结晶学基础第八章习题答案

Author:://抽沙船《结晶学基础》第八章习题答案8001(C)8002非。8003非。六方晶系只有简单六方一种点阵型式,六方晶胞中所含的两个球,均属一个结构基元。80041:2:18005(E)80060,0,0;1/3,2/3,1/2(或0,0,0;2/3,1/3,1/2)8007(1)63,6简单六方。(2)0,0,0;1/3,2/3,1/2。(3)(NA·34r3)/0.7405=13.95cm3(4)d002=2×1.633×160/2pm=522.6/2pm=261.3pm8008面;面8009(1)(1/3,2/3,1/4);(1/3,2/3,3/4);(2)(2/3,1/3,1/8);(2/3,1/3,7/8);(0,0,3/8);(0,0,5/8)Author:://分子占据面积r2;平行四边形面积2r×2r×sin60°rrr22866.02=0.9078011布拉格角:34.27°;40.56°;66.83°;指标:111;200;220。8012(1)a=352.4pm(2)d=VNnMA/=2432310524.31002.6/70.584g▪cm-3=8.906g▪cm-3(3)略8013A1型堆积为立方面心结构,第一对谱线的衍射指标为111a=362.0pmr=128.0pm立方面心,每个晶胞中有4个Cu原子,d=8.89g·cm-38014r=143pm;=19.3°8015a=400.4pmr=141.6pmA1堆积每个晶胞中有4个Al原子,d=2.793g·cm-38016(1)r=138.4pm(2)最多能得到(100)的4级衍射8017体心点阵Author:://=41(3×4292)1/2=185.8pm8019d(110)=330×sin45°pm=233.3pmsin=0.660,=41.3°8020d=21.45g·cm-3r=138.7pm8021a=405.0pm8021r=41(2×405.02)1/2pm=143.2pm8022a=b=2×146pm=292pmc=292×1.633pm=477pm8023对于体心立方,只能出现h+k+l=偶数之衍射线,即只出现(110),(200),(211),(220),(310),(222),(231),(004)等。sinhkl=a2(h2+k2+l2)1/2=0.2674(h2+k2+l2)1/2由于h2+k2+l2≥14,sinhkl1,所以只能得到下列6条衍射线:(110),(200),(211),(220),(310),(222)。其衍射角分别为:110=22.2°;200=32.3°;211=40.9°;220=49.1°;310=57.7°;222=67.9°。8024(1)点阵型式:简单立方;结构基元:1Cu,1Zn;r=138pm;Author:://抽沙船(2)点阵型式:体心立方;结构基元:21Cu,21Zn;r=133pm。8025(1)Cu的摩尔分数为x,Zn为1-x;63.5x:65.4(1-x)=75%:25%x=0.755,即Cu的原子百分数为75.51-x=0.245,即Zn的原子百分数为24.5(2)4.25×10-22g(3)V=0.5×10-22cm3(4)a=368pm;r=130pm。8026(1)a=320.9pm,c=524.0pm(2)1.727g·cm-38028(1)185.8pm;(2)0.967g·cm-3;(3)303.3pm8029(1)白锡变灰锡,体积膨胀;(2)增大26%。8030减少8031(1)a=200pm,c=326.6pm(2)22.5pm(3)(0,0,0.375);(0,0,0.625);(1/3,2/3,0.125);(1/3,2/3,0.875)。80331,1,280341,1,2Author:://(0,0,0);(1/3,2/3,1/2)。或(0,0,0);(2/3,1/3,1/2)8039禁带宽度不同(半导体Eg3eV)804074.05%8041V=AdNZM=5.00×10-23cm3a=367.7pm统计原子半径:r=(2/4)a=130.0pm8042Mo的原子半径:r=(3/4)a=136.26pmd100=314.70pmd110=222.56pm8043a=(8/3)r=648.96pmAuthor:://=a3=2.73×108pm3d=AVNZM=5.78g·cm-38044111;sin=[(/2a)2(h2+k2+l2)]1/2=0.3469=20.308045参看周公度《结构化学基础》图8.3.1(c)四方P结构基元:2Au,2Cu8046参看周公度《结构化学基础》图8.3.1(a)立方F结构基元:一个统计原子8047M=130.288048白锡:d=7.31g·cm-3灰锡:d=5.78g·cm-3白锡密度大,灰锡密度小,白锡转变为灰锡,由于体积骤然膨胀,使锡器碎裂80492+228hmE=08050参看周公度《结构化学基础》p.367Author:://。8052异:(1)A1:ABC|ABC|...堆积A3:AB|ABC|...堆积(2)A1:可取出面心立方晶胞A3:可取出六方晶胞(3)A1:密置层为(111)A3:密置层为(001)同:(1)每一层都是密置层,由密置层作最密堆积(2)配位数都为12(3)堆积系数都为74.05%(4)晶胞中球数、八面体空隙数、四面体空隙数的比值都为1∶1∶28053a=2rc=正四面体高×2=1.633×2rc/a=1.63380544r=3aV=a3=[(4/3)r]3堆积系数为68.02%805541/48280566Author:://hkl=[2a/(h2+k2+l2)1/2]sinhkl=∵sinhkl≤1∴h2+k2+l2≤12根据面心立方的消光规律,衍射图中将出现五条谱线:111,200,220,311,22229.11,34.18,52.60,68.69,76.678058a=408.57pmZ=4根据消光条件,Ag晶体属面心立方点阵,Ag原子的分数坐标应为:(0,0,0),(1/2,0,1/2),(1/2,1/2,0),(0,1/2,1/2)8059a=286.64pmZ=MdVNA=2根据消光条件,α-Fe属体心立方点阵,Fe原子的分数坐标应为:(0,0,0),(21,21,21)8060∵sinhkl≤1∴h2+k2+l2≤19根据面心立方的消光规律,衍射图上有9条衍射线,前三条为:110,200,21118.81,27.13,33.968061d=8.86g·cm-3Co原子半径为：a/2=125.35pm8062Author:://=8由sin2=(/2)2(h2/a2+k2/b2+l2/c2)得=31.478063Pd晶胞体积V=a3=5.89×107pm31cm3Pd含有的晶胞数为:(1×1030pm3)/(5.89×107pm3)=1.70×1022Pd晶胞中有4个八面体空隙和8个四面体空隙.1cm3Pd中含有的空隙数为:12×1.70×1022=2.04×1023700cm3H2即为0.03125molH2,含H2分子数为:0.0315×6.023×1023=1.88×1022H原子数为:2×1.88×1022=3.76×1022H原子所占空间的百分数为18.4%8064(4r)2=2a2r=a/(22)=137.5pmPd原子之间最短距离为:2r=275.0pmd=12.00g·cm-380651284垂直于三次轴方向8066a=2×158.3pm=316.6pmc=1.633×316.6pm=517.0pmd=5.85g·cm-38067a=4r/2=405.1pmd=2.70g·cm-3Author:://=2体心立方点阵(0,0,0);(1/2,1/2,1/2)8069a=4r/3=570.0pm相对原子质量为85.298070V=AdNZM=1.51×10-22cm3a=(1.51×10-22)1/3pm=532.1pmr=230.4pmd（110）=376.2pm8071(1)六方(2)六方P(hp)(3)2个,(0,0,0),(1/3,2/3,1/2)(4)128072一晶胞中共有四个A原子,另外三个坐标是(1/4,3/4,3/4),(3/4,1/4,3/4),(3/4,3/4,1/4)8073111=21.7°200=25.3°220=37.1°311=45.0°d=8.97g·cm-38074(1)8.61eV(2)7.01eVAuthor:://抽沙船(3)1.36:1(4)0.368075EF(0)=(h2/8m*)(3n/)2/3=4.72eV80762dhklsinhkl=dhkl=a/(h2+k2+l2)1/2a=hklsin2(h2+k2+l2)1/2='1781sin22.154×33pm=404.9pm8077(1)0.816R(2)2.45R8078(1)224hmLdE(2)224mLNh8079(1)由布拉格方程2dsin=得d=/(2sin)=80/(2×0.133)pm=300pm对立方体心结构,(200)面间距d200是晶胞边长的一半a=2d=600pm(2)晶体密度为d=2.0g/cm3d=2M/(NAV)=2M/(6.023×1023×63×10-24)∴M=130(3)立方体心晶胞的原子分数坐标:(0,0,0),(1/2,1/2,1/2)Author:://=21·(3/2)a=3a/4=259.8pm(4)空间利用率:晶胞中有两个原子2(4/3)(3a/4)3/a3=68.02%8080波矢空间E=EF的等能面称为费米面。自由电子的费米面是半径为RF=/2FmE的球面金属电子比热小的原因是由于只有费米面附近约kT范围内的电子受热激发才可能跃迁到较高能级对比热有贡献。8082垂直或平行于三重旋转轴。在(111)面上取6个圆,密堆积成正三角形,二维堆积系数为=(2×r2)/(21×4r×4r×3/2)=/(23)=90.65%8084○○○○○○○○○○○○○○○○○○○