晶体学与衍射技术Crystallography and Diffraction 4 晶体点阵常数的测定及应用晶体结构晶体结构晶胞参数晶胞参数晶胞内原子坐标参数晶胞内原子坐标参数晶体学与衍射技术Crystallography and Diffraction 3.3 倒易点阵 基于布拉格方程 从衍射实验峰位数据 所获得的一套面网间距，不同指数（hkl ）的面间距。衍射图片上的衍射点代表 一组平行面网的方向和面间距。如何方 便分析衍射花样，我们引入倒易点阵的 概念（reciprocal lattice）.Bragg diffractionk=k+GBragg diffractionCOD1/2GDk2Constructing Brillouin Zones1st B. Z. 2ndB. Z. 2p/aCos(px/a)Sin(px/a)Cos2(px/a)Sin2(px/a)高温高温X X射线照相射线照相精确测定晶体点阵常数的意义精确测定晶体点阵常数的意义确定新相（新化合物，新材料）确定新相（新化合物，新材料）Is the compound known? Crystallographic Structure DatabasesICSD (Minerals and Inorganics) http:/www.fiz-karlsruhe.de/ Minerals and Inorganic Over 60000 entriesCambridge Structure Data Bank ） http:/www.ccdc.cam.ac.uk Organics & Organometallics Over 250000 entriesICDD diffraction data http:http:/www.icdd.com/ Inorganic & Organic Over 140000 entriesNIST Crystal Data http:/www.nist.gov/srd/nist3.htm Inorganic & Organic Over 230000 entriesLa2(Co,Ti）17化合物Atom site xyzLa 6c 绿0.00.00.3470Co 9d 黄0.50.00.5Co 18f 兰 0.28600.00.0Co 18h 紫 0.50.00.1548*Co+Ta 6c 绿0.00.00.0961a= 8.5092(1), c= 12.3575(1) , V=774.9(1)3Q.L. Liu et al., Q.L. Liu et al., Appl. Phys. Lett. 71 (1997)1869 Q.L. Liu et al., Q.L. Liu et al., Appl. Phys. Lett. 71 (1997)1869 测定固溶体的类型和固溶度测定固溶体的类型和固溶度 测定相图的固溶线测定相图的固溶线Q.L. Liu et al, J.Phys.: Condens. matter 11 (1999)9797 Q.L. Liu et al, J. Alloys and Compounds 297 (2000)33Q.L. Liu et al, J.Phys.: Condens. matter 10 (1998)179 Ti1-xSnxO2体系化合物晶胞体积随成分的变化B.J. Sun, Q.L. Liu et al., J. Alloys Compounds, jalcom15480 (2007)Nonmagnetic semiconductors DMS1.A: Ferromagnetic semiconductors EuO, EuS, EuSe, CdCr2S4 (late1960s-early1970s)2.B: 稀磁半导体 DMS 3.C: Nonmagnetic semiconducorsH. Ohno, Science 281(1998)951Diluted magnetic semiconductors1.II-VI semiconductors 2. CdTe ZnS 1980s2.III-V semiconductors 3. GaAs GaN AlN 1990s 4. 3.Oxide semiconductorsZnO TiO2 SnO2 recently 3. T. Dietl et al, Science 287(2000)1019要求室温铁磁性和半导体性Interesting problems1.成分 dopants contentdirect Mn-Mn interaction: antiferromagnetic dilute: Mn-carriers-Mn: ferromagneticcarriers: holes /electronic concentration?orbital moment quenched? 2.构成和结构solid solutions, alloys 2. nanoclusters of the magnetic atoms 3. precipatates 4. second phase? 5. 3.生长条件Depend on the growth method and conditionsMn-doped ZnOJ. Luo, J.K. Liang, Q.L. Liu et al, J. Applied Physics 97(2005) No. 086106 Mn-doped ZnOJ. Luo, J.K. Liang, Q.L. Liu et al, J. Applied Physics 97(2005) No. 086106 Mn-doped ZnOJ. Luo, J.K. Liang, Q.L. Liu et al, J. Applied Physics 97(2005) No. 086106 Gd5(Si1-xGex)4 成分、温度、晶体结构和磁性的关系Q.L. Liu et al,J. Alloys Compounds 325(2001)50 Q.L. Liu et al,J. Alloys Compounds 325(2001)50 Gd5(Si1-xGex)4成分、温度、晶体结构和磁性的关系Lattice parameters, cell volume and Ln-O distances of Ln3GaO6F.S. Liu, Q.L. Liu, et al, J. Solid State Chem 177(2004)1796 Lattice parameters and cell volume of rare earth doped (4 at%) Y3GaO6F.S. Liu, Q.L. Liu et al., J. Luminescence 111 (2005)61Lattice parameters and cell volume of Tb and Tm doped Y3GaO6TbTmF.S. Liu et al., J. Solid State Chem 178 (2005)1064F.S. Liu, Q.L. Liu et al, J. Alloys and Compounds 425 (2006)278F.S. Liu, Q.L. Liu et al, J. Alloys and Compounds 425 (2006)278Saturation range of the PL intensityfor the Tb3+, Tm3+ doped Y3GaO6 TbTm420%15%F.S. Liu et al., J. Solid State Chem 178 (2005)1064F.S. Liu, Q.L. Liu et al, J. Alloys and Compounds 425 (2006)278F.S. Liu, Q.L. Liu et al, J. Alloys and Compounds 425 (2006)278衍射数据的指标化qn2（观察值）sin2qnq11420.0149q216140.0199q32320.0399q42740.0547q528160.0597q632500.0799q735500.0947q840300.1197q94340.1347qnhklq10.01493111 q20.01994200 q30.0399.8220 q40.054711311 q50.059712222 q60.079916400 q70.094719331 q80.119724422q90.134727空间群的确认空间群的确认晶格常数的修正晶格常数的修正hklsin2 0sin2 c 1110.01490.0150 2000.01990.0200 2200.0399.0.0399 3110.05470.0549 2220.05970.0599 4000.07990.0799 3310.09470.0949 4200.0999 4220.11970.1198333/5110.13470.1348压电效应 热电效应 旋光性 倍频效应 晶体光学 强度统计规律：N（Z） 函数法有无对称中心的确定 LaCoTiLaCoTi 2:17 2:17 4.26304.2630 4.12214.1221 3.54213.5421 3.17073.1707 2.96652.9665 2.85372.8537 2.72332.7233 2.54612.5461 2.46232.4623 2.37082.3708 2.13202.1320 2.11392.1139 2.07152.0715 2.06162.06161.48101.4810 1.46711.4671 1.42161.4216 1.39741.3974 1.34331.3433 1.33761.3376 1.33271.3327 1.31841.3184 1.30671.3067 1.29681.2968 1.27141.2714 1.23011.2301 1.22211.2221 1.21851.2185 1.19881.19881.89311.8931 1.85611.8561 1.82611.8261 1.76921.7692 1.71731.7173 1.70721.7072 1.67781.6778 1.63321.6332 1.61071.6107 1.59281.5928 1.57991.5799 1.51051.5105 1.50041.5004 1.48521.4852 1.48101.48101.19881.1988 1.18481.1848 1.17201.1720 1.15451.1545 1.13611.1361 1.09491.0949 1.06531.0653 1.06021.0602 1.05621.0562 1.04491.0449 0.99800.9980 0.98740.9874 0.98470.9847 0.97780.9778 0.97170.97170.96960.9696 0.95130.9513 0.94620.9462 0.94250.9425 0.92710.9271 0.92490.9249CEM=20,VOL=1500,CEM=20,VOL=1500, D1=0.0002,D1=0.0002, D2=0.0