5 Werkstofftechnik
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At high temperatures and in harsh environments ceramic springs are often superior to metallic ones and allow for innovative solutions. A further application was proposed by using ceramic springs as capacitive force sensor. Lower and upper coil surfaces are coated by electrically conducting layers. Deformation of such spring results in a change of capacity. Sensor application calls for helical springs with rectangular cross-section, a linear stress-strain characteristic over entire deformation range and low manufacturing tolerances relating to inner and outer diameter, coil cross section and spring pitch. Furthermore, complex spring design with integrated connecting elements has to be realized.
Alumina, zirconia (Y-TZP) and silicon nitride springs were produced by hard machining starting from sintered hollow cylinders. After external and internal cylindrical grinding the hollow cylinders were filled with hard wax, followed by multi-stage cutting of spring coils with custom-made cutting discs. Finally, hard wax was removed by melting and burnout. Best surface and edge qualities of springs were reached using Y-TZP material and hot isostatic pressed alumina. Y-TZP springs produced with material-specifically selected cutting discs and optimized process parameters show sharp coil edges without spallings and mean roughness values of inner surfaces < 0.2 μm. Manufacturing tolerances of spring diameters, spring pitch, height and width of coil cross section are in the range of ± 10 microns. Good reproducibility of spring geometry by optimized hard machining technology allows for production of Y-TZP springs with spring constants differing less than ± 1 % within a series.
According to DIN 2090 spring constant for rectangular coil cross section is proportional to the square of height and width of coil cross section and indirectly proportional to number of active coils and to the cube of the mean spring diameter. Hence, spring constants can be tailored over a range of many orders of magnitude by changing the spring dimensions. Good agreement was reached between calculated target spring constants and measured values on produced springs.
Alumina and zirconia springs were characterized relating to deformation behavior under dynamic compression load with various deformation speeds and under static tensile loads over long periods of time. Contrary to alumina springs, a non-linear stress-strain behavior of TZP springs was proved in both test series. It is supposed, that pseudoelasticity caused by stress-induced transformation of tetragonal to monoclinic phase is responsible for this special feature of TZP springs. Therefore, TZP material cannot be used for capacitive spring sensors.
Crack healing in glass ceramic solid oxide fuel cell (SOFC) sealants is of utmost importance as cracks caused by thermal cycling remain a bottleneck in developing durable SOFC. Whereas no or low crystal volume fraction seems most favorable for viscous crack healing, it does not for load bearing and undesired diffusion. On the other hand, crystals or filler particles can make the sealant less prone to these disadvantages but it could increase the effective composite viscosity and retard crack healing.
Against this background, the influence of crystal volume fraction, phi, on viscous crack healing in glass matrix composites prepared from soda lime silicate glass and zirconia filler particles was studied. Vickers indention induced radial cracks were healed isothermally during interrupted annealing steps and monitored with optical microscopy. Due to the slow crystallization of the glass under study, phi could be kept constant during crack healing.
For bulk glass samples (phi = =), the decrease in radial crack length was retarded by an initial increase in crack width due to crack rounding. Up to phi = 0.15 the increase in effective viscosity retarded this crack broadening thereby yielding faster crack healing. For phi > 0.15, crack broadening was progressively suppressed but the same was true for crack healing, which was fully prevented above phi = 0.3. Results indicate that optimum micro structures can prevent crack broadening limited by the global effective composite viscosity and this way promote crack healing limited by local glass viscosity.
Within the perspective of increasing reliability of AM processes, real-time monitoring allows part inspection while it is built and simultaneous defect detection. Further developments of real-time monitoring can also bring to self-regulating process controls. Key points to reach such a goal are the extensive research and knowledge of correlations between sensor signals and their causes in the process.
Single crystal superalloys usually contain pores of sizes 5-10 micro-m after casting and heat treatment. These pores can be reduced under compression by combined creep and diffusion in a subsequent treatment called Hot Isostatic Pressing (HIP). The paper presents a methodology to simulate pore shrinkage under HIP conditions in two dimensions (2D).
At the scale of the pores, which is also the scale of the sub-grains (<50 micro-m) the dislocation sources cannot be assumed to be homogeneously distributed. Thus, the applicability of classical crystal plasticity is questionable. In this case, the transport of dislocations under an applied stress from the location where they are nucleated must be explicitly modelled. This is done by solving the transport equations for the dislocation densities and the elasticity equations in 2D. The dislocations are assumed to be nucleated at Low Angle Boundaries. They glide or climb through the sub-grains with a stress dependent velocity.
The transport equations are solved by the Flux-Corrected Transport method, which belongs to the predictor-corrector class of algorithms. In the first step, an artificial diffusion is introduced, which suppresses spurious oscillations of the solution. In a second step, the solution is corrected in such a way that no additional extremes appear and that the extremes do not grow. The algorithm is validated by simulating the transport of simple distributions with a constant velocity field.
With the dislocation velocities and the computed dislocation densities, the inelastic shear rate at the slip system level is computed by integrating the Orowan equation. In the 2D-setting, three slip systems are considered. The contributions of these slip systems are summed up to obtain the total inelastic strain rate. Dislocation glide and climb and the coupling of climb with vacancies diffusion are considered.
The resolution of the equilibrium equations from the inelastic strains turned out to be prone to numerical instabilities. As an alternative, the stresses are directly computed from the distribution of geometrically necessary dislocations following the method presented in. The resulting boundary value problem is solved by the Least-Square Finite Element method.
Examples of simulations are presented for a representative region under creep tension and for a pore shrinking under external pressure.
Fiber-reinforced-polymers (FRPs) are in current research focus in the lightweight construction industry, because of their extraordinary characteristics (stiffness and strength-to-density relation). The structure of polymer matrix and the interaction with reinforcement are crucial for optimization of the mechanical and thermal properties of FRPs. Due to the macromolecular chain structure, the mechanical properties of a polymer strongly vary with temperature: Below the glass transition, the chain segments of a polymer are “frozen”. Regarding fracture, the total changed energy during fracture if only dissipates for the generation of the new surfaces. However, in the region of the glass transition, the polymer chain segments start to get “unfrozen”, and the energy is not only required for generating new surfaces, but also for irreversibly deformation. This irreversible deformation is affected by the global temperature and the local temperature near the crack tip, which is affected by the local strain rate and crack propagation velocity.
Hence, in this research project, the irreversible deformation of neat and reinforced polymers will be controlled by changing the global temperature as well as the local temperature. With using different fracture experiments, the amount of energy required for creating new surfaces and for the irreversible deformation will be separated. In this presentation, I summarized of the first 15 months the whole project. In this period, the basic crack propagation theory for neat polymers is established and the special fracture experiment sample is prepared and tested at room temperature. In addition, the model of the specimen is first established.
Crack propagation in polymers: Separation of surface energy and irreversible deformation energy
(2019)
Fiber-reinforced-polymers (FRPs) are in current research focus in the lightweight construction industry, because of their extraordinary characteristics (stiffness and strength-to-density relation). The structure of polymer matrix and the interaction with reinforcement are crucial for optimization of the mechanical and thermal properties of FRPs. Due to the macromolecular chain structure, the mechanical properties of a polymer strongly vary with temperature: Below the glass transition, the chain segments of a polymer are “frozen”. Regarding fracture, the total changed energy during fracture if only dissipates for the generation of the new surfaces. However, in the region of the glass transition, the polymer chain segments start to get “unfrozen”, and the energy is not only required for generating new surfaces, but also for irreversibly deformation. This irreversible deformation is affected by the global temperature and the local temperature near the crack tip, which is affected by the local strain rate and crack propagation velocity.
Hence, in this research project, the irreversible deformation of neat and reinforced polymers will be controlled by changing the global temperature as well as the local temperature. With using different fracture experiments, the amount of energy required for creating new surfaces and for the irreversible deformation will be separated. This poster is the summary of the first part of the whole project. In the first part, the basic crack propagation theory for neat polymers is established and the special fracture experiment sample is prepared and tested at room temperature. In addition, the fracture experiment at room temperature is validated numerically.
Fiber-reinforced-polymers (FRPs) are in current research focus in the lightweight construction industry, because of their extraordinary characteristics (stiffness and strength-to-density relation). The structure of polymer matrix and the interaction with reinforcement are crucial for optimization of the mechanical and thermal properties of FRPs. Due to the macromolecular chain structure, the mechanical properties of a polymer strongly vary with temperature: Below the glass transition, the chain segments of a polymer are “frozen”. Regarding fracture, the total changed energy during fracture if only dissipates for the generation of the new surfaces. However, in the region of the glass transition, the polymer chain segments start to get “unfrozen”, and the energy is not only required for generating new surfaces, but also for irreversibly deformation. This irreversible deformation is affected by the global temperature and the local temperature near the crack tip, which is affected by the local strain rate and crack propagation velocity.
Hence, in this research project, the irreversible deformation of neat and reinforced polymers will be controlled by changing the global temperature as well as the local temperature. With using different fracture experiments, the amount of energy required for creating new surfaces and for the irreversible deformation will be separated. The fracture tests include the conventional tensile test, the macroscopic peel test and the single fiber peel – off test.
Modern wind turbine rotor blades consist of sandwich shell segments made from glass fiber reinforced polymers. During manufacturing, defects can arise which could lead to failure of the whole component under dynamic mechanical and thermal loads. Hence during operation defects can arise which, if detected, can be repaired locally and in-situ by applying repair patches instead of taking the whole rotor blade down and repair it remotely. This method is much more time and cost effective, since the shut-down time of the energy converter is limited to a minimum. These repair patches can, however, also lead to new defects if not applied optimally. Therefore, it is necessary to control the quality of the repair patches to ensure the best possible restoration of structural integrity of the component. As a rotor blade is an object with a large aspect ratio, X-ray laminography is predestined to provide 3D information of the objective volume. To enhance the amount of information gained from laminographic reconstruction, we use in this study a photon counting and energy discriminating X-ray detector and apply a material decomposition algorithm to the data. By inherently separating the incident spectra within the detection process into two distinct energy bins, the basis material decomposition can provide material resolved images. Choosing glass and epoxy resin as basis materials and numerically solving the inverse dual-energy equation system, the reconstructed laminographic datasets contain highly valuable information about the distribution of the basis materials within the structure. Furthermore, cross- artifacts arising from the limited angle of the projection data can be reduced by this method which allows to investigate structures that were hidden underneath the artefacts.
Modern wind turbine rotor blades consist of sandwich shell segments made from glass fiber reinforced polymers. During manufacturing, defects can arise which could lead to failure of the whole component under dynamic mechanical and thermal loads. Hence during operation defects can arise which, if detected, can be repaired locally and in-situ by applying repair patches instead of taking the whole rotor blade down and repair it remotely. This method is much more time and cost effective, since the shut-down time of the energy converter is limited to a minimum. These repair patches can, however, also lead to new defects if not applied optimally. Therefore, it is necessary to control the quality of the repair patches to ensure the best possible restoration of structural integrity of the component. As a rotor blade is an object with a large aspect ratio, X-ray laminography is predestined to provide 3D information of the objective volume. To enhance the amount of information gained from laminographic reconstruction, we use in this study a photon counting and energy discriminating X-ray detector and apply a material decomposition algorithm to the data. By inherently separating the incident spectra within the detection process into two distinct energy bins, the basis material decomposition can provide material resolved images. Choosing glass and epoxy resin as basis materials and numerically solving the inverse dual-energy equation system, the reconstructed laminographic datasets contain highly valuable information about the distribution of the basis materials within the structure. Furthermore, cross- artifacts arising from the limited angle of the projection data can be reduced by this method which allows to investigate structures that were hidden underneath the artefacts.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Depending on the CO2 generating and the capture process as well as on consecutive purification steps applied, CO2 streams from different emitters may differ in their composition. When CO2 streams with different compositions are fed into a larger pipeline network, there are several aspects that must be considered: i) chemical reactions, such as acid formation, may occur within the joint CO2 stream; ii) there may be a variation of mass flow rate and CO2 stream composition within the pipeline network if the feed-in behavior of different CO2 sources changes with time. Potential impacts of changing CO2 stream compositions and mass flow rates in CCS cluster systems were investigated in the collaborative project "CLUSTER" (see also www.bgr.bund.de/CLUSTER). In this presentation, we focus on the experimental investigations of formation and condensation of strong acids and their impacts on the corrosion of pipeline steels. When SO2, NO2, O2 and H2O are present simultaneously in CO2 streams chemical cross-reactions may occur leading to the formation of strong acids such as sulfuric and nitric acid. To prevent this acid formation the concentration of at least one of these four impurities must be kept very low (e.g., Rütters et al., 2016). At temperatures below the acid dew point temperature, acids will condense, e.g., on pipeline steel surfaces. In turn, these acid condensates may trigger steel corrosion. To better understand the process of acid formation and condensation and its implications for steel corrosion, exposure tests were performed on pipeline steel X70 in dense CO2 with varying SO2, NO2 and O2 concentration under high pressure and at 278 K in an observable autoclave, in which water was added as droplets or as vapor. Further, electrochemical tests were carried out with X70 specimens immersed in 500 mL CO2-saturated synthetic condensate solution or in droplets of the same solution on the specimen’s surface. Depending on impurity concentrations in the CO2 streams, condensates consisting of different relative amounts of nitric and sulfuric acid were formed. In condensates containing both nitric and sulfuric acid, corrosion rates were higher than the sum of those of the individual acids. In addition, corrosion products and forms depended on the condensate composition. Investigations of water droplets on steel surfaces in impurity-containing dense-phase CO2 revealed the diffusion of SO2 and NO2, followed by cross-reactions forming corresponding acids. An increase in droplet size (from 1 to 5 µl) lead to higher corrosion rates. However, in comparison to measurements in bulk solution, corrosion reactions in droplets resulted in thick, high-resistance corrosion products and observed droplet corrosion rates were significantly lower. In addition, the possibility of acid droplet formation and growth in impure liquid CO2 is influenced by the wetting behavior of the acid droplet on the steel surface. Thus, the contact angle between a water droplet and the surface steel specimens in a CO2 atmosphere was investigated in a high pressure view cell following the sessile drop method. The contact angle wasand found to be larger at higher CO2 pressures (studied from 5 to 20 MPa) and at higher temperatures (e.g. 278 K to 333 K). Further, measured contact angles were larger on rough than on smooth metal surfaces. In addition, acid formation reduced the contact angle, i.e. lead to better wetting, thereby stimulating condensation that was followed by a corrosion process. These detailed insights on the complex interplay of acid formation, condensation, wetting behavior and corrosion allow a better assessment of material suitability for pipeline transportation of impure CO2 streams
Environmental conditions are known to influence sub-critical crack growth (SCCG) that starts from microscopic flaws at the glass surface, leading to stress corrosion phenomena at the crack tip. The processes at the crack tip are complex and water has been identified as a key component governing SCCG at low crack velocities (region I). In particular, the influence of humidity accelerating crack propagation is well studied for dry industrial soda-lime silicate glasses (< 1000 ppm water). To shed light on this influence, the effect of water is mimicked by studying SCCG in water-bearing glasses. For this purpose, water-bearing silicate glasses of up to 8 wt% total water were synthesized in an internally heated pressure vessel at 0.5 GPa and compared to dry glasses. SCCG was measured using the double cantilever beam technique. For dry glasses, three trends in the crack growth velocity versus stress intensity, KI, curve were found. The slope in region I, limited by environmental corrosion, increases in the order soda-lime silicate < sodium borosilicate < barium calcium silicate < sodium zinc silicate < sodium aluminosilicate glass. The velocity range of region II, reflecting the transition between corrosion affected and inert crack growth (region III), varies within one order of magnitude among these glasses. The KI region of inert crack growth strongly scatters between 0.4 and 0.9 MPam1/2. For hydrous glasses, it is found that water strongly decreases Tg, form a new sub-Tg relaxation peak caused by molecular water, and makes the glasses more prone to SCCG. The observed trends will be discussed in terms of the effects of Youngs Modulus on strain energy release rate and energy dissipation related to glass relaxation phenomena.
Efficient studies of scarce or expensive materials require material saving processes. Therefore, a high yield concept for small batch preparation of ready-to-press powder is exemplarily presented for yttria stabilized nano-zirconia (d50 < 50 nm).
The concept involves small batch preparation in an ultrasound resonator, dispersant selection based on zeta potential measurements, evaluation of slurry stability using an analytical centrifuge, and preparation of ready-to-press powder by freeze drying.
Freeze drying offers key advantages. Process efficiency and high yield above 95 % are independent of sample size. The dried product does not require further mechanical treatment like milling or grinding. Side effects like migration of additives are avoided.
An optimized freeze drying process tolerates slurries with moderate stability. Thus, efforts for slurry development can be reduced. Generally, identifying a suitable dispersing agent requires only 3-5 zeta potential measurements. Slurry stability is rechecked using an analytical centrifuge, which also accounts for steric stabilization. An ultrasound resonator is used to disperse the powder without contamination, which becomes critical for small batches.
The described route is exemplarily presented for the development of an additive recipe for nano-sized zirconia powder, targeting for good pressing behavior and high green density. Therefore, a variety of binding and lubricating agents were tested.
Following the presented route, 80 g zirconia powder were sufficient to conduct a study including slurry development and five sample sets with varying composition, each set comprising five discs (d = 20 mm and h = 2 mm).
Homogeneous introduction of organic additives is a key of ceramic powder processing. Addition of organics to ceramic slurries holds advantages compared to dry processing like organic content reduction and a more homogeneous additive distribution on the particle surface.
Investigations of the alumina slurries were primarily based on zeta potential measurements and sedimentation analysis by optical centrifugation. Both methods were combined to determine a suitable additive type, amount and composition, whereas the spray drying suitability has been ensured by viscosity measurements. Granules, yielded by spray drying of such ideally dispersed alumina slurries, are mostly hollow and possess a hard shell. Those granules cannot easily be processed and can only hardly be destroyed in the following shaping step, leading to sinter bodies with many defects and poor strength and density.
The precise slurry destabilization, carried out after ideally dispersing the ceramic powder, shows a strong influence on the drying behavior of the granules and hence on the granule properties. A promising degree of destabilization and partial flocculation was quantified by optical centrifugation and resulted in improved granule properties. Spray drying the destabilized alumina slurries yielded homogeneous “non-hollow” granules without the above mentioned hard shell. Sample bodies produced of these granules exhibited a reduction of defect size and number, leading to better results for sinter body density and strength.
The positive effect of the slurry destabilization has been further improved, by exchanging the atomizing unit from a two-fluid one to an ultrasound atomizer with only minor slurry adjustments necessary. The controlled destabilization and ultrasound atomization of the ceramic slurry show excellent transferability for zirconia and even ZTA (zirconia toughened alumina) composite materials.
The introduction of the 5G technology and automotive radar applications moving into higher frequency ranges trigger further miniaturization of LTCC technology (low temperature co-fired ceramics). To assess dimensional tolerances of inner metal structures of an industrially produced LTCC multilayer, computer tomography (CT) scans were evaluated by machine learning segmentation.
The tested multilayer consists of several layers of a glass ceramic substrate with low resistance silver-based vertical interconnect access (VIA). The VIAs are punched into the LTCC green tape and then filled with silver-based pastes before stacking and sintering. These geometries must abide by strict tolerance requirements to ensure the high frequency properties.
This poster presents a method to extract shape and size specific data from these VIAs. For this purpose, 4 measurements, each containing 3 to 4 samples, were segmented using the trainable WEKA segmentation, a non-commercial machine learning tool. The dimensional stability of the VIA can be evaluated regarding the edge-displacement as well as the cross-sectional area. Deviation from the ideal tubular shape is best measured by aspect ratio of each individual layer. The herein described method allows for a fast and semi-automatic analysis of considerable amount of structural data. This data can then be quantified by shape descriptors to illustrate 3-dimensional information in a concise manner. Inter alia, a 45 % periodical change of cross-sectional area is demonstrated.
The ProboStat is a multi-purpose measurement cell suitable for various electrical and physical measurements under different atmospheres and at high temperatures. Disc and bar shaped samples are sandwiched between platinum electrodes at the top of the tubular cell. The gas tight assembly can be inserted into a furnace. Different gases can be flushed through the tube. For this study, a ProboStat was adapted to measure volume resistivity of ceramic insulators at high temperatures according to standards.
The standardized measurement of volume resistivity of ceramic insulators requires the consideration of many specifications including sample diameter, thickness, electrode design, and the proportion of these characteristics. Measurements are ideally performed in a state of dielectric equilibrium. The time-related slope of resistivity of a specific sample follows a power function. Thus, care must be taken when choosing a charge time or defining the duration of a measurement. As fringing of the guarded electrode occurs under high voltage, the effective electrode area for evaluation of the results should be corrected with respect to sample thickness and electrode design. The demands of effective standards on sample geometry and electrode design are stricter for room temperature measurements than for high temperature measurements.
To perform high temperature measurements on ceramic samples that also fulfill the demands on room temperature measurements, a ProboStat was equipped with a dedicated large sample setup for discs with diameters of up to 60 mm. The volume resistivity of different alumina samples was first measured at room temperature in a standard test fixture and then compared to results obtained with the ProboStat. All measurements were performed for at least 100 min using a 26 mm guarded electrode. High temperature measurements at 500 °C were performed using the same samples. Room temperature values obtained with the standard test fixture are in the order of 10^17 Ohm·cm. The quantitative effect of electrode area correction is presented. Practical issues related to the use of the multi-purpose cell are addressed. These include electrode material selection, application of electrodes, and compensation of leakage currents. High temperature results of volume resistivity of the different alumina samples are presented. The validity is discussed with respect to the suitability of the multi-purpose cell for such measurements.
Localized patches are a cost- and time-effective method for repairing fiber-reinforced polymer (FRP) sandwich wind turbine rotor blade shells. To increase the understanding of their effect on the fatigue of the blades, this study examines the effect of various layup methods of localized repair patches on the structural integrity of composite sandwich structures. Manufactured with the vacuum-assisted resin infusion (VARI) process, the shell test specimens are produced as a curved structure with glass fiber reinforced polymer (GFRP) sandwiching a polyvinyl chloride (PVC) foam core. Patch repairs are then introduced with varying layup techniques, and material properties are examined with cyclic fatigue tests. The transition region between patch and parent material is studied in greater detail with finite element method (FEM) simulations, with a focus on the effect of fiber orientation mismatch. Damage onset, crack development, and eventual failure are monitored with in-situ non-destructive testing methods to develop a robust understanding of the effects of repair concepts on material stiffness and strength.
Up to now, oriented surface crystallization phenomena are discussed controversially, and related studies are restricted to few glasses. The vast majority of previous work does not consider possible effects of surface preparation and surrounding atmosphere. Moreover, very few observations of surface crystal orientation were made on separately grown crystals.
The aim of our project is to advance the basic understanding of oriented surface crystallization, e.g. whether preferred orientation of surface crystals results from oriented nucleation or reorientation mechanisms during early crystal growth. In both cases, crystal orientation may reflect the orientation of the glass surface or that of anisotropic active surface nucleation sites. Therefore, we focus on orientation of surface crystals separately growing under controlled conditions.
First results on diopside (MgCaSi2O6) and walstromite (BaCa2Si3O9) crystals growing from 18BaO·22CaO·60SiO2 and MgO·CaO·2SiO2 glass surfaces, respectively, indicate that different orientation mechanisms may occur.
Neighbored walstromite crystals were found to gradually reorient themselves when they are going to impinge each other during stepwise isothermal treatments (log η = 4,5 Pa*s) of polished glass samples. Nevertheless, no preferred crystal orientation was evident for separate crystals.
For diopside crystals growing from polished glass surfaces (1 μm diamond lapping foil), strong preferred orientation was observed for 3.5 to 85 min annealing at 850 °C. Electron Backscatter Diffraction (EBSD) studies showed that the c-axis of surface crystals is oriented parallel to the glass surface and that separated diopside crystals as small as 600 nm are already oriented. Studies on glass surfaces, polished with diamond lapping foils starting from 16 μm down to 1 μm grain, revealed that crystal orientation may scatter arround this preferential orientation and that this scatter progressively decreases with decreasing polishing grain size.