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1、晶胞参数的测定本讲稿第一页，共十九页OutlineExperimental Goal1.Background and Theory2.Example3.本讲稿第二页，共十九页Experimental Goal Determine the precise lattice parameters of materials本讲稿第三页，共十九页Background and TheoryImportance Useful in determining solid solubility limits of one component in another,coefficients of thermal e
2、xpansion,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.本讲稿第四页，共十九页Background and TheoryA material with a cubic structure本讲稿第五页，共十九页Background and TheoryMethodsDebye-Scherrer CamerasDiffractometersMath
3、ematizationExtrapolation Debye-Scherrer Cameras Bradley-Jay Nelson-Riley Diffractometers The least-square method本讲稿第六页，共十九页Background and TheoryDebye-Scherrer CamerasSources of error:Film shrinkage Incorrect camera radius Off-centering of specimen Absorption in specimen Divergence of the beam本讲稿第七页，
4、共十九页Background and TheoryDiffractometersSources 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本
5、讲稿第八页，共十九页Background and TheoryExtrapolation1.Since varies differently with different errors，a single extrapolation function is not satisfactory in this case2.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
6、enabling you to draw the best possible straight line本讲稿第九页，共十九页Background and TheoryThe least-square methodNormal Equations Drift constant本讲稿第十页，共十九页ExampleFIG 1X-ray diffraction pattern of aluminum showing only the high-angle regionThe least-square method-Aluminum本讲稿第十一页，共十九页ExampleTable 1 Calculat
7、ion of the Lattice Parameter of Aluminum本讲稿第十二页，共十九页ExampleTABLE 2 Data Required for Cohens Analytical Method本讲稿第十三页，共十九页Example 2674A+858.9C=96.77139858.9A+313.14C=31.08341A=0.0361895 C=7.810-7 本讲稿第十四页，共十九页ExampleFIG2 X-ray diffraction pattern of silicon showing only the highangle regionExtrapolati
8、on-Silicon本讲稿第十五页，共十九页ExampleTABLE 3 Work Table for Indexing the Diffraction Pattern of Silicon本讲稿第十六页，共十九页Examplea0=0.5430nmTrue value a0=0.5431 nmFIG 3 The straight line by extrapolating lattice parameters against 本讲稿第十七页，共十九页Examplea0=0.5430nmTrue value a0=0.5431 nmFIG 4 The straight line by extrapolating lattice parameters against 本讲稿第十八页，共十九页本讲稿第十九页，共十九页