Depth of x-ray penetration

These circumstances naturally pose the following question what is the effective depth of x-ray penetration Or, stated in a more useful manner, to what depth of the specimen does the information in such a diffraction pattern apply This question has no precise answer because the intensity of the incident beam does not suddenly become zero at any one depth but rather decreases exponentially with distance below the surface. However, we can obtain an answer which, although not precise, is at least useful, in the following way. Equation (4-14) gives the integrated intensity diffracted by an infinitesimally thin layer located at a depth x below the surface as 

This expression permits us to calculate the fraction of the total diffracted intensity which is contributed by a surface layer of depth x. If we arbitrarily decide that a contribution from this surface layer of 95 percent (or 99 or 99.9 percent) of the total is enough so that we can ignore the contribution from the material below that layer, then x is the effective depth of penetration. We then know that the 

Equation (9-4) can be put into the following form, which is more suitable for calculation  

Values of corresponding to various assumed values of are given in Table 9-1. 

Preferred orientation is not confined to metallurgical products. It also exists in rocks, ceramics, and in both natural and artificial polymeric fibers and sheets. In fact, preferred orientation is generally the rule, not the exception, and the preparation of an aggregate with completely random crystal orientations is a difficult matter. 

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For given values of B and n, which results in a greater effective depth of x-ray penetration, a back-reflection pinhole camera or a diffractometer ... 

Due to the low penetration depth of X-rays in heavy element samples, XRD patterns are not always significant for the structure of the bulk. In analogy to observations made on rare earth metal foils, fee phases observed occasionally after heating and interpreted as high temperature phases of the actinide metals, might be the product of a reaction between the metal surface and residual gas leading, e.g. to hydride etc. 

Different wavelengths are reflected at different depths. An x-ray penetrates the stack of layers until it arrives at the depth where the period resonates with its wavelength and angle. In this manner, a very broad band of reflection can be obtained, therefore, we call the reflectors extremely broad band or EBB multilayers. This system is not as critically dependent as the uniform period multilayer upon adhering to the optimum prescription of thickness versus depth. They were originally conceived for the reflection of slow neutrons (Mezei, 1976, and Mezd and Dalgleish, 1977). Christensen... 

In addition, by using glancing angles of incidence, the penetration depth of X-rays can be limited and the detection of a surface signal facilitated. 

Xps is a surface sensitive technique as opposed to a bulk technique because electrons caimot travel very far in soHds without undergoing energy loss. Thus, even though the incident x-rays penetrate the sample up to relatively large depths, the depth from which the electron information is obtained is limited by the "escape depth" of the photoemitted electrons. This surface sensitivity of xps is quantitatively defined by the inelastic mean free path parameter which is given the symbol X. This parameter is defined to be the distance an electron travels before engaging in an interaction in which it experiences an energy loss. 

The X-ray penetration depth in a material depends on the angle of incidence. It increases from a few tens of A near the total reflection region to several jim at large... 

Another major difference between the use of X rays and neutrons used as solid state probes is the difference in their penetration depths. This is illustrated by the thickness of materials required to reduce the intensity of a beam by 50%. For an aluminum absorber and wavelengths of about 1.5 A (a common laboratory X-ray wavelength), the figures are 0.02 mm for X rays and 55 mm for neutrons. An obvious consequence of the difference in absorbance is the depth of analysis of bulk materials. X-ray diffraction analysis of materials thicker than 20—50 pm will yield results that are severely surface weighted unless special conditions are employed, whereas internal characteristics of physically large pieces are routinely probed with neutrons. The greater penetration of neutrons also allows one to use thick ancillary devices, such as furnaces or pressure cells, without seriously affecting the quality of diffraction data. Thick-walled devices will absorb most of the X-ray flux, while neutron fluxes hardly will be affected. For this reason, neutron diffraction is better suited than X-ray diffraction for in-situ studies. 

Fig. 4.31. Variation of the coefficient of reflection and penetration depth for X-rays of 1.5405 A incident on a perfectly flat silicon surface.

The differences between x-ray and electron excitation must obviously stem from differences in the interaction of x-rays (1.11) and of electrons (1.4) with matter. Electrons are retarded rather quickly when they strike a sample, and they lose much of their energy in classical collision processes (4.1). Because electrons transfer their energy so rapidly, the critical thickness (Equation 6-8) for electron excitation is very much less than we saw it to be for x-ray excitation a.calculation based on experiments on a variety of materials53 gives 1CT3 cm (105 A) as a good value for the depth to which 50-kv electrons penetrate aluminum, and bears out the previous statement. Because the energy of every electron decreases as it penetrates, the x-ray excited by any electron will be of... 

The discussion just concluded is largely implicit in the earlier discussion of the excitation of a continuous x-ray spectrum by electron bombardment (4.1). Note that x-rays behave differently when they are used for excitation. An x-ray penetrates with little or no loss of energj" until it is absorbed, and it is the more likely to penetrate to greater depth (in regions of continuous abiorption) the greater its energy (or shorter its wavelength). 

The spatial resolution in quantitative analysis is defined by how large a particle must be to obtain the required analytical accuracy, and this depends upon the spatial distribution of X-ray production in the analysed region. The volume under the incident electron beam which emits characteristic X-rays for analysis is known as the interaction volume. The shape of the interaction volume depends on the energy of the incident electrons and the atomic number of the specimen, it is roughly spherical, as shown in Figure 5.7, with the lateral spread of the electron beam increasing with the depth of penetration. 

The spatial resolution of X-ray analysis carried out in the EPMA is limited to the size of the sampling volume, which is around 1 pm3. There may be many important features of a specimen which are smaller than 1 pm, and one way of overcoming the problem is by the use of thin specimens. We have seen (Figure 5.7) that the lateral spread of the electron beam increases with depth of penetration, so that in a sufficiently thin specimen the beam spread is much less. We will therefore next consider the analysis of thin foil specimens in the TEM. 

In practice, the application of x-ray measurement techniques to thin films involves some special problems. Typical films are much thinner than the penetration depth of commonly used x-rays, so the diffracted intensity is much lower than that from bulk materials. Thin films are often strongly textured this, on the other hand, results in improved intensity for suitable experimental conditions but complicates the measurement problem. Measurements at other than ambient temperature, not usually attempted with bulk materials, constitutes additional complexity. Since typical strains are on the order of 1 X 10 , measurements of interplanar spacing with a precision of the order of 1 X 10 are needed for reasonably accurate results hence, potential sources of error must be kept to a low level. In particular, the sample displacement error can be a major source of difficulty with a heated sample. The sample surface must remain accurately on the axis of the instrument during heating. 

X-ray fluorescence is a rapid and low-cost method that can be performed on solid samples. However, the depth of penetration of X-rays in most solid samples is relatively shallow. High-precision XRF on geological samples such as obsidian requires preparation of homogeneous, powdered samples pressed into pellet form. If some loss of precision and accuracy due to irregular size, shape, and thickness of samples is acceptable, obsidian specimens can be analyzed non-destructively. Samples smaller than 1 cm in diameter or with element concentrations less than 5 ppm are generally not suitable for XRF. XRF can determine about 10-15 elements in obsidian (K, Ti, Mn, Fe, Zn, Ga, Rb, Sr, Y, Zr, Nb, Pb, and Th). Fortunately, many of the measurable elements are the incompatible elements which provide discrimination between sources. 

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