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- 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 Fe4.50 Sketch the atomic packing of (a) the (100) plane for the BCC crystal structure, and (b) the (201) plane for the FCC crystal structure (similar to Figures 4.206 and 4.216).At room temperature and pressure RbI crystallizes with theNaCl-type structure. (a) Use ionic radii to predict the length ofthe cubic unit cell edge. (b) Use this value to estimate the density.(c) At high pressure the structure transforms to one witha CsCl-type structure. (c) Use ionic radii to predict the length of the cubic unit cell edge for the high-pressure form of RbI.(d) Use this value to estimate the density. How does this densitycompare with the density you calculated in part (b)?
- 2.) A newly designed superconductor material has 3 different types of atoms in its molecular formula and has a crystal structural similar to diamond cubic with an additional atom at the body-center (like BCC). Atom A orients on the 8 vertices of the cubic lattice and at the body center. Atom B orients at the center of each face. Atom C orients at 4 tetrahedral sites residing entirely within the cubic lattice. Each cubic crystal lattice has precisely the number of atoms that matches the molecular stoichiometry: AxByCz. What is the stoichiometry of this material?At room temperature and pressure RbI crystallizes with theNaCl-type structure. (a) Use ionic radii to predict the length ofthe cubic unit cell edge. (b) Use this value to estimate the density.(c) At high pressure the structure transforms to one witha CsCl-type structure. (c) Use ionic radii to predict the lengthof the cubic unit cell edge for the high-pressure form of RbI.(d) Use this value to estimate the density. How does this densitycompare with the density you calculated in part (b)?3.54 The accompanying figure shows three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms. k0.30 nm> 0.25 nm 0.20 nm (110) (101) (011) (a) To what crystal system does the unit cell belong? (b) What would this crystal structure be called? (c) If the density of this metal is 18.91 g/cm³, de- termine its atomic weight. 0.39 nm- F0.32 nm 0.36 nm-
- The crystal structure of lithium sulfide (Li2S), is pictured in the text on p. 553 (10th Ed.). The length of the unit cell is 5.88 x 102 pm. For this structure determine: (a) the coordination numbers of Li+ and S2–: (b) the number of formula units in the unit cell:(c) the density of Li2S:3.54 The accompanying figure shows three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms. k0.30 nm 0.25 nm 0.20 nm (110) (101) (011) (a) To what crystal system does the unit cell belong? (b) What would this crystal structure be called? 0.39 nm- F0.32 nm 0.36 nm-1) Assume that the elemental atoms are hard spherEs of radius r. Calculate the maximum packing rate t obtained when this element CIvstallizes into the following structures: (a) simple cubic (sc) (b) body-centered cubic (bcc) (c) face-centered cubic (fcc) (d) diamond (e) hexagonal close packed (hcp) (first calculate the optimal c/a relation) Using these results. determine the value of the lattice parameter(s) of the following real cIystal systems where d is distance between nearest neighbors: (f) magnesium (hcp), d = 3.20 Å (g) aluminum (fcc), d = 2.86 Å (h) silicon (diamond), d= 2.35 Å Hints: A B (b) For e) (a) Three-dimensional filling of the hexagonal close packed (left) and face-centered cubic (right) structures.
- (b) Using the cubic unit cells below, draw the directions and plane indicated on each figure. [101] [010] (002)Why are there no more than 7 crystal systems ? What are quasicrystals ?Diatomic body-centered cubic crystal structure Consider a diatomic body-centered cubic crystal structure. The atoms at the corners of the cube have radii of 1.5 Å while those at the center of cube have radii of 3.0 Å. Using hard-sphere approximation, (a) Determine the lattice-constant a of the crystal. (b) Calculate the atomic packing factor for this crystal. (c) Calculate the number of atoms per em of the crystal. (d) Calculate the number of atoms per cm? on the (111) plane of the crystal.