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| REGRESSIVE SOLUTION FOR QUANTITATIVE PHASE ANALYSIS BY X-RAY DIFFRACTION WITHOUT STANDARD SANPLES |
| CHEN Minghao Central Iron and Steel Research Institute; Ministry of Metallurgical Industry; Beijing№14 Lab;Central Iron and Steel Research Institute;Ministry of Metallurgical Industry; Beijing |
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Cite this article:
CHEN Minghao Central Iron and Steel Research Institute; Ministry of Metallurgical Industry; Beijing№14 Lab;Central Iron and Steel Research Institute;Ministry of Metallurgical Industry; Beijing. REGRESSIVE SOLUTION FOR QUANTITATIVE PHASE ANALYSIS BY X-RAY DIFFRACTION WITHOUT STANDARD SANPLES. Acta Metall Sin, 1988, 24(3): 280-285.
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Abstract The sum of squares of deviations of the equation for calculating kwas constructed using the measured data of m samples. By deriving the minimumof the sum of squares of deviations of n equations, i.e. let ?sum from j=1 to m(M_j--sum from i=1 to n I_(ij)k_s~i)~2'/?k_s~i=0,the regressive coefficients of the n equations can be obtained (m>n). The k valuescan be deduced from the matrix equation Δ_k=Δ_I~(-1), Δ_M, and the n unknown phasesmay be calculated subsequently. It is expected that the trouble of error expansionduring solving the polynomial equation might be overcome by minimizing the sumerror through regression. The above method has been used to analyse precipitatesin high speed steel W_9Mo_3Cr_4V.
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Received: 18 March 1988
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