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A Review of Materials Characterisation by Quantitative Microscopy

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Abstract:

Quantitative microscopy techniques for manually measuring parameters on light, scanning, and transmission electron microscope images are presented in this review. The numerical techniques contained in this paper are also employed in the algorithms of automated image analysers. Only the most important parameters are covered in detail and these are grain and particle sizes in addition to the volume fractions and mean free path of the microconstituents. Apart from metallic materials, some of the techniques which are described in this review can also be used for polymeric, ceramic and biological materials.

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International Journal of Engineering Research in Africa Vol. 4

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International Journal of Engineering Research in Africa (Volume 4)

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35-57

DOI:

https://doi.org/10.4028/www.scientific.net/JERA.4.35

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Online since:

May 2011

Authors:

C.C. Chama

Keywords:

Stereology, 2D Quantitative Analysis, Mechanical Property, Microstructure

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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[56] has been the most popular technique for determining the hardness and elastic moduli of thin films. The hardness was calculated from equation (IIIa). H=PmaxA (IIIa) where H = hardness, Pmax = maximum load observed during indentation and A = projected contact area between indenter and film. The contact area was calculated from a polynomial equation which is function of depth of penetration of the indenter into the film hc; the parameter hc is measured in the AFM. The hardness data determined from equation (IIIa) are shown in Table 2 for different values of hc and the average was 8. 40543 GPa. The standard deviation and variance for the hardness were 2. 0993 and 4. 4071, respectively. A 95% confidence interval, for example, can be determined for the average hardness in the following manner. H ±tα2SHn IIIb where H = average hardness, tα2 = t-distribution, SH = standard deviation and n = number of measurements. Equation (IIIb) is valid for n less than 30. Using the values shown above and n = 16, equation (IIIb) becomes 8. 40543 ±1. 1184 This gives a 95% confidence interval for the average hardness of 7. 28703 to 9. 52383 GPa. In the calculation of the Young's modulus, the following approach was adopted S=dPdh (IIIc) where S = stiffness and was determined from the load-displacement curve obtained in the AFM. Er=π2SA (IIId) where Er = reduced modulus. It has been shown that.

[56] 1Er=1-ν2E+1-νi2Ei (IIIe) where E = modulus of the specimen, Ei = indenter modulus, ν= Poisson's ratio of the specimen and νi = Poisson's ratio of the indenter. The elastic modulus of the diamond indenter Ei is taken as 1141 GPa and Poisson's ratio νi as 0. 07.

DOI: 10.1111/j.1744-7402.2010.02522.x

[56] The Poisson's ratio ν for the Cu-6at. %Ag film was assumed to be 0. 34. The only unknown quantity now is E and this can be calculated from equation (IIIe). The Young's moduli calculated for different penetration distances of indenter hc are shown in Table 2 and the average was 154. 5157 GPa. The standard deviation and variance for the Young's modulus hardness were 41. 3608 and 1710. 7151, respectively. A 95% confidence interval, for example, can be determined for the average Young's modulus by using equation (IIIb) and gives 154. 5157±22. 0350. This gives a 95% confidence interval for the average Young's modulus of 132. 4807 to 176. 5507 GPa. Although the AFM is not really a microscope for obtaining images as is the case with the optical microscope, SEM and TEM, it is a very useful tool for determining mechanical properties of thin films. This is achieved by utilizing its capability to very accurately measure indentation depths with corresponding loads during penetration. Apart from this, the AFM can be used to measure film roughness and grain size. Table 2. Hardness and Young's Modulus of the Cu-6at. %Ag Thin Film.