Linear decorations defining edges of an internal octahedron within a natural diamond: observations and an explanation

Linear decorations defining edges of an internal octahedron within a natural diamond: observations and an explanation

CRYSTAL GROWTH Journal of Crystal Growth 143 (1994) 46-57 ELSEVIER ______________________ Linear decorations defining edges of an internal octahedr...

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CRYSTAL GROWTH Journal of Crystal Growth 143 (1994) 46-57

ELSEVIER

______________________

Linear decorations defining edges of an internal octahedron within a natural diamond: observations and an explanation F.C. Frank b

a

J.w. Harris b

K. Kaneko

a

AR. Lang

a,*

‘H.H. Wills Physics Laboratory, University of Bristol, TyndallAvenue, Bristol BS8 I TL, UK Department of Geology and Applied Geology, University of Glasgow, Lilybank Gardens, Glasgow G12 8QQ, UK Received 14 April 1994; manuscript received in final form 21 June 1994

Abstract A 2.13 carat weight natural diamond, a slightly flattened octahedron with roughly-pitted surfaces, exhibits an internal framework of dense black “lines” located a short distance below the present surface. Most of the lines lie closely parallel to (110) and connect up to delineate edges of an octahedron concentric with and slightly smaller than the present body. The lines are agglomerations of thin black discs (thickness too small to be measured in situ by optical microscopy), diameters ranging from 1 to 40 ~m (but mainly in the 5 to 20 ~m range), equantly distributed on diamond (111), and consistent with graphite. Special optical techniques were developed for examining this specimen and they provided control of relative visibility of internal versus superficial features. Optical micrographs taken in all eight (111) directions are discussed. Synchrotron X-ray topography detected the internal linear framework with good contrast, and helpfully displayed spatial relations between its segments. Findings from eathodoluminescence topography are described. An explanation of the phenomenon is outlined. It proposes a sequence of pressure and temperature conditions and of resulting stresses between diamond and encasing solid matrix whereby graphitization was caused to occur locally along edges of an octahedron, which was subsequently enclosed by further diamond growth. Implications for the origin of the edge grooves frequently exhibited by diamond octahedra are suggested.

1. Introduction It can safely be assumed that natural diamonds crystallized within their field of thermodynamic stability, which lies on the higher-pressure, lower-temperature,side of the diamond-graphite phase boundary. The likely ranges of pressure and temperature of diamond formation can be

________

*

Corresponding author,

inferred by combining physical, geological and

mineralogical data (summarized in Ref. [1]). Crystallization occurred at a depth not less than about 150 km below the Earth’s surface (ambient pressure 5 GPa), and, for the majority of diamonds, a crystallization temperature not more than 200 to 400°Cbelow the diamond—graphite equilibrium line is envisaged (i.e. crystallization between 900 and 1200°C). It follows that if diamonds are warmed considerably above these temperatures (at constant pressure), or raised by a few tens of kilometres within the Earth, they will

0022-0248/94/107.00 © 1994 Elsevier Science By. All rights reserved SSDI 0022-0248(94)00409-F

F.C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

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pass into the graphite stability field. Under these conditions disintegration through graphitization will occur rapidly. This paper embraces the topic of diamond graphitization. However, it is not concerned with processes through which the whole diamond is transported out of the domain of its thermodynamic stability. Instead, it deals with interactions between the diamond and its environment that subject the former to non-hydrostatic stresses of such nature as to cause limited, highly localized graphitization. Despite the study material for this work being just a single and highly unusual diamond, it is believed that the observations and their proposed interpretation may hold the key to understanding a puzzling morphological feature widely exhibited by natural diamonds. The specimen studied was a rough-surfaced, rounded, slightly flattened octahedron of weight 2.13 carats (0.43 g). It came from an unknown African source. The overall distance between the two largest near-octahedral surfaces, an opposite pair, was 4.6 mm. They were indexed (111) and (111). The maximum overall distance between opposite rounded vertices was 7.5 mm. There was a uniform slightly grey body colour. Surface topography was unusual: the entire surface was scalloped by large, mutually contacting pits, diameters ranging mainly between 0.2 and 1.0 mm. The sloping sides of adjacent pits met in sharp ridges that had suffered severe abrasion. The remarkable visible feature exhibited by this specimen was an internal framework of dense black “lines” located a short distance below the present surface. Most of the lines lay closely parallel to <110) and connected up to delineate edges of an octahedron concentric with and slightly smaller • than the present body. Optical micrography was the method of study

expands upon the implications for natural diamond morphology.

of the black lines upon which most effort was expended. An account of micrographic techniques and observations is presented first, in Seetion 2. X-ray topography was informative; some findings therefrom are displayed in Section 3. Other techniques applied are described in Seetion 4. Then follows, in Section 5, a proposed reconstruction of the crystal’s growth history that explains the black lines. The concluding section

diamond was of cubic shape, edge length 10 mm. It was partly filled with fragments of MgO crystals to provide a bed for the specimen upon which it could be readily manipulated into the desired orientations, and which raised it so that only a minimum depth of fluid lay between it and the cover slip topping the cell. The refractive indices of MgO and CH212 match closely, rendering the immersed MgO fragments almost in-

2. Optical micrography

2.1. Techniques The optical requirements for satisfactory photomicrographic mapping of the black lines ineluded (1) low-magnification optics providing good depth of focus without undue sacrifice of resolution, (2) convenient means for orienting the specimen to give views along each of the eight <111> directions in turn, (3) illumination optimizing contrast of the black lines relative to the spatially highly variable scattering from the specimen surfaces, and (4) minimization of image perturbation by refraction at the specimen’s irregular surface. Control of the last item was the least effective: the immersion medium used, diiodomethane, ~D 1.74, went only part way towards matching the high refractive index of diamond, nD 2.42. More success attended achieving conditions (1) to (3), after lengthy cxperimentation. The special set-up assembled could serve for photographing interiors of any irregular-shaped and rough-surfaced crystal, so the contrivances adopted under headings (1) to (3) will be described. (1) A metallurgical microscope was modified to allow direct projection by a Macro-Nikkor f/4.5, 35 mm focal length lens on to 35 mm film. Low magnification, x 3.15, enabled the whole diamond image to be captured on one film frame. The lens had an internal iris: stopping down to f/5.6 gave increased depth of focus when needed. (2) The CH2 ~2 immersion cell containing the =

=

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F. C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

visible. Light scattering by the diamond-supporting bed was thereby substantially eliminated, (3) The side walls of the immersion cell were alternately clear and frosted, allowing choice of direct or diffuse illumination from a horizontally directed light beam when a dominantly silhouetting mode of illumination of the black lines was required. Alternatively (or in addition) illumination from above was provided by an annular 45° reflector interposed between lens and cell top. One or two fibre-optic illuminating probes fitted with condensing tips were used. One of these probes was mounted on a cross-slide working in a vertical plane that provided precise control of light source position horizontally and vertically, Photography through deep yellow Kodak-Wratten filter number 12 usefully reduced image impairments due to the high dispersion of diamond, Ilford Pan F black and white film was used. 2.2. Observations In Fig. 1 the specimen surface (simplified into that of a regular octahedron) is laid out to provide identification of the eight views normal to octahedral planes shown in Figs. 2a—2h. On the micrographs and in the associated text, the labelling A, A, B, etc., for vertices pointing respectively towards [100], [100], [0101, etc., is adopted as a convenient shorthand, which is useful also for identifying octahedron edges, i.e. AB denotes the edge corresponding to the black line that is horizontal in Fig. 2a. From the outset it should be noted that in many instances the black lines are actually of more uniform thickness and more closely parallel to <110) directions than appears in the optical micrographs; image disruption by refraction at surface scalloping is everywhere severe. For example, the black line BC in Fig. 2a is apparently “dislocated” in three places. This is unreal, the “dislocations” being purely artefacts due to refraction. (In addition to the large-scale surface pitting, there was also present everywhere a scaly or pig-skin-like roughening of the surfaces lining the pits, on a scale of 5—10 j~mtypically, that formed a further barrier to photography of sub-surface features.) Consider now some major facts about the in-

ternal lines. First, it appears that the internal octahedron delineated by them was flattened in a manner that reduced the distance between the (111) and (111) surfaces, similar to the flattening of the present overall external shape. The flattening produces a hexagonal rather than triangular periphery of the internal (111) face: it is an alternating hexagon having longer and shorter sides about 4 and 1 mm long, respectively. The ratio of these sides corresponds to the periphery of the surface (111) displaced inwards by 0.4 of the perpendicular distance between centroid and surfaces of the regular octahedron. In the views showing the three octahedral surfaces that contam one of the longer edges of the hexagonal figure bounding the (111) surface (Figs. 2a, 2c and 2e), the two short edges adjacent to the long edge can be seen dipping away from the observer, and going out of focus in consequence. A second major observation is that the octahedral framework is absent in the vicinity of vertex C. (This lack is very clearly displayed in the X-ray topographs, shown in Section 3.) It is also seen that major areas of three of the four faces that would, if triangularly bounded, meet in C, are in olo

001

100

(111)

(111)

a

c (111)

b 100

010 -

- -

010

001

g (II!) f

(111) •

h

S 001

010

Fig. 1. Key to indexing of octahedron surfaces viewed in photographs Figs. 2a—2h. The black dot in each triangle indicates the vertex that appears uppermost in Figs. 2a—2h.

F. C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

fact fully enclosed, having a fourth bounding line that gives them a periphery roughly trapezoidal. See Figs. 2d, 2g and 2h. Thirdly, the dissolution processes that have

C

~‘

a

produced the rounded and pitted present crystal shape have in some places exposed part of the octahedral framework. In the case of the (111) surface, Fig. 2g, the present surface is roughly

A

b

A

C

C

I~ ii

49

C

e

Fig. 2. Micrographs focusing on the internal octahedral framework. Specimen immersed in CH

7~C

fi

2 12 and illuminated as described in Section 2.1. Vertex notation explained in Section 2.2, e.g. A, ~, and B point towards [1001,[100] and [0101, respectively; and the octahedron surface with vertices A~C(a) is (111), etc. Magnification the same in all photographs: the scale is given by the lengths of sides of the equiangular triangle of black lines in (a), which is 4 mm.

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F. C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

tangential with the internal framework, and all edges of the latter bounding (111) are exposed. From these edges most of the black material has been removed; only a limited amount remains, consisting of matter still enclosed just below the present surface. Instead of the black material, one sees a dense band of small cracks in the ri~l~oc~a1~c5e a visible in Fig. 2g. Faces that share a <110) edge with (111) are outlined by a combination of lines of black matter with one line of crazing. Illumination that gives good contrast to black lines does not do so well for crazing. This accounts for the inferior visibility of edges parallel to BC in Fig. 2d, to AB in Fig. 2f and to AC in Fig. 2h. After allowing for image irregularities due to refraction, it is evident that the black lines maintam a noteworthy uniformity of cross-section. Under low magnification they appear as somewhat diffusely bounded opaque threads, mean diame-



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~ -

, *

~

.~

~

l

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Fig. 3. Micrograph at higher magnification showing individual black discs in the region on (111) arrowed in Fig. 2b. These discs lie 0.4 mm below the average level of the rough external surface of the specimen. Field width 0.67 mm, scale mark 50 tim. Microscope objective x25, 0.5 NA.

Fig. 4. Synchrotron X-ray topographs of the whole diamond, wavelength 0.09 nm, 111-type reflections, Bragg angle O~= 12.6°. Magnification 1.3 times that in the optical micrographs, Fig. 2. Crystal axis [011] vertical. View looking along diffracted beam towards crystal. Octahedron face (111) closest to observer. (a) Reflection 111, diffraction vector points to left, diffracted beam makes 19.5°+ 12.6°= 31.1°with [111].(b) Reflection 111, diffraction vector points to right, diffracted beam makes 19.5°—12.6°= 6.9° with [1111.

F.C. Frank et al. /Joumal of Crystal Growth 143 (1994) 46—57

ter about 200 ~m. Under higher magnification they are seen to be composed of dense agglomerations of small black discs. Excluding the domain that lies within about 1.5 mm from the predicted position of the C vertex of the internal octahedral framework, the parallelism of the framework with <110) directions is close. The principal exception is on (111), Fig. 2b, where the AB edge is incompletely delineated. It was on (111), in the locality where the dense black line that runs from the B corner into the face interior and then disintegrates (arrowed in Fig. 2b), that a field was found where fairly satisfactory micrographic images of individual black particles could be obtained. Fig. 3 shows a loosely clustered band of black discs in which a fair number rather larger than average disc size can be seen. Observed disc diameters range between 1 and 40 ~m. They lie in all {111} planes with apparently equal frequency. Discs lying on (111), (111) and (111) seen in Fig. 3 are ellipses with axial ratio equal to 3, which is sec 70.5°,as expected. The larger discs tend towards development of straight (110) segments in their peripheries. No measurements of disc thicknesses have been achieved: values less than 1 j.tm can be safely assumed.

(a)

51

3. X-ray topography A synchrotron radiation source is particularly effective for X-ray topographic assessment of diamonds having thicknesses like that of this specimen since it allows choice of the optimum wavelength, which in this case lies between those of available conventional sources, Mo Ka, A 0.07 nm, and Cu Ka, A 0.154 nm. (Use of too short a wavelength, while ensuring little absorption loss in the specimen, involves loss of resolution in the diffraction-contrast imaging of lattice defects because the dynamical diffraction extinction distances in the perfect-crystal matrix are inversely proportional to wavelength [21.)The topographs shown in Figs. 4a and 4b form a stereopair of the hkl, hkl type [21.The whole surface of the crystal contributes a background of diffraction contrast, displaying a mottled or flecked image texture arising from the peppering of the surface by abrasion damage. The internal linear framework stands out clearly. All the black lines photographed in Fig. 2 produced strong contrast. The lines that lie in (111), from which most black matter has been lost, still show with moderate contrast, which is attributable to the strain fields =

=

(b)

B

Fig. 5. Correspondence of lines of strong diffraction contrast in Figs. 4a and 4b with the visible internal (incomplete) octahedral framework. Heavily-drawn lines identify diffraction-contrast images of black lines lying in the (111) surface of the internal octahedron, those drawn thinly identify contrast from the lines of crazing lying in its (iii) surface. Lines of diffraction contrast that run between (111) and (111) are identified by arrowing directed towards the observer. Larger lettering identifies the nearer vertices. (a) Key to Fig. 4a. (b) Key to Fig. 4b.

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F. C. Frank et a!. /Journal of Crystal Growth 143 (1994) 46—57

associated with the multitude of small cracks visually observed. Fig. 4b provides a view of the specimen only 7° off normal to (111). Hence shapes of those parts of the internal framework that lie in (111) and (111) are negligibly distorted in this topograph. To match Figs. 4a and 4b with Fig. 2b, the optical micrograph needs to be rotated 60° anticlockwise in its own plane; and to match with Fig. 2g, the latter should be reflected right to left across a vertical line and then rotated 60° clockwise in its own plane. The effective stereo-optical convergence angle in pairs such as Figs. 4a and 4b is twice the Bragg angle 0B’ and in this pair 20B 25°.That is rather too high for comfortable stereoviewing, but it is possible to lock-on to 3D visualization when viewing the original X-ray plates at low magnification. The drawings Figs. 5a and Sb explain the spatial relations of the framework segments imaged in the topographs. It is fortunate for the visibility of the linear features that other contrast-producing imperfections within the crystal volume are quite restricted in spatial extent. They show up as two diffuse dark areas on the images of Figs. 4a and 4b. Both areas are less than 1 mm in diameter, One lies a little above the image centre, the other, which is somewhat sheet-like, is at centre level. No dislocations have been detected in X-ray topographs of this diamond, which appears to be a highly perfect crystal except in the vicinity of the defects revealed in Figs. 4a and 4b. There are some complexities in the images of the black lines not yet fully understood. However, the basic structure of these images can be understood on a geometrical-optical basis: strongest X-ray reflection comes from volume elements where the greatest long-range-correlated lattice curvature is produced by elastic deformation of the diamond matrix. The continuous spectrum of synchrotron radiation can enhance contrast arising from lattice bending compared with that recorded on X-ray topographs using conventional sources. In the latter, the standard strict collimation of the incident beam combined with the limited wavelength spread of the characteristic X-ray emission lines limits the angular range of misoriented crystal that can Bragg reflect at a given specimen

orientation setting to not more than about one arc minute, under the usual conditions for recording the 111 reflection from diamonds, With the present specimen, supplementary experiments with synchrotron radiation showed that in the images of the octahedral framework the synchrotron radiation topographs are recording significant diffracted intensity from volume elements misoriented up to about 2 arc mm away from the orientation of the perfect bulk of the crystal.

=

4. Other observations Diamonds are conventionally classified according to their optical properties, in particular their absorptions in the 7—20 ~m infrared range that depend upon the concentration and states of aggregation of the principal known impurity dcment in diamond, nitrogen. Though there was no reason to suspect that the phenomena reported here are related to nitrogen impurity content, it was important to check whether the infrared absorption spectrum of this unusual specimen presented exceptional characteristics. (Important features of the nitrogen-impurity-dependent infrared absorption spectra and their nomenclature are described by Woods [31and Clark, Collins and Woods [4]; and Evans [5] considers their geological implications.) The absorption spectrum of the present specimen turned out simply to be like that most commonly observed, falling in the classification type IaA/B and verging towards the limiting type IaA. Because of the relatively large specimen thickness, the absorption at the principal peak due to nitrogen in A-defect form, at 1282 cm~, was too high to be measurable, but the much weaker related peak at 500 cm could be easily measured, Referring the absorption at 500 cm’ to that due to the intrinsic diamond absorption at 2000 cm~ yielded an estimated absorption coefficient of 55 cm at the 1282 cm1 peak. Applying a weighted mean of recent determinations of the factor converting absorption coefficient at 1282 cm~ to concentration of nitrogen in A-defect form [6—8]gave 900 atomic -



F.C. Frank eta!. /Journal of Crystal Growth 143 (1994) 46—57

- .~‘

-~

Fig. 6. Cathodoluminenscence topograph of (Ill) face, onented similarly to Fig. 2g. Electron beam energy 30 kV, current density 2~sAmm . Direction of incidence of electron beam makes 30°with [iii], being tilted towards the right-hand vertex ~. Hence surface (111), on left, is not directly electron-irradiated, and is seen only by internally reflected and scattered light. On the other hand, for surfaces (111) upper right and (111) lower right the electron beam makes a smaller angle (~58 ) with their normals than the angle between their normals (~70.5°)and the viewing direction; this geometry enhances brightness of (111) and (111) relative to that of (iii).

ppm for that concentration. This is, of course, a mean value taken along a diameter of the crystal. The (111) surface was chosen for cathodoluminescence (CL) observations because it allowed comparison of material at the level of the (111) face defined by the octahedral framework with other material slightly further from the crystal centre. The technique of direct CL photomicrography applied was basically similar to that described by Lang and Meaden [9], but with the modification that the specimen surface was viewed via a mirror enabling the angle between specimen mean surface normal and the imaging electron beam to be reduced to 30° in order to cut down imaging artefacts due to electron beam shadowing in areas of high topographic relief [10]. In Fig. 6 high brightness arises from two distinct causes. First, internally trapped CL is strongly

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scattered out of the crystal towards the observer by all surface cracks and even by the abraded crests of the ridges between surface pits. Such scattering facilitates correlation of Fig. 6 with Fig. 2g. Second, this monochrome print emphasizes the extra luminosity where a green component is added to the overall deep blue CL that is characteristic of natural diamonds belonging to this specimen’s infrared spectral type. (The green component is easily differentiated from the blue background visually or by colour photography; Fig. 6 is an orthochromatic rephotograph of a colour print.) The extra overall brightness in the triangular field between vertex C and the curved band of cracking and pitting that forms the fourth side of the trapezoidal quadrilateral upper field arises principally from the addition of green CL, and such CL is also present along all the bands of cracking that bound the quadrilateral field. Both the triangular and quadrilateral fields exhibit a bnghtness pattern showing that layers parallel to (111) differing in CL intensity are intersected by the scalloped specimen surface. Consequently, within the ABC triangle, outcrops of these layers delineate contours of the external specimen surface relative to a (111) datum level. For example, the highest point lies within the crescent-shaped area of weak CL near the upper left corner of the generally bright triangular field containing C; but its height above the cracked surface exposed at the mid-point of the boundary between triangular and quadrilateral fields is only 150 ~m. The most likely origin of the localised green CL (indeed the only possible origin known to the authors) is alpha radiation damage of the diamond due to contact of its surface with a medium containing alpha-emitting components. Variationsof green-emission intensity in bands parallel to (111) could arise from three causes, acting singly or in combination: (1) variations of growth rate, (2) growth into a mobile medium not uniformly radioactive, and (3) dependence of the green emission upon concentration and state of aggregation of nitrogen impurity. It is believed that cause (3) is important, probably dominant: there appears to be some correlation of bands of stronger blue in the upper field with those of stronger green emission in the lower field. The

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F.C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

alpha radiation damage commonly observed in CL of diamonds is usually confined within a “skin”of thickness corresponding to the maximum range of alpha particles entering from outside the diamond surface, which is most frequently a post-growth solution surface, or is localised in haloes surrounding points or patches on the external surface; and radiation damage haloes surrounding inclusions of non-diamond minerals also occur [11]. In the case of the present specimen, the external surfaces of both the quadrilateral and triangular fields are identically scalloped, and can be assumed to have had similar post-growth exposures to a possibly-radioactive surrounding medium, Consequently, the absence of green CL in the quadrilateral field is unexpected. However, interpreting the distribution of green emission on a surface topographic basis is complicated by evidence that some green emission observed is photoluminescence rather than CL, and comes from depths below the surface greater than the electron penetration range, which is about 5 ~m. Observations of the specimen’s birefringence were greatly hampered by the rough surface. An internal source of birefringence appeared to correspond in position with the source of the diffuse patch of X-ray diffraction contrast seen above the image centre in Figs. 4a and 4b. Localized birefringence in diamond matrix surrounding the

black lines could not be recognised against the high background luminosity present. Birefringence associated with the octahedral framework was best in evidence within the bands of cracks exposed on (111). Conditions for Raman microspectroscopic probing of the black material were not propitious. The only locality where it could be certain that the argon-ion laser probing beam impinged on a black line was on the dense segment that runs from vertex B towards the (111) face centre, Fig. 2b. Here the black material lies on average about 400 ~m below the specimen surface. The sensitivity limit of the experiments performed was about 1% of the peak of the sharp diamond Raman line. So in view of the long probing beam trajectory within diamond, failure to detect other substance than diamond was not surprising.

5. Interpretation Although not yet verified from findings of microanalytical experiments, there can be little doubt from optical microscopic observations, as exemplified in Fig. 3, that the black discs are graphite; there is close similarity with those seen in other diamonds, where their graphite identity has been proven [12,13]. Here a history of the present specimen is proposed that can explain

Fig. 7. Stages in the growth history proposed. (a) The diamond, grown as a sharp-edged octahedron, has become completely encased in a solid matrix (shown by hatching). XY is a grain boundary in the encasing material, viewed edge-on, that wraps around diamond surfaces sharing vertex ~. (b) Encasing material shrinks relative to the diamond, by whose edges it is indented, producing short cracks (symbolized by little half-loops). Case-material also cracks where grain boundary XY meets diamond surfaces. (c) Local graphitization (symbolized by black discs) occurs within diamond in proximity to crack-openings in the surrounding case. (d) After removal of case-material, diamond overgrowth, forming a larger octahedron, encapsulates the linear agglomerations of graphite discs produced in stage (c). (e) The final stage: dissolution reduces the volume of the diamond, producing a roughly pitted surface. Graphite that has become exposed on surface (111) is dissolved away.

F.C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

how an octahedral framework of localised graphitization can be generated as a result of pressure (P) and temperature (T) changes acting on the diamond and a solid matrix encasing it. Although the model proposed involves variations of P and T, it is assumed that throughout its history the general ambient P and T conditions remain within the field of diamond stability. Initially, the diamond grows as an octahedron in a mainly fluid medium, and hence without mechanical constraints, so that all edges are sharp and straight, parallel to <110). Then, perhaps by reason of increase in P or decrease in T, non-diamond substance crystallizes to encase the whole diamond within a solid matrix, terminating diamond growth for the time being. This stage is shown schematically in Fig. 7a. The grain size of the encasing matrix is unknown, but to account for specific observations surrounding apex C of the specimen,it is suggested that a grain boundary in the matrix lies in a surface schematically shown edge-on along XY. Encasing material lying above and below XY in Fig. 7a may have different mechanical properties. A subsequent, further increase in P or decrease in T causes deviant stresses in the system diamond plus non-diamond case. It can be taken for granted that the compressibility and coefficient of thermal expansion of the non-diamond encasing material are both greater than they are for diamond, so that either of these changes shrinks the case on to the diamond. The mechanical implications of these changes are as follows. If the diamond were spherical,and the case also spherical or alternatively, whatever its shape, large compared with the diamond, the stress changes due to this shrinkage would be an isotropic increase of pressure in the diamond, assuming that elastic anisotropy may be neglected. In consequence there would be in the surrounding case an increase of radial compressive stress and decrease of tangential compressive stress. All principal stress components would remain compressive if pressure increase is the cause of shrinkage, and equally so if the cause is temperature decrease unless that decrease is particularly large. However, the diamond is not spherical, but a sharp-edged octahedron, This sharp edge will

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cause stress concentration by a factor of essentially unlimited magnitude at the edge of the elastic discontinuity. The situation will be similar to that for a rigid sharp-edged indenter pressed into an elastically softer material. The edge is a re-entrant one for the case-material. There will be enhancement, by an essentially unlimited factor, of the tensile stress change, in the casematerial, for a direction normal to the octahedral edge and to the radius. Stress in this direction will become tensile, even though P is large. This condition will extend for a short distance from the diamond, beyond which the general ambient compressive stress P will dominate. The consequence will be short cracks in the case-material extending outwards from each edge of the diamond. (Cracks might also occur at grain boundaries in the case-material where these boundaries meet the diamond surface). Once these cracks have formed, and opened to crack-openings of more than atomic dimensions, there is no radial compression on the diamond opposite the mouths of these cracks, so that the diamond close to an octahedron edge is undoubtedly thermodynamically unstable relative to graphitization (and presence of shear stresses is also likely to promote this conversion kinetically). The consequences should be formation of graphite along every salient edge of the diamond crystal, and on an octahedral surface where this meets a grainboundary crack in the case-material. These interactions between diamond and case are illustrated in Figs. 7b and 7c. In Fig. 7b cracking is depicted, outside the octahedron; Fig. 7c symbolizes the local graphitization, which occurs within the bounding surfaces of the octahedron. The representation separately of cracking and graphitization events is for clarity of illustration: it does not imply significant temporal separation. Circumstances that render vertex C and its surrounds different from the other vertices may be as follows. The case material below XY may deform plastically as well as by fracture, and plastic deformation within the volume more distant from XY may relieve stresses sufficiently to avoid fracturing along octahedron edges close to C. Alternatively, a parting of case-material over

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F.C. Frank et a!. /Journal of Crystal Growth 143 (1994) 46—57

the grain-boundary surface XY may take place, with similar stress-relieving effects that halt propagation of cracks towards C. These two happenings are not mutually exclusive. A parting on XY necessarily involves filling the space between the parted surfaces. This is most easily achieved by infiltration of fluid, which might introduce radioactive substance. (Recall the CL evidence for presence of radioactive substance in case-material close to octahedron edges, presumably infiltrated during the period of local pressure reduction t crc, As regards the black line that runs towards the (111) face centre from corner B, it is geometrically possible that this could mark the locus of an incursion on to (111) by a segment of the XY surface; or it could arise from a meeting with a different grain boundary. Passing on to the next stage in the history, it is supposed that probably by decrease of P or increase of T, or possibly by change in the chemistry of the environment, reversion back to conditions similar to those under which the diamond crystal formerly grew takes place: the non-diamond encasing material dissolves away and diamond crystallization resumes, enclosing the lines of graphite disc concentrations within a larger octahedral diamond (Fig. 7d). Finally, further environmental change causes the diamond surface to undergo dissolution, making a coarsely pitted and, grossly considered, more rounded diamond (this being consistent with the fact that almost all natural diamonds show signs of dissolution at the end of their growth history). This final, present state, is sketched in Fig. 7e. Dissolution, or perhaps cleavage parallel to (111), has exposed the lines of graphitization on (111). Most of the discs have been dissolved out, leaving the bands of cracking and small-scale pitting now seen.

6. Concluding remarks Although the majority of diamonds have undergone much rounding as a result of post-growth dissolution, often to the point where {111} faces have disappeared, the flat-faced octahedron is an important naturally occurring habit. Its octahe-

Fig. 8. Diamond octahedron, slightly rounded, with grooved edges.

dral surfaces may be bounded by a single sharp edge parallel to <110) (though inevitably mechanically damaged, as optical microscopy and X-ray topography make evident); or, in place of a single edge, a substantial re-entrant groove, usually coarsely stepped parallel to <110), may be seen. Fig. 8 (after Pough [141) is a standard drawing of this edge-grooved morphology. The magnitude of edge grooves far exceeds that which could arise from etching away mechanical damage on a single edge along <110). Edge grooves are not expected under conditions of diffusion-limited growth of a polyhedral crystal, when concentration gradients favour growth at edges. If arising from dissolution processes that act all over the crystal surface, the strong development of edge grooves is often out of proportion to the small scale of etch pit (tngon) development on {111} surfaces. Hence a reason for diminished resistance to removal of material in the vicinity of octahedral edges is sought. One such reason could be presence along those edges of linear concentrations of graphite discs, as illustrated above; however, it may well be thought that edge-grooved morphologies in natural diamonds are too common to be all interpreted in this way. The sequence of P and T conditions postulated to cause such local graphitization cannot be very rare, but preservation of the graphite within a diamond overgrowth may be freakish. Perhaps this study of one specimen, albeit a freak, can contribute towards understanding the morphology of many.

F. C. Frank et al. /Journal of Crystal Growth 143 (1994) 46—57

Acknowledgements Mr. Joe Sisey is thanked for bringing to the notice of the authors this unusual diamond, and the Diamond Trading Company are also thanked for the donation of this stone for scientific study. The Director and Staff of the SERC Daresbury Laboratory are thanked for the provision of cxperimental facilities, and the assistance of Mr. A.P.W. Makepeace, University of Bristol, and Dr. M. Moore, Royal Holloway, University of London, during the synchrotron X-ray topographic experiments is gratefully acknowledged.

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