Diamonds are formed at depths of 200 km or more inside the earth, and often contain inclusions of other minerals. The chemistry and crystal structure of these mineral inclusions are of great interest to earth scientists, since they represent the deepest samples available of the earth's interior.
Some diamonds are transparent, and optical microscopy can be used to locate and identify mineral inclusions in such diamonds. However, many diamonds are opaque, and the goal of these experiments was to see if x-ray microtomography could be used to locate mineral inclusions in such opaque diamonds. After locating such inclusions, the goal would be to study their crystal structures using x-ray diffraction. The inclusions would not be removed from the diamonds for such studies, but rather the diffraction data would be collected with the inclusion in-situ.
The samples were provided by Dr. John Parise of SUNY Stony Brook. Four diamonds were studied, two transparent and two opaque.
For each diamond below there are two transmission x-ray images, which have been corrected for dark current and flat field, and are displayed on a logarithmic intensity scale. The full data set for each crystal consists of 360 such images, collected from 0 degrees to 179.5 degrees in 0.5 degree steps. The tomographic reconstructions are done using filtered backprojection for all of the angles in a given row. Ring artifacts (due to detector driftt, detector non-linearity, or higher harmonic x-ray energies in the beam) have been reduced with a low-pass filter.
The pixel size in each image is about 6 microns, and this appears to be close to the true spatial resolution. With a different microscope objective (and more computer power!) images with resolutions down to 1 or 2 microns are almost certainly feasible.
Diamond 1 This a large transparent, facetted crystal. There is a single large inclusion near the top of the diamond, which is clearly visible both optically and in the transmission radiographs below.
|View 2. 1 degree rotation. The large inclusion near the top and the facetted nature of the crystal are clearly seen.|
|View 90. 45 degree rotation|
|Slice 96. This is a tomographic reconstruction of row 96 in the above images. The location and size of the inclusion within the diamond are clear, as well as the fact that there is only a single inclusion in this plane.|
Diamond 2 is a large opaque crystal. The crystal appears black in the optical microscope and it is not possible to see any inclusions in it with visible light.
|View 0. 0 degree rotation. A group of inclusions of various sizes can be clearly seen in the lower left part of the sample in this view.|
|View 180. 90 degree rotation. The inclusions have rotated closer to the center of the image in this view.|
|Slice 213. This is a tomographic reconstruction of row 213 in the above images. A highly absorbing inclusion is seen on the left side of the diamond in this plane. The embayed shape of the crystal is clear, as are voids (or fluid inclusions?) on the lower edge of the image. A 3-d reconstruction of this data set would be very helpful for determining whether these apparent voids connect to the exterior of the crystal, or are enclosed voids or inclusions.|
|Slice 264. This is a tomographic reconstruction of row 264 in the above images. Two highly absorbing inclusions are seen on the left side of the diamond in this plane. Again, several voids or fluid inclusions are seen, and some are quite small.|
Diamond 3 is a small roughly spherical opaque crystal. In the optical microscope it is not possible to see any inclusions in this sample.
|View 90. 45 degree rotation. A set of inclusions is clearly seen near the center of the crystal in this view.|
|View 270. 135 degree rotation. The inclusions are also near the center of the image in this view.|
|Slice 140. This is a tomographic reconstruction of row 140 in the above images. A single small highly absorbing inclusions is seen near the center of the diamond. A void or fluid inclusion is seen on the left, and an intermediate absorption inclusion is seen just above the center. It appears that cracks have propagated through the crystal through each of the inclusions, probably because of strain localization around them.|
|Slice 190. This is a tomographic reconstruction of row 190 in the above images. A single small highly absorbing inclusions is seen near the center of the diamond. Again, it appears that cracks have propagated through the crystal through this inclusion. One puzzle is that the cracks are dark in these images, which implies a higher absorption than the surrounding diamond. This means that the cracks might be filled with a higher atomic number material than diamond. Another possibility is that this is an x-ray optics refraction effect similar to the apparent rims around the crystals discussed below.|
Diamond 4 is a small transparent prismatic crystal, about 1.5x3x5mm in size.
|View 90. 45 degree rotation. The prismatic shape of the crystal is clear, as is the rough (broken?) top surface. A number of very small inclusions are visible throughout the crystal. The large dark area at the bottom of the image is a contaminant in the wax used to mount the crystal.|
|View 270. 135 degree rotation. The small inclusions are again visible throughout the crystal.|
|Slice 189. This is a tomographic reconstruction of row 189 in the above images. A medium sized, absorbing inclusions is seen near the lower right of the diamond.|
|Slice 308. This is a tomographic reconstruction of row 189 in the above images. A very small, highly absorbing inclusion is seen near the right center of the diamond. A set of cracks or planar inclusions is also visible.|
These diamonds are of course, single crystals, and we are illuminating them with monochromatic x-rays. One might expect to observe x-ray diffraction when collecting these tomographic data, which would be manifested by the crystal becoming completely dark when it diffracted the incident beam in a direction away from the detector. However, diamond has a simple crystal structure, and thus relatively few diffraction planes. If the diamonds are unstrained then their rocking curves will be only a few arcseconds wide. Since we are collecting only 360 static images at 0.5 degree spacing, the probability of the crystal being in the diffraction condition is very low. However, in each diamond we have observed images like the the following:
|Diamond 3, view 1. This is a view of diamond 3 at a rotation angle of 0.5 degrees.|
|Diamond 3, view 0. This is a view of diamond 3 at a rotation angle of 0 degrees, or only -0.5 degrees from view 1 above. Note the apparently planar regions of very low x-ray intensity.|
|Diamond 1, view 44. This is a view of diamond 1 at a rotation angle of 22 degrees.|
|Diamond 1, view 43. This is a view of diamond 1 at a rotation angle of 21.5 degrees, or only -0.5 degrees from view 44 above. Note the irregularly shaped regions of very low x-ray intensity.|
Our current interpretation of the low-intensity features in the above images is that they are the result of x-ray diffraction. The entire crystal is not in the Bragg diffraction condition, but there are locally strained regions which are. These strained regions have either slightly different lattice constants or slightly different orientations from the bulk diamond. An alternative explanation could be planar regions of a polycrystalline material, such a graphite, which has a distinct preferred orientation. At certain orientations these graphite crystals are in the diffraction condition. This latter explanation seems unlikely since these features are observed even in optically very clear diamonds.
In the four diamonds which we have examined so far these diffraction features are observed in perhaps 10% of the images. Fortunately the diffraction does not introduce serious artifacts into the tomographic reconstructions.
X-rays behave differently from visible light, because their velocity in solids is actually greater than their velocity in vacuum or air. The refractive index of solids is thus less than 1 for x-rays, and when x-rays strike a solid-air interface they are refracted into the air, rather than into the solid, as is the case for visible light. X-ray refraction is normally difficult to observe, because the refraction angles are very small, and the source-size for laboratory x-ray sources is quite large. However, with these synchrotron imaging experiments, with a high resolution detector, we are clearly observing x-ray refraction, or phase contrast. This is seen in the following images.
|Diamond 3, view 270. Note that immediately outside the crystal the x-ray intensity is higher than in the surrounding air. The increase in intensity is about 10%, and the thickness of the bright halo is about 15 microns. The distance from the sample to the phosphor screen was about 175 mm. This implies a refraction angle of roughly 100 microradians.|
|Diamond 3, slice 190. The refraction the above
image causes the reconstructed slice to have a bright ring around it, with another shell
inside that of lower intensity. The object thus appears to have a rim of higher
absorption, because the x-rays which should have been transmitted directly through that
outer layer have instead been refracted into the surrounding air. While this is an
undesirable artifact for a pure absorption tomogram, this phase contrast can be
employed to good effect to image surfaces between materials with very little
absorption contrast. In particular, researchers at the ESRF have used phase
contrast tomography to image small biological samples with high-energy x-rays where the
absorption is very low.
One can control the amount of phase contrast in the image simply by choosing where the phosphor screen is placed relative to the sample. If the screen is placed very close to the sample then the refraction/phase contrast will be small, because the separation of the direct and refracted beam will be small. If the phosphor screen is placed far from the sample then the phase contrast will be greatly enhanced.