Brittle Single Crystals Research Articles

On dynamic surface instabilities of cracks in brittle crystals

We investigated fracture surface instabilities generated during interaction of dynamic cracks with atomistic scale defects in brittle single crystals. We show that the initiation of the surface instabilities is caused by several well-defined variables. We generalized the phenomenon of surface instabilities by cleaving cubic silicon and germanium crystals with a variety of point defects.Well-defined low-speed atomistic-height wedge such as jogs were observed in cubic brittle silicon crystal doped with boron substitutional and oxygen interstitial, but not with phosphorus, and not in cubic germanium crystal doped with gallium. Pile-ups of the jogs are ended with a low speed sub-micron height ridges.A continuum based theoretical model using energy minimization law suggests that the generation of the jog-like surface instabilities in cubic crystals is conceivable due to the proximity of two low energy cleavage planes and depends upon crack speed and local internal chemical strain induced by the defect atom, as well as by the macroscopic asymmetry of the crystal. The jogs are formed to reduce the defect induced local chemical strain energy by creating new surfaces. Based on the current finding, we postulate that the fracture surface of ideal brittle crystals will presumably be stable (flat) at all crack speeds.

Understanding the effect of surface flaws on the strength distribution of brittle single crystals

AbstractThe dependence of strength on the surface quality of brittle single crystals is highly relevant in microelectronic applications, where a certain roughening of the crystal surface is required to guarantee or enhance the functional properties of the final component. In this work, the effect of surface conditioning on the strength distribution of single crystals is assessed on LiTaO3 and LiNbO3 samples with distinct surfaces (i.e., polished, grinded, and scratched). Artificial surface cracks (scratches) were introduced using a Berkovich nanoindenter tip oriented under various angles with respect to the most critical {012} cleavage plane. Biaxial tensile tests were performed using the ball‐on‐three‐balls test, supported by fractographic analyses to interpret the strength results. A direct correlation between sub‐surface damage and strength was observed, associated with the hardness and elastic constants of the material, being strongly dependent on the crystal orientation with respect to the loading axis. Furthermore, we provide an explanation for the usually low Weibull modulus in single crystals and discuss the validity of the biaxial tests on scratched specimens for fracture toughness evaluation.

The dynamic cleavage energy of brittle single crystals

Crack initiation in brittle materials is usually dictated by the energy required to create two new surfaces. This energy is known as Griffith barrier and equals twice the free and relaxed surface energy, 2γs. This value is usually taken as the cleavage energy for crack propagation as well. We investigated, experimentally, the fundamentals of cracks dynamics in brittle single crystals, with emphasis on the cleavage energy at initiation and during propagation. Silicon single crystal, which has a diamond cubic symmetry, served as a model material. The experiments were performed using the Coefficient of Thermal Expansion Mismatch method (CTEM), developed in our laboratory in recent years. The CTEM method possesses the advantage of controlling the quasi-static energy release rate (ERR) gradient to the crack front, dG0/da, denoted here Θ.The cleavage energies at initiation and propagation of dynamic cracks on two Low-Energy Cleavage Systems (LECSs) of brittle silicon crystal, (110)[11¯0] and (111)[112¯], were evaluated by comparing the experimental energy–speed relationship with the theoretical one, manifested by Freund theory for cracks dynamics, known as Freund equation of motion. The ERR, G0, was evaluated using quasi-static, anisotropic Finite Element Analysis (FEA), and the crack speed was measured using Potential Drop Technique (PDT).The experiments revealed that the energy required to initiate and propagate a crack is governed by Θ. When Θ > 0.7 J/m2mm, the cleavage energy at initiation is higher than 2γs and linearly increase with increasing Θ for both LECSs of silicon. Surprisingly, the cleavage energy for initiation and propagation remain constant during the event of fracture for a prescribed Θ, meaning, it is not crack speed dependent. Moreover, we show that all the variables participating dynamic cleavage are linearly dependent on Θ, which provides the evidences that the ERR gradient is the controlling variable governs cracks dynamics.Finally, we suggest that the physics of the above fundamental behavior is laying on the way crack initiate and propagate at the atomistic scale, i.e., the bond breaking mechanisms in form of kinks.

Evaluating the Cleavage Energy of Brittle Single Crystals

Abstract Evaluating the cleavage energy of brittle crystals is challenging due to the need to generate a controlled deformation of only a few microns; to introduce a straight and planar, atomistic thick precrack, perfectly aligned with the plane of propagation; to align the external loading with that plane; and above all, to grip the specimen while avoiding premature cleavage. In addition, achieving a relatively slow crack upon initiation is another requirement that needs special treatment. Consequently, we designed an experimental method that fulfills the above requirements. It consists in gluing a thin, rectangular specimen, with an atomistic sharp precrack, inside a rectangular hole in an aluminum loading frame, using thin layers of epoxy resin. Crack initiation and propagation occur upon heating the assembly on top of an electrical heating stage by only a few °C, due to the coefficients of thermal expansion mismatch between the specimen and the aluminum frame. Finite element analysis is used to evaluate the strain energy release rate. We describe it in full through cleavage experiments of two low energy cleavage systems of silicon crystal under pure Mode I, under room conditions and argon gas at atmospheric pressure.

Plastic deformation of piezoelectric lanthanum-gallium tantalate crystals during cyclic mechanical actions

The microstructure of piezoelectric lanthanum-gallium tantalite single crystals is shown to change substantially during cyclic mechanical actions at room temperature and during thermal shock: the dislocation density increases, twinning takes place, and a mesostructure forms. This effect is related to the appearance of piezoelectric fields, which significantly decrease the temperature of the onset of plastic deformation of these brittle single crystals, during mechanical actions.

Fractography of Dynamic Crack Propagation in Silicon Crystal

The phenomena occurring during rapid crack propagation in brittle single crystals were studied by cleaving silicon specimens on the low energy cleavage planes under tensile and bending. The experiments revealed new phenomena not previously reported, and new crack path instabilities in particular. The well defined boundary conditions of the tested specimens and crack velocity measurements enabled rationalization of the observed phenomena and the velocity-surface instabilities relationship in particular. In contrast to amorphous materials, the observed instabilities are generated at relatively low velocity, while at high velocity the crack path remains stable. No evidences for mirror, mist, and hackle instabilities, typical in amorphous materials, were found.

Crack growth modelling in single crystals based on higher order continua

This work presents several regularized crack growth models in brittle single crystals based on a combination of the micromorphic approach and continuum damage mechanics. First, a variant of micromorphic continuum, the microstrain theory, is chosen to explore the regularization capabilities of enhanced continua sparing three degrees of freedom compared to the full micromorphic approach. The difficulties in reaching final fracture of a sample are pointed out and an alternative damage criterion is proposed as a remedy which leads to a different localization pattern. Secondly, the microdamage formulation which enhances the numerical efficiency and also eliminates the final fracture difficulty is presented in detail. For all presented models, analytical solutions for governing differential equations are provided for 1D and the corresponding finite element simulation results are discussed.

Lead magnesium niobate‐lead titanate single crystal thick films on silicon substrate for high‐frequency micromachined ultrasonic transducers

Some new clinical applications requiring ultrasonic frequencies higher than 30 MHz are emerging, such as ophthalmological and dermatological imaging and intravascular imaging with probes mounted on catheter tips. High frequency ultrasonic transducer (HFUT) has thus been a growing research area in recent years. Most of the HFUTs reported are using piezoelectric PZT ceramic thin plates, ZnO films or PVDF films as the transducer materials. The PMN‐PT ((1‐x)Pb(Mg1/3Nb2/3)O3‐xPbTiO3) single crystal, although possessing the highest piezoelectric coefficients, has seldom been used for this purpose because it is difficult to lap down the brittle single crystals to thin plates and handle them in conventional way of transducer fabrication. In this work, a novel high‐frequency ultrasonic transducer structure is realized by using PMN‐PT‐on‐silicon technology and silicon micromachining. A hybrid processing method involving wafer bonding, mechanical lapping and wet chemical thinning is successfully developed. PMN‐PT thick films with thickness ranging from several to tens of microns have been demonstrated and they have properties comparable to those of PMN‐PT bulk samples. A prototype high frequency ultrasonic transducer is being fabricated and characterized. Acknowledgement Financial support from the Innovation and Technology Fund (K‐ZP21) is acknowledged.

Dynamic instabilities in {1 1 1} silicon

The phenomena occurring during rapid crack propagation in brittle single crystals was studied by cleaving strip-like silicon specimens along the {1 1 1} low-energy cleavage plane under bending. The experiments reveal phenomena associated with rapid crack propagation in brittle single crystals not previously reported, and new crack path instabilities in particular. In contrast to amorphous materials, the observed instabilities are generated at relatively low velocity, while at high velocity the crack path remains stable. The experiments demonstrate that crack velocity in single crystals can attain the theoretical limit. No evidence for mirror, mist, and hackle instabilities, typical in amorphous materials, was found. The important role played by the atomistic symmetry of the crystals on controlling and generating the surface instabilities is explained; the importance of the velocity and orientation-dependent cleavage energy is discussed. The surface instabilities are generated to satisfy minimum energy dissipation considerations. These findings necessitate a new approach to the fundamentals of dynamic crack propagation in brittle single crystals.

Surface Characterization in Diamond Turning of Highly Anisotropy Brittle Crystals: A Multi-Spectrum Analysis Approach

This paper presents a multi-spectrum analysis method for the characterization of the surface generation in single-point turning of brittle single crystals. The features on the diamond turned surfaces were extracted and analysed by the power spectrum analysis of the surface roughness profiles measured at a number radial sections of the workpiece. By the analysis of the variation of the spectral patterns in the multi-spectrum plots, the surface roughness and materials effect on surface generation are found to be strongly related to the power spectrum. This provides an important means to explain quantitatively the effect of factors affecting the surface generation in diamond turning brittle crystals.

Wavelength decomposition analysis of surface generation in the ultraprecision machining of brittle single crystals

Brittle single crystals present special characteristics that are not encountered in ultraprecision machining of ductile materials. The conventional surface characterization approaches based on surface roughness parameters and power spectrum analysis are inadequate for characterizing the surface generation. In this paper, a wavelength decomposition analysis is proposed that provides a component-by-component wavelength decomposition of the surface roughness profiles at a finite number of radial sections of the machined surfaces. Experimental results indicate that wavelength decomposition analysis provides an effective way of characterizing quantitatively the effect of different surface generation mechanisms such as the brittle-ductile transition on surface roughness in the ultraprecision machining of brittle single crystals.

Influence of cutting friction on anisotropy of surface properties in ultra-precision machining of brittle single crystals

This paper deals with the effect of cutting friction on the surface properties in diamond turning of brittle single crystals. Experimental results indicate that the anisotropy of the surface roughness decreases with increasing cutting friction which is related to the mechanism of brittle–ductile transitions in surface generation. As cutting friction increases, the brittle single crystals are more susceptible to the brittle fracture than ductile mode cutting. This finding provides an important means for the improvement of surface quality in diamond turning of brittle single crystals.

Large local deflections of a dynamic crack front induced by intrinsic dislocations in brittle single crystals.

We show that intrinsic dislocations in brittle single crystals can be a source of strong local perturbations along the crack path. A theoretical model was developed which predicts substantial crack front deflections. Investigating the crack surfaces in Si crystals with induced dislocation density of 10(9)-10(10) cm(-2) revealed a significant amount of crack front perturbations in the form of V-shaped grooves, which were completely missing in dislocation-free Si specimens. The measured depths of the perturbations were in the range of 2-20 nm and in excellent agreement with the theoretical model.

Anisotropy of surface roughness in diamond turning of brittle single crystals

This paper deals with an investigation of the effect of crystallographic orientation and process parameters on the surface roughness of brittle silicon single crystals in ultraprecision diamond turning. The process parameters involve the depth of cut, feed rate, and spindle speed. Experimental results indicate that anisotropy in surface finish occurs when the cutting direction relative to the crystal orientation varies. There exists a periodic variation of surface roughness per workpiece revolution, which is closely related to the crystallographic orientation of the crystals being cut. Such an anisotropy of surface roughness can be minimized with an appropriate selection of the feed rate, spindle speed, and depth of cut. The findings provide a means for the optimization of the surface quality in diamond turning of brittle silicon single crystals.

Tetraammin‐Lithium‐Kationen zur Stabilisierung phenylsubstituierter Zintl‐Anionen: Die Verbindung [Li(NH3)4]2[Sn2Ph4

Tetraammine Lithium Cations Stabilizing Phenylsubstituted Zintl‐Anions: The Compound [Li(NH3)4]2[Sn2Ph4]Ruby‐red, brittle single crystals of [Li(NH3)4]2[Sn2Ph4] were synthesized by the reaction of diphenyltin dichloride and metallic lithium in liquid ammonia at −35°C. The structure was determined from X‐ray singlecrystal diffractometer data: Space group, P1, Z = 1, a = 9.462(2) Å, b = 9.727(2) Å, c = 11.232(2) Å, α = 66.22(3)°, β = 85.78(3)°, γ = 61.83(3)°, R1 (F ⩾ 4σF) = 5.13%, wR2 (F02 ⩾ 4σF) = 10.5%, N(F ⩾ 4σF) = 779, N(Var.) = 163.The compound contains to Sb2Ph4 isosteric centres [Sn2Ph4]2− as anions which are connected to rods by lithium cations in distorted tetrahedral coordination by ammonia. These rods are arranged parallel to one another in the b,c‐plane, but stacked along [100].

Na 2Au 6In 5, the first compound in the system sodium-gold-indium

Silver coloured brittle single crystals of a hitherto unknown Na 2Au 6In 5 were synthesized by the reaction of sodium azide, gold sponge and indium at 550°C. The structure was determined from X-ray single-crystal diffractometry data: space group Pm 3, Z = 3, a = 9.245(4) A ̊ , R/R w (w = 1) = 0.038/0.054 for 363 structure factors with F o 2 ⩾ 3 σ( F o 2) and 23 variables. Na 2Au 6In 5 crystallizes with the Mg 2Cu 6Al 5 structure type. The gold and indium atoms form a framework structure with a caesium chloride-like arrangement of indium centred Au 12 icosahedra and empty Au 6 octahedra. The indium environment and the interconnecting pattern of these building units can be described by the formula { Au 12 in 8 2 i−iin 12 4 a−a} {Au 6in 8 2 i−i(in 2) 6 4 a−a } 8 8 , according to Schäfer and von Schnering's notation for transition metal clusters.

Rb 2Au 3, eine schichtstruktur im system rubidium-gold

Silver-coloured brittle single crystals of a hitherto unknown Rb 2Au 3 were synthesized by the reaction of RbN 3 and gold powder at 450 °C. The structure was determined from X-ray single-crystal diffractometry data: space group Immm; Z = 2; a = 4.942(2) A ̊ ; b = 5.442(3) A ̊ ; c = 10.601(6) A ̊ ; R/ R w ( w = 1) = 0.057/0.066; Z( F 0 2) ≥ 3 σ( F 0 2) = 152 and Z(var.) = 12. Rb 2Au 3 crystallizes in a layer structure. The gold atoms form plane 3.6.3.6. + 3 26 2(1:2)-nets. These layers are separated by rubidium atoms along [001]. The stacking sequence is characterized by A Rb B Rb A Rb B. The structural relationships between Rb 2Au 3 (Ca 2GaCu 2-type) and the K 2PtS 2- and W 2CoB 2-type are discussed.

Single crystal cleavage of brittle materials

Cleavage of brittle single crystals is reviewed and the historical criteria for the phenomenon are critically examined. Previously proposed criteria, including those based on crystal structure (crystal growth planes, the planes bounding the unit cell, and planar atomic packing) and crystal properties (ionic charge of possible cleavage planes, bond density, elastic modulus, and surface free energy), are found to be applicable only to particular crystals or to isostructural groups, but each lacks universal application. It is concluded that the fracture toughness (K Ic) of the crystallographic planes is the most appropriate criterion. Measurements reveal that the ‘cleavage toughnesses’ of brittle single crystals are usually about 1 MPa m1/2 or less. Measurements of the fracture toughnesses of brittle polycrystalline aggregates are then compared to the single crystal cleavage values in those instances where reliable results are available for the same crystal structures. Polycrystalline toughnesses are consistently higher, in part because of the lack of continuity of cleavage cracks through the polycrystalline aggregates. However, the increment of toughness increase is only 1–2 MPa m1/2. The role of grain texture or preferred crystal orientation is also addressed. It is concluded that polycrystalline aggregate toughnesses are often highly anisotropic and that the values for intensely oriented microstructures may approach those for single crystal cleavage.

Eine neue verbindung im system rubidium-gold: synthese und struktur von Rb 3Au 7

Silver-coloured brittle single crystals of the hitherto unknown compound Rb 3Au 7 were synthesized by the reaction of RbN 3 and gold powder at 500 °C. The structure was determined from X-ray single-crystal diffractometer data: space group Cmmm, Z= 2, a= 5.585(2) A ̊ , b= 13.252(2) A ̊ , c= 7.258(1) A ̊ , R/R w (w= 1)=0.046/0.057, N(F o 2)⩾3o(F o 2)= 405 and N (var.)=22 . The structure consists of a three-dimensional gold framework. Rubidium atoms occupy channel-like cavities within the gold partial structure.

Einkristallzüchtung und Strukturverfeinerung von KAu 5 und RbAu 5

Green gleaming brittle single crystals of KAu 5 and RbAu 5 were obtained by the reaction of the alkalimetal azides with gold powder at 700 °C. The structures were determined from single-crystal diffractometer data: space group P6/ mmm, Z = 1; KAu 5, a = 5.663(1) A ̊ , c = 4.483(1) A ̊ , R/R w (w = 1) = 0.036/0.041, N( F o 2) ⩾ 3 σ(F o 2) = 234 and N(var.) = 9; RbAu 5, a = 5.762(2) A ̊ , c = 4.442(2) A ̊ , R/R w (w = 1) = 0.048/0.073, N( F o 2) ⩾ 3 σ(F o 2) = 248 and N(var.) = 9. Both compounds crystallize in the CaCu 5-structure type with negligible deviation from the ideal 1:5 composition.