# Ciência e Engenharia dos Materiais (CAP03)

(Parte 3 de 4)

A = 0.866 a2 ao 2ao π ao

28The Science and Engineering of MaterialsInstructor’s Solution Manual

3–79Determine the minimum radius of an atom that will just fit into (a) the tetrahedral interstitial site in FCC nickel and (b) the octahedral interstitial site in BCC lithium.

Solution:(a) For the tetrahedral site in FCC nickel (ao =3.5167 Å):

r/rNi=0.225 for a tetrahedral site. Therefore: r=(1.243 Å)(0.225) =0.2797 Å

(b) For the octahedral site in BCC lithium (ao =3.5089 Å):

r/rLi=0.414 for an octrahedral site. Therefore: r=(1.519 Å)(0.414) =0.629 Å

3–86What is the radius of an atom that will just fit into the octahedral site in FCC copper without disturbing the lattice?

Solution: rCu = 1.278 Å r/rCu=0.414 for an octahedral site. Therefore: r=(1.278 Å)(0.414) =0.529 Å

3–87Using the ionic radii given in Appendix B, determine the coordination number expected for the following compounds.

Solution:(a) Y2O3(b) UO2(c) BaO(d) Si3N4 (e)GeO2(f)MnO (g)MgS (h)KBr

0.42 1.96 rNi Å

Point 0, 0, 0

Point 1,1,1

CHAPTER 3Atomic and Ionic Arrangements29

3–88Would you expect NiO to have the cesium chloride, sodium chloride, or zinc blende structure? Based on your answer, determine (a) the lattice parameter, (b) the density, and (c) the packing factor.

Solution:rNi+2=0.69 ÅrO−2=1.32 ÅrNi

Acoordination number of 8 is expected for the CsCl structure, and a coordination number of 4 is expected for ZnS. But a coordination number of 6 is consistent with the NaCl structure.

(a) ao =2(0.69) +2(1.32) =4.02 Å

3–89Would you expect UO2to have the sodium chloride, zinc blende, or fluorite structure? Based on your answer, determine (a) the lattice parameter, (b) the density, and

(c) the packing factor.

The radius ratio predicts a coordination number of 8; however there must be twice as many oxygen ions as uranium ions in order to balance the charge. The fluoritestructure will satisfy these requirements, with:

U =FCC position (4)O =tetrahedral position (8)

 4(238.03 g/mol) +8(16 g/mol)

3–90Would you expect BeO to have the sodium chloride, zinc blende, or fluorite structure? Based on your answer, determine (a) the lattice parameter, (b) the density, and (c) the packing factor.

Solution: rBe +2=0.35 ÅrO

 4(9.01 +16 g/mol)

30The Science and Engineering of MaterialsInstructor’s Solution Manual

3–91Would you expect CsBr to have the sodium chloride, zinc blende, fluorite, or cesium chloride structure? Based on your answer, determine (a) the lattice parameter, (b) the density, and (c) the packing factor.

Solution: rCs +1=1.67 ÅrBr

 79.909 +132.905 g/mol

3–92Sketch the ion arrangement on the (110) plane of ZnS (with the zinc blende struc- ture) and compare this arrangement to that on the (110) plane of CaF2(with the flourite structure). Compare the planar packing fraction on the (110) planes for these two materials.

Solution: ZnS:

ao =0.596 nm

ao =0.536 nm

PPF nm

2 ππ π πr a ao 2ao

PPF nm

Zn S

2 ππ π πr a

3 CHAPTER 3Atomic and Ionic Arrangements31

3–93MgO, which has the sodium chloride structure, has a lattice parameter of 0.396 nm.

Determine the planar density and the planar packing fraction for the (1) and (2) planes of MgO. What ions are present on each plane?

Solution:As described in the answer to Problem 3–71, the area of the (1) plane is 0.866ao

 2 Mg

1.450 nm, bo =0.569 nm, and co

=0.740 nm. The chemical formula for the propy- lene molecule, from which the polymer is produced, is C3H6. The density of the polymer is about 0.90 g/cm3. Determine the number of propylene molecules, the number of carbon atoms, and the number of hydrogen atoms in each unit cell.

Solution:MWPP=3 C +6 H =3(12) +6 =42 g/mol

 (xC3H6)(42 g/mol)

3–101The density of cristobalite is about 1.538 g/cm3, and it has a lattice parameter of

0.8037 nm. Calculate the number of SiO2ions, the number of silicon ions, and the number of oxygen ions in each unit cell.

 (xSiO2)[28.08 +2(16) g/mol]

ao 2ao

32The Science and Engineering of MaterialsInstructor’s Solution Manual

3–105Adiffracted x-ray beam is observed from the (220) planes of iron at a 2uangle of 9.1owhen x-rays of 0.15418 nm wavelength are used. Calculate the lattice parameter of the iron.

Solution:sin u=l/2d220 sin(9.1/2) =

(Parte 3 de 4)