Evaluation of true interlamellar spacing from microstructural observations
- PDF / 736,732 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 38 Downloads / 231 Views
Vilupanur A. Ravi Department of Chemical and Materials Engineering, California State Polytechnic University, Pomona, California 91768
G. Jeffrey Snydera) Materials Science, California Institute of Technology, Pasadena, California 91125 (Received 22 February 2008; accepted 19 June 2008)
A method for evaluating true interlamellar spacing from micrographs is proposed for a multidomained lamellar structure. The microstructure of these materials is assumed to be composed of many domains with the lamellae aligned roughly parallel to each other within each domain and with the domains themselves randomly oriented relative to one another. An explicit expression for the distribution of apparent interlamellar spacing is derived assuming that the distribution of the true interlamellar spacing is Gaussian. The average interlamellar spacing is close to the peak interlamellar spacing observed in the distribution. The theoretical distributions are compared with experimental ones obtained by analyzing micrographs of PbTe–Sb2Te3 lamellar composites.
I. INTRODUCTION
Studies on the microstructures of alloys continue to be crucial because of their significant effect on functional and structural properties in many cases. Alloys that have lamellar structures, e.g., pearlitic steel, are in practical use and have been studied extensively. Interlamellar spacing is an important attribute of such lamellar structures. It is therefore essential to quantify this microstructural feature. For this purpose, the analysis on micrographs such as scanning electron microscopic or optical microscopic images is the simplest and the most direct method. In the analysis of micrographs, it is important to note the fact that the interlamellar spacings in the micrographs are not the true spacings because the lamellae are not necessarily oriented perpendicular to the observation planes. If the microstructure in the sample is oriented in a particular direction, e.g., because it has been unidirectionally solidified, the true interlamellar spacing can be determined by a procedure proposed by Bansal,1 where micrographs on two sections for each lamellar domain are required. However, it is not realistic to use this method for samples that have microstructures with randomly oriented polydomains. For materials with polydomains, Pellisier et al.2 have derived the expression for the
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0308 2538
J. Mater. Res., Vol. 23, No. 9, Sep 2008
distributions of apparent interlamellar spacing in terms of the distribution of the angle between lamellae and the observation plane. Furthermore, since true interlamellar spacing itself is not constant in most cases, methods to determine the distribution of the true interlamellar spacing from the cumulative area have been developed by several workers.2–5 In these methods, the true interlamellar spacing within each domain was assumed to be constant; however, there could be a distribution of true interlamellar spacing within domains as well a
Data Loading...
