æ¦oµ¨¹ (crystal structure) ª´»¦³rµ¦«¹¬µ • µ¦´Á¦¸¥´ª °°³°¤Ä °Â È 2109101 Engineering Materials • ¨´¬³Ã¦¦oµ¨¹ °Ã¨®³ • ¨ °µ¦´Á¦¸¥´ªn°ªµ¤®µÂn °ª´» ¦´Ê¸É Ó Ã¦¦oµ¨¹ °ª´» (Crystal Structure) • ª´»¨¹Á¸É¥ªÂ¨³ª´»®¨µ¥¨¹ (³¨nµª¹ÄÁ¦¸¥¦´Ên°Å) • ¨ °¨¹n°¤´· °ª´» (³¨nµª¹Ä¤´·µ¨) 1 2 µ¦Á¦¸¥´ª °°³°¤Ä °Â È µ¦Á¦¸¥´ªÂ random packing • Á}µ¦Á¦¸¥´ª¸ÉŤnÂn • ŤnÁ}£µª³¸É¡¨´µÉε» Á}µ¦Á¦¸¥´ª¸ÉÂn • ¡¨´µÉε¸É» Energy typical neighbor bond length typical neighbor bond energy µ¦Á¦¸¥´ªÂ regular packing • ª´»¸É¤¸Ã¦¦oµ¨¹ º° ª´»¸ÉÁ·µ°³°¤¸É¤¸ µ¦´Á¦¸¥´ª°¥nµÁ}¦³Á¸¥ ¤¸Â °µ¦ Á¦¸¥´ª¸ÉÂn°Ä3¤·· ¡Ä讳 Á¦µ¤·nª Ä®n¨³¡°¨·Á¤°¦rµ· r ª´»¸ÉŤn¤¸Ã¦¦oµ¨¹ º° ª´»¸É°³°¤£µ¥Ä Ťn¤¸µ¦´Á¦¸¥´ª°¥nµ¤¸Â¸ÉÂn° °µÁ· µµ¦Á¥È´ª°¥nµ¦ªÁ¦Èª µ¦´ÊÁ¦¸¥ªnµ °´µ ®¦º° amorphous Energy typical neighbor bond length r typical neighbor bond energy 3 crystalline SiO2 Adapted from Fig. 3.18(a), Callister 6e. Si Oxygen noncrystalline SiO2 Adapted from Fig. 3.18(b), Callister 6e. 4 µ¦Á¦¸¥´ª °°³°¤Â¨³®nª¥Á¨ •°³°¤Á¦¸¥´ª°¥nµÁ}¦³Á¸¥ •¦¼¨nµ»Âµ¦Á¦¸¥´ª ° °³°¤Á}æ¦oµ¨¹Ã¥Ä®o ¦¨¤Á}´ªÂ °°³°¤ µ¦Á¦¸¥³ª¸ÉÁ}¸ʵ¤µ¦ÂnÁ}®nª¥ ¥n°¥¸ÉÁ¨È¸É»¹ÉÁ¦¸¥Êεdz Á¦¸¥ªnµ ®nª¥Á¨ (unit cell) ¦¼Â®nª¥Á¨ °¨¹Ä¦¼¨nµ 5 6 7 8 โครงสรางผลึก ๗ ประเภท 1. Cubic 2. Tetragonal 3. Rhombohedral 4. Hexagonal 5. Orthorhombic 6. Monoclinic 7. Triclinic สามารถแบงยอยเปน bravais lattice (บราเวส แลททิส) ได ๑๔ ประเภท 9 æ¦oµ¨¹ °Ã¨®³ -- ªÃo¤¸É³¤¸ªµ¤®µÂn¼ ÁºÉ°µ •¤¸°³°¤®¨´Á¡¸¥·Á¸¥ªÎµÄ®o¦´«¤¸°³°¤Ánµ´®¤ Atomic Packing Factor -- °´¦µµ¦¦¦»°³°¤n°®¹É®nª¥Á¨ •¡´³Ã¨®³Á}¡´³¸ÉŤn¤¸·«µ APF = Volume of atoms in unit cell* Volume of unit cell •Á¤ºÉ°°³°¤Á¦¸¥··´Ä®o¤¸ªµ¤®µÂn¼ÎµÄ®o¡¨´µ¤¸nµÉε µ¦Á¦¸¥´ª °°³°¤Îµ®¦´Ã¨®³ nª¤µ³Á¦¸¥´ª´°¥nµnµ¥ ¹É Ânµµª´»¡ª¡°¨·Á¤°¦r¨³Á¦µ¤·¹É³¤¸Ã¦¦oµ´o° *assume hard spheres æ¦oµ¨¹°¥nµnµ¥¸É¡¤µÄ讳°µÂn°°ÅoÁ} Coordination number εª°³°¤ oµÁ¸¥¸É°¥¼n·´°³°¤¸ÉÄ • °¸ÁÈÁ°¦r·ª· body-centered cubic, BCC • Á¢ÁÈÁ°¦r·ª· face-centered cubic, FCC 10 æ¦oµ¨¹Â°¸ÁÈÁ°¦r·ª· body-centered cubic, BCC • Á±³Ã°¨Ã¨Â¡ hexagonal close-packed, HCP APF: BCC • APF °Ã¦¦oµ body-centered cubic = 0.68 2 1 Close-packed directions: length = 4R = 3a 3 4 5 8 Unit cell c ontains: 1 + 8 x 1/8 = 2 atoms/unit cell 7 R • Coordination # = 8 Adapted from Fig. 3.2, Callister 6e. a atoms unit cell APF = 2 4 3 a3 12 11 S( 3a/4 ) 3 volume atom volume unit cell 13 æ¦oµ¨¹ÂÁ¢ÁÈÁ°¦r·ª· face-centered cubic, FCC APF: FCC • APF for a face-centered cubic structure = 0.74 Close-packed directions: length = 4R = 2a • Coordination # = 12 Unit cell c ontains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell a Adapted from Fig. 3.1(a), Callister 6e. atoms unit cell APF = 4 4 3 a3 14 S( 2a/4 ) 3 volume atom volume unit cell 15 ¦³¨¹¸É¡Ä讳nªÄ®n (90%) æ¦oµ¨¹ÂÁ±³Ã°¨Ã¨Â¡ hexagonal close-packed, HCP • BCC (Body-Centered Cubic) Án Fe (D), Mo, V, Cr • FCC (Face-Centered Cubic) Án Fe (J), Al, Cu, Ag, Au, Ni • HCP (Hexagonal Close-Packed) Án Zn, Ti (D), Mg, Be • Coordination # = 12 • APF = 0.74 16 17 £µ¡°´¦¼ • £µ¡°´¦¼ (Polymorphism or Allotropy) º° £µ¡¸É讳®¹É ¤¸¦³ ¨¹Åo®¨µ¥¦³ ¹Ê´ °»®£¼¤· Án • Ti HCPÆBCC 234°C • Zr HCPÆBCC 872°C • Na BCCÆHCP -233°C 18 19 ¦³µÃ¨Â¡ (close packed plane) Á·Äæ¦oµÂFCC¨³HCP µ¦°ÎµÂ®nÄæ¦oµ¨¹¸É¤¸Â®¨´ 3  c FCC a » 1 ¦´ <000> a c » 2 ¦´ <100> » 3 ¦´ <110> HCP a » 5 ¦´ <½ ½ ½> » 6 ¦´ <001> c a c b » 7 ¦´ <101> b » 8 ¦´ <111> » 9 ¦´ <011> b b » 4 ¦´ <010> 20 ¦³µ¡ºÊ ¦³µÃ¨Â¡ ° FCC ¨³ HCP ¤¸µ¦´Á¦¸¥´ª°³°¤Ä°¤·· (¦³µ) ¸ÉÁ®¤º°´ 21 µ¦Á¦¸¥ °¦³µÃ¨Â¡ Á¤ºÉ°´Ê¦Á¦¸¥´ªµ¤ÎµÂ®n A ´Ê¸É2°µÁ¦¸¥ µ¤ÎµÂ®nB®¦º°C oµ´Ê¸É2Á¦¸¥µ¤ÎµÂ®n FCC B ´Ê¸É3°µÁ¦¸¥Åo¸Éε®n A®¦º°C¹É³Ä®o µ¦Á¦¸¥Ânµ´ FCC HCP 22 23 THEORETICAL DENSITY, U HCP # atoms/unit cell Atomic weight (g/mol) U Volume/unit cell (cm 3 /unit cell) nA Vc N A ´ª°¥nµ °Â • æ¦oµ¨¹ = FCC: • • Avogadro's number (6.023 x 10 23 atoms/mol) 4 atoms/unit cell Êε®´°³°¤ = 63.55 g/mol (1 amu = 1 g/mol) ¦´«¤¸°³°¤ R = 0.128 nm (1 nm = 10-7 cm) Vc = a 3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10 -23 cm 3 Result: theoretical UCu = 8.89 g/cm3 Compare to actual: UCu = 8.94 g/cm3 24 25
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