Impact-Induced Damage Accumulation at Micro- and Nanostructural Scale Levels in Sintered Powders SiO2, SiC, and Al2O3 and in Their Single Crystal Counterparts

The acoustic emission (AE) and fractoluminescence (FL) techniques were applied to study the impact damage in sintered powders of SiO2, SiC and Al2O3 and their single crystal counterparts. The measured AE intensities and FL amplitudes are proportional to the energy release in events of microcrack nucleation and chemical bond breakage, respectively. In crystals, the AE method showed the random energy release in crystals, and the scaling energy distributions in powders. The FL method evidenced the self-similar energy distributions in αSiO2 and α-SiC due to nanostructural heterogeneity inherent even to homogeneous solids, while luminescence from α-Al2O3 was specific for the random process.


Introduction
In terms of thermodynamics, the porous ceramic materials are hierarchic systems [1] with well-pronounced self-similar (fractal) properties [2,3].Structural self-similarity results from the long-range interactions between sintering particles at the stage of the thermal treatment.The fractal particle/pore shape and surface profile determine in a good measure the properties of ceramic materials in various important applications [3][4][5].In particular, the porous silicon carbide ceramics are used in aerospace engineering [6] and some armour configurations [7].In this light, a consideration of the destructive process in SiC ceramics under impact forcing could be of interest from the viewpoint of the role of self-similar structures in the mechanism of damage initiation in this material.
A distinguishing feature of fracture in heterogeneous materials is the multiple nucleations of microcracks, the clustering and growth of which lead to the formation of a number of macroscopic cracks with final failure of a loaded body.The diffused damage accumulation with subsequent localized fracture was well established with the help of the acoustic emission (AE) technique in such materials as ceramics [8,9], rocks [10,11], composites [12], etc.The energy release in nucleating microcracks is characterized by the power law dependence of number of events on event size (scaling) [12][13][14][15].The scaling evidences the self-similarity of the fracture process at different scale levels; in other words, the energy distribution in individual fracture events forms a fractal energy domain.The scaling phenomena manifest themselves efficiently over an area much greater than is predicted by elasto-dynamic interactions, which decay exponentially with distance.
Brittle homogeneous materials do not exhibit correlated (scaling) behavior at the microscopic scale level due to the lack of pre-failure cracking, and, correspondingly, the AE method cannot be informative in this case.However, the real damage initiation occurs at the nanostructural level where primary defects nucleate through the chemical bond breakage both in hetero-and homogeneous materials.This process is accompanied with the light emission from the electronic structures reconfigured during bond ruptures.Historically, this phenomenon was called "triboluminescence"; however, in recent decades the definition of the effect has been subject to some refinement.Nowadays, the term "triboluminescence" is commonly referred to the light generated through rubbing a material, while the photon emission from deformed or fractured solids is more frequently called "mechanoluminescence".Kawaguchi [16] introduced a specific term "fractoluminescence" (FL) to stress the difference between the strain-and fracture-induced effects.The latter term is used in this communication, which describes the application of the FL method for studying the primary stage of damage initiation in three sintered materials as compared with it in their crystal counterparts.Taking into account that all conventional homogeneous materials possess unavoidable nanostructural heterogeneity, one could expect that the formation of primary (nano-) defects in ceramics and crystals at this scale level would manifest some trends specific to multiple-site damage nucleation.
In this work, the laboratory samples of both monolithic and sintered quartz, silica carbide, and sapphire were damaged by falling weight, and the time series of light emission were detected.In order to put in direct comparison the fracture processes occurring at microand nanostructural levels, the FL experiments were supplemented with the AE measurements.

Experimental 2.1. Materials 2.1.1. SiO 2
The commercial silica ceramics ("Kersil" in Russian nomenclature [17]) is manufactured by the water slip forming of finely dispersed silica.A dried preform is sintered at temperature 1200 °C.According to the manufacturer's specifications, the porosity of the final product is about 10 %; the apparent density is ~ 2 g/cm 3 ; the OH -content is ~ 10 3 ppm.This ceramics is close in physical and mechanical properties to the material Corning 7941.
α-SiO 2 synthesized by the hydrothermal method served as a crystal counterpart.
α-SiC single crystals were synthesized by the PVT method.

Al 2 O 3
A fine-grained powder of γ-Al 2 O 3 sintered at temperature close to the γ → α phase transition was used as an analogue of alumina ceramics, which, however, has not special additives (purity about 99 %).

Experimental setup
A schematic diagram of the experimental setup is depicted in Fig. 1.The samples were placed on a massive metal support covered with a grease layer.A surface damage was produced by the hard pointed striker established on the upper face of the sample, on which a 100 g weight dropped.In single crystals, the impact was directed along the principal axis.The data acquisition system was triggered in the moment of contact between the weight and the striker.The FL radiation from samples was collected with a quartz lens and directed onto a photomultiplier FEU136.The single-electron pulse duration of the FEU136 was 8 ns.The characteristic time of the resistance-capacitance network (cables + photomultiplier) was 5 ns.An analogue-to-digital convertor ASK-3106 provided the dynamic range 2 mV to 10 V (70 dB) in the time range 10 ns to 100 s.
The AE signals from growing cracks were detected by a broadband piezotransducer made of ceramics Pb(Zr x Ti 1−x )O 3 .The digital low frequency sound filtration was applied at the level of 80 kHz in order to cut off parasitic oscillations of the sample and setup.
The converted (digital) FL and AE signals were stored in a PC.The duration of all recorded time series was 0.9 ms.

Time series
The FL amplitude (A FL , total energy of detected photons) and the AE intensity (amplitude squared of elastic wave, I AE = A 2 AE ) are proportional to the energy release, E, in damage events at nano-and microstructural scale, respectively (A FL ∝ E nano and I AE ∝ E micro ).
Fig. 2 shows sweeps of the AE and FL activity in impact-fractured sintered powders.The time series of AE and FL pulses emitted from crystals are depicted in Fig. 3.A delay of about 70-90 μs between the instances of weight-striker contact and the series beginning was determined by the traveling time of the elastic wave through the striker.

Energy distribution
The time series shown in Fig. 2 and Fig. 3 were used for constructing distributions of the energy release in fracture events occurred at atomic and microscopic scale levels in sintered powders and crystals, respectively.Fig. 4 and Fig. 5 represent these distributions in the form of dependences log 10 N(E>E′) versus log 10 E′, where N(E>E′) is the number of damage events characterized by the energy release E exceeding a varying value E′.One can see that both AE and FL distributions in sintered materials (Fig. 4) contain log-linear portions corresponding to the relation: log 10 N(E>E′) ∝ -blog 10 E′, (1) which represents the power law dependence: N(E>E′) ∝ E′ -b (1a) indicative of scaling damage accumulation (here b is the constant).A deviation from the loglinear behavior for low-energy damage events is caused by the lack of effective interactions between distantly occurred "weak" events.The log-linear dependences for the "strongest" events are also violated because of insufficient number (statistical insignificance) of large damages.
The energy distributions based on the AE time series for single crystals (Fig. 5a) do not exhibit the log-linear dependences (1), while the FL dependences of this kind were observed in crystals α-SiC and α-SiO 2 (Fig. 5b).At the same time, the FL distribution in α-Al 2 O 3 occurred to be similar to that in all AE time series (Fig. 5a), which had not linear portions in their log 10 N(E>E′) versus log 10 E′ plots.In order to determine the actual character of the FL energy release in the latter material, the FL energy distribution for α-Al 2 O 3 was replotted in semi-logarithmic coordinates (with linear scale along the horizontal axis, see cutin in Fig 5b).In this case, the FL distribution followed the relation: which is shown with a straight line in the cut-in (here a is the slope of line).Relation ( 2) is equivalent to the exponential law: N(E>E′) ∝ exp(-aE′) (2a) which is typical for random events occurring independently from each other.
The shown difference between crystals in damage accumulation at nanostructural level was quite surprising.At the same time, there is a particular property that distinguishes the latter crystal from two others: α-Al 2 O 3 exhibits certain microplasticity, which influences to some extent its structural behavior [19,20].This situation could have relevance to our case.

Discussion
Fractal properties of ceramics manifest themselves in geometric, temporal, and energy aspects.The geometric aspect characterizes the fractal pattern of a fragmented body [21][22][23], while two other ones arise from self-similar (power law) behavior of loaded solids.In general, the experimentally revealed power law dependence evidence the identity of the fracture process at different scale levels available to the given technique because the power law distribution function of detected events N(P) such as Eq.(1a) (the function argument P can represent size, time, or energy in dependence of the considered scope) is a single resolution of the scaling equation: ) where λ is the scaling factor.
Scaling distributions of fragment sizes [23,24], recurrence times between events [25], and energy release [26,27] in loaded/fracturing porous ceramics were established at microscopic and laboratory scale levels using the fractographic and acoustic techniques.The earlier revealed trends were confirmed in our AE tests: the energy distributions functions in sintered powders followed the power law thus demonstrating the presence of long-range interactions between newly-formed damages.In single crystals, the exponential AE energy distribution was typical for uncorrelated fracture process: a limited number of fast growing macroscopic (in dimensions of laboratory samples) cracks did not affect each other in these homogeneous materials.
In contrast of microscopic studies, there are very few investigations were focused on the damage accumulation occurring in ceramics at the nanostructural level.Meanwhile, one could expect some deviations from the scaling behavior caused by very small dimensions of primary defects and ultrashort time of bond breaking events.The rearrangement of the electronic structure, which results in the light emission, occurs within τ ~ 0.1 ns.The speed of elastic waves in brittle solids, which provide dynamic interactions between multiple individual failures, is about V =10 3 m/s (10 3 nm/ns), therefore the correlation radius of interactions between primary defects in ceramic materials is close to τV ≅ 0.1 μm.Only "weak points" that are separated by this distance could interact among themselves.Correspondingly, the time correlation is possible if the time of any defect formation is longer than the time needed for elastic wave to reach a neighboring "weak point".
A recent application of the FL method to studying the fractal properties of sintered materials [28] was carried out with ZrO 2 ceramics.The authors have shown that both geometric and time dependences N(P>P′) vs P′ (where P represented either fragment size or recurrence time) followed the power law.The results obtained in our experiments replenish their finding by the demonstration of nanostructural energy scaling in porous ceramics thus completing a "triad" of possible scaling aspects.Moreover, the scaling energy distributions in FL time series were observed in homogeneous single crystals SiO 2 and SiC, in which the AE tests did not show any features of the correlated dynamics in view of the lacking of multiplicity of microscopic failures.
At the same time, the FL experiments with α-Al 2 O 3 brought less unambiguous result: time series exhibited the Poisson-like behavior in this single crystal thus evidenced the absence of the long-range cross-coupling between newly-appearing nanostructural damage sites.
At first glance, the damage accumulation at the nanostructural scale level should be identical both in ceramics and crystals correlated because the multiple bond breakage takes place both in homogeneous and heterogeneous solids.However, one should take into account that the plastic deformation prior to the bond rupture (if ever occurs) could produce substantial structural perturbations, which would reduce the interactions between nucleating defects.The role of material fragility in the establishing of the power law characteristics of fracture was deduced from impact-loading experiments with various materials [29].It seems, α-Al 2 O 3 is the case.Under loading, this material exhibits a trend to twinning, which does not involve the structural bond breaking.Plastic deformation in this material was concluded long ago from the existence of the fatigue (pre-failure) phenomena in loaded single crystals [19,20] and sintered alumina [30][31][32].More recently, plastic effects were observed under compression of micropilars [33] and when indenting α-Al 2 O 3 [34].Obviously, the elastic long-range interactions between individual damages, which are responsible for scaling in brittle solids, becomes suppressed by localized plastic deformation, at least, at the nanostructural scale level.Intragrain microplasticity is unlikely in sintered materials, in which the loading-induced deformation proceeds mainly through rearrangements of particles with multiple brittle cracking along their boundaries.Therefore, the energy release in sintered alumina was similar to that in every other powders despite a particular plastic properties of monocrystals.Thus, the nucleation of nanostructural defects in fracturing sintered ceramics occurs always in a correlated mode and does not depend on the brittle-ductile properties of their crystalline counterparts.

Conclusion
The impact loaded sintered powders of SiO 2 , SiC and Al 2 O 3 showed similar energy distributions both in AE and FL time series, which followed the power law indicative of correlated process of multiple damage nucleations at micro-and nanostructural scale levels, respectively.Their crystalline counterparts demonstrated the stochastic (exponential) energy distributions in AE time series typical for homogeneous materials.At the nanostructural scale level, where the heterogeneity takes place even in homogeneous solids, the damage accumulation in SiO 2 and SiC single crystals followed the power law dependence similar to that in highly heterogeneous powders, while luminescence from α-Al 2 O 3 was specific for the random process.This difference in mechanical behavior between α-Al 2 O 3 and two other crystals was explained by certain microplasticity caused by the twinning phenomenon, which disturbs long-range elastic interactions between primary damage events.Microstructural microplasticity of crystalline components does not manifest itself noticeably in impact-loaded sintered ceramics due to prevailing cracking along intergrain boundaries.Therefore, the nucleation of both microscopic and nanostructural defects in loaded sintered powders proceeds always in a correlated (self-similar) manner, which does not depend on the brittleductile properties of their monocrystalline counterparts.

Fig. 3 .
Fig. 3. Time series of AE (a) and FL (b) signals from single crystals.

Fig. 4 .
Fig. 4. Energy release distributions in AE (a) and FL (b) time series from sintered powders.Straight lines fit the power law.

Fig. 5 .
Fig. 5. Energy release distributions in AE (a) and FL (b) time series from crystals.Straight lines fit the power law.Cut-in: log 10 N(E>E′) vs log 10 E′ dependence for α-Al 2 O 3 plotted in semi-logarithmic coordinates; straight line fits the exponential law.