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and d-spacing formula: radius ratio identify the crys- stant of the element. he data of the Table 1. etal is palladium, would you

and d-spacing formula: radius ratio identify the crys- stant of the element. he data of the Table 1. etal is palladium, would you

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Problem 01: An x-ray diffractometer (XRD) recorder chart for an element which has either the BCC or the FCC crystal structure showed diffraction peaks at the following 20 angles: 40.663°, 47.314°, 69.144°, and 83.448°. (The wavelength 2 of the incoming radiation was 0.15405 nm.) Now using the Bragg's law and d-spacing formula: (a) Generalize the concept of radius ratio identify the crystal structure of the element. (b) Determine the lattice constant of the element. (c) Identify the element use the data of the Table 1. (d) If you were told that the metal is palladium, would you be surprised? How do you identify the discrepancy? You can use this table for interpretation. Table: 1: Selected metals that have the BCC, FCC, HCP crystal structure at room temperature (20°C) and their lattice constant, atomic radius, density, melting point temperature. Lattice Constants 20°C, nm Melting Paint, °C Atomic Radins, nm Crystal Structuret (20°C) Element Symbol Aluminum AI Sb 660 Antimony Arsenic 630 817 2.70 6.70 5.72 0.143 0.138 FCC Rhombohedral 0.40496 0.45067 0.4131 As 0.125 Rhombohedralt BCCE НСРЕ 0.5019 0.22856 Barium Ba 714 3.5 0.217 Beryllium Boron 0.113 0.097 Be 1278 1.85 0.35832 в 2030 2.34 Orthorhombie Bromine Br -7.2 3.12 0.119 Orthorhombic НСРЕ FCC 0.29788 0.5582 0.24612 Cadmium 0.561667 Cd Ca 321 846 8.65 1.55 2.25 0.148 0.197 0.077 Calcium Carbon (graphite) Cesium Chlorine Chromium 3550 Hexagonal ВСС 0.67078 28.7 -101 1875 Cs 1.87 0.190 CI Cr 1.9 7.19 0.099 0.128 Tetragonal BCC НСР+ 0.28846 0.125 0.128 0.071 0.135 Cobalt Co 1498 8.85 0.2506 0.4069 Copper Fluorine Gallium Germanium Gold Cu 1083 8.96 FCC 0.36147 -220 1.3 5.91 5.32 19.3 F Ga Orthorhombic 29.8 937 Ge 0.139 Diamond cubic 0.56576 1063 -270 -259 157 FCC НСР Au 0.144 0.40788 Helium Не Hydrogen Indium Iodine H. In 0.046 0.162 0.136 0.135 О.124 0.175 Hexagonal FC tetragonal Orthorhombie FCC BCC FCC ВСС 7.31 0.45979 0.49467 114 2454 1536 327 4.94 Iridium Ir 22.4 0.38389 Iron Lead Lithium Fe 7.87 11.34 0.53 0.28664 Pb 0.49502 Li 180 0.157 0.35092 Lattice Constants 20°C, nm Melting Point, °C Density. R/cm Atomic Radius, nm Crystal Structuret (20°C) Element Symbol 0.32094 0.89139 Magnesium Manganese Mercury Molybdenum Neon Nickel Mg Mn 650 1.74 0.160 НСР 0.52105 1245 -38.4 7.43 14.19 0.118 Cubicț Rhombohedral 0.155 Hg Mo 2610 -248.7 10.2 1.45 0.140 0.160 ВСС 0.31468 Ne FCC 0.125 0.143 Ni 1453 8.9 FCC 0.35236 2415 -240 2700 Niobium Nb 8.6 1.03 22.57 ВСС 0.33007 Hexagonal НСР Cubict FCC Nitrogen Osmium N 0.071 Os О.135 0.27353 0.43191 -218 1552 Oxygen Palladium Phosphorus (white) Platinum 1.43 0.060 0.137 0.110 Pd 12.0 0.38907 P 44.2 1.83 Cubicț 0.139 0.238 0.138 Pt 1769 21.4 0.86 FCC 0.39239 Potassium K 63.9 ВСС 0.5344 Rhenium Re 3180 21.0 НСР 0.27609 0.44583 1966 Rhodium Ruthenium 0.38044 0.27038 Rh 12.4 0.134 FCC 0.125 0.160 НСР FCC Ru 2500 12.2 0.42816 Scandium Se 1539 2.99 0.4541 Silicon Si 1410 2.34 0.117 Diamond cubic 0.54282 10.5 0.97 FCC ВСС Silver 0.144 Ag Na Sr 961 0.40856 Sodium 97.8 0.192 0.42906 Strontium Sulfur (yellow) Tantalum 76.8 2.60 0.215 FCC# Orthorhombic 0.6087 2.07 16.6 119 0.104 Ta 2996 0.143 ВСС 0.33026 О.158 0.147 Tin Sn 232 7.30 Tetragonali НСР: 0.58311 0.31817 1668 3410 4.51 19.3 0.29504 0.31648 Titanium Ti 0.46833 Tungsten Uranium 0.141 ВСС 1132 1900 О.138 0.136 О.137 19.0 Orthorhombict ВСС 0.2858 0.3039 0.4955 Vanadium V 6.1 0.26649 0.32312 Zine Zn 419.5 7.13 НСР 0.49470 Zirconium Zr 1852 6.49 0.160 HCP; 0.51477 Page 2 of 3
Transcribed Image Text:Problem 01: An x-ray diffractometer (XRD) recorder chart for an element which has either the BCC or the FCC crystal structure showed diffraction peaks at the following 20 angles: 40.663°, 47.314°, 69.144°, and 83.448°. (The wavelength 2 of the incoming radiation was 0.15405 nm.) Now using the Bragg's law and d-spacing formula: (a) Generalize the concept of radius ratio identify the crystal structure of the element. (b) Determine the lattice constant of the element. (c) Identify the element use the data of the Table 1. (d) If you were told that the metal is palladium, would you be surprised? How do you identify the discrepancy? You can use this table for interpretation. Table: 1: Selected metals that have the BCC, FCC, HCP crystal structure at room temperature (20°C) and their lattice constant, atomic radius, density, melting point temperature. Lattice Constants 20°C, nm Melting Paint, °C Atomic Radins, nm Crystal Structuret (20°C) Element Symbol Aluminum AI Sb 660 Antimony Arsenic 630 817 2.70 6.70 5.72 0.143 0.138 FCC Rhombohedral 0.40496 0.45067 0.4131 As 0.125 Rhombohedralt BCCE НСРЕ 0.5019 0.22856 Barium Ba 714 3.5 0.217 Beryllium Boron 0.113 0.097 Be 1278 1.85 0.35832 в 2030 2.34 Orthorhombie Bromine Br -7.2 3.12 0.119 Orthorhombic НСРЕ FCC 0.29788 0.5582 0.24612 Cadmium 0.561667 Cd Ca 321 846 8.65 1.55 2.25 0.148 0.197 0.077 Calcium Carbon (graphite) Cesium Chlorine Chromium 3550 Hexagonal ВСС 0.67078 28.7 -101 1875 Cs 1.87 0.190 CI Cr 1.9 7.19 0.099 0.128 Tetragonal BCC НСР+ 0.28846 0.125 0.128 0.071 0.135 Cobalt Co 1498 8.85 0.2506 0.4069 Copper Fluorine Gallium Germanium Gold Cu 1083 8.96 FCC 0.36147 -220 1.3 5.91 5.32 19.3 F Ga Orthorhombic 29.8 937 Ge 0.139 Diamond cubic 0.56576 1063 -270 -259 157 FCC НСР Au 0.144 0.40788 Helium Не Hydrogen Indium Iodine H. In 0.046 0.162 0.136 0.135 О.124 0.175 Hexagonal FC tetragonal Orthorhombie FCC BCC FCC ВСС 7.31 0.45979 0.49467 114 2454 1536 327 4.94 Iridium Ir 22.4 0.38389 Iron Lead Lithium Fe 7.87 11.34 0.53 0.28664 Pb 0.49502 Li 180 0.157 0.35092 Lattice Constants 20°C, nm Melting Point, °C Density. R/cm Atomic Radius, nm Crystal Structuret (20°C) Element Symbol 0.32094 0.89139 Magnesium Manganese Mercury Molybdenum Neon Nickel Mg Mn 650 1.74 0.160 НСР 0.52105 1245 -38.4 7.43 14.19 0.118 Cubicț Rhombohedral 0.155 Hg Mo 2610 -248.7 10.2 1.45 0.140 0.160 ВСС 0.31468 Ne FCC 0.125 0.143 Ni 1453 8.9 FCC 0.35236 2415 -240 2700 Niobium Nb 8.6 1.03 22.57 ВСС 0.33007 Hexagonal НСР Cubict FCC Nitrogen Osmium N 0.071 Os О.135 0.27353 0.43191 -218 1552 Oxygen Palladium Phosphorus (white) Platinum 1.43 0.060 0.137 0.110 Pd 12.0 0.38907 P 44.2 1.83 Cubicț 0.139 0.238 0.138 Pt 1769 21.4 0.86 FCC 0.39239 Potassium K 63.9 ВСС 0.5344 Rhenium Re 3180 21.0 НСР 0.27609 0.44583 1966 Rhodium Ruthenium 0.38044 0.27038 Rh 12.4 0.134 FCC 0.125 0.160 НСР FCC Ru 2500 12.2 0.42816 Scandium Se 1539 2.99 0.4541 Silicon Si 1410 2.34 0.117 Diamond cubic 0.54282 10.5 0.97 FCC ВСС Silver 0.144 Ag Na Sr 961 0.40856 Sodium 97.8 0.192 0.42906 Strontium Sulfur (yellow) Tantalum 76.8 2.60 0.215 FCC# Orthorhombic 0.6087 2.07 16.6 119 0.104 Ta 2996 0.143 ВСС 0.33026 О.158 0.147 Tin Sn 232 7.30 Tetragonali НСР: 0.58311 0.31817 1668 3410 4.51 19.3 0.29504 0.31648 Titanium Ti 0.46833 Tungsten Uranium 0.141 ВСС 1132 1900 О.138 0.136 О.137 19.0 Orthorhombict ВСС 0.2858 0.3039 0.4955 Vanadium V 6.1 0.26649 0.32312 Zine Zn 419.5 7.13 НСР 0.49470 Zirconium Zr 1852 6.49 0.160 HCP; 0.51477 Page 2 of 3
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