Observation of Defects in Crystalline Polymers by HREM
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cient to obtain information about molecular packing. "Lattice imaging" refers to the contrast in high-resolution micrographs that develops due to the interaction of the incident wave with the crystalline "lattice" structure of the sample. The resulting image contains "fringes" due to regular spacings between molecules. Lattice images are the real space equivalent of diffraction peaks in scattering methods. However, imaging techniques are more powerful scattering methods because they retain information about the size, shape, and relative orientation of crystalline domains. Thus, high-resolution imaging is important for the study of defects and the specific arrangement of these crystalline domains. The fundamentals of contrast development and other practical considerations of HREM imaging have been detailed elsewhere.2"4 We will outline the essentials of the transfer theory of the imaging to emphasize that details in HREM images must be interpreted cautiously. History has shown that an improper understanding of high-resolution imaging can lead to interpreting anomalous features in electron micrographs as some sort of "fine structure" in the specimen, when these features can be explained as defocus artifacts.56 A schematic of the HREM imaging process is shown in Figure 1. We are interested in information about the threedimensional structure of the sample, represented as some characteristic of its wave function 4>(xl,x2,x3,t) where
(x-[,x2lx3,t) is a vector in four-space. In structural studies it is usual to consider the structure to be independent of time, (x},x2,x3). Radiation damage will cause changes to as f increases, but usually the primary interest is the undamaged specimen structure (xux2,x3). In order to reconstruct (j>(xl,x2,x3) from I(xux2) two problems must be solved. First, it is necessary to determine how the structure scatters the incident electron wave to give rise to an exit wave ifie. Then, it is necessary to know the effect of the microscope on taking this exit wave and producing an image wave i|/,. The effect of the microscope on the exit wave of the sample is represented as a mapping between the intensity of frequencies k in the Fourier transform of the exit wave ifje and those in the Fourier transform
0L
(j)Cf)
{•T Incident Wave
Sample
Exit Wave
— *i
VTA
Image
Objective Lens Figure 1. Schematic of the HREM imaging process. MRS BULLETIN, NOVEMBER 16/DECEMBER 31, 1987, PAGE 27
of the image wave i//,. This mapping function is known as the transfer function of the microscope. Ideally, it would be best to have a transfer function T = 1.0 for all frequencies; then the intensity in the image could be directly related to the intensity of frequencies in the exit wave. However, T is actually a sensitive function of the optics of the microscope and varies substantially from unity. Indeed, T can even be zero or negative, meaning that some frequencies might be completely lost and some passed in reverse contrast. The functional form of T in the weak phase object approximation is: T = sin X(k) D^k) D
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