单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Precise Lattice Parameter Measurement,Class One,2008-12-4,Precise Lattice Parameter Meas,1,Outline,Experimental,Goal,1.,Background and Theory,2.,Example,3.,OutlineExperimental Goal1.Bac,2,Experimental Goal,Determine the precise lattice parameters of materials,Experimental Goal D,3,Background and Theory,Importance,Useful in determining solid solubility limits of one component in another,coefficients of thermal expansion,and true densities of materials.,The magnitudes of changes in the lattice parameters due to a change in solute content or temperature are so small.,Background and TheoryImportanc,4,Background and Theory,A material with a cubic structure,Background and TheoryA materi,5,Background and Theory,Methods,Debye-Scherrer Cameras,Diffractometers,Mathematization,Extrapolation,Debye-Scherrer Cameras,Bradley-Jay,Nelson-Riley,Diffractometers,The least-square method,Background and TheoryMethodsDe,6,Background and Theory,Debye-Scherrer Cameras,Sources of error:,Film shrinkage,Incorrect camera radius,Off-centering of specimen,Absorption in specimen,Divergence of the beam,Background and TheoryDebye-Sch,7,Background and Theory,Diffractometers,Sources of error:,Misalignment of the instrument,Use of a flat specimen instead of a specimen curved to conform to the focusing circle,Absorption in the specimen,Displacement of the specimen from the diffractometer axis,Vertical divergence of the incident beam,Background and TheoryDiffracto,8,Background and Theory,Extrapolation,1.Since varies differently with different errors，a single extrapolation function is not satisfactory in this case,2.It is necessary to have as many reflections as possible in the high-angle region of the diffraction pattern so that you will have many Points,enabling you to draw the best possible straight line,Background and TheoryExtrapola,9,Background and Theory,The least-square method,Normal Equations,Drift constant,Background and TheoryThe least,10,Example,FIG 1X-ray diffraction pattern of aluminum showing only the high-angle region,The least-square method-Aluminum,ExampleFIG 1X-ray diffraction,11,Example,Table 1 Calculation of the Lattice Parameter of Aluminum,ExampleTable 1 Calculation of,12,Example,TABLE 2 Data Required for Cohens Analytical Method,ExampleTABLE 2 Data Required f,13,Example,2674A+858.9C=96.77139,858.9A+313.14C=31.08341,A=0.0361895 C=7.810,-7,Example 2674A+858.9C=96.77139,14,Example,FIG2 X-ray diffraction pattern of silicon showing only the highangle region,Extrapolation-Silicon,ExampleFIG2 X-ray diffraction,15,Example,TABLE 3 Work Table for Indexing the Diffraction Pattern of Silicon,ExampleTABLE 3 Work Table for,16,Example,a,0,=0.5430nm,True value a,0,=0.5431 nm,FIG 3 The straight line by extrapolating lattice parameters against,Examplea0=0.5430nmTrue value a,17,Example,a,0,=0.5430nm,True value a,0,=0.5431 nm,FIG 4 The straight line by extrapolating lattice parameters against,Examplea0=0.5430nmTrue value a,18,Thanks for your attention!,Thanks for your attention!,19,