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晶胞参数的测定

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晶胞 参数 测定
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Precise Lattice Parameter Measurement Class One 2008-12-4 Outline Experimental Goal1. Background and Theory2. Example3. Experimental Goal Determine the precise lattice parameters of materials 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 Theory A material with a cubic structure Background and Theory Methods Debye-Scherrer Cameras Diffractometers Mathematization Extrapolation * Debye-Scherrer Cameras ● Bradley-Jay ● Nelson-Riley * Diffractometers ● ● The least-square method 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 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 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 Theory The least-square method Normal Equations Drift constant Example FIG 1.X-ray diffraction pattern of aluminum showing only the high-angle region The least-square method-Aluminum Example Table 1 Calculation of the Lattice Parameter of Aluminum Example TABLE 2 Data Required for Cohen's Analytical Method Example 2674A+858.9C=96.77139 858.9A+313.14C=31.08341 A=0.0361895 C=7.8×10-7 Example FIG2 X-ray diffraction pattern of silicon showing only the high—angle region Extrapolation-Silicon Example TABLE 3 Work Table for Indexing the Diffraction Pattern of Silicon Example a0=0.5430nm True value a0=0.5431 nm FIG 3 The straight line by extrapolating lattice parameters against Example a0=0.5430nm True value a0=0.5431 nm FIG 4 The straight line by extrapolating lattice parameters against
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