1、Precise Lattice Parameter MeasurementClass One2008-12-4OutlineExperimental Goal1.Background and Theory2.Example3.Experimental Goal Determine the precise lattice parameters of materialsBackground and TheoryImportance Useful in determining solid solubility limits of one component in another,coefficien
2、ts 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 TheoryA material with a cubic structure222lkhdasin2/dcot/ddBackground and TheoryMethodsDebye-Scherrer CamerasDiffra
3、ctometersMathematizationExtrapolation Debye-Scherrer Cameras Bradley-Jay Nelson-Riley Diffractometers The least-square method22cossincos2cos2cossincos2Background and TheoryDebye-Scherrer CamerasSources of error:Film shrinkage Incorrect camera radius Off-centering of specimen Absorption in specimen D
4、ivergence of the beamBackground 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 t
5、he incident beamBackground and TheoryExtrapolation1.Since varies differently with different errors，a single extrapolation function is not satisfactory in this casedd2.It is necessary to have as many reflections as possible in the high-angle region of the diffraction pattern so that you will have man
6、y Pointsenabling you to draw the best possible straight lineBackground and TheoryThe least-square methodNormal Equations CA22sin22sinCA2024/aA222lkh10/DC 2sin102Drift constantExampleFIG 1X-ray diffraction pattern of aluminum showing only the high-angle regionThe least-square method-AluminumExampleTa
7、ble 1 Calculation of the Lattice Parameter of AluminumExample222hklTABLE 2 Data Required for Cohens Analytical Method210sin 2ExampleCA22sin 22sinCA2674A+858.9C=96.77139858.9A+313.14C=31.08341A=0.0361895 C=7.810-7 0/20.40491aAExampleFIG2 X-ray diffraction pattern of silicon showing only the highangle
8、 regionExtrapolation-SiliconExampleTABLE 3 Work Table for Indexing the Diffraction Pattern of SiliconExample00.050.10.150.20.250.30.350.40.54240.54260.54280.5430.54320.54340.5436cos2Lattice Parameter(nm)a0=0.5430nmTrue value a0=0.5431 nmFIG 3 The straight line by extrapolating lattice parameters against 2cosExample00.050.10.150.20.250.30.350.40.450.54240.54260.54280.5430.54320.54340.5436cos2/sinLattice Parameter(nm)a0=0.5430nmTrue value a0=0.5431 nmFIG 4 The straight line by extrapolating lattice parameters against sincos2
