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What is the distance from the center of one Si atom to the center of its nearest neighbor if the lattice constant is 4.25 A?
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- Figure below shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used. Intensity (relative) 40.0 Peak 1: Peak 2: Peak 3: 50.0 Peak 4: 70.0 Diffraction angle 20 a) Index (i.e., give h, and I indices) for each of these peaks. 60.0 Diffraction pattern for polycrystalline copper. 80.0 90.03. Atomic vibrations in a metal. Consider point ions of mass M and charge e immersed in a uniform sea of conduction electrons. The ions are imagined to be in stable equilibrium when at regular lattice points. If one ion is displaced a small distance r from its equilibrium position, the restoring force is largely due to the electric charge within the sphere of radius r centered at the equilibrium position. Take the number density of ions (or of conduction electrons ) as 3/(47R³), which defines R. (a) Show that the frequency of a single ion set into oscillation is @= (e²/MR³) ¹/2. (b) Estimate the value of this frequency for sodium, roughly. (c) From (a), (b), and some common sense, estimate the order of magnitude of the velocity of sound in metal.Consider spherical nanoparticles of copper with diameters of 10 and 100 nm. A) Calculate the total number of atoms in the particles,considering the lattice parameter of bulk Cu. B) Calculate the number of atoms at the grain boundaries for a typical grain boundary thickness of 1nm.
- The volume density of atoms for a simple cubic lattice is 3 x 1022 cm-. Assume that the atoms are hard spheres with each atom touching its nearest neighbor. Determine the lattice constant and the radium of the atom.A/The volume density of atoms for a simple cubic lattice is 3 x 1022 cm. Assume that the atoms are hard spheres with each atom touching its nearest neighbor. Determine the lattice constant and the radium of the atom and APF. 15 M B/A th 0 051 ig diff oli calt0.4 nm 0.3 nm +x -0.5 nm- Direction 2 Fig. Q3(b) c) Calculate the atomic packing factor for the face-centered cubic (FCC) crystal structure. Formula Sheet nA V.NA p= djkl Direction 1 APF = = V V nλ = 2d hk sin 0 S +y a √h² +k² +1²
- The density of an unknown metal is 2.64 g/cm3 and its atomic radius is 0.215 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal.The spacing between vibrational energy levels in CO molecule is found to be 8.44 x10 eV. Given that the reduced mass of CO is 1.14×10 º kg, Planck's constant –26 -34 -19 is 6.626x104 Js and leV =1.6×10 J. The force constant of the bond in CO %3D molecule isAn empirical interatomic pair potential for xenon atoms, in units of eV, and nm, and the lattice parameter of Xenon is equal to 0.630 nm. V(r) = 12.6 X 10-7 31.8 X 10-4 712 The calculated interatomic separation (nearest-neighbour) distance is: A. 0.2227 nm. B. 0.3536 nm C. 0.4455 nm D. 1.414 nm
- constant = 1. If 1 × 1015 boron atoms per cm³ are uniformly added to silicon (diamond structure, lattice 0.543 nm) as a substitutional impurity, determine what percentage of the silicon atoms are displaced in the single crystal lattice, i.e., the concentration of boron as an impurity in silicon.The overlap integral, S, between atomic orbitals on different atoms is sometimes approximately equal to 0. True FalseThe packing efficiency of simple cubic lattice is 52.4%. Find the amount of space occupied by the atom in a simple cubic lattice whose edge is 2 nm. (in nm^3)
