uniaxial) with its axis k lying in the y-z plane and making angle 45° with the optic (or z) axis. Assuming no 1.507 and ne 1.467, obtain phase velocities of the ordinary and extraordinary waves. What is the angle between E and D vectors for the two waves?
3.12 An infinite, thin, plane sheet of conducting material has a circular hole of radius a cut in it. A thin, flat disc of the same material and slightly smaller radius lies in the plane, filling the hole, but separated from the sheet by a very narrow insulating ring. The disc is maintained at a fixed potential V, while the infinite sheet is kept at zero potential. (a) Using appropriate cylindrical coordinates, find an integral expression involv- ing Bessei functions...
Question 4-9
1. What are the four types of bonding observed in solids? c ndeCavalent bonang 2. Rank the four types of bonding from strongest to weakest. io<>coaletxalic>H-ro İ 3.1 Derive an algebraic expression for the equilibrium spacing, re of an ionic bond that follows the equation E, in terms of A, B, n, and E. 4. 5. What is the force between the two atoms at the equilibrium spacing? atonic force What is the number of atoms per unit...
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