15.10 How many (a) nearest neighbours, (b) next-nearest neighbours are there in a body-centred cubic structure? What are their distances if the side of the cube is 600 nm?
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- (a) Draw an orthorhombic unit cell, and within that cell a (210) plane. (b) Draw a monoclinic unit cell, and within that cell a (002) plane.9. For a two dimensional lattice with, a1= a a2= a/2 P- T1/3 (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).9. For a two dimensional lattice with, az= a/2 a1= a (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).
- (a) The density of diamond is 3.5 g/cm3, and that ofgraphite is 2.3 g/cm3. Based on the structure of buckminsterfullerene,what would you expect its density to berelative to these other forms of carbon? (b) X-ray diffractionstudies of buckminsterfullerene show that it has aface-centered cubic lattice of C60 molecules. The length ofan edge of the unit cell is 14.2 Å. Calculate the density ofbuckminsterfullerene.3) Draw two different projections of a monoclinic unit cell with a = 3 Å, b = 4 Å, c = 5 Å, B = 119⁰. (Don't forget to indicate the basis vectors.) One atom is located at (0.2, 0.3, 0.4), another one at (0.2, 0.7, 0.4). Determine the interatomic distances < 2.5 Å.Which of the following schemes for the repeating pattern of close-packed planes are ways of generating close-packed lattices? Explain your answer. (i) АВССАВС .. (ii) АВАС ... (ii) ACCA.. (iv) АВСВС .. (v) АВВАВС (vi) АВСВ
- 1. For a two dimensional lattice with a₁ = a, (a) what is the area of a primitive cell? (b) show that the lattice is a rectangular lattice? a F/3 π (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).Calculate the volume in Å3 of each of the following types ofcubic unit cells if it is composed of atoms with an atomic radiusof 1.82 Å. (a) primitive (b) face-centered cubic.How will you distinguish between the following pairs of terms:(i) Tetrahedral and octahedral voids(ii) Crystal lattice and unit cell
- 2.4 2.5 The unit cell for Platinum (Pt) has atoms which are located at each of the corners and at the centre of all the unit cell faces. The density and atomic weight of Pt are 21.45 g/cm³ and 195.08 g/mol, respectively. Given that the Avogadro's Number is 6.023 x 1023 atoms/mol, (a) sketch the atomic arrangement on the (010) plane of the unit cell. (b) determine the lattice constant, a of Pt atom. (c) calculate the atomic radius of Pt atom. A sample of BCC iron (Fe) was placed in an X-ray diffractometer using incoming X-rays with a wavelength, λ = 0.1541 nm. Diffraction from the {110} planes was obtained at 20 = 44.704°. Assuming that the order of reflection is 1, calculate: (a) the interplanar spacing of the planes (b) the value for the lattice constant, a for BCC FeHow many (a) nearest neighbours, (b) next-nearest neighbours are there in a body-centred cubic structure? What are their distances if the side of the cube is 600 nm?A unit cell has a=5Å, b=5Å, c-8Å, a=90°, B-90° ad y=90°. What will be the Bravais lattice for this unit cell? Mention the following for each of the given crystallographic cubic planes. (a) Intercepts in the x, y and z coordinates (b) Reciprocals (c) Final index of the crystal plane 1/2