Home Search Collections Journals About Contact us My IOPscience Imaging diamond with x-rays This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2009 J. Phys.: Condens. Matter 21 364217 (http://iopscience.iop.org/0953-8984/21/36/364217) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 129.49.56.80 The article was downloaded on 30/06/2010 at 16:59 Please note that terms and conditions apply. IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 21 (2009) 364217 (15pp) doi:10.1088/0953-8984/21/36/364217 Imaging diamond with x-rays Moreton Moore Department of Physics, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK E-mail: [email protected] Received 5 April 2009 Published 19 August 2009 Online at stacks.iop.org/JPhysCM/21/364217 Abstract The various techniques for imaging diamonds with x-rays are discussed: x-radiography, x-ray phase-contrast imaging, x-ray topography, x-ray reciprocal-space mapping, x-ray microscopy; together with the characterization of the crystal defects which these techniques reveal. 1. Introduction may also be sharp characteristic peaks superimposed upon the continuous spectrum, characteristic of the target material. X-rays may be used to image whole diamonds, or selected These come from the brief promotion of electrons dislodged regions, by radiography or by using various techniques from target atoms to discrete higher energies. These (or other) employing a Bragg reflection for x-ray diffraction contrast. electrons drop back to their original energies and, in so doing, The x-rays may be chosen to be parallel or divergent, to have emit x-rays of a particular energy (or particular wavelength). a broad range of wavelengths or to be monochromatic. They Kα radiation arises from electrons dropping back to the K-shell may be produced from conventional metal targets or from a from the L-shell; and Kβ radiation from those transferring synchrotron. The various possibilities are discussed in this between the M- and K-shells. There are only a few such review. allowed transitions (grouped into series) associated with each elemental metal and they give rise to very intense narrow peaks 2. X-rays (often called ‘lines’) in the spectrum. The Kβ radiation may be filtered out by a thin metal foil (such as 20 μmofNifor It is well known that x-rays are a form of electromagnetic Cu Kβ, or 100 μmofZrforMoKβ) which halves the intensity radiation of short wavelength, discovered by Wilhelm of Kα but reduces the Kβ to less than 1%. Such radiation is not Roentgen in 1895. Their wavelengths span a wide range, which exactly monochromatic but it is nevertheless useful for many may be sub-divided (somewhat arbitrarily) into hard x-rays of simple applications. To achieve monochromatic radiation, one approximately 0.01–0.1 nm and soft x-rays of 0.1–10.0 nm. or more Bragg reflections from crystals are employed. The angstrom unit is still in popular use: 1 A˚ = 0.1nm = Synchrotron radiation is a continuous electromagnetic 10−10 m. These wavelengths correspond to energies (in kilo- spectrum extending from x-rays, through ultra-violet, the electron-volts, E = hc/λ, h = Planck’s constant, c = velocity narrow visible range, infrared and beyond to radio waves. By of light) of 124–12.4 keV for hard x-rays; and 12.4–0.124 keV analogy with the visible spectrum of many colours, a broad for soft x-rays. The range for soft x-rays (a factor of 100) continuous range of x-rays is called ‘white’, in distinction from is thus ten times as wide as that for hard x-rays (a factor of ‘monochromatic’. This radiation is produced by accelerating 10), but it should be emphasized that these are just convenient charged particles (usually electrons) at speeds close to the numbers and are open to further discussion. speed of light on a curved path in a magnetic field. The X-rays may be produced by accelerating electrons, of radiation is emitted mainly in the forwards direction within a energies in the above ranges, towards a metal target (positive very narrow cone of angle typically a fraction of a milliradian. electrode). The abrupt stoppage of electrons by the atoms in the The angle is approximately mc2/E,wherem is the rest mass target converts these high energies into the emission of x-rays. of the electron and mc2 = 0.511 MeV. Thus, for an electron The spectrum is broad, but with a sharp cut-off at the short energy E = 2 GeV, this angle is 0.25 mrad, (equivalent to a wavelength end, corresponding to the accelerating voltage vertical height of 10 mm at a distance of 40 m). The magnetic applied. This radiation is sometimes called Bremsstrahlung fields may simply turn the electrons through a gently curved (breaking radiation). The metal target may be static, as in path (from a bending magnet) or cause the electrons to move a sealed x-ray tube; or moving, as in a rotating-anode x-ray through paths of smaller radius of curvature (from wigglers and generator. In addition, at sufficiently high voltages, there undulators) [1]. 0953-8984/09/364217+15$30.00 1 © 2009 IOP Publishing Ltd Printed in the UK J. Phys.: Condens. Matter 21 (2009) 364217 M Moore Table 1. Transmission of x-rays of various wavelengths through diamond. (Note: the wavelengths (λ) of four characteristic Kα emissions from silver, molybdenum, copper and chromium are given. Values for the mass absorption coefficient (μ) are listed for these wavelengths together with two popular wavelengths from synchrotron radiation. (ρ is the density of diamond.) The transmission of such x-rays through various thicknesses (t) of diamond are given in the lower four rows.) Radiation Ag Kα Mo Kα Synch.rad. Cu Kα Synch.rad. Cr Kα λ (nm) 0.056 0.071 0.100 0.154 0.200 0.229 Energy (keV) 22.1 17.4 12.4 8.04 6.20 5.41 μ/ρ (cm2 g−1) 0.374 0.576 1.32 4.51 9.86 15.0 μ (cm−1) 1.315 2.025 4.640 15.85 34.66 52.73 t = 0.3 mm 0.96 0.94 0.87 0.62 0.35 0.21 t = 1.0 mm 0.88 0.82 0.63 0.20 0.031 5.1 × 10−3 t = 3.0 mm 0.67 0.54 0.25 8.6 × 10−3 3.1 × 10−5 1.4 × 10−7 t = 10.0 mm 0.27 0.13 9.7 × 10−3 1.3 × 10−7 8.9 × 10−16 1.3 × 10−23 At an experimental station designed for hard x-rays, the transmission I/I0 for various thicknesses of diamond, taking radiation usually emerges from a beryllium window on the end the density ρ of diamond as 3.515 g cm−3 and values of μ/ρ of an evacuated beam-pipe; and therefore a long wavelength from [3]. One can see that it does not take much diamond to limit of 0.25 nm is set both by the window material and absorb the less energetic x-rays. One millimetre of diamond by absorption in air thereafter. The spectrum on the short transmits just one-fifth of Cu Kα radiation but only a half of wavelength side of maximum intensity falls off steeply. The one per cent of Cr Kα radiation. useful wavelength range from a bending magnet extends from X-rays are also absorbed in air. Ten centimetres of air about 0.05 to 0.25 nm, giving a factor of 5 in wavelength. A transmits 99% of Mo Kα and 89% of Cu Kα, but only 68% wiggler magnet makes the electron-beam curve more sharply of Cr Kα. One metre of air transmits 90% of Mo Kα, 31% of and the entire x-ray spectrum is shifted to shorter wavelengths: Cu Kα and only 2% of Cr Kα radiation. the range is increased to approximately 0.01–0.25 nm: (a factor Radiography usually employs a divergent beam from of 25). a small distant source. For the best resolution and least There are many advantages of synchrotron radiation [2] distortion, the specimen is placed close to, or in contact with, as will be discussed later. Apart from the wide range of x- the photographic film. Sometimes cracks in gem diamonds are ray energies (wavelengths) available, the narrow divergence filled with an optically transparent material of high refractive (excellent collimation), the high intensity (giving short index (such as lead glass or silicone oil) but which is more exposure times), the linear polarization and the pulsed time absorbent to x-rays than the diamond. X-radiography can structure are all useful for particular experiments. And as far as therefore be used to reveal such filled cracks, especially if diamond is concerned, radiation damage is not usually evident several different views are taken with x-rays of low energy. in the relatively short exposure times used for imaging. 4. X-ray phase-contrast imaging 3. Radiography: x-ray absorption When a specimen, such as diamond, is made of light elements The iconic x-ray image of the hand of Roentgen’s wife is (Z 8), it hardly absorbs x-rays of wavelength of, say, certainly the earliest x-ray picture of rings, but it is probably 0.15 nm (energy 8 keV); so conventional radiography is rather not the earliest such picture of a diamond.