顯微結(jié)構(gòu)的量化處理及組織分析的教程lecturen(1)-資料下載頁
2025-01-08 08:37本頁面
【正文】 decrease as the total number of measurements gets larger, in line with the statistical principles discussed before. 3 R L Higginson and C M Sellars, Worked Examples in Quantitative Metallography, (2022) Maney, London Quantification of Microstructure and TextureSize from Planar Sections R Goodall, October 2022 9 Worked Example 3 In worked example 1, we measured the mean grain size of the example microstructure to be 177。 181。m with 95% confidence limits by treating each of the lines as a separate measurement. If we wanted to estimate the expected error before doing this experiment, or if we decided to take all the measurements together and needed to estimate the error, we can use Eqn. (8). In worked example 1, we had 231 intercepts (we can assume that the number of grains examined, n is equal to the number of grain boundary intercepts) in a total line length of 10 mm, giving a mean linear intercept length of 181。m. This is slightly different from the value determined in worked example 1, as the way we are summing the values and their consequent weighting is slightly different. Using Eqn. (8) gives an estimated relative standard error of (% of the measured value), which corresponds to an absolute standard error of ( 181。m) = 181。m. In order to set the 95% confidence limits, we need to multiply this by the value of t(95, n1), which for a large sample such as this we can assume is approximately equal to 2, giving us a final grain size of 177。 181。m with 95% confidence limits. This pares very well with the value calculated with more steps in worked example 1. Other Measures of the Size of Features The linear intercept method works well if a large enough area can be imaged. However, we are sometimes faced with the need to determine the size of a relatively small number of second phase particles or inclusions. In this case, we can make individual measurements of the particles (although it must be remembered that if the number in the sample is small, the statistical significance of the result will be low). There are a number of ways of measuring the dimensions of isolated particles, which are really all different ways of deciding what to consider the characteristic size of a particle。 its “diameter”. Most of these can be performed by hand or, increasingly, using automated image analysis software. Some of these account in different ways for the fact that the shape of the particles may not be spherical (it may be anisotropic). Caliper Diameter / Feret Diameter These measures are the shortest distance between two straight parallel lines that are tangent to the object of interest’s surface. Normally a direction would need to be specified (. horizontal or vertical in the image) for the direction in which the measurement is taken, as this will vary for nonspherical particles. Length / Breadth Normally the length would be the largest Feret diameter (of all the angles possible around an object). The breadth would be the Feret diameter at 90176。 to this. Such measurements are most easily made using image analysis Software, as will be described later, although for some anisotropic particle shapes the dimensions are self evident. Equivalent Circles If the particles are roughly spherical, then their intersections with the imaged plane will be roughly circular. One way of classifying their size is with the use of a sheet perforated by holes of different sizes. The sheet can be placed on the image and the particle matched with the hole that just covers it. This will produce a histogram of particle size distribution, from which a mean may be determined. Note that this method cannot be used if the particles are anisotropic.
公司管理相關推薦
鄂ICP備17016276號-1