High temperature creep deformation of nanocrystalline diamond films

1 Introduction

Diamond is a material well-known for its combination of exceptional material properties, such as extreme hardness and high elastic modulus. Chemical vapor deposition using the hot-filament technique allows the formation of 3-dimensional coatings of nanocrystalline diamond films on different substrates on an industrial scale [1]. Nanocrystalline diamond films usually consist of small, nearly-equiaxed grains, which give rise to relatively smooth film surfaces [2]. An important mechanical property, the fracture strength, can be as high as 5.0 GPa [3]. This makes nanocrystalline diamond films a strong candidate for applications that rely on good mechanical properties, ranging from hard, wear resistant coatings to robust sensor devices [4, 5].

Nanocrystalline materials often display different properties compared with their coarse grained variants due to their small crystallite sizes and the large volume fractions of grain interfaces [6]. It is necessary to understand such size-dependent phenomena since they might limit or enhance the possible applications of nanocrystalline materials. Most of the investigations to date are focused on the properties and behavior of nanocrystalline metallic materials [6]. In contrast, the present work reports an investigation of the creep behavior of nanocrystalline diamond. In very fine grained metallic as well as ceramic materials it is observed that grain boundary sliding is the dominant mechanism of plastic deformation and not dislocation generation and motion [7]. In non-metals plasticity is also based on deformation mechanisms involving the grain boundaries rather than dislocation activity that commences in the grain interior.

Diamond possesses grain boundaries with an atomic structure that is different from those of grain boundaries in other materials with the same crystal structure, e.g. silicon [8], [9], [10]. In diamond, in contrast to silicon, a fraction of the grain boundary excess energy is relaxed by changing the hybridization of carbon atoms. This leads to structurally more ordered sp²-bonded carbon structures within the grain boundary [8, 9]. As a result, chemically more disordered grain boundaries involving sp²- and sp³-bonded carbon atoms are formed [8, 9].

It has already been demonstrated that the structure and chemical composition of a grain boundary significantly affects the grain boundary sliding velocity [11, 12] and hence the rate of plastic deformation [13, 14] of polycrystalline materials.

Covalently bonded materials are usually brittle below their Einstein- or Debye- temperature and become ductile above it [15]. The Debye temperature of diamond is 2200 K [16] (1926.85 °C) but the brittle–ductile transition in diamond does not follow the aforementioned rule, since diamond is a metastable phase at low pressures and starts to transform to graphite at temperatures of 1500–1800 °C [17], [18], [19]. This transformation is found to start from the surface, since the higher specific volume of graphite would lead to high pressure on a graphite nucleus inside the material which corresponds to the stable region of diamond in the phase diagram of carbon [17], [18], [19], [20]. Plastic deformation of diamond was first reported in 1924 by Friedel and Ribaud to commence at 1880 °C [21], [22], [23]. Later, Evans and Wild reported the range for brittle–ductile transition for diamond to be between 1400 °C and 1600 °C [23, 24]. Weidner et al. measured the yield strength of diamond at 1000 °C to be 10 GPa and showed that plastic deformation takes place due to crystal plasticity [25]. More recent investigations revealed dislocation-mediated plasticity in microcrystalline diamond powder that had a yield stress of 7.9 GPa at 1000 °C [26].

If nanocrystalline diamond is exposed to high temperature, one could examine whether the unique grain boundary structures can give rise to plastic flow at much lower temperatures and stresses. In this work we investigate plastic deformation of nanocrystalline diamond films at a high temperature.

2 Experimental procedure

Nanocrystalline diamond films were grown by means of hot filament CVD on 4 inch (10.16 cm) silicon wafers. Before growth, the silicon substrates were pretreated by ultrasonic seeding [1, 27, 28]. The seeding density usually achieved is in the range of 10¹¹ cm⁻² [1]. The nanocrystalline diamond film was grown by a CH₄/H₂/NH₃ gas mixture, similar to what was used in the process explained in [3]. The film was grown up to a thickness of h = 50 µm.

The film thus grown was structured by a 1064 nm diode laser, followed by the dissolution of the silicon substrate in a potassium hydroxide solution. This way, free standing rectangular samples (b = 4 mm, l = 13 mm, h = 50 µm) made of nanocrystalline diamond could be fabricated. Investigation of the sample cross-sections in a scanning electron microscope (SEM) showed that no visible changes in the microstructure resulted from the laser cutting. Only a thin (a few microns thick) layer of non-diamond carbon was formed close to the cut but it mostly disappeared during sample cleaning. An SEM image of the surface morphology of a sample grown as described above is shown in Figure 1a. A cross-sectional SEM image of a laser structured, free standing nanocrystalline diamond sample is shown in Figure 1b.

Figure 1:

SEM images of the prepared samples: (a) the nanocrystalline diamond sample surface morphology, (b) the cross-section of a laser structured, free standing nanocrystalline diamond sample.

The strong reaction of diamond with oxygen at elevated temperatures makes it necessary to perform the creep measurements in an ultra-high vacuum environment. Secondly, the brittleness of the diamond samples makes tensile tests of specimens extremely difficult. These limiting conditions and the small sample sizes rule out creep tests using conventional equipment. Consequently, we built a simple three-point bending setup, constructed of molybdenum. The test setup was placed in an evacuated tube furnace, schematically shown in Figure 2a. The pressure inside the tube furnace was between 10⁻⁵ and 10⁻⁶ mbar during the experiments. One of three constant loads (F = 0.414 N, 0.443 N, 0.666 N) was applied by placing the corresponding mass on top of the punch.

Figure 2:

Experimental setup: (a) Schematic drawing of measurement setup, (b) the simple three-point bending apparatus placed in the evacuated tube furnace, prior to load application at room temperature, (c) on load application, after 30 min of creep at 1000 °C.

The sample was heated in a contact-less fashion by the radiation of a heating system consisting of heating coils surrounding the tube furnace. The heating system was movable such that the sample could be heated up and cooled down quickly.

The downward displacement of the sample at the load point was measured using optical photographs of the samples (see, for example, Figure 2b and c), taken by a camera mounted in a fixed position relative to the bending setup.

A well-known analysis for the three-point bending creep test was used to examine the displacement data [29]. The steady state creep rate is described by Norton’s equation,

where B is a material constant, n is the creep stress exponent, ε ̇ s s is the steady-state strain rate and σ is the applied stress. The test specimen is a straight, rectangular beam of width b, height h that rests on two simple supports separated by a distance l. The vertical along which the load is applied (called load point) is half-way between the two supports. See Figure 3.

Figure 3:

Schematic drawing of the 3-point bending setup.

Following [29], the steady-state displacement rate of the load point is calculated as

which can be simplified as,

with

The parameter B is calculated from N as

From Equation (3), a linear relation between the logarithm of the steady-state displacement rate δ ̇ s s and logarithm of the applied load F is obtained. In such a plot, the slope will be equal to the creep stress exponent n and the intercept on the ordinate yields the value of N. The parameter B can be calculated from Equation (5) once N and n are known.

From the three-point bending experimental measurements, the equivalent stress that would be experienced in a tensile specimen is obtained as [29, 30],

and the equivalent steady-state strain rate is given by,

If one integrates Equation (7) with respect time, remembering that at t = 0, ε = 0, one would get the linear relation between ε and δ.

3 Results and discussion

Prior to the creep tests, the specimens were subjected to X-ray diffraction using Cu-K_α (λ = 1.54 Å) radiation. Based on X-ray diffraction peak broadening of the (111) peak and the Scherrer equation, the average grain size was estimated as 7.9 nm. Additional X-ray diffraction measurements were also made on samples that were annealed for 90 min at 1000 °C. Figure 4 shows the diamond 111-peak before and after annealing.

Figure 4:

XRD measurements of the nanocrystalline diamond 111-peak reveal no evidence for grain growth after 90 min at 1000 °C.

The results revealed that within the experimental time frame, no evidence is available for grain growth in the nanocrystalline diamond specimens studied.

The elastic modulus and hardness of the samples were measured at room temperature by nanoindentation using a Berkovich indenter [31], [32], [33]. Indentations into a standard fused silica sample before and after the indentation into the nanocrystalline diamond film confirmed the integrity of the diamond indenter. Using the Oliver–Pharr method [31], [32], [33], the hardness was found to be H = 36 ± 6 GPa and the elastic modulus to be E = 403 ± 55 GPa, assuming that the Poisson’s ratio of nanocrystalline diamond p = 0.2 [3]. In qualitative agreement with these experimental results, simulations have reported a reduction in elastic modulus with decreasing grain size and increasing sp² fraction in the grain boundaries [34, 35].

The mass density of the diamond film produced was determined using the Archimedes method and found to be 2.77 ± 0.13 g cm⁻³. This is a significantly smaller value than the mass density of single-crystal diamond (3.51 g cm⁻³ [36]). The reduced mass density is attributed to the relatively large grain boundary volume present in the nanocrystalline films and porosity.

For a grain size of about 7.9 nm, the mass density of the grain boundary is estimated to be around 1.6 g cm⁻³ (46 % of the density of a single crystal), which is a typical value for hydrogenated amorphous carbon [37]. This is a much smaller value than the one predicted by molecular dynamics simulations for impurity-free diamond [38, 39]. These simulations predict that the grain boundaries have an increased volume per unit area of 10–14 %, compared with the grain interior [38, 39]. Moreover, HRTEM studies of meteorites reveal that complex diamond–graphene crystalline nanostructures can exist in cubic diamond [40, 41]. These so-called diaphite nanocomposites possess a much larger specific volume than diamond [40, 41] and could also exist in nanocrystalline diamond films. Finally, an incorporation of impurities, such as hydrogen, into the grain boundaries could be an additional factor contributing to the reduced mass density and reduced elastic modulus [42].

The measurements in three-point bending made for 70 min at T = 700 °C did not reveal any evidence for irreversible, plastic deformation. Within the limits of experimental accuracy, on unloading, the samples straightened.

When the same measurements were made at a temperature of T = 1000 °C, the samples exhibited transient creep deformation – see Figure 5 – initially, which eventually settled down to a steady state strain rate, characteristic of the applied load. On unloading, the samples did not straighten back to their original radius of curvature, which indicates the presence of inelastic/permanent strain. Figure 5a shows the displacement data recorded during such an experiment. As was pointed out earlier, by an integration of Equation (7), the strain in the sample can be calculated. This is displayed in- Figure 5b.

Figure 5:

Creep deformation of nanocrystalline diamond films at 1000 degrees C: (a) The displacement and strain at load application point as a function of time at a temperature T = 1000 °C, and load F = 0.414 N. (b) Equivalent strain calculated for the sample during bending. At t = 0 (still at room temperature), purely elastic bending is seen. For longer times, the displacement/strain increases, showing the presence of creep deformation in the samples.

What is described above is clear evidence for time-dependent inelastic deformation (also known as creep deformation; the initial transient region is known as Andrade creep or logarithmic creep) being present in the samples. Following the standard practice in creep literature [43] the strain–time relationship in Figure 5b is described in a continuum model as

ε ( t ) = α l n ( t ) + c , w i t h α = 4 × 1 0 − 5 , c = 6 × 1 0 − 4 a n d t h e c o e ffi c i e n t o f c o r r e l a t i o n , R 2 = 0.6797 .

Interestingly, as early as in 1963 logarithmic creep was reported in graphite deformed at temperatures below 1500 °C [44]. It has also been widely reported in metals and alloys of fcc, bcc and hcp crystal structures. Although what we have employed above is the most common form of representing logarithmic creep behavior, a close examination reveals that this equation fails at t = 0 because it suggests that at t = 0, the strain rate is infinite, which is physically not true. Therefore, it is expressed by the “purists” in an equivalent form ε = α ₁ ln(1 + νt), where α ₁ and ν are fitting constants, with ν having the dimension t i m e − 1 [43]. It is straightforward to evaluate the constants of the alternative equation also in a manner very similar to that used to determine α and c in the former equation.

In addition, the following comments are pertinent. When creep measurements are made, the measured total strain, ε _tot, consists of three parts: the initial elastic strain, ε _e, the subsequent plastic/inelastic strain, ε _p, both of which are instantaneous (time-independent), and the creep strain, ε _c, which is time-dependent. Using an additive law, it is written that ε _tot = ε _e + ε _p + ε _c. In most of the creep analyses, including the one adopted in this paper, ε _e, which in most materials is governed by Hooke’s law, is neglected and the measured strain (really ε _tot) is taken as equal to ε _c, as both ε _p and ε _c are inelastic strains. Strictly, in tension and compression testing systems there are ways of deducting ε _e from ε _tot to obtain the total inelastic strain. But, with the experimental system used here (three-point bending) this is not possible, certainly not done by most of the researchers.

During transient (Andrade) creep the total strain measured is rather small. Therefore, not deducting ε _e from ε _tot could lead to an overestimation of ε _c. This is not considered in the present analysis. But, it is well known that the shape of the strain–time curve in a stress relaxation test (done by stopping the cross-head motion in a tension or a compression test without load removal) is very similar to that of the transient creep curve and numerically the strain recovered in a stress relaxation test is ≈ε _e for some materials. Therefore, an indirect way of knowing ε _e in the present case exists. As the accuracy of this method is not known, no such correction was attempted in the present analysis. Nor has it been done in those of the other researchers who also used the same method.

These experiments were performed at 3 different loads (F = 0.414 N, 0.443 N, 0.666 N) at 1000 °C for a maximum duration of 60 min. In addition, some creep measurements were made for a maximum duration of 24 h. They revealed that for each of the applied loads a time-independent, steady-state creep rate is present. Figure 6 shows the steady state displacement rates obtained at different loads.

Figure 6:

Steady-state displacement rate (mm⋅s⁻¹) as a function of loading (N) plotted on a log–log scale.

Using Equations (3) and (5), we obtain from the slope and the intercept of Figure 6 the values n = 1.6886, N = 1.9494⋅10⁻⁸, B = 4.0784⋅10⁻²¹. With this, the equivalent stresses, strains and strain rates can be obtained using Equations (6) and (7).

Figure 7 presents the steady-state strain rate as a function of stress (Equation (6)). From the slope of Figure 7 (a plot of log  ε ̇ s s vs. log (σ _ss)) n is evaluated as 1.79, which is close to the value of 1.69 calculated from Figure 6. This establishes the internal consistency present in the calculations at all stages.

Figure 7:

Dependence of the steady-state strain rate (s⁻¹) on stress (GPa) for the investigated nanocrystalline diamond films at 1000 °C.

The applied load led to a maximum stress in the samples of only 0.3–0.8 GPa (corresponding to a steady state stress between 0.08 and 0.13 GPa). Suzuki et al. [45] have presented a universal scaling law for the temperature-dependent critical shear stress of materials of diamond lattice structure (Si, Ge, SiC, diamond). According to their model, the critical shear stress for diamond at 1000 °C should be significantly greater than 1 GPa [45]. The yield strength at 1000 °C in diamond poly-crystals was observed in the investigations of Weidner et al. [25] and Yu et al. [26] to be 10 GPa [25] and 7.9 GPa [26] respectively. The theoretically estimated resolved shear stress [43] and the experimentally determined yield stresses [25, 26] in the above cases are also significantly greater than the stresses applied in the present experiments.

It is well established that in very fine grained metallic systems, grain boundary sliding becomes the dominant plastic deformation mechanism because the stresses needed for dislocation formation in the grain interior and its motion are considerably more than the stresses needed for grain boundary sliding when the grain size goes below one micrometer [7, 46, 47]. In the present case also, the grain boundaries of nanocrystalline diamond films, having a strongly reduced shear modulus [3], are expected to deform through a mechanism dominated by grain boundary sliding. In addition, in these experiments, a value for the stress exponent, n, of 1.69–1.79 is obtained. It has been observed in several experiments that, depending on the experimental conditions, the value of n for grain-boundary-sliding dominated processes hovers in the range 1 < n < 3, with the value close to 2 for many alloys [47] – another supporting argument in favor of a grain-boundary-sliding dominated process being responsible for deformation in this case.

It is known that diamond grain boundaries can undergo structural changes when annealed above 800 °C [48], [49], [50], [51]. To quantify the impact of the grain boundary structural changes by annealing at 1000 °C, nanoindentation tests at room temperature on samples that were annealed for 1 h at 1000 °C were carried out. These tests also revealed a similar elastic modulus and hardness (E = 414 ± 71 GPa, H = 37 ± 8 GPa) compared with the values obtained on the as-grown samples (E = 403 ± 55 GPa, H = 36 ± 6 GPa). Density measurements on as-prepared samples and on samples that were annealed for an hour at 1000 °C show a similar density of 2.87 ± 0.13 g cm⁻³ after annealing, compared with that of their as-grown state (2.77 ± 0.13 g cm⁻³).

Using the grain boundary sliding controlled flow model [7, 52], [53], [54], [55], [56], [57] a priori predictions of the shear modulus, G, and the elastic modulus, E, are possible.

In this analysis, grain boundary sliding controlled deformation in different classes of materials is accurately accounted for if it is proposed (and subsequently verified experimentally) that grain boundary sliding (GBS) develops to a mesoscopic scale (defined to be of the order of a grain diameter or more) and controls the rate of the deformation process. It is reasonable to postulate that if the barriers to boundary sliding at triple junctions and other grain boundary obstacles are accommodated by faster accommodation processes of dislocation emission (in a barrier-free manner or during a thermal event) from sliding grain/interphase boundaries, highly localized atom shuffles of fractions of interatomic distance and/or grain rotation, GBS can develop to a mesoscopic scale and form plane interfaces, which by interconnection can form a 3D-continuous network of deforming high-angle grain boundaries and lead to superplastic flow. Experimental evidence for mesoscopic boundary sliding/plane interface formation has been reported in many classes of materials. For a summary, see, for example, [58, 59]. The length of the plane interfaces formed is a function of temperature and grain size. Evidently, plane interface formation gives rise to a long-range threshold stress (as shuffling/rearrangement of atoms in the vicinity of grain boundaries over mesoscopic scale dimensions is involved), which is subtracted from the applied stress to determine the effective stress that drives the deformation. The actual accommodation process(es) will depend on the type of the grain boundary obstacles, chemical composition of the material, phases present and the experimental conditions. Such a description has already been shown to explain grain boundary sliding controlled flow in metallic materials of fcc, bcc or hcp crystal structures, ceramics, composites, bulk metallic glasses, intermetallics, nanostructured materials, geological materials and ice/ice-mixture. It can also explain how the grain shape remains near-equiaxed even after extreme specimen elongation [57, 58].

For mathematical development at the level of atomistics that extends to a mesoscopic scale, the basic sliding unit in a high-angle grain boundary is assumed to be an oblate-spheroid-shaped atomic ensemble that contains excess free volume of about 10 % (over and above that contained by a grain boundary) and has dimensions of 5 atom diameters along the boundary plane and 2.5 atom diameters (≈average grain boundary width, W [60]) in height measured at the center of the oblate spheroid in the direction perpendicular to the boundary plane. The oblate spheroid is assumed to be located symmetrically on either side of the grain boundary between the two grains that define the grain boundary. Such a choice of dimensions for the basic sliding unit permits GBS controlled flow in crystalline and non-crystalline (e.g., bulk metallic glasses) materials to be explained on a common basis, in addition to this assumption being consistent with experimental observations [7, 61, 62]. Sliding at a grain boundary results from a sequential shear of oblate spheroids of atom ensembles, containing the excess free volume described above, until it gets blocked at a grain boundary obstacle, e.g. a triple junction. As stated above, such an obstacle gets eliminated by faster (than the rate of GBS) by dislocation emission in a barrier-free manner or during a thermal event or highly localized atomic shuffling in the vicinity of the triple junction and/or grain rotation arising from unbalanced grain boundary shear stresses [63]. In a real situation, if the basic boundary sliding unit is not an oblate spheroid, but of an irregular shape, this can be taken care of by introducing a form factor, f, of value close to unity [7].

In real materials there are also grain size distribution and grain shape irregularities. In this analysis these are replaced by equivalent (in volume/area, depending on whether 3D or 2D situations are considered) rhombic dodecahedral grains (closest to the shape of real crystals [64]) of uniform size. This average grain size is obtained from a secondary rate equation that expresses the instantaneous grain size as a function of temperature, strain and time of deformation.

Such an analysis leads to the following equations:

Here von Mises yield behavior is assumed. Using any other yield criteria, e.g. Mohr–Coulomb, will introduce only negligible changes in the final results [65, 66]. For an oblate spheroid shape, β 1 = 0.944 ( 1.590 − p ) ( 1 − p ) , β 2 = 4 ( 1 + p ) 9 ( 1 − p ) , with p the Poisson’s ratio [67]. According to the von Mises criterion, the shear strain rate γ ̇ = 3 0.5 ε ̇ , where ε ̇ is the normal strain rate one obtains from plots like Figure 7. The grain boundary width W is assumed to be ≈ 2.5 × atomic diameter – see above. The unit shear strain produced in a basic sliding event γ ₀ is equal to 3 0.5 ε 0 , where ɛ ₀ is the instantaneous dilatational strain present as one half of the oblate spheroid shears and goes over the saddle point during the shear of a basic unit of grain boundary sliding, ν is the thermal vibration frequency, L is the average grain size, τ is the applied shear stress, which, for the present case is derived from any of the points shown in Figure 7 (along with the corresponding strain rate), τ ₀ is the threshold stress needed for the onset of mesoscopic boundary sliding, V ₀ is the volume of the above described oblate spheroid (= 2 3 πW ³), ΔF ₀ is the activation energy for the rate controlling GBS deformation process, k is Boltzmann’s constant, T is the temperature of deformation on the absolute scale, G is the shear modulus of the oblate spheroid located in the grain boundary region, which, in turn, is equal to E 2 ( 1 + p ) , with E the Young’s modulus of the material, N is the number of grain boundaries that align to form a plane interface, γ _B is the specific grain boundary energy, which is assumed to be isotropic in this analysis, and “a” is a constant, which is a measure of the grain coarsening tendency of the material due to both static and dynamic grain growth. By analyzing more than 50 materials of different classes (metals and alloys, ceramics, metal-matrix as well as ceramic-matrix composites, intermetallics, nanostructured materials, bulk metallic glasses, geological materials, ice/ice-mixture), it has been suggested that the following (mean) numerical values can be assumed for the four 4 constants of this mesoscopic scale analysis [57]:

γ B = 0.776 5 ≈ 0.78 J ⋅ m − 2 ; a = 0.203 6 ≈ 0.20 ; N = 6.7 6 − 7 , γ 0 = 0.213 4 ≈ 0.21 .

It is noted here that in the real situation the values of the above four constants are material-dependent. The mean values are useful for order of magnitude calculations for a new, untested situation to predict the likely behavior. It should also be kept in mind that there could be situations where the specific grain boundary energy is anisotropic. For such a case, the analysis has to be developed further because the present analysis assumes isotropic specific grain boundary energy.

For the present case, p = 0.2 (Poisson’s ratio of nanocrystalline diamond [3]). Thermal vibration frequency, ν = 10¹³ s⁻¹, the average grain size, L = 7.9 nm for both the as-prepared samples as well as the specimens pre-annealed at T = 1000 °C and the atomic diameter of diamond is 0.1828 nm. The normal strain rate values ε ̇ , are taken from Figure 7, along with the corresponding values of the steady state stress.

Using the above data and Equations (8)–(11), the average values of the shear modulus, G and the Young’s modulus, E for nanocrystalline diamond (Figure 7) are predicted as G = 105.38 GPa and E = 252.92 GPa (an average of 6 stress/strain rate combinations taken from Figure 7). In the present calculations, following the classical analysis of Eshelby [67], the activation energy for the rate controlling process (Equation (10)) is obtained. Therefore, G should correspond to the shear modulus of the oblate spheroid of atom ensemble that contains free volume. In our experiments involving nanoindentation testing we have obtained an experimental value for E of ∼403–414 GPa. When one considers the size of the tip of the nanoindenter, it becomes clear that the experimentally determined value corresponds to the elastic modulus of a region significantly larger than that of the grain boundary width. The present authors are not aware of any experimental technique for measuring the shear modulus of the oblate spheroid located within a high-angle grain boundary. However, it is safe to say that an average value of E = 252.92 GPa for the grain boundary region is certainly consistent with an average value of E = 403–414 GPa for bulk nanocrystalline diamond.

In all the materials examined till now, see, for example [57], for the validation of the grain/interphase boundary sliding controlled flow model, it was assumed that the elastic constants of the oblate spheroid, representing the basic sliding unit, are similar to those of the surrounding material. This assumption is valid for the systems examined so far because the grain sizes were rather coarse (microcrystalline or sub-microcrystalline) in comparison with the present grain size of 7.9 nm and at least in metallic materials the elastic constants decrease only by ∼10–20 % even when the grain size goes below about 20 nm. (No such measurements are available for non-metallic materials.) In contrast, not only the average grain size of the present bulk nanocrystalline samples is 7.9 nm, but also at the test temperature of 1000 °C, grain boundaries of diamond are known to relax and become significantly less rigid. Therefore, in our opinion, by applying the grain/interphase boundary sliding controlled flow model successfully to understand in a quantitative manner the creep behavior of nanocrystalline diamond, we have demonstrated the relevance of this model in a new situation where the mechanical properties of the grain boundaries are distinctly different from those of the grain interior – an important step forward, in our opinion, in view of recent developments in nanocrystalline materials and nanoglasses.

It should be noted at this stage that we have been able to account quantitatively and accurately for the steady state creep deformation of ultra-nanocrystalline diamond in terms of a mesoscopic scale grain boundary sliding rate controlled deformation process, which was earlier found suitable to explain structural superplastic deformation in different classes of materials on a common basis. But direct experimental evidence for grain boundary sliding in the present samples during their deformation is yet to be provided. This could be done by comparing the grain boundary appearance of the as-prepared, annealed for an hour at 1000 °C and deformed at 1000 °C specimens, as has been done in the past in the case of other materials [68]. This would require the careful preparation of thin foils by focused ion beam (FIB) for examination under a modern low-voltage, low-dose, transmission electron microscope (TEM). Such an investigation is planned for the future.

4 Conclusions

The transient as well as the steady state inelastic deformation of a nanocrystalline diamond film at high temperatures was investigated in a three-point bending apparatus using a constant load. It was shown that at 700 °C the deformation is fully elastic, while at 1000 °C, the samples exhibit time-dependent inelastic deformation (creep). On account of the very low stresses that were applied to deform the samples (0.3–0.8 GPa), the creep behavior is suggested to arise from grain-boundary-dominated processes, rather than crystal plasticity arising from dislocation motion originating within the grains. The deformation behavior was initially transient such that the rate of deformation decreases with increasing time to eventually reach a steady-state value. The transient creep region is shown to be an example of the well-known logarithmic creep behavior of standard materials and the steady-state creep results are demonstrated to be consistent with the predictions of a physics-based model for grain/interphase boundary sliding controlled flow.