Assessing Diamond and cBN Quality for Tooling Applications
by Dr Sergio Carbonini
Diamond and cBN are of the hardest materials known to man.Consequently, it can be quite difficult to measure the strength of these materials with accuracy. RE.TEK. is the leader in the field of diamond strength testing for more than 20 years and RE.TEK. diamond testing equipment is widely used in the industry to measure the strength and quality of diamond provided to toolmakers.
In this the first article on the measurement of the strength of diamond, we delve into some technical aspects of the test and then provide an outline of the procedure for accurately testing diamond strength and determining the quality and consistency of material provided by the diamond producers.
Those who are less interested in the technical details can skip to the section titled “F.I Measurement in Practice”.In a subsequent article we will explore in more depth the practical use of the RE.TEK. friability tester equipment.
The growth in the number of companies manufacturing superabrasive materials, diamond and cubic boron nitride, cBN, for tooling applications has brought benefits and disadvantages in recent years. The downward trends in diamond price and consequent reduced the costs of the manufacturing process have been positive for tooling companies buying the materials. However, this has meant that diamond processing, a particularly costly part of the production process, is generally, not as secure i.e. as controlled and consistent as before due to the increased cost sensitivity of the manufacturing process.
For tooling producers, their customers require tools which have consistent quality and guaranteed performance, but with the fluctuation in diamond quality between and within material supplier batches, tool producers often can’t guarantee the properties of the raw materials used and this could have a detrimental effect on the final tool performance.
This is one of the reasons why testing of diamond and cBN materials before they enter the tooling production is so vitally important. The Abrasives Hub has talked to the founder member and technical manager Dr Sergio Carbonini, of RE.TEK. s.a.s., to explain the theory and practice of friability testing for diamond and CBN. Since 1989, the Italian company has been a leader in the development of testing equipment and its machines are now used all over the world.
Dr Carbonini has been a key force in developing the theory of measuring diamond strength alongside different methods to test of quality of super-materials like diamond and cBN. As Dr.Carbonini explains, determining the Friability Index, F.I., is one of the most accurate and useful measures of diamond quality. Additionally, the Toughness Index, T.I., can easily be established from the F.I. using a simple algorithm.
The Theory of Friability Testing
“In the majority of diamond tools for machining stone materials the cutting action is roughly similar to hammering, i.e. it acts by crushing pressure waves or impact. Hence it is paramount to know the shock strength of the diamond, that is, how hardness and resiliency are balanced,” explains Dr Carbonini.The cutting properties of a tool are not only influenced by the strength of the diamond but are also affected by the correct combination of the diamond properties with the bonding agent hardness and resiliency.
This is why synthetic diamonds are supplied complete with the applicable commercial grading, dividing them according to their application area, substantially based on impact strength and the decay of that property as a result of temperature and sintering time. “For an independent, state-of-the-art design and control of diamond tools for machining stone materials, it is particularly crucial to know, besides the bonding agent properties, the diamond specifications, measured directly before and after sintering,” says Dr Carbonini.
Toolmakers are able to accurately control the properties of the bonding agent and the toolmaking process.However, these toolmakers need to rely on the diamond producers to ensure that the properties of the key component of the tool consistently meet the expected values (standards).Therefore they need a means of verifying the consistency of the supplied product.
A measurement can be reliable only if that measurement is repeatable and predictable. “Repeatability means that measuring equal materials according to the same procedures, the resulting numerical results are the same or have as small a deviation as possible,” notes Dr Carbonini.
Measurements can be divided into absolute or relative measurements. Measurements are regarded as absolute when, these measurements can be compared to a defined standard and units for the measurement exist. For example, the measurement of length is absolute in that a defined standard exists; the unit of measurement (metre) is clearly defined and
, everybody knows what measuring a sample length means.
“Relative measurements are those where the obtained datum is not directly related to the physical condition of the sample under examination but, for instance, it is an expression of a property of the material that does not fall under direct observation,” explains Dr Carbonini.
“Of course, in this case standards and methods can be the most varied. For instance, hardness measurement defines the relationship between the penetration of the inching tool and an assumed number intended for classifying the hardness property. Just think about the various methods: Brinnel, Rockwell, Vickers … Each one of these methods makes use of different measurement systems, based on their own relative scale, features a specific area of application, expresses properties that are similar, but not exactly the same, and sometimes for the same material measurements are not comparable,” notes Dr Carbonini.
Further he states, “The impact strength value or diamond, expressed by the F.I. friability index, is a repeatable, predictable and relative measurement. It expresses a diamond property that cannot be directly evaluated against physical parameters, but must be set in relationship with an average of combinations of hardness-resiliency of a limited number (ratio) of diamond grains assumed as representative sample or the material under investigation.”
Setting the assumptions
Consider a diamond sample (distribution) consisting of a sufficiently large number of crystals sharing similar shape, dimensions and quality which, under controlled conditions, undergo a series of destructive impacts. The quality of diamond is known to be related to the amount of impurity in the diamond crystals.These impurities are in the form of carbon inclusions. Crystals are assumed to have uniform quality when they contain in the same number, dimensions and positions of these inclusions or faults.
When the crystals are subjected to impact energy, the variation in the number of unbroken crystals follows the statistical equation:
dN= -KNdE 
dN = variation in the number of unbroken crystals
N = number of sound crystals
dE = variation of the destructive impact energy
K = constant of impact diamond breakage probability
The – sign proves that as the breakage energy increases the number of unbroken crystals decreases.
When diamond crystals are broken by impact a relationship exists between breaking energy and number of unbroken crystals, and this relationship depends on a K factor that can be experimentally determined, and if the material is uniform K is constant.
Integrating , and calculating the ancillary conditions, a law is obtained, which gives the number of unbroken crystals as a function of the breaking energy supplied to the system:
NE = number of unbroken crystals as a function of the destructive impact energy E
N0 = number of originally unbroken crystals
E = destructive impact energy
e = base of natural logarithms (2,718…).
Now assuming that the diamond sample consists only of perfectly octahedral crystals with the same dimensions and uniform quality we can also assume that all diamonds have the same density and, therefore, a weight unit (i.e. 1 mg) will always contain the same number of crystals. Based on this, the number of crystals can be simply “counted” by weighing them. (According to the same principle of the piece counter balance), thus formula  becomes:
PNF = weight of the uncrushed diamond after applying a crushing energy E
PT = original diamond weight
Supplying the crushing energy
The system used to provide the impact force consists of a capsule, with a suitably shaped inner cavity, into which the diamond is placed together with a hardened metal ball. The capsule is oscillated at high-frequency in the direction of the larger axis of the cavity and hence at each oscillation (back and forth) the ball is violently projected against the capsule walls “squashing” the diamond that is between the wall and the ball. This diamond strength testing process is also known as “comminution”.
At every oscillation two impacts are produced between the ball and the diamond grains.
It can be assumed that at each impact the diamond is given a small constant quantity of breaking energy. By further simplification, since the number of oscillation cycles is accurately measured (counted) with respect to every single impact, we can replace the energy value with the number of shaking (impact) cycles, of course adequately changing the K constant.
The formula  can thus be re-written
PNF =PT e-HC
H = new constant of probability of the diamond breaking setting the relationship between shaking cycles and the destructive impact energy
C = shaking cycles.
Fig. 1 shows the curve expressing the trend of formula .
The vertical axis can be thought of as the percentage of unbroken crystals while the horizontal axis is the number of crushing cycles that the diamond experiences (or the time of crushing).At the start, the unbroken crystal percentage will be 100% as the number of crushing cycles increase (i.e. the time of crushing increases), the percentage of unbroken crystals decreases.
It can be observed how PNF features an exponentially decreasing trend as a function of the shaking cycles.The above reported law should be a mere theoretical exercise if it was not experimentally observed that synthetic diamonds can be produced and selected, having different impact strength, and this allows diamond producers to process the diamond into the various diamond commercial grades.
This difference in grades is mathematically expressed by different H values in formula  and hence leading to different breaking curves for each diamond quality; in detail, the “best” diamonds feature, being the supplied energy equal, higher breaking curves, as shown in Fig. 2.
This higher strength curve can be intuitively understood as follows: the stronger the diamond, the less the probability that the crystals will fracture when subjected to an impact force.Therefore more impacts are needed to reduce the percentage of unbroken crystals.In contrast, the weaker crystals break more easily and this leads to the relatively lower strength curve shown in the figure above.
So determining H provides knowledge of the “quality” of the diamond under examination.
From : PNF/PT=e-HC
From which: ln(PNF/PT)= -HC
and, based on the properties of logarithms, ln(PT/PNF) = HC
And expressing the formula in terms of H
H= ln(PT/PNF)/C 
If we define the “quality” of the diamond as the proportion from the number of original crystals to the number of crystals that break, due to the number of the impact C, then Function  shows how H, the probability constant, decreases as the diamond “quality” increases, tending to 0 as more diamond crystals are able to withstand the impact breaking. While formula  is mathematically correct, it is more intuitive to define the strength in terms of the inverse of this function so that the value of the constant increases as the quality of the diamond increases (i.e. as the properties of the diamond improve).
This is why it was preferred to define the friability index F.I. as the inverse of formula 
F.I.= 1/H = C/ln(PT/PNF) 
This gives a number (F.I.) that qualifies the diamond as a direct function of the capability to withstand impact breaking. Should the above number be used as it was defined, it is not possible to compare data surveyed by different measurement systems in that the value scale depends on the geometric and operating conditions of the testing equipment. Furthermore, even it is true that every point surveyed on the curve permits to calculate the friability index (F.I.), when PNF value is low the error due to inaccuracy in the weighing process is too large and leads to unacceptably poor accuracy in F.I. determination.
To remedy these limitations an arbitrary multiplication factor and a PNF range within which measurements are reliable were defined.
It was found that the initial sample weight needed for the test was PT = 400 mg ± 0.5 %, in order to ensure that F.I. could be measured with sufficient accuracy.Furthermore, the accuracy of the weighing needed to be to within ± 1mg for a final uncrushed material mass of PNF = 200 mg ± 5 %.
Next, it was necessary to normalise the formula such that F.I. = 100 when the uncrushed diamond PNF is equal to 50% of the original diamond PT, and the number of cycles required for this condition to take place is C = 2500.
The above conditions lead to the formula:
F.I.= 0.027726C/ ln(PT/PNF) 
As a simple check, replacing in formula  the vlnalues: PT = 400, PNF = 200 and C = 2500, it results F.I. = 100.
It was decided that a reliable measure of the strength of the diamond is the number of impact cycles C needed to crush 50% of the diamond.Therefore a procedure was needed for determining the C50 value, i.e. the number of cycles by which 50% of the material is crushed, in case that with the first measurement PNF does not fall within the acceptable range.
In order to do this, an arbitrary number of cycles are used in the first test based on the size of the grains and the natural or synthetic diamond type, PNF is weighed and F.I. calculated from formula 7.
Since F.I. is a constant, by a simple equation it results:
0.27726C/ln(PT/PNF) = F.I.= 0.2776C50/ln(PT/50%PT)
This simplifies to:
C50 = 0.693142C/ ln(PT/PNF)
Making use of formula  it is then possible, in case the first test did not result in PNF values within the preset validity range (200 mg ± 5%) to calculate the number of cycles required to perform a second test in which the PNF value is as close as possible to 200 mg, and hence the calculated F.I. value is affected as little as possible by the errors involved by the weighing system.
F.I Measurement in Practice.
The tests can be carried out for two main purposes:
a) checking the F.I. value in diamonds with known quality
b) determining the F.I. value in diamonds of unknown quality
In case a)where the quality of the investigated material is known one test is sufficient. In fact, it is sufficient to set the Friability Tester on the number of cycles C50 previously determined on the last batch of diamond received with the same quality, and to perform a shaking cycle. Should the weight of uncrushed diamond PNF be equal to 50 % ± 5 % of total weight PT, the examined diamond can be classified as standard (F.I. may vary by ± 7 % as a maximum).
In case b)at least two measurements are required, except where 50 % crushing takes place immediately (through luck or experience of the user). The first measurement is aimed at roughly determining the diamond quality, whereas the second precisely determines the F.I. value. Should the first determination still largely deviate from 50 %, a third test may be required to determine the correct F.I. value.
While the approach described above is quite straightforward and diamond is a material with complex properties, RE.TEK. has demonstrated with its testing equipment that its F.I. measurement is both reliable and repeatable, helping tool companies to accurately and repeatably distinguish between the various qualities of diamond available on the market. The test is very sensitive to the size of the diamond presented top the test.The test assumes that the diamond is accurately sized according to the ANSI/FEPA sizing specification (ISO6106).
InitiallyRE.TEK. developed its original machine only to test diamonds for stone tools applications. An advanced electronic controller has been added to the original mechanics, and this has made the RE.TEK. Friability Tester even more versatile. Consequently, over the years, some customers requested new standards to test diamond for mechanical tools applications, for glass and polishing tools applications, and for cBN. RE.TEK. developed a new machine with two standards: the first to test diamond for stone tools applications, the second selected from one of the others three standards. In 1995 RE.TEK. upgraded the equipment by incorporating a new advanced electronic controller, and now all the four standards are possible with the ST4 Friability Tester version. In addition, equipment operation is even more reliable and does not require any calibration checks.
The company set up in the late 1980s and now has a number of areas of activity including:
Friability Tester and Spare Parts (capsules) production
Recovery from sintered scraps and requalification of diamonds
Analysis of diamonds and sintered segments
Micro-diamond suspensions production.
Cobalt diacetate for animal feed integration production
The first Friability Tester was developed in 1988 initially with only one standard to test diamond for stone tools. Over the years, some customers requested new standards to test diamond for mechanical applications, for glass and polishing, for diamond and cBN. Now there are two types of machines, with one or four standards.
In 1992 the company developed a sonic sieve, and, finally, a splitting equipment to divide the diamond in quality steps.RE TEK operates a small plant with all the equipment necessary to polish, select and remix diamond (size 20-80 mesh).As part of the diamond recovery process, RE TEK, in 1999, developed a small plant to recover and purify the cobalt, producing cobalt diacetate for animal feed integration. This plant and production is under CE control.
In 1994, RE.TEK took over a firm that produced diamond suspensions (water or oil base). These media products are real suspensions (non-Newtonian solutions) and not slurries, with application to polish special materials.