Phase shifting interferometry of growth patterns on the octahedral faces of natural diamonds

Journal of Crystal Growth 119 (1992) 177—194 North-Holland

o~o~

CRYSTAL GROWTH

Phase shifting interferometry of growth patterns on the octahedral faces of natural diamonds W.J.P.

van Enckevort

Drukker International BV~Be~ersestraat20, 5431 SH Cuijk, Netherlands Received 6 December 1991; manuscript received in final form 17 January 1992

Phase shifting interferometry, a relatively new method for quantitative mapping of surface height profiles, has been applied to investigate the original growth patterns on the {111) faces of natural diamond. To avoid interference from post-growth etching phenomena, the specimen crystals were selected for the absence of dissolution features such as surface trigons and rounded edges between adjacent facets. Two types of growth features were encountered. The first were shallow growth hillocks, presumably related to dislocations. Below the growth surfaces, at a depth of a few micrometres, cathodoluminescence topography revealed trigonal patterns related to the hillocks. These patterns are a result of a difference in impurity uptake by growth steps of different Orientations which advance at different velocities. Secondly, steep hillocks, emitting extended, trigonal step patterns were found. The (flat) summits of these elevations are characterized by a difference in surface morphology and impurity content, which is indicative of fluid—fluid—solid growth via a different phase on top of the hillocks. Finally, step bunching phenomena, leading to the formation of macro-steps are described.

1. Introduction To obtain an insight into the formation history of natural diamond, several approaches have in the past been pursued in-depth. Information on the chemical environment, temperature, pressure and time of diamond growth has been obtained from inclusion studies [1] and from the investigation of xenocrystals coexisting with diamond in kimberlite rocks [21.Knowledge of the history and mechanism of crystal growth was obtained from defect studies using spectroscopic [3] and several topographic techniques [4—6]. A very powerful method for studying crystal growth processes is surface topography with the help of phase sensitive optical microscopy [7]. Until the beginning of the seventies, Tolansky and co-workers [8,9] examined the surfaces of numerous diamonds by means of multiple beam interferometry. Although often misinterpreted as being “as-grown”, their work was mainly confined 0022-0248/92/$05.OO © 1992

—

to post-growth dissolution phenomena [10]. Since practically all diamonds were corroded to some extent during their ascent to the earth’s surface, only little work was done on the microtopography of unaffected diamond faces. Examples are the first observation of shallow growth hillocks on an octahedral diamond face by Frank and Lang [11] and the important contribution by Sunagawa et al. [121,who were able to correlate the summits of these trigonal features to the outcrops of screw dislocations. The present paper describes the morphology of some original growth features on the surfaces of carefully selected natural diamonds. These patterns were imaged by phase shifting interferometry, which is a relatively new technique for quantitative mapping of surface height profiles. This optical method has rarely, if at all, been applied to the investigation of crystal growth processes. Therefore, in the first part of this work, the merits of this technique will be compared to

Elsevier Science Publishers B.V. All rights reserved

I 78

WI. P.

an Lnckei or!

I’S! ot grov~’thpatterns on octahedral face.s of natural diamonds

I or one measurement of a givcn surfacc protilc hLv. v). three interferogranis arc digitized. each with the reference mirror shifted over a distance equal to one eighth of the wavelength, A. of the monochromatic light usLd for illumination 1-rom this set of interferograms. the spatial distribution of phase shift, e(x, v), and thus h( .v, v), is cornputed. I hi analytical h tsis for the numeric ii is ilu i tion of the height profilc from thrcc two hi tin interferogr tms is provided by the following con sidcration In i two beam interlerometcr thc hi im rcflectcd from thc rcferincc surf tic is di scrihed by

-

4

—

4

H

] 11 U

H

Fig. I. Phase shifiing interferomciry: schematic representa-

=

R E1 cos( oat

+

—

ii

~/2)

.

(1

tion.

In this equation. L11 is the amplitude of the incident beam, R, is the coefficient of reflection those of conventional techniques for crystal surface topography, such as Nomarski interference contrast and phase contrast microscopy [7].

for the reference mirror and ar is the phase jump upon reflection. An extra phase shift n~/2,with n 0 1 or 2, is introduced by translation of the reference mirror in two steps of A/8. In a similar manner, the rays reflected from the specimen

2. Phase shifting interferometry as a method for the investigation of growth and dissolution patterns on crystal surfaces

surface are given by

=

.

L

~.t,

.

~

~ ~

-

~x. ~ -

Xcos[wt+s5(x,v)+E(x,v)].

(2)

2.!. Principles

Since phase shifting interferometry (PSI) is not very well known as a technique for crystal surface examination, its technical and physical principles [13] will be explained briefly in this section. Fig. 1 gives a schematic view of the arrangement of optical and electronic components in the micro-PSI interferometer. The microscope is provided with a two-beam interferometer (Michelson, Mirau, Linnik or other type), the reference mirror of which can be translated accurately with the help of a piezoelectric clement. The interferograms obtained by this device are projected onto a two-dimensional CCD array, which is connected with a microcomputer via an analogue— digital converter. After transfer, the intensity I(x, y) of all the individual picture elements (pixels) of the CCD array are stored as elements of an image matrix in the computer’s memory. -

.

.

where R,(x, y) is the coefficient of reflection for the specimen surface, a5(x, y) is the phase shift upon reflection and (x, y) is the phase shift due to height variations. It is assumed that the cornposition of the specimen is uniform over its surface (x, y) or a,(x, y) constant and R5(x, y) R5 constant. The intensity distribution of the recombined beam, i.e., the interferogram I (x, y), is =

=

I~( ~,

~)

+

=

=

E5(

~.

~)

+

I~(x. v)

10Rr + I~1R5+ 2i~~~R1 ~Rh

xcos ~ (x, v) +11(x, y),

.

‘I

with

~

~,

y)

=

cx.,

—

ar + e( x. y) +

n~r/2.

(3)

W.J. P.

Enckeeori

tan

/ PSI of growth patterns on

Ih(x, y) is an additional term due to (incoherent) background illumination, for example from the rear surface of a transparent specimen, and J~ E~. Subtracting pairs of interferograms followed by calculation of the appropriate ratio gives Cia =

=

a,

—

—

11(x, -s’) I1(x, y) 1

1

—cos[iia

~) +

+ E(X,

(4)

~/2}}_i

which, after some algebra becomes tan[~1a +(x

y)

—i~/4]

=tan[8(x

~)]15\ S

I

where O(x, v) ~ia + (x, y) ~/4. Since ~ia — ir/4 *f(x, y), 0(x, y) is the phase shift due to height differences, but now considered from another reference point than for ~(x, y). Since the surface profile h(x, y) is equivalent to 6(x, y)A/4ir, it follows that =

A. =

2.2. Comparison with other optical methods

.

>
h(x, .v)

several standard image processing techniques, such as smoothing, sharpening and masking of some surface areas.

mercially available WYKO TOPO-3D PSI microinterferometer [14]. The 10 x and 40 X objectives used are provided with a Mirau interferometer. The measurement principles of this instrument, which are described elsewhere [13], are slightly different from those formulated above.

=tcos~~ct+e(x,y)+~n —cos[L%a + e(x, y) + ir/2])

=

179

During the present surface topographic studies of natural diamond, use was made of the com-

ar):

12(x, Y) 10(x, y)

octahedralfaces of natural diamonds

—

—i

tan

12(x, y) —I~(x,y) I(x y) —11(x, ~

.

(6)

From eq. (6) it follows that from three digitized interferograms, each with the reference mirror shifted over A/8, the complete profile of the specimen surface can be calculated. The height distribution matrix h(x, y), which is stored in the computer’s memory, can be represented in many ways. Fig. 2 shows a shallow trigonal hillock on diamond imaged in several modes: (a) colour as a measure of height; (b) colour as a measure of slope; (c) three-dimensional height profile; (d) two-dimensional height profile. Other possibilities for display of h(x, y) are: grey level or colour as a measure of slope or curvature along the x or y directions, its frequency spectrum (Fourier transform) and its autocorrelation function. Prior to its representation, the height distribution matrix can be subjected to

Instead of three, now five interferograms, again each with the reference mirror shifted over A/8, are used to evaluate the height profile h(x, y). Compared to other optical methods for quantitatir’e mapping of surface profiles, such as twobeam interferometry (TBI) and multiple-beam interferometry (MB!) [71,PSI is by far superior. Its resolution of about 1 nm is similar to that of MB! and considerably better than that of TB!. In the application of PSI the main disadvantages of MBI, namely the necessity to silver the surfaces, laborious experimenting and often difficult interpretation of fringe patterns, are avoided. Therefore the development of phase shifting techniques, by which the results are readily obtained, can be considered as a breakthrough in optical interferometry. As demonstrated in figs. 2a, 2b and 3a, PSI is also suitable as a method for qualitatice imaging of step patterns on crystal faces. The best images of surface steps were obtained after 5 x 5 or 7 x 7 median noise filtering [15], followed by a grey level or colour display of the x, y or radial slope. In this case the image contrast looks similar to that acquired by differential interference contrast microscopy (DICM), as shown in fig. 3. The lowest steps that could be imaged by PSI were about I nm. This is comparable to DICM, but considerably higher than for phase contrast microscopy (PCM), which is capable of imaging steps down to 0.2 nm [7]. Other advantages of PSI with respect to DICM and PCM are: (i) There is no need to silver the specimen surfaces [7], since the background term

Wi

180

I~

U

p. ian Encket Ott

/ P.S’!

of growth pattern.s on octahedral tacet of natural diamonds

P1

I

sJa~awOUE~ 5-~

______________________

I N cn~ i~i

-~ ~_.

~

,~ — p

1)

WJ.P. van Enckevort / PSI of growth patterns on octahedralfaces of natural diamonds

Ib(x, y) in eq. (3) is cancelled in deriving the phase shift via eqs. (4) and (5). (ii) Quantitative and qualitative information are available simultaneously. A disadvantage of PSI is that for a given resolution only a limited surface region can be imaged. This is due to the limited size (256 x 256 pixels) of the CCD detector used. Summarizing, it can be stated that PSI, for quantitative and qualitative mapping, DICM for

181

quickly scanning and PCM for revealing the lowest steps form a most appropriate team for the topographic investigation of crystal surfaces.

3. Specimen selection It has been suggested that almost all natural diamonds were formed in the upper mantle at a

a

.

Fig. 3. Comparison ot several optical methods for ~urlace microiopograph~of crvsials: (a) PSI; (h) DICM; (c) PCM. The surface area imaged is a stepped terrace between three ‘~pointcontacting” shallow hillocks on a Siberian diamond.

I 84

/ PSI of grois’th

WJ.f’. Ian Lnc*eiort

patterns on octahedral faces of natural diamonds

depth of 1Sf) to 200 km [16]. Very probably the crystals formed from a liquid solution [121 (silicate magma containing CO, and CH4 [16]) at temperatures of 900 to 1300°C and pressures of about Sf) khar [17]. In general the growth form of the crystals is octahedral. After a period of residence in the upper mantle, which might go up to 3 x 10u years. the crystals were brought up to the earth’s surface via volcanic eruption [181. Although the details of the process of diamond ascent are unknown, it is well established that

_________

_____ ______

____________ _________________________________________

• ~ ~ —

- __________

hedrally shaped crystals were dissolved to rounded dodecahedrons [19—21].In other cases the edges between adjacent {] ll} faces became rounded, and trigonal etch pits (trigons) were formed on the diamond surfaces [10,12]. An implication of this dissolution process is that iii almost all cases the original growth patterns are no longer available for surface microtopographv. lo allow the investigation of as-grown surfaces to he made, the diamond crystals used in this study were chosen on the basis of being almost free from post-growth dissolution. Two sources of diamonds were used for selection: (i) From a 50 carat hatch of well-facetted, octahedral Siberian diamonds, about twenty crystals were picked out. The specimens were characterized by sharp edges between adjacent (111) faces and were free from trigons. The volume of each

the manufacturc of high prcssurc ins ils tnd othir products, four sharp edged octahedrons were selected. The crystals were probably of African origin. The specimen surfaces were only slightly etched, as could he deduced from the occurrence of small-sized, shallow trigons superimposed on the growth patterns. The selection of the crystals was carried out with the help of Nomarski interference contrast microscopy.

b

25nm a

during this period practically all diamonds were etched to some extent. In extreme cases the octa-

4. Morphologies of as-grown surface patterns {iii} natural diamond

~

on

All the octahedral surfaces investigated are planar and have steps ranging from less than 1 nm to 102 nm in height (fig. 4). The steps are sometimes curved, but usually they are straight and parallel to K 1 l0~. In this section, attention will he paid to the different types of centres at

12a

179 229

a

C2

12,

the

~t

124

SM,

ar~

of

129

249

Sor~

Fig. 4. IIigh mag nil I eat ion PSI images a sorness list hunched step irain emiiied from a shallow growth centre: (a) grey level as a measure slope: (Is) height profile.

of

growth steps are generated. For each case properties of steps and their implication on the distribution of point defects in the crystals will he considered. which

WJ.P. tan Enckei’ort / PSI of growth patterns on octahedral faces of natural diamonds

4.1. Shallow hillocks

4.1.1. General features Fig. 2 gives a typical PSI image of a shallow growth hillock on an octahedral face of one of the Siberian diamonds. The orientation of this category of hillocks was found to be invariably “negative” [11], i.e., the sloping sides are of the form (1, 1, 1 — ~}. This means that on the (111) surface the steps are parallel to /110/ and slope down towards /112/. In the following, /hkl/ is defined as the set of the [hkl] vector plus its symmetrical equivalents in a given plane (u, v, w). As can be deduced from the X-slope map and the height profiles in figs. 2c and 2d, respectively, the hillock inclination amounts to about 0.10. Similar hillocks were also encountered on two diamonds from other sources. The PSI micrograph fig. 5 shows negatively oriented, somewhat rounded, growth centres on a Cape Yellow diamond, presumably of African origin. Their summits are decorated by point-bottomed trigons [11], which is indicative of a relation with dislocation outcrops [12]. As will be discussed in section 4.1.3, the rounding off is due to post-growth dissolution. All the hillocks investigated in this study showed some bunching [22], i.e., accumulation of lower steps into higher ones. The height of the macro-steps is in the order of 10 nm. The rare occurrence of shallow, trigonal growth hillocks on {111) natural diamond has also been reported by Frank and Lang [11] and by Van Enckevort and Seal [23]. Sunagawa et al. [12] were able to relate such centres to the outcrops of screw dislocations by X-ray diffraction topography. This suggests a spiral mechanism for natural diamond growth. In general, crystal growth proceeds in three steps: first, volume diffusion of growth units towards the growing surface, second, lateral diffu-

Fig. 5. PSI micrographs of shallow growth hillocks on the octahedral surface of a diamond of African origin: (a) grey level as a measure of slope; (b) height profile. A correlation with the distribution of point defects in the crystal volume underneath (a) and (b) is demonstrated in cathodoluminescence topograph (c).

153

.

.

5%

—

75 nm

Ci,-

b a 23~

95~

0

249

49~

D~t~nc~

y

744

992

(M,o,-o,-,~)

_________

________________________ _________________________

____________ _______

-

.

.

-

II

I 84

Wi. P. tan Lncket ort / I’S! of grout/i patterns on octahedral faces of natural diamonds

sion over the crystal surface towards tile steps, and finally, incorporation at the step or kink positions. If the isotropic process of volume diffusion is rate determining in diamond growth, then the crystals would be “hoppered” or dendritic and, if still present, the growth hillocks would be circular, elliptical or dendritic in shape. In fact, the velocity of natural diamond formation is almost completely governed by surface kinetics. If mass transport in the mother-phase limits growth to some extent, then an increased supersaturation near the edges and corners of the crystals is expected to occur [24], which again leads to a local acceleration of step advancement. This was not encountered during the present investigation, Neither decrease in hillock inclination nor bending of steps was found near the periphery of the octahedral faces, The angular dependence of the diffusion of adsorbed growth units on a crystal surface can he described by an orientation dependent diffusion constant. According to the theory of irreversible thermodynamics, this constant is a two-dimensional, second order symmetrical tensor, which can he represented as an ellipse [25]. According to a two-dimensional version of Neumann’s principle [25]. all properties of a crystal surface should include the symmetry elements of its two-dimensional point group. The planar point group symmetry of (111) diamond is 3m. Since a circle is the only ellipse that fulfils this symmetry, it can he concluded that here the surface diffusion constant is isotropic. A consequence of this is that the growth hillocks on the octahedral faces must he circular if surface diffusion is the rate determining step in diamond formation. Since the actual hillock shape is sharply pointed triangular (see also section 4.1.3), it follows that integration of the growth units at step or kink sites, rather than surface diffusion, is rate determining in natural diamond growth. 4.1.2. Lateral anisotropy of step aduancement From the morphology of the as-grown octahedial diamond surfaces it can be inferred that the advancement rate of growth steps is strongly dependent on orientation. The ledges with minimal

velocities Oil {l II) are parallel to /i10/ and slope down towards / 112/. This follows from the negative” orientation of the trigonal elevations and the fact that the sides of a growth hillock arc hounded by the slowest advancing steps [261. Steps of other directions move considerably faster. When slowly advancing steps emitted from two adjacent growth centres collide, then they form a V-shaped pattern with a sharp reentrant corner. As a result of an increased effective supersaturation near the region of very large step curvature [27], in the first instance, the reentrant corner is quickly “filled in” and becomes rounded. Because now a whole range of step orientations with enhanced step velocities is created, tile ledges quickly sweep away from the point of collision. This leads to the formation of weakly inclined terraces with low step densities between the hiliocks. The whole process is outlined in fig. 6a. It accounts for the fact that only hillocks having their corners in point contact with tile sides of their neighbours (fig. 6b) were found. No overlapping or isolated hillocks were encountered during the present study, neither on the Russian nor on the African diamonds. Point contacting growth hillocks can also he recognized in fig. 5 of ref. [12]. The reverse case of point contacting etch pits (trigons) on natural diamond has been examined and analysed by Frank, Puttick and Wilks [10] and Frank and Lang [11]. The fact that no overlapping or isolated hillocks, but only hillocks touching their neighhours at one predictable point were observed can straightforwardly be explained if one assumes that the features are due to growth. To explain the patterns as being caused by dissolution requires the introduction of a long distance (> 100 /sm) correlation between steps moving towards the hillocks and the exact location of the summits of these elevations. Since this is highly improbable. it is once more confirmed that the surface patterns of the present diamonds-are formed by growth rather than by post-growth dissolution. It is very probable that the acceleration of steps in the flat terraces between the hillocks is a steady state process. This means that for a given pair of successive steps, the separation at each point is proportional to the local rate of step

WIP. ian Enckeiort / PSI ofgrowth patterns on octahedral faces of natural diamonds

advancement. In other words, the angular variation of step velocity can be determined by measlightly curved steps as a function of orientation (fig. 6a). Fig. 6c gives the dependence of step velocity on crystallographic orientation for the surement of the distance between two successive, Siberian diamonds as determined from the micrographs in figs. 3 and 6b. The slowest steps on (Ill) slope down towards /112/, while the fastest are oriented towards the reversed direction /112/ and proceed 5.4 times faster. Fig. 7 gives an atomic view of a growth layer on (111) diamond bounded by a [112] sloping step and an opposite [112] sloping step. From the figure it follows that the atoms at the [112] step are characterized by one dangling bond, except for those at the kink positions which possess one additional free bond [10,26]. Upon changing the step orientation with an angle 6 with respect to /112/, the number of kinks per unit step length increases sin 6towards (0°<0 /112/ <60°) [28]. 0proportionally 60°the stepwith slopes and isAtfully kinked. According to the first order broken bond model there is no essential difference between a growth unit adsorbed at a /112/ step and one attached at the bare (Ill) surface. Both are connected with one bond. However, atoms adsorbed at kink positions are two-fold bonded and thus are more easily added to the crystal lattice. Therefore, the lateral advancement of steps is expected to be governed by attachment at the kink sites along the ledges. If one assumes that the advancement rate of a step is proportional to its density of kink positions [28,29], then this velocity should vary as sin 9 for different angles. Comparison of such a theoretical relationship with measured values in fig. 6c shows a reasonable agreement. This mdicates that the kink positions at steps play a decisive role in diamond growth. =

185

-

-

i __________ _________

/

:

FL.

T I

t

.

.

~:cr

(a)

~.

F

+E~15 F:1r

-

F

_______ _______

I,~. _____

—

—~

~ -~—-—~--,—r-r--

1.0 .‘~

••••• -~ °-~

7..

Theory Observations

H ~

//

~ 0.6

So 0 0.4

C 0.2

Fig. 6. Lateral anisotropy of step velocity on {ltl) diamond: (a) acceleration ofof(c) steps terraces asbetween hillocks; (b)a DICM photograph “point shallow hillocks Siberian diamond; stepat contacting” velocity a function of on step orientation.

Cl) 0.0

o

10 2F0

~

4F0

50

0

60

I 86

WI.!’. iso bicket SrI

I’S! of growth patterns on oita/ii’dra/ faces of miatural diumno,id.s

broken bond interface energy (5.3 J/m7 [32]) of an ideal (II l} diamond—vacuum interface, so that the wetting of the octahedral diamond surface

7 I

,~I ~

~

F

was considerable. From the above, it can he inferred that natural diamond probably was formed from a liquid solu-

I I

~

.

.

~

T

I

--~

~

.

~

~

-~

...

-

-

I

aver on the (Ill) surface of diamond, hounded Is~a [1)2] and a [t12[ step. S: three-fold hooded atoms at step sites: K: two-fold bonded atoms at kink p051 iofls 1-ig. 7. lop view of a growth

Although the sin 0_dependence of step velocity suggests that /112/ (0 0°) ledges do not advance at all, the surface topographs of the Siberian diamonds point to an actual /112/ step propagation rate which is about 20% of the fully kinked /112/ steps. This can he attributed to the occurrence of — 20% kinks at /112/ generated by statistical fluctuations. By using simple Bolzmann statistics, it can he shown that the fraction of kinked positions along a step is given b =

2

exp( —p/2kT)/[l

+ 2

exp( ~/2kT)1.

In this relation ~ equals ~sl ~. where and ~ ft~1~Cthe solid—fluid, solid—solid and fluid—fluid nearest neighbour interaction energies [30]. respectively. In fact, tile ahove given fraction of kink positions at a / 112/ step on (111) diamond is the same as for a / 100/ step on the (001) face of a Kossel crystal [31]. From the “observed’ kink density of 2ft%, it follows that ip/kT 4.2. This corresponds with a standard temperature ((.).88l38kT/~)of 0.21. which is 33~ of the roughening temperature of the {l I I} face of a diamond lattice [30]. Assuming a growth temperature of 1400 K [16], it follows that the (11 l} surface free energy during diamond formation amounted 0.73 J/m. This is l4~ of the ~.

~,

=

(ion. advancing /112/ step direction pointsThe to slowest a condensed (solid or liquid) mother phase. In such systems, the dangling bonds at the growing diamond surface are saturated to such an extent that no step reconstruction occurs and the surface morphology is in accordance with a first order broken bond model [26]. If the mother phase had been a solid solution, probably mass transport would he rate limiting in crystal growth. Besides, the surface patterns are completely determined by the symmetry of the crystal face and the location and type of growth centres. IThis tmplies that the diamond interface characteristics are both isotropic and uniform over the whole growth face. This is indicative for an isotropic. homogeneous liquid phase, rather than a (poly) crystalline solid rock at any one instant in time. As can he inferred from the occurrence of growth bands in the crystals [4.5.20]. the overall composition, temperature or pressure of the liquid might change during growth. 4. 1.3.

Implication t~rthe distribution

of p0011 de-

t~’cts

Io investigate the influence of step orientation on the capture of impurities during crystal growth. cathodoluminescence topography [5] was used as a method for imaging the distribution of point defects in crystal volumes just (a few micrornetres) underneath the as-grown surfaces. The topographs were recorded with the help of a scanning electron microscope, fitted with a cathodoluminescence accessory. Fig. Sc gives the distrihution of luminescence intensity below the surface area shown in the PSI niicrograph of fig. Sa. Clearly fossil images of growth hillocks can he recognized. The darker areas correspond with volumes., the growth of which was governed by the slowest /112/ steps. The brighter areas are diamond volumes formed via (faster) steps of other orientations. Since the dependence of cathodoluminescence intensity on

W.J.P. ia,i Eni lot ott / PSI of growth patterns on octahedral faces of natural diamonds

~—

--

-

_

.

.

defect concentration is unknown, no answer can be given to the question which step type captures more impurities. The cathodoluminescence micrograph of fig. 8 shows a group of fossil hillocks elsewhere on the same African diamond seen in fig. 5. Also for the Siberian crystal of fig. 3, luminescent replicas of shallow hillocks were found. Although many hillocks were replicated as cathodoluminescent images, no one-to-one correlation was found. In several cases additional luminescent triangles were observed. These result probably from previous hillocks which were overgrown by others at the last stage of diamond growth. The presence of luminescent hillock patterns gives additional proof that the surface patterns discussed here are authentic growth phenomena. In contrast to the associated hillock patterns, the cathodoluminescence replicas are marked by more or less straight / 110/ edged and pointed vertices. This means that the extensive rounding off of the surface features as shown in figs. 3, 5 and 6 is introduced by dissolution after termination of growth. The original hillocks were almost strictly triangular. In the micrograph of fig. 5c, the trajectories of the angular points of the trigonal step patterns are imaged as brighter traces .

.

.

.

.

~IJ1h~

_____

Hg. 5. ( .iihodoluminescenee topogiaph of a group of fossil sh.illov. growth hillocks on the {l 11) surface of an African. Cape Yellow diamond.

-

187

300 nm 239

479

7 17

(b) 8

249 12

RMS: RA:

at

496 a,,oe

744

I H,

992

,-o,sa I

PROFILE

tG4nrn

PV:

Gl5nrn

Use,- Ft

4~396~O

(c) 0

223

a -223

160 D:~to~~e

323

498

surface

850

913

~ M:~ro~s (t~.9X,

979

Fig. 9. PSI images of three hillocks on an as-grown {Il I) . _ surface of a Siberian diamond: (a) grey level as a measure of height; (h) three-dimensional height profile: (c) two-dimensional height profile.

I 88

U .1!’

i

an Liii l.ii ott

I’ SI of p nit-i/i I/alt

1/Li ott oi ta/us/ru! fa: e,s of ,iatii,sil dtaoio,id.s

on (Ill). Examples, with typical heights ranging from 200 to 501) nm. are given in the PSI micrographs of fig. 9. The steep hillocks were never _~

A L

~

~

___________ __________________

_______________

J

Fig II). Dl( M mitrograph of the distribution of lowet steps emitted from two neighbouring steep hillocks

parallel to / 112/, which radiate from the growth centres. This suggests that during crystal growth the shallow hiliocks were rounded off very slightly near their vertices, where steps with directions deviating from / 112/ capture different amounts of impurities. A final characteristic of the cathodoluminescent triangles is the same mutual ‘‘point contact’’ relation as described for the hillocks in the previous subsection. 4.2

teejI lu/locks

4.2.1. Morphology The growth steps on the octahedron surfaces of the Siberian diamonds usually did not originate from shallow hillocks, as discussed in the previous section. hut nucleated from steep trigonal elevations. The orientation of the raised growth features was invariably negative, i.e.. with edges parallel to /110/ declining towards /112/

encountered on the African diamonds. As can he seen in fig. 10. the lower steps emitted from the elevated growth centres expand laterally over the whole (Ill) surface. forming triangular, shallow patterns with ledges parallel to / 110/. From this DICM photograph it was deduced that the most rapidly advancing /112/ steps propagate 6.5 times faster than the slowest /112/ steps. Further it was found that the positively oriented patterns centred around each summit only have one point in contact with each neighbouring step system. From these and other observations it follows that the properties of the lower steps, with heights to a few tens of nanornetres. are identical to those described ill tue preyoils section. Therefore, in the remaining part, attention ~viII only he focused to the morphology of the growth centres. The summits of the central hillocks may he pointed (fig. II a), planar (fig. 11 h) or mtermeiii— ate (fig. I 2a). on those point—topped hillocks that were not affected by post-growth dissolution, patterns related to the original crystallization pro-

cess were observed. This growth morphok)gy is completely different from the rest of the surface. Fig. II a shows a triangular growth hillock of positite orientation on top of a negative steep hillock. Fig. I 2a gives a SEM niicrograph ~if a hillock centre, which is characterized by a rough surface texture. These observations indicate that at tile summits discussed here, the state of tile

solid—fluid interface and thus the conditions and mechanisms of crystal growth were altered to a large extent. In contrast to the other hillocks, the surfaces of the fiat—topped elevations are very smooth and free from features detectable by the PSI method (fig. II h). In general, the top area of these hilloeks is considerably larger than for the other steep centres. It is thought that originally the flattopped hillocks were point-topped (or ‘‘intermediate-topped”). However, at a given moment the alternative growth mechanism which promoted vertical growth stopped, and extended plateaus were formed by subsequent lateral cx-

WJ.P tan Encket ort / PSI of growth patterns on octahedral faces ot natural diamonds

189

s/i

—

8

0

62 124 196 Ijiatance (M,crona)

249

Fig. 11. High magnification surface topographs of steep growth centres: (a) point-topped summit (DICM): (b) planar summit (PSI).

pansion of steps and hillock edges via the same crystallization process as elsewhere on the surface. 4.2.2. Relation with point defects It is well established that the segregation of impurities and the formation of lattice imperfections is strongly influenced by the characteristics of the solid—fluid interface and the mode of crystal growth. Therefore, if the deviating surface structure at the tops of the steep hillocks is due to an alternative growth process, this should be marked as a difference in the point defect concentration in the crystal volumes underneath. To

search for such a correlation, use was made of cathodoluminescence topography. Fig. 12b gives the distribution of luminescent defects just (to 1 ~sm) below the hillock given in the SEM micrograph of fig. 12a. The roughened surface area is clearly replicated as a triangle of high intensity luminescence. As can be seen in the cathodoluminescence topograph of fig. 13a, enhanced luminescence was also encountered for the crystal volume associated with the pointtopped centre of fig. 1 la. From this relationship between the positions of steep centres and the distribution of defects it can be concluded that these summits were formed by a growth process

I 9(1

II / I’

ui

Iii,

~

: ~tt

1511

rs ‘wt/i pattern.s on octahedral faces of un tiural ilutunonil

the middle of the plateau. These observations strongly advocate the point-topped origin i/I tile

____________________________________________________________

_______

__________

_____________________ ________________

______

tisilili

_____

.—

—-—-—_____

planar elevations. The triangles of increased luminescence are in fact the fossils of growth cciitres where crystallization took place via tile alternative mechanism.

4.2.3. Fluid—fluid—-solid growl/u The alternative mode of crystal growth at the tops of the steep centres might he explained by the occurrence of a droplet of a foreign fluid this fluid, which

-_

---,-

Fi’a. l2. ( ot elation hct’,teen sin Lice inoipho!oes aid di. cu_I ui in ints.’imi.’di.iie topped - hillock: I i) 81 51 mi— .ionraph: (hi c,ithodolumincscc’nce topograph.

b

strueluje

which differs from that elsewhere on the crystal surface. To verify that the flat-topped centres are the remainders of point-topped hillocks after cessation of vertical growth, a cathodoluminescence micrograph (fig. 13b) was recorded from the crystal volume underneath the elevation in fig. 1 lb. The distribution of luminescence intensity shown in this micrograph is uniform over the hillock plateau, except for a small region of high intensity. The same pattern was also found for the other flat—topped hillocks. In these cases the bright spot was clearly triangular and centred at

i.t~!

Fig I .‘. ( ilhodoliimiiieseence iuipuinr.iph’. inippins die di’Ii i hution of lurninesu_cot defcs_h underne,ith li Ia point lopped ,oul Ib) a plan.ii-topped hillock.

WJ.P. i ‘an Enckei ‘ort / PSI of growth patterns on octahedral faces of natural diamonds

solution, was a liquid or essentially the same a compressed supercritical gas with a high solubil ity of carbon species. This leads, with respect to the rest of the growing (1111 face, to an increased surface wetting and a lowering of step free energy [33]. Causing a higher rate of two-dimensional nucleation, this again promotes the vertical growth at the hillock centres. The mechanism of fluid—fluid—solid (FFS) growth suggested here is very similar to the case of two-dimensional vapour—liquid—solid (VLS) growth as described by, amongst others, Binsma et al. [34] for several crystals formed from the gas phase. Because of the altered interface properties below the droplets, the FFS mechanism straightforwardly accounts for the deviating surface morphology at, and defect structure underneath, the summits of the point-topped hillocks. When during crystal growth the droplet vanishes, two-dimensional nucleation stops and a planar top will develop. The composition of the droplet phase is unknown. One might speculate about highly cornpressed CH4, CO2 or H20 gas bubbles adhered —

—

to the crystal surfaces. The latter two compounds have been observed in micro-inclusions occurring in cubic diamonds [35]. Very probably the foreign phase is not a solid particle since in that case a limited diffusion rate would hamper crystal growth and a crater-like pattern would be formed.

191

_________________ -_______

_______________

—

___________

-~

350nm

en8

120

179

(b) 239

0

62 i24 i86 D,atance (M,cron~)

249

4.3. Other sources of steps 4.3.1. Growth pits On the octahedral faces of one of the African diamonds growth features of a peculiar kind were found. As shown in fig. 14 these were hexagonally shaped depressions with edges parallel to /110/, centred in an elevated, negatively oriented triangular plateau bounded by ledges facing towards /112/ on (111). The diameters and depths of all the craters on the crystal faces were similar and amounted to about 200 p.m and 200 nm respectively. Fig. 15 gives a schematic view of an idealized crater pattern derived from the morphologies of several tens of pits. The presumed low steps emitted from the triangular plateaus were not found on the actual crystal surfaces, but this kind of ledge might have been removed by slight

_______

_____ _____

ii

~ _____

.

.

Fig. 14. Craier-like hexagonal gro~hpit on ihe (Ill) surface of an African Cape Yellow diamond: (a) general view (DICM); . . . (b) height profile of central depression (PSI). The sudden jumps in height indicated by the arrows are artifacts inherent to the PSI method; (c) cathodoluminescence topograph.

192

141]. P. i a/i Lnckei Ott

//

!‘.SI of growth pattern.s on octahi-dral fuce,s of natural duiunonu/v

crystal growth is hampered and a crater is formed.

.

I

//~\

A -

tended s,,ps

I I

Fig. l~.Schematic representation of an idealized growth pit.

post-growth dissolution. That such etching indeed took place was inferred from the occurrence of numerous fiat-bottomed trigons on the diamond faces, If not obstructed by other plateaus, the protruding angular points of the trigonal elevations extended over the whole growth surface in directions parallel to /1T2/. This indicates that the crater patterns must have been formed by growth. since the dissolution hypothesis requires an unrealistic, long distance correlation between step behaviour and crater positions. Confirmation was obtained by cathodoluminescence topography (fig. 14c) which revealed fossil images of the hexagonal depressions in a similar manner to that discussed previously for the steep and shallow hillocks. It should be noted that the growth pits reported here are essentially different from the hexagonal etch pits described by Moore [36]. A possible mechanism for the formation of crater-like patterns is as follows. During crystal growth, droplets of a fluid which is immiscible with the mother phase, or alternatively, crystallographically oriented solid particles, are positioned on the diamond surfaces. In contrast to the previously described FFS growth, here the solubility or the diffusion velocity of carbon in the foreign phase is less than in the growth solution. This implies that below the droplet or particle,

At the rim of the contact surface between foreign body and diamond, nucleation of new steps is facilitated. In the manner explained in fig.3 of

rows of parallel (macro-) steps, which covered four adjacent fIll) growth faces. As can he inferred from the ccmposite PSI topograph in fig. 16, the step trains are nucleated at one cornmon point, namely the octahedron apex common to the four octahedron faces in question. At the centre of this figure the octahedral diamond is drawn in its projection along [001]. Around this sketch the PSI micrographs of the four step trains and the corresponding one-dimensional height profiles are given. The formation of steps is most probably due to contact nucleation, introduced by a solid or fluid particle touching the diamond top. Just before termination of growth, the activity of the step source was diminished and planar areas on the (111) surfaces close to the common angular point were formed. The foreign particle prohably lost contact with the diamond. Since the above-mentioned diamond top was fractured to some extent, scanning electron microscopy could not give additional information on the growth centre.

5. Conclusions In combination with other methods, such as phase contrast and interference contrast microscopy, SEM and cathodoluminescence topography, phase shifting interferometry is a very powerful tool for the quantitative investigation of growth or dissolution patterns on crystal surfaces. The present surface topographic investigation of the (11 1) faces of several natural diamonds proved that growth steps on the crystal surfaces

WJ.P. ian Enckec’ort / PSI of growth patterns on octahedralfaces of natural diamonds

~

193

)

~

~..

//

/

________

// /

.

//

.

~‘u’-’:

fl;.,

‘N

--15; Si er y’eters

Fig. 16. Collage of PSI topographs showing extended step trains nucleated from one octahedron apex.

can be nucleated in different ways: (i) generation at the outcrops of dislocations, resulting in the formation of shallow hillocks; (ii) fluid—fluid—solid growth leading to steep hillocks; (iii) nucleation caused by solid or fluid particles in contact with

the growing diamonds, The large variation in surface morphology indicates that the conditions and mechanisms of crystal growth are not unique. Although evidence exists for crystallization from a liquid phase, there is definitely no question of

94

If-l/.P i-api Lrukei op-I / P_SI of growl/i patterns o;i octahedral fdce.s of natural dia,nond,s

one single, universal model for natural diamond

[Ill F.(’. Frank and AR. Lang. iii: l’hvsicah l’roperties of

formation. The major problem in interpreting the results of cx situ, a posteriori surface topographic studies

[l2] ISunagawa, K. Tsukamoto and I Yashuda. in: Materials Science of the Earths Interior. Ed. I Sunagawa (Terra.

of crystal surfaces is the fact that the information is only valid for the last stage of crystal growth. It is not clear whether the surface patterns de. . . scrihed in this paper are also representative for tile earlier stages of diamond crystallization. The most appropriate way to gather insight in this is to search for cathodoluminescence images of fossil growth hillocks on { 111 } plates, cleaved paralId with a given octahedral diamond growth face.

Diamond. Ed. R. Berman ((‘larcndon, Oxford.

965) p.

Tokyo. 1984) p.131 [131 iC. Wyant CI,. Koliopoulos. B. Bushan and I). Basila. Trans. ASME i. Trihology 108 0986) 1. [14] WYKO corporation. I 95~East Sixth Street. I ueson. AL 85719. USA. [IS] E. hall. Computer Image Processing arid Rceogodion (Academic Press. London. 1979) p. 21)7.

[16] H.O.A. Meyer. Am. Mineralogist 7(1 (1985) 344. [17] H.O.A. Meyer. in: Mantle Xenohiths, Ed. P.11. Nixon (Wiley, c’hiehester, 1987) p. 51)1. [18] V.A Milashev. Explosion Pipes (Springer. Berlin, 988) [19] M. Miss_ire ancf AR. Lang, i. Crystal Gro8Ih 2~i(1974)

Acknowledgements

[20] M.Seal. Am. Mineralogist 5)) (1965) 05.

The author is grateful to Dr. M. Seal for critical reading of the manuscript and to Mr. D.J. Andriesse for providing a batch of Siberian di~tmonds from which specimens suitable for surface topography were selected.

[21] M. Seal. Phys. Status Solidi 3 (1963) 658. [22] P. Bennema and 0.1-1. Gilnier in: Crystal Growth, An Introduction, Ed. P Hartman (North-Holland, Amsterdani. 1973) p. 310 [23] W.J.P. van Enekevort and M. Seal, Phil. Mag. 57 (1988)

References [I] J.W. llarris and i.J. Gurney, in: The Properties of Diamood, Ed. i.E. Field (Academic Press, London, 1979) pp. 555~59l. [21 PH. Nixon. Ed., Mantle Xenoliths (Wiley. c’hichester. 987): see also: J.B. Dawson, Kimherliies and their Xcnoliths (Springer. Berlin. 1980). [3] See, for example: J. Walker, Rept. Progr. Phys. 42 (1979) 1605. [4] AR. Lang. i. Crystal Growth 24/25 (1974) 108. [5] P.L. Hanky, I. Kiflawi and AR. Lang, Phil. Trans. Roy. - Soc. London A 284 (1977) 329. 16] W.J.P. van Enckevort and M. Seal, Phil. Mag. 55 (1987) 631. [7] WJ.P. van Enekevort, Progr. Crystal Growth Characterization 9 (1984) 1. [8] S. Tolansky. The Microstructures of Diamond Surfaces (N.A.G. Press, London. 1955). [9] S. Tolansky, in: Physical Properties of Diamond, Ed. R. Berman (Clarendon. Oxford, 1965) p. 135. [10] F.c. Frank, K.E. Puttick and F.M. Wilks. Phil. Mag. ~ (1958) 1262: F.C. Frank and K.E. Puttick, Phil. Mag. 3 (1958)1273.

[24] A. Seeger, Phil. Mag. 44 (1953) I. [25] iF. Nyc, Physical Properties of Crystals. Their Representation by Tensors and Matrices (Clarendon. Oxford. 1987). [26] W.J.P. van Enckcvort and Li. Oiling. i. Crystal c;iu_tn-ih 45 (1978) 90. [27] B. van s_Icr Hock, J.P. van der Eercten and P. Bennema. J. Crystal Growth 56(1982)11)8. 128] i. Nishizawa, Y. Kato and M. Shimf,o. J. Crystal Growth 31(1975) 291) [29] I-I. MdlIer-Krumbhaar, T.W. Burkhardf and D.M. Kroll, i. c’~-~~t~d Growth 38 (1977)13. [30] W.i.P. van Enekevort and J.P. van der Eerden, J. (‘iystal Growth 47(1979) 501. [31] i. Frenkel, Zh. Fiz. Khim. 9(1945)392. [32] i.E. Field, in: The Properties of Diamond, Ed. i.E. Field (Academic Press, London, 1979) p. 284. [33] P. Bennema and i.P. Van dcr Eerden. in: Morphology of (‘rystals, Ed. I. Sunagawa (Terra, Tokyo, 1987) pp. 1-75. [34] i.J.M. Binsma, W.J.P. van Enckevort and G.W.M. Starink. i. Crystal Growth 61(1983)138. [35] 0. Navori. 1.0. 1-lutcheon, G.R. Rossman and G.i. Wasserhurg, Nature 335 (1988) 784. [36] M. Moorc, in: Properties of Diamond, Ed. J. Field (Academic Press, E,ondon, 1979) p 245