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Posted on Jul 18, 2024

The intermetallic Al Zr can exist in the L1, structure (informally described as a face-centered-cubic atom arrangement with Zr atoms at cube corners or vertices

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The intermetallic Al Zr can exist in the L1, structure (informally described as a face-centered-cubic atom arrangement with Zr atoms at cube corners or vertices and Al atoms at face centers). Bonding between Zr and Al atoms in this intermetallic is mostly metallic but likely has some covalent bonding which will affect the atomic radii. The density of AlzZr has been reported to be 4.1 g/cm. a. For Al Zr, report/specify the following: i. the Bravais lattice and basis, ii. the prototype crystal; iii. the Strukturbericht designation, and iv. the Pearson symbol. b. Given the measured density above, determine the mixed-bond bonding distance; i.e., (rA + rz:). Compare this distance to the values (2) computed using the metallic an ionic radii for Al and Zr given in Callister. C. Calculate the atomic packing factor for AlzZr. Melting Point (C) 660.4 -1892 725 1278 2300 -7.2 321 Cd 48 839 (sublimes at 3367) 28.4 -101 1875 1495 1085 - 220 BCC - Au - Characteristics of Selected Elements Atomic Density of Crystal Atomic Tonic Most Atomic Weight Solid, 20C Structure, Radius Radius Common Element Symbol Number (amu) (g/cm) 20C (nm) (nm) Valence Aluminum AI 13 26.98 2.71 FCC 0.143 0.053 3+ Argon Ar 18 39.95 Inert Barium Ba 56 137.33 3.5 BCC 0.217 0.136 2+ Beryllium Be 4 9.012 1.85 HCP 0.114 0.035 2+ Boron B 5 10.81 2.34 Rhomb. 0.023 3+ Bromine Br 35 79.90 0.196 1- Cadmium 112.41 8.65 HCP 0.149 0.095 2+ Calcium Ca 20 40.08 1.55 FCC 0.197 0.100 2+ Carbon 6 12.011 2.25 Hex. 0.071 -0.016 4+ Cesium Cs 55 132.91 1.87 0.265 0.170 1+ Chlorine 17 35.45 0.181 1- Chromium 24 $2.00 7.19 0.125 0.063 3+ Cobalt Co 27 58.93 8.9 HCP 0.125 0.072 2+ Copper Cu 29 63.55 8.94 FCC 0.128 0.096 1+ Fluorine F 9 19.00 0.133 Gallium Ga 31 69.72 5.90 Ortho. 0.122 0.062 3+ Germanium Ge 32 72.64 5.32 Dia cubic 0.122 0.053 4+ Gold 79 196.97 19.32 FCC 0.144 0.137 1+ Helium He 2 4.003 Inert Hydrogen H 1 1.008 0.154 1+ Iodine 1 53 126.91 4.93 Ortho 0.136 0.220 1- Iron Fe 26 55.85 7.87 BCC 0.124 0.077 2+ Lead Pb 82 207.2 11.35 FCC 0.175 0.120 Lithium 3 6.94 0.534 BCC 0.152 0.068 1+ Magnesium Mg 12 24.31 1.74 HCP 0.160 0.072 2+ Manganese Mn 25 54.94 7.44 Cubic 0.112 0.067 2+ Mercury Hg 80 200.59 0.110 2+ Molybdenum Mo 42 95.94 10.22 BCC 0.136 0.070 4+ Neon Ne 10 20.18 Inert Nickel Ni 28 58.69 8.90 FCC 0.125 0.069 2+ Niobium Nb 41 92.91 8.57 BCC 0.143 0.069 5+ Nitrogen N 7 14.007 0.01 0.02 5+ Oxygen O 8 16.00 0.140 2- Phosphorus P 15 30.97 1.82 Ortho. 0.109 0.035 Platinum Pt 78 195.08 21.45 FOC 0.139 0.080 2+ Potassium K 19 39.10 0.862 BCC 0.231 0.138 1- Silicon Si 14 28.09 2.33 Dia cubic 0.118 0.040 4+ Silver Ag 47 107.87 10.49 FCC 0.144 0.126 1+ Sodium Na 11 22.99 0.971 BCC 0.186 0.102 1+ Sulfur S 16 32.06 2.07 Ortho. 0.106 0.184 2- Tin Sn SO 118.71 7.27 Tetra 0.151 0.071 4+ Titanium TH 22 47.87 4.51 HCP 0.145 0.068 4+ Tungsten W 74 183.84 19.3 BCC 0.137 0.070 4+ Vanadium V 23 50.94 6.1 BCC 0.132 0.059 S+ Zinc Zn 30 65.41 7.13 HCP 0.133 0.074 2+ Zirconium Zr 40 91.22 6.51 HCP 0.159 0.079 4+ "Dia = Diamond, Hex. - Hexagonal; Ortho. - Orthorhombic, Rhomb. - Rhombohedral, Tetra. - Tetragonal. 29.8 937 1064 -272 (at 26 atm) -259 114 1538 327 181 649 2+ 1244 -38.8 2617 -248.7 1455 5+ 2468 -209.9 -218.4 44.1 1772 63 1410 962 98 113 232 1668 3410 1890 420 1852 The intermetallic Al Zr can exist in the L1, structure (informally described as a face-centered-cubic atom arrangement with Zr atoms at cube corners or vertices and Al atoms at face centers). Bonding between Zr and Al atoms in this intermetallic is mostly metallic but likely has some covalent bonding which will affect the atomic radii. The density of AlzZr has been reported to be 4.1 g/cm. a. For Al Zr, report/specify the following: i. the Bravais lattice and basis, ii. the prototype crystal; iii. the Strukturbericht designation, and iv. the Pearson symbol. b. Given the measured density above, determine the mixed-bond bonding distance; i.e., (rA + rz:). Compare this distance to the values (2) computed using the metallic an ionic radii for Al and Zr given in Callister. C. Calculate the atomic packing factor for AlzZr. Melting Point (C) 660.4 -1892 725 1278 2300 -7.2 321 Cd 48 839 (sublimes at 3367) 28.4 -101 1875 1495 1085 - 220 BCC - Au - Characteristics of Selected Elements Atomic Density of Crystal Atomic Tonic Most Atomic Weight Solid, 20C Structure, Radius Radius Common Element Symbol Number (amu) (g/cm) 20C (nm) (nm) Valence Aluminum AI 13 26.98 2.71 FCC 0.143 0.053 3+ Argon Ar 18 39.95 Inert Barium Ba 56 137.33 3.5 BCC 0.217 0.136 2+ Beryllium Be 4 9.012 1.85 HCP 0.114 0.035 2+ Boron B 5 10.81 2.34 Rhomb. 0.023 3+ Bromine Br 35 79.90 0.196 1- Cadmium 112.41 8.65 HCP 0.149 0.095 2+ Calcium Ca 20 40.08 1.55 FCC 0.197 0.100 2+ Carbon 6 12.011 2.25 Hex. 0.071 -0.016 4+ Cesium Cs 55 132.91 1.87 0.265 0.170 1+ Chlorine 17 35.45 0.181 1- Chromium 24 $2.00 7.19 0.125 0.063 3+ Cobalt Co 27 58.93 8.9 HCP 0.125 0.072 2+ Copper Cu 29 63.55 8.94 FCC 0.128 0.096 1+ Fluorine F 9 19.00 0.133 Gallium Ga 31 69.72 5.90 Ortho. 0.122 0.062 3+ Germanium Ge 32 72.64 5.32 Dia cubic 0.122 0.053 4+ Gold 79 196.97 19.32 FCC 0.144 0.137 1+ Helium He 2 4.003 Inert Hydrogen H 1 1.008 0.154 1+ Iodine 1 53 126.91 4.93 Ortho 0.136 0.220 1- Iron Fe 26 55.85 7.87 BCC 0.124 0.077 2+ Lead Pb 82 207.2 11.35 FCC 0.175 0.120 Lithium 3 6.94 0.534 BCC 0.152 0.068 1+ Magnesium Mg 12 24.31 1.74 HCP 0.160 0.072 2+ Manganese Mn 25 54.94 7.44 Cubic 0.112 0.067 2+ Mercury Hg 80 200.59 0.110 2+ Molybdenum Mo 42 95.94 10.22 BCC 0.136 0.070 4+ Neon Ne 10 20.18 Inert Nickel Ni 28 58.69 8.90 FCC 0.125 0.069 2+ Niobium Nb 41 92.91 8.57 BCC 0.143 0.069 5+ Nitrogen N 7 14.007 0.01 0.02 5+ Oxygen O 8 16.00 0.140 2- Phosphorus P 15 30.97 1.82 Ortho. 0.109 0.035 Platinum Pt 78 195.08 21.45 FOC 0.139 0.080 2+ Potassium K 19 39.10 0.862 BCC 0.231 0.138 1- Silicon Si 14 28.09 2.33 Dia cubic 0.118 0.040 4+ Silver Ag 47 107.87 10.49 FCC 0.144 0.126 1+ Sodium Na 11 22.99 0.971 BCC 0.186 0.102 1+ Sulfur S 16 32.06 2.07 Ortho. 0.106 0.184 2- Tin Sn SO 118.71 7.27 Tetra 0.151 0.071 4+ Titanium TH 22 47.87 4.51 HCP 0.145 0.068 4+ Tungsten W 74 183.84 19.3 BCC 0.137 0.070 4+ Vanadium V 23 50.94 6.1 BCC 0.132 0.059 S+ Zinc Zn 30 65.41 7.13 HCP 0.133 0.074 2+ Zirconium Zr 40 91.22 6.51 HCP 0.159 0.079 4+ "Dia = Diamond, Hex. - Hexagonal; Ortho. - Orthorhombic, Rhomb. - Rhombohedral, Tetra. - Tetragonal. 29.8 937 1064 -272 (at 26 atm) -259 114 1538 327 181 649 2+ 1244 -38.8 2617 -248.7 1455 5+ 2468 -209.9 -218.4 44.1 1772 63 1410 962 98 113 232 1668 3410 1890 420 1852