Specialized bombardment techniques

4.7 Specialized bombardment techniques

4.7.1 Neutron diffraction

The advent of nuclear reactors stimulated the application of neutron diffraction to those problems of materials science which could not be solved satisfactorily by other diffraction techniques. In a conventional pile the fast neutrons produced by fission are slowed down by repeated collisions with

a ‘moderator’ of graphite or heavy water until they are slow enough to produce further fission. If

a collimator is inserted into the pile, some of these slow neutrons 9 will emerge from it in the form of a beam, and the equivalent wavelength λ of this neutron beam of energy E in electron-volts is given by λ = 0.0081/E. The equilibrium temperature in a pile is usually in the range 0–100 ◦

C, which corresponds to a peak energy of several hundredths of an electron-volt. The corresponding wavelength of the neutron beam is about 0.15 nm and, since this is very similar to the wavelength of X-rays, it is to be expected that thermal neutrons will be diffracted by crystals.

The properties of X-ray and neutron beams differ in many respects. The distribution of energy among the neutrons in the beam approximately follows the Maxwellian curve appropriate to the equilibrium temperature and, consequently, there is nothing which corresponds to characteristic radiation. The neutron beam is analogous to a beam of ‘white’ X-rays, and as a result it has to be monochromatized before it can be used in neutron crystallography. Then, because only about one in

10 3 of the neutrons in the originally weak collimated beam are reflected from the monochromator, it is necessary to employ very wide beams several inches in cross-section to achieve a sufficiently high counting rate on the boron trifluoride counter detector (photographic detection is possible but not generally useful). In consequence, neutron spectrometers, although similar in principle to X-ray diffractometers, have to be constructed on a massive scale.

Neutron beams do, however, have advantages over X-rays or electrons, and one of these is the extremely low absorption of thermal neutrons by most elements. Table 4.3 shows that, even in the most highly absorbent elements (e.g. lithium, boron, cadmium and gadolinium), the mass absorption coefficients are only of the same order as those for most elements for a comparable X-ray wavelength, and for other elements the neutron absorption is very much less indeed. This penetrative property of the neutron beam presents a wide scope for neutron crystallography, since the whole body of a specimen may be examined and not merely its surface. Problems concerned with preferred orientation, residual stresses, cavitation and structural defects are but a few of the possible applications, some of which are discussed more fully later.

Another difference concerns the intensity of scattering per atom, I a . For X-rays, where the scattering is by electrons, the intensity I a increases with atomic number and is proportional to the square of the atomic-form factor. For neutrons, where the scattering is chiefly by the nucleus, I a appears to be quite

9 These may be called ‘thermal’ neutrons because they are in thermal equilibrium with their surroundings.

Characterization and analysis 231 Table 4.3 X-ray and neutron mass absorption coefficients.

Element At. no.

Neutrons ( λ = 0.18 nm) Li

X-rays ( λ = 0.19 nm)

Table 4.4 Scattering amplitudes for X-rays and thermal neutrons. Element

At. no.

Scattering amplitudes × 10 −12 X-rays for sin θ/λ = 0.5

Neutrons ∗

H 1 0.02 −0.4 Li

3 0.28 Li 6 0.7 Li 7 −0.25

22 2.68 −0.38 Fe 26 3.27 Fe 56 1.0 Fe 57 0.23

0.59 Ag 47 6.71 Ag 107

∗ The negative sign indicates that the scattered and incident waves are in phase for certain isotopes and hence for certain elements. Usually the scattered wave from an atom is 180 ◦ out of phase with the incident wave.

unpredictable. The scattering power per atom varies not only apparently at random from atom to atom, but also from isotope to isotope of the same atom. Moreover, the nuclear component to the scattering does not decrease with increasing angle, as it does with X-rays, because the nucleus which causes the scattering is about 10 −12 mm in size compared with 10 −7 mm, which is the size of the electron cloud that scatters X-rays. Table 4.4 gives some of the scattering amplitudes for X-rays and thermal neutrons.

The fundamental difference in the origin of scattering between X-rays and neutrons affords a method of studying structures, such as hydrides and carbides, which contain both heavy and light

232 Physical Metallurgy and Advanced Materials Experimental

stations

Storage ring

10 15 Wiggler (center pole)

5 T field 10 13

Normal bending magnet 1.2 T field

Booster

(photons per second per mrad)

0.01 0.1 1.0 10 100 1000 Linac

Wavelength (nm)

(b) Figure 4.59 (a) Layout of SRS, Daresbury. (b) Wavelength spectrum of synchrotron radiation

(a)

(after Barnes, 1990, by permission of the Institute of Materials, Minerals and Mining). atoms. When X-rays are used, the weak intensity contributions of the light atoms are swamped by

those from the heavy atoms, but when neutrons are used, the scattering power of all atoms is roughly of the same order. Similarly, structures made up of atoms whose atomic numbers are nearly the same (e.g. iron and cobalt, or copper and zinc) can be studied more easily by using neutrons. This aspect is discussed later in relation to the behavior of ordered alloy phases.

The major contribution to the scattering power arises from the nuclear component, but there is also an electronic (magnetic spin) component to the scattering. This arises from the interaction between the magnetic moment of the neutron and any resultant magnetic moment which the atom might possess. As a result, the neutron diffraction pattern from paramagnetic materials, where the atomic moments are randomly directed (see Chapter 5), shows a broad diffuse background, due to incoherent (magnetic) scattering, superimposed on the sharp peaks which arise from coherent (nuclear) scattering. In ferromagnetic metals the atomic moments are in parallel alignment throughout

a domain, so that this cause of incoherent scattering is absent. In some materials (e.g. NiO or FeO) an alignment of the spins takes place, but in this case the magnetization directions of neighboring pairs of atoms in the structure are opposed and, in consequence, cancel each other out. For these materials, termed anti-ferromagnetic, there is no net spontaneous magnetization, and neutron diffraction is a necessary and important tool for investigating their behavior (see Chapter 5).

4.7.2 Synchrotron radiation studies

Very large electrical machines known as synchrotron radiation sources (SRS) provide a unique source of electromagnetic radiation for materials characterization. 10 Electrons from a hot cathode

10 In 1980, the world’s first totally radiation-dedicated SRS came into operation at Daresbury, England. Electrons are ‘stored’ in the main ring for 10–20 h, traversing its 96 m periphery more than 3 × 10 6 times per second.

Characterization and analysis 233 are accelerated in three stages by a linear accelerator (Linac), a booster synchrotron and an evacu-

ated storage ring (Figure 4.59a). As bunches of electrons travel around the periphery of the storage ring they attain energies of up to 2 GeV and velocities approaching that of light. At these relativistic velocities, electron mass becomes 4000 times greater than the rest mass. Dipole and quadrupole magnets constrain the bunches into an approximately circular orbit and, by accelerating them cen- tripetally, cause electromagnetic radiation to be produced. The spectrum of this synchrotron radiation is very wide, extending from short-wavelength (‘hard’) X-rays to the infrared range (Figure 4.59b).

A wiggler magnet produces a strong (5 tesla) field and can extend the spectrum to even shorter wavelengths. Compared with more orthodox sources of electromagnetic radiation, the synchrotron offers the advantages of very high intensity, short wavelengths, precise collimation of the beam and

a smooth, continuous spectrum. The high radiation intensity permits exposure times that are often several orders of magnitude shorter than those for comparable laboratory methods. The risk of beam damage to specimens by the flashes of radiation is accordingly lessened. Specimens of metals, ceram- ics, polymers, semiconductors, catalysts, etc. are placed in independent experimental stations located around the periphery of the ring chamber and irradiated in order to produce spectroscopic, diffraction or imaging effects.

In the technique known as extended X-ray absorption fine-structure spectroscopy (EXAFS), attention is directed to the small discontinuities on the higher-energy flank beyond each vertical, characteristic ‘edge’ which appears in a plot of mass absorption versus X-ray wavelength. These ‘fine structure’ (FS) features derive from interference effects between electron waves from excited atoms and waves back-scattered from surrounding atoms. Mathematical treatment (using a Fourier trans- form) of the EXAFS spectra yields a radial distribution plot of surrounding atomic density versus distance from the excited atom. By selecting the ‘edge’ for a particular type of atom/ion and studying its fine structure, it is thus possible to obtain information on its local environment and coordination.

This type of information is of great value in structural studies of materials, such as glasses, which only exhibit short-range order. For instance, the EXAFS technique has demonstrated that the network

structure of SiO 2 –Na 2 O–CaO glass is threaded by percolation channels of modifier (sodium) cations.

4.7.3 Secondary ion mass spectrometry (SIMS)

This important and rapidly developing technique, which enables material surfaces to be analyzed with great chemical sensitivity and excellent resolution in depth, is based upon the well-known phenomenon of sputtering. The target surface is bombarded with a focused beam of primary ions that has been accelerated with a potential of 1–30 kV within a high-vacuum chamber (10 −5 –10 −10 torr). These ions generate a series of collision cascades in a shallow surface layer, 0.5–5 nm deep, causing neutral atoms and, to a much smaller extent, secondary ions to be ejected (sputtered) from the specimen surface. Thus, a metallic oxide (MO) sample may act as a source of M, O, M + ,O + ,M − ,O − , MO + and MO − species. The secondary ions, which are thus either monatomic or clustered, positive or negative, are directed into a mass spectrometer (analyzer), wherein they are sorted and identified according to their mass/charge ratio. Exceptionally high elemental sensitivities, expressed in parts per million and even parts per billion, are achievable. All elements in the Periodic Table can be analyzed and it is possible to distinguish between individual isotopes. Studies of the self-diffusion of oxygen and nitrogen have been hindered because these light elements have no isotopes that can be used as

radioactive tracers. SIMS based on the stable isotope 18 O provides a rapid method for determining self-diffusion coefficients. The physical process whereby ions are ejected is difficult to express in rigorous theoretical terms; consequently, SIMS is usually semiquantitative, with dependence upon calibration with standard samples of known composition. SIMS is a valuable complement to other methods of surface analysis.

234 Physical Metallurgy and Advanced Materials The available range of beam diameter is 1 µm to several millimeters. Although various types of ion

beam are available (e.g. Ar − , 32 O + 2 , 16 O − , Cs + , etc.) positively charged beams are a common choice. However, if the sample is insulating, positive charge tends to accumulate in the bombarded region, changing the effective value of the beam voltage and degrading the quality of signals. One partial remedy, applicable at low beam voltages, is to ‘flood’ the ion-bombarded area with a high-intensity electron beam. In some variants of SIMS laser beams are used instead of ion beams.

Of the large and growing variety of methods covered by the term SIMS, the dynamic, static and imaging modes are especially useful. Materials being investigated include metals, ceramics, polymers, catalysts, semiconductors and composites. Dynamic SIMS, which uses a relatively high beam current, is an important method for determining the distribution and very low concentration of dopants in semiconductors. The beam scans a raster, 100–500 µm in size, and slowly erodes the surface of the sample. Secondary ions from the central region of the crater are analyzed to produce a precise depth profile of concentration. Static SIMS uses a much smaller beam current and the final spectra tend to be more informative, providing chemical data on the top few atomic layers of the sample surface. Little surface damage occurs and the method has been applied to polymers. The imaging version of SIMS has a resolution comparable to SEM and provides ‘maps’ that show the lateral distribution of elements at grain boundaries and precipitated particles and hydrogen segregation in alloys. Imaging SIMS has been applied to transverse sections through the complex scale layers which form when alloys are

exposed to hot oxidizing gases (e.g. O 2 , CO 2 ). Its sensitivity is greater than that obtainable with conventional EDX in SEM analysis and has provided a better understanding of growth mechanisms and the special role of trace elements such as yttrium.