Review of Indenter Materials for High Temperature Nanoindentation
Elevated temperature nanomechanical testing techniques, predominantly nanoindentation and microcompression, are becoming increasingly popular due to the lower cost of sample manufacture/preparation, shrinking length scale of devices, and speed of testing. However, testing at high temperatures reintroduces challenges for indenter material selection which were addressed during the first advent of hot hardness testing. With the smaller length scales and greater precision involved in instrumented nanoindentation testing than hot hardness testing, a review of indenter materials  and their properties with a view towards high temperature nanoindentation may be useful to many practitioners as a guide for selecting the correct indenter material for their sample material at high temperatures.
The choice of indenter is normally based on what is the hardest, highest stiffness material available. This criterion ensures that the indenter receives the least amount of damage (Figure 1) possible from the high reciprocal stresses it might experience during indentation. However, at elevated temperatures, there are several addition criterions for selection of indenter material. Will the material remain inert in the high temperature environment? At the desired temperature, is this material still the hardest, highest stiffness material available? Will the indenter material remain chemically inert with respect to the sample and not react with the sample?
Figure 1: Secondary electron micrograph of a damaged conospheroidal diamond indenter.
The material of choice for a specific high temperature indentation test must satisfy all these questions. Furthermore, the properties of this material must be well-characterized as a function of temperature, so that its properties at the test temperature can be used to analyze the resulting load-displacement relationships. In the remainder of this article, the answers to all these questions will be discussed in relation to all the existing literature.
In order to perform a hardness test, the indenter material must be a minimum of 20% higher hardness than the sample in order to generate plastic deformation [2, 3]. In order to avoid rapid blunting of a sharp indenter tip, the indenter material should be significantly (>100-1000%) harder than the sample. To provide an overview of the hot hardness of various indenter materials, the data shown in Figure 2 has been assembled.
Figure 2: Hot Vickers (HV) and Knoop (HK) hardness of indenter materials as a function of temperature [4-9].
Diamond is the obvious frontrunner for hardness at ambient temperature, but its hardness decreases somewhat rapidly at elevated temperature. However, at temperatures below 1000 °C, diamond is still the hardest material available and is recommended for testing of very hard materials, such as ceramics, tool bit coatings, semiconductors, et cetera.
The next hardest material at ambient temperature is cubic boron nitride or cBN. However, its hardness decreases very quickly with temperature, and it retains only half of its hardness by 500°C. Boron carbide (B4C), silicon carbide (SiC), and tungsten carbide (WC) maintain their hardness at elevated temperatures significantly better. Boron carbide maintains its high hardness best of all materials; by 900 °C its hardness surpasses diamond. ReB2 also displays promising high temperature hardness. However, knowledge of its other properties and its commercial availability are still limited.
In summary, diamond and boron carbide appear to be the materials of choice for indenting hard materials at elevated temperatures. However, additional concerns such as indenter/ sample reactivity might make other materials with lower hardness have a chemical advantage for indenting specific materials systems. This is further discussed in a later section.
One of the chief advantages of instrumented indentation over previous hot hardness methods is the ability to extract hardness and elastic modulus without imaging of the residual impression. In the Oliver and Pharr  analysis, since the indenter tip is not perfectly rigid, it elastically deforms simultaneously with the sample. It can be shown that the apparent “reduced” modulus, Er, is given by
where B is a geometric constant, S is the contact stiffness, and A is the contact area. This reduced modulus is the convolution of both the indenter and sample elastically deforming during contact according to the relation
where Ei, νi and Es, νs the Young’s modulus and Poisson’s ratio of the indenter and sample, respectively. This equation demonstrates necessity of accurate knowledge of the indenter properties in order to apply instrumented indentation to measure the mechanical properties of a sample. Since the values of Young’s modulus, as well as all other mechanical properties, change with temperature, it is important to know the correct values of the indenters elastic properties at the test temperature in order to accurately extract sample properties at that temperature. An illustration of the change in elastic properties of various indenter materials is shown in Figure 3.
The raw data for Young’s modulus as a function of temperature shown in Figure 3 is taken from various literature sources [11-18]. The fitted lines shown connecting the points are a regression fit to Wachtman’s equation :
where E0 is the Young’s modulus at 0 °K, A is an exponential fitting parameter, and T0 is the elevated temperature in °K where the Young’s modulus approaches a linear relationship with temperature. A summary of the parameters used to fit the data in Figure 3 is given in Table 1. This equation also accommodates the athermal regime at low temperatures and yields values which approach 0 °K with zero slope in accordance with the third law of thermodynamics. Poisson's ratio also changes as a function of temperature, but both the magnitude of this change and its effect on indentation results are suggested to be almost negligible.
|Indenter Material||E0 (GPa)||A||T0 (°K)||V|
|Tungsten Carbide, WC||706.7||0.0824||879.64||0.194|
|Tungsten Carbide with 6% Cobalt, WC-6% Co||541.7||0.0648||707.91||0.20|
|Cubic Boron Nitride, cBN||681.6||0.0442||526.52||0.15|
|Boron Carbide, B4C||461||0.0548||114.5||0.21|
|Silicon Carbide, 6H-SiC||515.7||0.0218||79.25||0.17|
Table 1 - Summary of elastic parameters for Equations 2 and 3 for various indenter materials.
For the case of tungsten carbide indenters, special caution is needed. Typically, tungsten carbide indenters are sintered cermets containing polycrystalline tungsten carbide grains and some fraction of cobalt as a binder. This has a significant effect on the elastic properties as can be seen in Figure 3. The effect of the grain size and the fraction of cobalt binder on the elastic modulus of the cermet is known , but specific knowledge of the exact microstructure of your indenter would be required to use these relationships.
Figure 3: Young’s modulus of indenter materials as a function of temperature [11-18].
For diamond, WC and cBN and SiC, this change is only a few percent over 500 °C. However, for B4C and sapphire, the change over the same interval is ~6%. This is significant, given that the modulus variation of the sample material may be similarly small.
Damage due to oxidation
The danger of oxidative damage to diamond indenters at temperatures > 400 °C is now fairly well known [20, 21] in the community. At temperatures ≤ 400 °C, diamond indenters can be nominally stable for years. Most other indenter materials are also susceptible to oxidation damage at similar or slightly higher temperatures than diamond - Table 2.
|Indenter Material||Behavior in Oxygen|
|Diamond||Forms CO & CO2 > 400°C|
|Boron Carbide, B4C||Forms B2O3 layer > 450°C|
|Silicon Carbide, 6H-SiC||Forms SiO2 > 750°C|
|Tungsten Carbide, WC||Forms WO3 > 500°C|
|Cubic Boron Nitride, cBN||Forms B2O3 layer > 700°C|
Table 2 – Onset temperature and product of oxidation for various indenter materials in dry air [20, 22-25].
These onset temperatures are typical for oxidation of fine powders with sizes similar to that of sharp indenter radii. However, it is important to note that all of these onset temperatures can be reduced by the introduction of water vapor. Extra caution is warranted during testing in humid environments, since water vapor not only decreases the onset temperatures but also increases the oxidation rates.
For operation at temperatures higher than the onset temperatures in Table 2, a high purity inert gas [21, 26] or high vacuum [27, 28] environment can be used to protect the indenter from oxygen.
Damage due to Indenter/Sample Reactions
Even if the indenter is sufficiently stiff and hard to indent the sample material without significant mechanical blunting or wear, the indenter could still be at risk to chemical reactions between itself and the sample. The classic example of this is the indentation of steel with a diamond indenter at high temperature. Despite the extraordinary chemical stability of diamond, most exemplified by its complete resistance to attack by acids, the diamond disintegrates and reacts with the steel to form Fe3C carbides. This process can completely destroy an indenter, as shown in Figure 4. This demonstrates the necessity of using the appropriate indenter material for various classes of sample materials to ensure that they remain chemically inert during indentation.
Figure 5: Secondary electron micrograph of the remnant of a diamond indenter after contact with a steel sample at 500 °C.
However, this situation is complicated by the extremely high stresses applied during indentation. An appropriate ‘rule of thumb’ for a maximum temperature for indentation with known reactive indenter/sample combinations, such as staying below the creep regime of the material or below the formation temperature of the carbide, remains elusive, since the tip can be lost at temperatures below these criteria - Figure 4.
Table 3 – Overview of indenter and sample material classes and their reactivities at high temperature [20, 26, 29-36].
A systematic empirical study of the influence of stress on these solid state reactions has been avoided thus far due to the prohibitive cost of the number of consumable indenters required to conduct such a study. In the absence of this knowledge, indenter/sample material combinations where reactions have been observed to occur at any elevated temperature are recommended to be avoided completely.
Some limited anecdotal information on safe temperature regimes and indenter/sample material combinations for high temperature indentation exists in the literature on hot hardness from the 1940’s-60’s, but much of this technical expertise seems to have been lost. By combining the limited picture remaining from hot hardness literature with the literature on high temperature wetting, a general picture of the reactivities of various classes of indenter/sample material combinations has been constructed – Table 3.
Diamond indenters show excellent resistance to materials which chemically attack indenters: alkali metals, alkaline earth metals, and metalloids. However, diamond is vulnerable to attack by materials which aggressively form carbides or dissolve carbon: the early and late transition metals.
Tungsten carbide appears to be the most chemically stable of all the indenter materials. It only appears to be vulnerable in combination with tungsten, titanium, and iron at very high temperatures where the carbon could diffuse into the sample. Both indenter materials which contain boron, cBN and B C, 4 show a similar tendency to react with the more energetic early transition metals, late transition metals, and metalloids as well as with oxygen. Sapphire, or more accurately corundum, is perhaps the most reactive indenter material. The majority of the transition, noble, and coinage metals are inert in combination with sapphire. However, significant exceptions exist in almost all categories. The strongest recommendations for using sapphire are its immunity to oxidation, low cost, and good machinability.
The literature properties of various indenter materials have been reviewed with respect to their performance for high temperature nanoindentation. Diamond and boron carbide are the materials of choice for indenting hard materials at elevated temperatures due to their excellent retained hardness at high temperatures. The temperature dependence of the elastic properties of the various indenter materials including formulae for their values has been given along with the possible errors resulting from using incorrect values. The thermal properties of the materials have been briefly described in relation to their impact on high temperature indentation behavior. Lastly, the chemical reactivity of the indenter materials with various elements was reviewed. High to ultra-high vacuum is necessary to prevent oxidation of most indenter materials above ~400 °C with the exception of sapphire. Tungsten carbide showed the lowest reactivity of the indenter materials surveyed and is likely the most universal solution for indentation of metals and alloys without sample- indenter reactions. Further information on indenter material behavior at high temperature can be found in the full review article .
Anton Paar would like to thank Dr. Jeffrey M. Wheeler (now at ETH Zurich) and Dr Johann Michler from EMPA in Thun (Switzerland) for the redaction of this applications report. Figures and sections of this article are reprinted with permission from Review of Scientific Instruments 84 (10), 101301. Copyright 2013, AIP Publishing LLC.
1. J. M. Wheeler and J. Michler, Review of Scientific Instruments 84 (10), 101301 (2013).
2. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids. (Clarendon, Oxford, 1986).
3. D. Tabor, Br. J. Appl. Phys. 7, 159-166 (1956).
4. N. Novikov, Y. V. Sirota, V. Mal’Nev and I. Petrusha, Diam. Relat. Mater. 2 (9), 1253-1256 (1993).
5. M. Lee, MTA 14 (8), 1625-1629 (1983).
6. A. Atkins, Proceedings of the Royal Society. London, Series A. 292, 441 (1966).
7. T. Hirai and K. Niihara, J. Mater. Sci. 14 (9), 2253-2255 (1979).
8. V. Mukhanov, O. Kurakevych and V. Solozhenko, Journal of Superhard Materials 32 (3), 167-176 (2010).
9. R. D. Koester and D. P. Moak, Journal of the American Ceramic Society 50 (6), 290-296 (1967).
10. W. C. Oliver and G. M. Pharr, Journal of Materials Research 7 (6), 1564-1583 (1992).
11. F. Aguado and V. G. Baonza, Physical Review B 73 (2), 024111 (2006).
12. R. R. Reeber and K. Wang, Journal of the American Ceramic Society 82 (1), 129-135 (1999).
13. J. B. Wachtman and D. G. Lam, Journal of the American Ceramic Society 42 (5), 254-260 (1959).
14. J. B. Wachtman, Jr., W. E. Tefft, D. G. Lam, Jr. and C. S. Apstein, Physical Review 122 (6), 1754-1759 (1961).
15. T. Goto, O. L. Anderson, I. Ohno and S. Yamamoto, Journal of Geophysical Research 94 (B6), 7588-7602 (1989).
16. S. R. Murthy, Journal of Materials Science Letters 4 (5), 603-605 (1985).
17. W. Köster and W. Rauscher, Zeitschr. f. Metallk 39, 111-120 (1948).
18. Z. Li and R. C. Bradt, International Journal of High Technology Ceramics 4 (1), 1-10 (1988).
19. H. Doi, Y. Fujiwara, K. Miyake and Y. Oosawa, Metall and Materi Trans 1 (5), 1417-1425 (1970).
20. J. M. Wheeler, R. A. Oliver and T. W. Clyne, Diam. Relat. Mater. 19 (11), 1348-1353 (2010).
21. J. C. Trenkle, C. E. Packard and C. A. Schuh, Review of Scientific Instruments 81 (7), Art. No.: 073901 (2010).
22. L. M. Litz and R. Mercuri, Journal of The Electrochemical Society 110 (8), 921-925 (1963).
23. J. Quanli, Z. Haijun, L. Suping and J. Xiaolin, Ceramics International 33 (2), 309-313 (2007).
24. A. S. Kurlov and A. I. Gusev, International Journal of Refractory Metals and Hard Materials (0), In Press (2013).
25. A. W. Weimer, Carbide, nitride and boride materials synthesis and processing. (Springer, 1997).
26. N. M. Everitt, M. I. Davies and J. F. Smith, Philos. Mag. 91 (7-9), 1221-1244 (2011). 27. S. Korte, R. J. Stearn, J. M. Wheeler and W. J. Clegg, Journal of Materials Research.
27. S. Korte, R. J. Stearn, J. M. Wheeler and W. J. Clegg, Journal of Materials Research 27 (1), 167-176 (2011).
28. J. M. Wheeler and J. Michler, Review of Scientific Instruments 84 (4), 064303 (2013).
29. C. H. Philleo and D. H. Sale, U. S. ARMY WEAPONS COMMAND - DTIC Report Report No. SWERR-TR- 72-63, 1972.
30. N. Eustathopoulos, G. Nicholas and B. Drevet, Wettability at High Temperatures. (Elsevier Science, 1999).
31. G. E. Spriggs, in Powder Metallurgy Data. Refractory, Hard and Intermetallic Materials, edited by P. Beiss, R. Ruthardt and H.Warlimont (Springer Berlin Heidelberg, 2002), Vol. 2A2, pp. 118-139.
32. M. G. S. Naylor and T. F. Page, J. Microsc.-Oxf. 130 (JUN), 345-360 (1983).
33. S. Kleiner, F. Khalid, P. Ruch, S. Meier and O. Beffort, Scripta Materialia 55 (4), 291-294 (2006).
34. E. Paul, C. J. Evans, A. Mangamelli, M. L. McGlauflin and R. S. Polvani, Precision Engineering 18 (1), 4-19 (1996).
35. S. Kalogeropoulou, L. Baud and N. Eustathopoulos, Acta Metallurgica Et Materialia 43 (3), 907-912 (1995).
36. J. A. Arsecularatne, L. C. Zhang and C. Montross, International Journal of Machine Tools and Manufacture 46 (5), 482-491 (2006).