Simple Cubic (review) H d h t h l b di l 2R a ar sp eres ouc a ong cu e agona ? a= Number of atoms per unit cell n = 1, Atomic packing factor, APF = 0.52 Coordination number: # of atoms touching, CN = 6 Body-Centered Cubic (review) H d h t h l b di l 4R/?3 a ar sp eres ouc a ong cu e agona ? a= Number of atoms per unit cell n = 2, Atomic packing factor, APF = 0.68 Coordination number: # of atoms touching, CN = 8 Face-Centered Cubic (review) R ? a a Hard spheres touch along diagonal ? a= 2R 2 Number of atoms per unit cell n = 4, . Atomic packing factor APF = 0 74 (maximum possible), . Coordination #: CN = no. of neighbors = 12 Find density of Al if in FCC crystal with R= 0.143nm FCC n = 4 ; a = 2?2 R NA =6.02x1023atoms/mol A= 26.98 g/mol Find ? =2 71g/cm3 . . Chap 3 (cont) Densities of some FCC metals Interstitial Sites (spaces in lattice) Carbon interstitial atom in BCC iron FCC, BCC, HCP: void space relatively small Æ atomic radius of interstitial << than host different types of sites defined by their coordination number SC larger void space (smallerAPF) Hexagonal Close-Packed (HCP) ? Non-cubic unit cell Stacking of Billiard Balls Close-packed Structures (FCC and HCP) FCC: ABCABCABC ? HCP: ABABAB. FCC & HCPÆAPF =0 74 (maximum value) Close-packed Structures (FCC and HCP) . FCC: ABCABCABC ? HCP: ABABAB. FCC and Close-Packed Planes A B C Unit cell axes have labels for important directions [x,y,z] Linear density (LD) 2 atoms along a line of length 4R Crystal planes labeled by where they intersect axes (1,1,1) Called Miller indices Planar Density (PD) 4R a = 2?2 R 2 atoms in an area (4R x a) What is the PD for the (1,1,0) of a BCC X-ray diffraction lets us measure h l it e att ce parameters Single Crystals and Polycrystalline Materials Si l t l i di ti t i lng e crys a : per o c array over en re ma er a Polycrystalline material: many small crystals (grains) with varying orientations. Atomic mismatch where grains meet (grain boundaries) 18 Grain Boundary Polycrystalline Materials 19 Atomistic model of a nanocrystalline solid Polymorphism & Allotropy Polymorphism Æ more than one crystal structure If l t l lid ll d ll t an e emen a so ca e : a o ropy (carbon: diamond, graphite, amorphous carbon, fulerene?s, etc.) Remember IONIC BONDING and CRYSTAL STRUCTURE A key feature of an ionic bond is that: A) It is strongly directional B) It is completely non-directional C) Acts between identical atoms D) It results in electrostatically neutral atoms E) It is typical of metals The electronegativity of an atom is a f it t d tmeasure o s en ency o: A) Form a covalent bond )B Attract electrons C) R l lepe e ectrons D) A l i ittract e ectropos t ve atoms E) N f th bone o e a ove IONIC BONDING & STRUCTURE cation as an interstitial (not required at this time) Ch N li CaF2: Ca 2+ F- i+? arge eutra ty cation F- an ons --General form AmXp d t i d b h t litm, p e erm ne y c arge neu ra y ? Structure stability - - - - + - - - - + - - - - + unstable stable stable Ionic Bonding (strong and non-directional) ? Electron transfer reduces energy of the system e- Na Cl Ionic Bonding (strong and non-directional) ? Electron transfer reduces energy of the system e- Na Cl Na+ Cl- ? Na shrinks and Cl expands rNa+/rCl-= 0.097nm/0.181nm = 0.536 ? Electron transfer reduces energy of the system e- Ionic Bonding (strong and non-directional) Na Cl Na+ Cl- ? Na shrinks and Cl expands rNa+/rCl-= 0.097nm/0.181nm = 0.536 ? Electron transfer reduces energy of the system e- Ionic Bonding (strong and non-directional) Na Cl Na+ Cl- ? Na shrinks and Cl expands rNa+/rCl-= 0.097nm/0.181nm =0.536 Why an FCC crystal for NaCl?? COORDINATION # AND IONIC RADII think of the cation as an interstitial ? Coordination # increases with rcation ranion rcation Coord # ZnS Covalent Structure to be ranion < .155 (zincblende) 2 discussed .155-.225 .225-.414 NaCl (sodium chloride) 3 4 Face Centered Cubic FCC .414-.732 CsCl (cesium 6 Simple Cubic SC .732-1.0 chloride)8 ml7q Microsoft PowerPoint - LectChap3b.ppt [Compatibility Mode]
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