A parametric relationship for synthesized diamond powder

Diamond & Related Materials 15 (2006) 61 – 66 www.elsevier.com/locate/diamond

A parametric relationship for synthesized diamond powder A.L.D. Skury *, G.S. Bobrovnitchii, S.N. Monteiro Universidade Estadual do Norte Fluminense, Campos dos Goytacazes, RJ, CEP 28013-600, Brazil Received 5 July 2004; accepted 6 July 2005 Available online 26 August 2005

Abstract Diamond powders synthesized in different solvent/catalyst systems at high pressure and high temperature conditions contain crystals that could be separated into groups of distinct size and defect morphology. These groups differ by their mechanical compressive resistance, given by the fracture load, which could be used to classify them for potential industrial applications. In the present work a parametric relationship between the defect morphological aspects, the granulometry and the compressive resistance of diamond powders synthesized in a concave anvil high-pressure device at 4.7 GPa and 1250 -C was established. Results were obtained by measuring the fracture load, using the single grit test of individual crystals, and comparing the average value for crystals with different defect morphology and corresponding grain sizes. The parametric relationship permitted to classify each diamond crystal by its size and defect morphology in association with its compressive resistance. It is therefore suggested that this parametric relationship be used as a new method to evaluate a diamond powder in terms of crystal size, defect morphological aspects and mechanical resistance. D 2005 Elsevier B.V. All rights reserved. Keywords: Synthetic diamond; Mechanical resistance; Parametric relationship

1. Introduction Diamond synthesis can be performed in different types of systems associated with a variety of high pressure devices (multi-piston, Belt, anvil, and others) with compression chambers technologically adapted to a number of hydraulic presses [1,2]. High pressure and high temperature, HP –HT, gradients established inside the compression chamber may vary from one system to another. It is well known that temperature gradients exert strong influence on the characteristics and mechanical properties of the diamond [1]. The multi-piston is considered one of the best devices for quality crystal productions. The Belt device provides special conditions for large crystal synthesis in which single crystals with pre-established properties can be obtained [2]. The anvil device with central concavity produces diamond powders with a broad range of morphology, properties and sizes with the same synthesis parameters normally used in

* Corresponding author. E-mail address: [email protected] (A.L.D. Skury). 0925-9635/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2005.07.008

other devices [3 –6]. This is due to the high pressure and temperature gradients attained inside the compression chamber. Consequently, the size of diamonds synthesized in this device may vary from very small powder particles to 0.5 mm crystals. In general the diamond powders obtained in the central concavity anvil type device are composed of crystals or agglomerated particles exhibiting defects with different morphological aspects, from very small flaws to grain boundaries. Moreover, the defect morphology also varies for distinct range of particles sizes [6], which allows the diamond crystals to be classified in corresponding groups. In general the strength of diamond particle is affected by its surface condition, shape, defect concentration and other factors [7]. Quantitative interpretation of the effect caused by these factors was reported on monocrystalline dust or grit type of particles. For instance, smooth particles were found to be, on average, 43% stronger than rough while blocky particles 40% stronger than needle-shaped [7]. In the present work, morphological group will correspond only to defect morphology and not to crystalline shape or surface condition. In practice, a certain class of powder with

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A.L.D. Skury et al. / Diamond & Related Materials 15 (2006) 61 – 66 Table 1 Morphological and granulometric groups

specific defect and size, which could be used for a given industrial application, can be obtained, as a group, from the synthesis product. This would be convenient if information on the properties of a given diamond powder could be provided in association with corresponding morphological groups. However, the producers do not provide other technical information on the properties than the average size and, exceptionally, the hardness of the diamond powder as a whole. Since in a same batch of synthesized diamond powder the mechanical properties of individual crystals may be related to their size and morphological aspect, the present work attempts to establish a relationship between compressive resistance, given by the fracture load, and crystals morphology in the distinct granulometric groups that comprise a batch of diamond powder. In principle this relationship is of considerable interest since it could serve as a convenient guide for selecting both the adequate crystal size and the morphology required in specific industrial applications such as high speed cutting tools and drilling equipments.

Code Morphological group

Code Granulometric groups Size range Average (Am) granulometry (Am)

M1 M2 M3 M4 M5 M6 M7 M8

Crystals with minor, unimportant defects Crystals with surface defects only Fragments of crystals Crystals with internal defects only Crystals with both internal an surface defects Pair or triplet geminated crystals More than three geminated crystals Small grain polycrystalline diamonds

G1

20 – 28

24.0

G2 G3 G4 G5

28 – 40 40 – 50 50 – 63 63 – 80

34.0 45.0 56.5 71.5

G6 G7 G8

80 – 100 90.0 100 – 125 112.5 125 – 160 142.5

then established. No account was made for the variation in the thermocouple e.m.f. due to the applied pressure. After a pre-determined 8 min synthesis cycle, an agglomerate composed of transformed diamond crystals, non-transformed graphite, metallic alloy and carbides was formed inside cell. The diamond crystals were extracted from the agglomerate by applying an alkaline melt process [8]. In the present work 22 agglomerates were investigated and their transformed diamonds crystals were manually separated by morphological groups with the help of a magnifying glass. Diamond crystals in each morphological groups were then granulometric classified in terms of their size distribution. This granulometric classification disregarded crystals outside the size interval from 20 to 160 Am. The amount of disregarded crystals did not exceed 9.5% of the total number and were not statistically significant to be analyzed according to the proposed methodology. The statistically considered crystals, with sizes between 20 and 160 Am, were classified in the eight morphological groups presented in Table 1. The order of classification of these morphological groups increases with the amount of structural imperfections. For example, M1 is the group with lesser imperfections while M8, for diamonds with many

2. Experimental procedure Diamond crystals were synthesized in a 2500-ton press using an anvil with concavity type of high-pressure device. Powder of the graphite precursor and the catalyst/solvent alloy Ni – Mn were thoroughly mixed in a 1:1 wt ratio and compacted into the reaction assembly shown in Fig. 1. The mixture was then subjected to a pressure of 4.7 GPa and a temperature of 1250 -C. The pressure calibration was done at room temperature by observing the phase transitions in Bi (I –II) at 2.55 GPa and PbSe at 4.3 GPa. Since the pressure inside the reactive cell is not constant and may vary due to several factors, the actual pressure during the synthesis can differ from calibrated values by T5%. The temperature was calibrated with a cromel-alumel thermocouple which was diametrically inserted into the center of the reactive cell. The electric current to be supplied and its temperature correlation was θ58

1

30

1 – Graphite heating caps 2 – Calcite protection disks 3 – Calcite deformable gasket 4 – Reactive mixture

3 4 2 θ30 Fig. 1. Geometry of the compact cylinder containing the reactive mixture and other components (dimensions in mm).

A.L.D. Skury et al. / Diamond & Related Materials 15 (2006) 61 – 66

grains, is the group with greater amount of imperfections. Fig. 2 illustrates, for each morphological group, the aspect of a corresponding diamond particle. In the particular case of crystals with internal defect only, group M4, the visual selection was based on surface holes that indicate the existence of a significant defect inside the crystal. All SEM pictures in Fig. 2 were obtained in a Jeol, model JSM 6460 LV, microscope operating at 20 kV. Each morphological group, in Table 1, was separated in eight granulometric groups. The size interval and the average granulometry for each group are also shown in Table 1. This 8 by 8 matrix of morphological vs. granulometric groups was the basis for the establishment of a parametric relationship between crystal morphology and mechanical resistance.

M1

M2

M3

M4

There is no simple way to assign quantitative values to crystal morphological aspects. However, the strength of a crystal depends on its amount of defects in a way that the greater this amount is the lower is the mechanical resistance. Consequently it is proposed that the average mechanical strength ( F MX ) for crystals with same morphology serves as value to represent each morphological group, MX, shown in Table 1. For the synthesis parameters applied, no flawless diamond crystals were found. Therefore the M1 morphological group of crystals with minor defects was considered the standard in terms of comparison. This group was given a relative strength (R M) equal to 100. The strength for each one of the other morphological groups was evaluated in corresponding relative units as compared to that of M1. The measurement of the mechanical resistance of the diamond crystals was performed by the single grit method in a DA-2 equipment of the Technocrystal Company, Moscow, Russia. Here, an individual diamond is mechanically compressed between two hard metal (96% WC – 4% Co) anvils until the crystal begins to break. The equipment has an automatic loading for the crystals and the applied force associated with the breaking of the crystal is also automatically registered. Being softer than the diamond, the hard metal anvil allows less stress-raising at local sharp points on the particles. However, bedding-in of the particles might still occur, in which case results could be misleading [7]. In the present work 10 crystals were randomically selected from a specific morphological group and a specific granulometric group. Each one of these selected crystals was mechanically tested and no bedding-in actually occurred. The average, F G, of these 10 individual tests defined the mechanical resistance for crystals associated with a given granulometry in a given morphological group. One should bear in mind that the mechanical resistance referred in the present work corresponds to fracture load and not stress. The relative mechanical resistance, R M(X), for a given morphological group, MX, was evaluated through the following equation:  RM ð X Þ ¼

M5

M6

63

FMX FM1

 100

ð1Þ

where F MX is the mean value of the crystal mechanical resistance for all granulometric groups in the same morphological group MX.

3. Results and discussion

M7

M8

Fig. 2. Typical diamond particles exemplifying each one of morphological groups considered in this work.

Table 2 shows the average mechanical resistance, F G, corresponding to each group of diamond crystals associated with a given granulometry in a given morphological group. In this table, the average mechanical resistance for each morphological group, F M, and its relative mechanical resistance, R M, given by Eq. (1), are also shown. It is worth mentioning that, for any single grit test performed,

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Table 2 Average mechanical resistance, F G, for diamond crystals in morphological and granulometric groups F G (N) M1 M2 M3 M4 M5 M6 M7 M8

G1

G2

G3

G4

G5

G6

G7

G8

18 13 9 – – – – –

20 15 12 8 2 – – –

23 17 13 10 6 5 – –

26 19 15 12 8 6 – –

27 27 21 14 9 7 3 –

30 27 22 17 11 8 5 3

33 26 24 19 14 11 6 4

– – 26 21 15 13 8 6

F M (N)

RM

25.3 20.0 17.8 14.4 9.3 8.3 5.5 4.3

100 79 70 57 37 33 22 17

bedding-in of diamond particles into the anvil was not observed. From the results in Table 2, it can be seen that, for each set of granulometry, the mechanical resistance tends to decrease as the crystal defects increase. This is expected since any crystal imperfection, in principle, act as a microcrack or weak point during mechanical straining. Using the data from Table 2, curves corresponding to the dependence of the average mechanical resistance, F G, with the average granulometry ( G) for each morphological group investigated, were plotted in Fig. 3. As observed in this figure, for any of the investigative group, the resistance increases with the average granulometry. This indicates that diamonds with greater size tend to be individually stronger. Similar result was reported by Field et al. [9] for diamond dusts in which the smaller particles withstand lower loads, though have largest strengths (load/area). This size effect has not been equated before and its justification appears to be related to the nature of the compressive test. Smaller crystals have more surface area and hence more external corners, which may serve as stress raisers. Therefore, the smaller the crystal is, the greater is the number of stress raisers per volume to promote fracture. In spite of deviations, it is possible to consider that the points in a given morphological group follow a linear fit as 40

a ¼ 0:1165F0:0135 N=lm:

b ¼  0:0069F0:0006 lm1 :

25

ð3Þ

If the straight plots in Fig. 4 were parallel lines, which nearly they are, a mathematical expression exists for the combined F G vs. G and ln(R M) vs. G relationships. Lets then assume a relationship for an ideal parameter P, replacing the real values of ln(R M), in which all lines were perfectly parallel. In this case, the following equation holds: P ¼  ðb=aÞFG þ bG þ C

ð4Þ

where the coefficient a is given in Eq. (2) and b in Eq. (3). These coefficients correspond to the inclination of the straight lines in Figs. 3 and 4. The constant C is given by the 5,0

M1 M2 M3 M4 M5 M6 M7 M8

30

ð2Þ

Small deviations upwards in some points belonging to M2 and M3 can be explained by the fact that, during growth, the crystal might improves its structure. This has also been reported by Novikov [6]. According to Fig. 3, it is also relevant to mention that, for a certain granulometry, the mechanical resistance decreases with the amount of imperfection, as one should actually expect. Another relationship was found between the logarithm of the relative mechanical resistance, ln(R M) representative of morphological groups, and corresponding average granulometry, G. Fig. 4 depicts the graphic representation of the ln(R M) versus G points. These points were obtained at the intercepts of constant F G horizontal lines with the linear plots in Fig. 3. For example, a dashed horizontal line at F G = 20 N intercepts the linear plots corresponding to M1, M2, M3 and M4 at values of G, respectively, of 33.3, 58.4, 87.1 and 124.4 Am. These four values are shown in Fig. 4 as open circles. Similar plots were obtained at other constant F G intercepts. Within a good approximation, the points corresponding to a constant F G can be associated with straight lines with an average inclination of:

Morphological Group

35

4,5

20

ln (RM)

FG (N)

depicted in Fig. 3. From the mean value of the straight-line inclinations one may define a ratio of increase of the mechanical resistance with the diamond size. This mean inclination was found to be:

15

4,0

3,5 5N 10N 15N 20N 25N

10 5

3,0

0 0

20

40

60

80

100

120

140

160

Granulometry (µm)

2,5 0

20

40

60

80

100

120

140

160

Granulometry (µm) Fig. 3. Dependence of the average mechanical resistance with the average granulometry for each morphological group.

Fig. 4. Graphic representation of the ln(R M) vs. G.

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A.L.D. Skury et al. / Diamond & Related Materials 15 (2006) 61 – 66 5,0

4,5

ln RM

4,0

3,5

3,0 ln RM = 1.013P + 0.263

2,5 2,5

3,0

3,5

4,0

4,5

5,0

P = 0.0592FG - 0.0069G + 3.29 Fig. 5. Master curve for the parametric relationship associated with Eq (5).

value of ln(R M) simultaneously associated with F G = 0 and G = 0. In Fig. 3, there is no experimental line passing exactly at the origin ( F G = 0, G = 0). To avoid unnecessary mathematical manipulation, the average ln(R M) corresponding to the M6 (open squares) and M7 (solid lozenge) lines, just above and below the origin, was considered. This average was found to be 3.29. Therefore, with actual figures, Eq. (4) becomes P ¼ 0:0592 FG  0:0069 G þ 3:29:

ð5Þ

This parametric relationship permits to correlate the mechanical resistance of each diamond crystal, synthesized under the conditions applied in the present work, with its size and defect morphology, now associated with P. Moreover, Eq. (5) may be used to interpolate and, eventually, to extrapolate data for crystals obtained under the same experimental conditions. Fig. 5 shows the graphic representation of Eq. (5) for all experimental points given in Table 2. This representation defines the master curve for the parametric relationship presented in Eq. (5). It is relevant to notice that the master curve in Fig. 5 could be adjusted to a linear relationship between ln(R M) and the parameter P, within the band limited by the dashed lines, which contains all points. The mean equation for the best linear fit corresponding to this master curve was found to be: lnðRM Þ ¼ 1:013 P þ 0:263:

ð6Þ

The interval associated with the limits of the experimental points containing band corresponds to approximately T 0.32 for ln(R M) and T 0.31 for P. It is beyond the scope of the present work to speculate on the theoretical predictions behind the mathematical interpretation of the master curve in Fig. 5. In practice, however, with the proper extrapolation one could estimate the maximum resistance attained by a diamond crystals synthesized in a HP –HT system that follows a parametric relationship. For instance, if one considers an almost

65

flawless diamond crystal with size of 500 Am, which is about the largest that can be obtained in a concave anvil with central concavity high pressure device [6], its F G would be estimated, using Eq. (6), as 75.0 T 7.94 N. This is a value almost 50 times greater than the smallest in Table 2. Moreover, it is relevant to mention that, in practice, similar values are specified by the Russian norm GOST9206-80 for relatively large diamond crystals [10,11]. As an example, this norm indicates a mechanical resistance of 80 N for a 450-Am crystal. Using Eq. (6) for an almost flawless crystal with 450 Am in size, a F G of 70N is obtained. Therefore the possibility of separation diamond crystals according to their defect morphology and size could strongly improve the selection for a given technological application associated with a certain mechanical resistance. The limited nature of the present results does not permit to consider the parametric relationship expressed by Eq. (5) as a general behavior for diamonds powders. It should not possibly apply with the same numerical parameters for natural diamonds or even for those synthesized in different systems such as multi-pistons and belt. At the moment, investigations are being carried out on diamond powders obtained in the same concave anvil HP – HT system but at different operational conditions. Preliminary results indicate that similar parametric relationships apply. In a future publication the possibility to further extend this parametric method to classify diamond crystal shall be discussed.

4. Conclusions A parametric relationship has been proposed to correlate the defect morphological aspects of diamond crystals with their size and compressive mechanical resistance, given by the fracture load in single grit tests. These three characteristics were experimentally evaluated in diamond powders synthesized in a concave anvil HP – HT device at 4.7 GPa and 1250 -C. A quantitative value for the defect morphological aspect was assigned based on the relative compressive resistance of a crystal group with the same defect morphology in comparison with that of the most perfect group. The parametric relationship was associate with a master curve that, at least for crystals synthesized in the same HP – HT device, allows for interpolation and extrapolation of any two characteristics to obtain the third one.

Acknowledgements The authors would like to express their thanks to the financial support provided by the Brazilian agencies: FAPERJ, CNPq and CAPES. The permission for using the SEM facilities at COPPE/UFRJ is gratefully acknowledged.

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[7] J.E. Field, The Properties of Diamond, Academic Press, London, 1979. [8] A.V. Eliutin, A.L.D. Skury, A.A. Potemkin, R.I. Polushin, Superhard Mater. 1 (2001) 4. [9] J.E. Field, H.M. Hauser, I.M. Hutchings, A.C. Woodard, Ind. Diamond Rev. 8 (1974) 255. [10] Diamond Powders for Grinding, Russian State Standard GOST 920680. [11] V.G. Gargin, Superhard Mater. 4 (1983) 27.