Local Lattice Research Articles

Point-defect-driven flattened polar phonon bands in fluorite ferroelectrics

The scale-free ferroelectric polarization of fluorite MO2 (M = Hf, Zr) due to flat polar phonon bands are promising for nonvolatile memories. Defects are also widely introduced to improve the emergent ferroelectricity. However, their roles are still not fully understood at the atomic-level. Here, we report a significant effect of point-defect-driven flattening of polar phonon bands with more polar modes and polarization contribution in doped MO2. The polar phonon bands in La-doped MO2 (M = Hf, Zr) can be significantly flattened, compared with pure ones. However, the lower energy barrier with larger polarization of VO-only doped MO2 compared with La-doped cases suggest that VO and local lattice distortion should be balanced for high-performance fluorite ferroelectricity. The work is believed to bridge the relation between point defects and the generally enhanced induced ferroelectricity in fluorite ferroelectrics at the atomic-level and inspire their further property optimization via defect-engineering.

Hierarchically polar structures induced superb energy storage properties for relaxor Bi0.5Na0.5TiO3-based ceramics

Electrostatic capacitors are fundamental components in electronics and electric power systems because of their inherent superiorities of charging/discharging speed and power density. However, energy storage properties (ESPs) of the top promising relaxor ferroelectric (RFE) are intimately entwined symmetry of local lattice and dynamics of nano-scaled polar structure. Herein, hierarchically polar structure and oxygen octahedral tilting can be induced in the 0.7Bi0.5Na0.5TiO3-0.3Na0.91Bi0.09Nb0.94Mg0.06O3 (BNT-NBNM) matrix with the addition of CaZrO3 (CZ) to achieve outstanding comprehensive ESPs. The chemically induced coexisting triple phases of tetragonal P4bm, orthorhombic P21ma and Pnma2 bring forth hierarchically polar structure, featuring nanodomains and slush-like polar clusters embedded in stripe submicro-domains, as indicated by morphological observations, splitting of diffraction spots and polar state distributions. Accordingly, an ultrahigh recoverable energy storage density Wrec = 7.5 J cm−3 concurrent with a high-efficiency η = 94.5 % at a breakdown electric field of 510 kV cm−1 can be attained in BNT-NBNM-0.05CZ RFE ceramic. In addition, the optimal composition also displays excellent stability (Wrec = 5.1 ± 0.1 J cm−3, η = 92.7% ± 1%, 20–170 °C and Wrec = 5.2 ± 0.2 J cm−3, η = 92.1% ± 1.3%, 5–500 Hz) at 410 kV cm−1. The present work provides a new perspective for designing lead-free RFE ceramics with ultra-high ESPs that benefit from hierarchically polar structures.

A ductility metric for refractory-based multi-principal-element alloys

We propose a quantum-mechanical dimensionless metric, the local-lattice distortion (LLD), as a reliable predictor of ductility in refractory multi-principal-element alloys (RMPEAs). The LLD metric is based on electronegativity differences in localized chemical environments and combines atomic-scale displacements due to local lattice distortions with a weighted average of valence-electron count. To evaluate the effectiveness of this metric, we examined body-centered cubic (bcc) refractory alloys that exhibit ductile-to-brittle behavior. Our findings demonstrate that local-charge behavior can be tuned via composition to enhance ductility in RMPEAs. With finite-sized cell effects eliminated, the LLD metric accurately predicted the ductility of arbitrary alloys, which compares well with existing tensile-elongation experiments. To validate further, we qualitatively evaluated the ductility of two refractory RMPEAs, i.e., NbTaMoW and Mo72W13Ta10Ti2.5Zr2.5, through the observation of crack formation under indentation, again showing excellent agreement with LLD predictions. A comparative study of three refractory alloys provides further insights into the electronic-structure origin of ductility in refractory RMPEAs. This proposed metric enables rapid and accurate assessment of ductility behavior in the vast RMPEA composition space.

Atomic-scale manipulation of single-polaron in a two-dimensional semiconductor

Polaron is a composite quasiparticle derived from an excess carrier trapped by local lattice distortion, and it has been studied extensively for decades both theoretically and experimentally. However, atomic-scale creation and manipulation of single-polarons in real space have still not been achieved so far, which precludes the atomistic understanding of the properties of polarons as well as their applications. Herein, using scanning tunneling microscopy, we succeeded to create single polarons in a monolayer two-dimensional (2D) semiconductor, CoCl2. Combined with first-principles calculations, two stable polaron configurations, centered at atop and hollow sites, respectively, have been revealed. Remarkably, a series of manipulation progresses — from creation, erasure, to transition — can be accurately implemented on individual polarons. Our results pave the way to understand the physics of polaron at atomic level, and the easy control of single polarons in 2D semiconductor may open the door to 2D polaronics including the data storage.

The influence of hafnium removal on the microstructure and properties of 8YSZ ceramics

The effects of hafnium removal on the sinterability, phase composition, and microstructural, mechanical, and electrical properties of 8YSZ (8 mol% yttrium stabilized zirconia) were investigated using SEM, XRD, Raman spectroscopy, EBSD, three-point bending, Vickers indentation, and impedance spectroscopy. The 8YSZ and 8YSZ0 (8 mol% yttrium-stabilized hafnium-free zirconia) ceramics were prepared via dry pressing and atmospheric sintering, respectively. The overall mechanical properties of the 8YSZ0 ceramic were poor. However, at a sintering temperature of 1450°C, the relative density of 8YSZ and 8YSZ0 ceramics was almost identical. 8YSZ0 had a slightly smaller grain size and activation energy, and its electrical properties were slightly better than those of the 8YSZ ceramics. The presence of tetragonal secondary phases in the cubic structure of 8YSZ ceramics inhibited crack propagation and led to an increase in the mechanical properties and a decrease in the ion conductivity. In terms of the crystal structure, the increase in the cubic phase lattice parameters and tetragonal phase c/a values of the 8YSZ0 ceramics was attributed to the larger Zr4+radius, reduced local lattice distortion, and increased matrix oxygen vacancy concentration and cubic phase content. The EBSD analysis results indicated that there was no significant difference in grain orientation between the two types of ceramics, but the content of 8YSZ ceramics in large angle grain boundaries was slightly higher, especially in special grain boundaries Σ3 and Σ9. Therefore, this material can be used as a solid-state electrolyte candidate.

Atomic-scale deformation mechanism of nano Cu precipitate along the rolling process of ferritic steel

The deformation behavior of nanoscale precipitates and their interaction with the matrix in the alloys have been rarely explored. In this study, the deformation mechanism of nanoscale soft Cu precipitates and its interaction with ferritic matrix during rolling deformation were studied at the atomic scale. The ellipsoidal Cu precipitates with an average diameter of about 34 nm are flattened into slender rods under rolling reduction of about 70% and are elongated along the rolling direction. The initial K-S orientation relationship was transformed into N-W orientation relationship after rolling deformation. The shear deformations are induced in Cu precipitate near the interface and the serrated boundary are formed combined with the plastic flow of the matrix. A successive lattice torsion band with a width of 1.5 ∼ 10 nm was formed at the serrated interface, while there is only local lattice distortion at the smooth interface. The Cu precipitates maintained good deformability and excellent strain coordination ability under severe deformations. These results have important value for understanding the deformation mechanism of Cu precipitates.

Ab initio study of the lattice distortion and the vacancy defects in multi-anion oxycarbonitride ceramics TiCNO and TiZrCNO

Multicomponent ceramics have received much attention due to the tunning physicochemical properties and the huge compositional space, while multicomponent ceramics with the mixing of multi-anion are rarely studied. In this work, the local lattice distortion and vacancy formation energy in TiCNO and TiZrCNO are systematically investigated by density functional theory calculations combining with the special quasi-random structure model. The present results show that multi-anionic mixed oxycarbonitride ceramics exhibit obvious local lattice distortion. The quantified displacive distortions of C, N, and O in TiCNO are relatively large, being in order of C < N < O, although metallic elements Ti has larger distortion than nonmetals. Within incorporative mixing of Zr in cation sublattice, the distortions of Ti, C, N, and O increase evidently, the distortion degree for nonmetal elements is still in order of C < N < O. The distortion of Ti is still the largest, whereas Zr possesses almost the smallest distortion. The electronic structure shows a close association with the degree of distortion, the larger DOS at the Fermi level corresponds to the larger distortion. The vacancy defects are further studied. Our consequences show that the vacancy formation energies of non-metal elements with large local distortions are relatively low, suggesting that the local chemical environment profoundly affects the vacancy formation energy and defect-related properties. The present study reveals the important correlation of lattice distortion with electronic structure and vacancy generation, so it is valuable to deepen the understanding of the excellent properties of multicomponent ceramics with multi-anion mixing, and develop novel multicomponent ceramics with polyanionic structures.

Regulating phase ratio of β/α and static recrystallization of Ti-5Al-5Mo-5Cr-3Nb-2Zr with high plasticity alloyed by vanadium

To research the recrystallization mechanism without deformation of the α phase and control the phase ratio of β/α, Ti-5Al-5Mo-5Cr-3Nb-2Zr alloys with different vanadium contents were melted. The results indicate that with increasing vanadium content, the content and aspect ratio of the primary α (αp) and secondary α (αs) phases decrease, and the ratio of the β phase increases from 7% to 88%. The degree of recrystallization of αp and grain boundary α (αGB) phases increases, and their morphology changes from lath to equiaxed. The mechanism of static recrystallization is that the enrichment of V aggravates the local lattice strain and leads to the migration of the α phase interface. The V element aggravates the atomic size mismatch and the local lattice strain and reduces the β transition temperature of the enrichment region. The strength in the Ti-0 V alloy is the highest at ∼1056 MPa and then decreases. The Ti-2 V alloy had the highest toughness of ∼68.4 MPa·m1/2. The elongation of the Ti-6 V alloy is the highest at ∼16.1% due to the increase of β phase content and α phase recrystallization, which is ∼1.8 and ∼ 1.7 times that of the Ti-0 V and Ti-8 V alloys, respectively. The equiaxed αp phase and αs phase lead to shortening of the crack deflection path, and crack propagation is easier due to the increase of β phase content, which causes the crack propagation path to change from tortuous to straight.

Ab initio study of effects of Al on the defect behaviors of AlxCoCrFeNi high entropy alloys

The influence of Al on the defect behaviors of AlxCoCrFeNi high-entropy alloys (HEAs) is studied by ab initio calculations. The lattice distortion, defect formation energies, and defect migration energies were calculated for different Al concentrations ranging from 0 to 6.25 at. %. First, the increase in the lattice distortion of AlxCoCrFeNi by the addition of Al is demonstrated, but the increment is smaller than that predicted by the atomic size difference of constituent elements. Second, although formation energies of Al vacancies and dumbbells containing Al are higher, the addition of Al decreases the average formation energies of vacancies and interstitials, which is probably due to the Al-induced local strain field and lattice distortion. The migration energies of interstitials and vacancies exhibit opposite variations, the migration energies of interstitials are increased while that of vacancies are decreased with the Al content. Moreover, the distributions of formation and migration energies of both defects are significantly broadening with increasing Al content, which could further enhance the characteristic effects of HEAs and play a more important role in the irradiation resistances of HEAs. Based on the calculation results, the effects of Al on the irradiation responses of AlxCoCrFeNi are discussed.

High-resolution 3D strain and orientation mapping within a grain of a directed energy deposition laser additively manufactured superalloy

The industrialization of Laser Additive Manufacturing (LAM) is challenged by the undesirable microstructures and high residual stresses originating from the fast and complex solidification process. Non-destructive assessment of the mechanical performance controlling deformation patterning is therefore critical. Here, we use Dark Field X-ray Microscopy (DFXM) to map the 3D subsurface intragranular orientation and strain variations throughout a surface-breaking grain within a directed energy deposition nickel superalloy. DFXM results reveal a highly heterogenous 3D microstructure in terms of the local orientation and lattice strain. The grain comprises ≈ 5 μm-sized cells with alternating strain states, as high as 5 ×10−3, and orientation differences <0.5°. The DFXM results are compared to Electron Backscatter Diffraction measurements of the same grain from its cut-off surface. We discuss the microstructure developments during LAM, rationalising the development of the deformation patterning from the extreme thermal gradients during processing and the susceptibility for solute segregation.

Dislocation arrangements in 4H-SiC and their influence on the local crystal lattice properties.

Two wafers of one 4H-silicon carbide (4H-SiC) bulk crystal, one cut from a longitudinal position close to the crystal's seed and the other close to the cap, were characterized with synchrotron white-beam X-ray topography (SWXRT) in back-reflection and transmission geometry to investigate the dislocation formation and propagation during growth. For the first time, full wafer mappings were recorded in 00012 back-reflection geometry with a CCD camera system, providing an overview of the dislocation arrangement in terms of dislocation type, density and homogeneous distribution. Furthermore, by having similar resolution to conventional SWXRT photographic film, the method enables identification of individual dislocations, even single threading screw dislocations, which appear as white spots with a diameter in the range of 10 to 30 µm. Both investigated wafers showed a similar dislocation arrangement, suggesting a constant propagation of dislocations during crystal growth. A systematic investigation of crystal lattice strain and tilt at selected wafer areas with different dislocation arrangements was achieved with high-resolution X-ray diffractometry reciprocal-space map (RSM) measurements in the symmetric 0004 reflection. It was shown that the diffracted intensity distribution of the RSM for different dislocation arrangements depends on the locally predominant dislocation type and density. Moreover, the orientation of specific dislocation types along the RSM scanning direction has a strong influence on the local crystal lattice properties.

Anomalous thermal conductivity of alkaline-earth-metal-substituted EuTiO3 induced by resonant scattering

We have investigated thermal conductivities (κ) of polycrystalline Eu1–xAxTiO3 (A = Ca, Sr, Ba, 0 ≤ x ≤ 0.8) bulk materials in the temperature range of ∼ 2 K <T < 1173 K. The EuTiO3 demonstrates anomalous glass-like κ(T) behavior at low temperatures. Partial substitutions with Sr2+ and Ba2+ do not cause a significant change in the κ(T) behavior, while a κ(T) peak, which looks like a manifestation of a typical crystalline solid, appears only in the Ca-substituted samples with an orthorhombic structure when x ≥ 0.4. After excluding the magnetic effects on κ and discussing the possible phonon scattering mechanisms in depth, together with heat capacity Cp measurements and high-resolution X-Ray diffraction characterization, we find that the unusual low κ at low temperatures is attributed to resonant scattering induced by the intrinsic disordered local structure and lattice instability in EuTiO3. Due to the different lattice dynamics of ATiO3, the lattice structure of Eu1–xCaxTiO3 can be regarded as formed by a part-soft (from EuTiO3) part-rigid (from CaTiO3) sublattice. The anomalous κ(T) behavior of Eu1–xCaxTiO3 results from the combined effect of phonon transport between the normal phononic heat transport in the rigid sublattice and the strong damping of heat conduction in the soft sublattice.

Statistical analysis of slip transfer in Al alloy based on in-situ tensile test and high-throughput computing method

Slip transfer mechanism is studied based on in-situ tensile tests performed on an Al-Mg alloy and high-throughput computing. A statistical analysis of slip transfer is performed for over 1180 grain boundaries and 155,250 slip pairs while considering the local lattice rotation, grain boundaries, and slip system geometries. Two new slip transfer parameters, N and B, representing the alignment of the slip planes and the activation of slip systems in adjacent grains, are proposed. A decision tree model is built to evaluate the prediction accuracy of the slip transfer parameters. The optimized results of the decision tree classifiers show that the two new parameters are more effective than the Luster–Morris parameter, m′. The improvement in the classification accuracy is attributable to the information regarding the slip plane geometry and orientation evolution contained in N and B. The new slip transfer parameters improve our understanding of the slip transfer mechanism and can be integrated into plasticity models to predict the deformation and fracture behaviors of polycrystalline materials.

Local instability in GdBa2Cu3O7-x/La0.7Sr0.3MnO3 superconducting bilayer: Temperature-dependent EXAFS study

This study investigated the effect of local structural coupling between the buffer and the superconducting layers on the superconductivity of a GdBa2Cu3O7-x (GdBCO)/La0.7Sr0.3MnO3 (LSMO) bilayer. Epitaxial bilayers consisting of GdBCO with varying thicknesses (100, 300, and 500 nm), with and without LSMO (100 nm), were fabricated on a (001) SrTiO3 substrate. To investigate the local structural distortion within the GdBCO/LSMO system, the temperature-dependent extended X-ray absorption fine structure (EXAFS) spectra were measured at the Mn- and Cu–K absorption edges. The EXAFS analyses revealed local structural non-uniformity, which manifested as anomalies in the temperature dependence of both the Mn–O and Cu–O bond distributions. A strong correlation exists between the local structural distortion of the Mn–O bond and the degree of lattice instability in the CuO2 plane, which exhibits a strong thickness dependence. The inter-atomic potential of oxygen oscillations with an anharmonic approximation was adopted to interpret the structural anomalies. As a result, a double-well potential was obtained near Tc, owing to the occurrence of longer Cu–O bonds in the CuO2 plane. The difference in the degree of structural anomalies depending on the GdBCO thickness manifested as a difference in the distance between the two wells, which closely correlates with the appearance of a superconducting state. These experimental results demonstrate the role of local lattice fluctuations in the superconducting mechanism of the GdBCO/LSMO bilayer.

Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-Tc cuprate superconductor Bi2Sr2CaCu2O8+{\delta} revealed a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B1 and E representations in the C4v group of the lattice, which coincides with the uni-directional d-symmetry CDW (dCDW) previously identified within the CuO2 planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the X-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally-frozen version of the soft phonons identified by the X-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.

Quantitative analysis of atomic-scale local lattice distortions in high-entropy fluorite oxide (Zr0·2Ce0.2Hf0.2Y0·2Al0.2)O2-δ

Novel high-entropy oxides have attracted considerable attention as promising candidates for high-temperature structural applications. The lattice distortion effect in such materials is closely related to their microstructural evolution and thermophysical performance. In this study, the local lattice distortions in the high-entropy fluorite oxide (Zr0·2Ce0.2Hf0.2Y0·2Al0.2)O2-δ were observed at the atomic scale using aberration-corrected scanning transmission electron microscopy and studied quantitatively using geometric phase analysis. The results showed that the radius and brightness of the atomic column projections exhibit slight variations owing to the random distribution of the cations, resulting in differences in the relative contents of the five elements in each atomic column. The anions were influenced by both the random distribution of the cations and the large number of oxygen vacancies, leading to M-O-M (M = Zr, Ce, Hf, Y, and Al) bond angles of 80–105°. The distributions of strains εyy and εxx (along the lattice spacing direction and vertical direction, respectively) within the crystal structure were mainly centred around ±4%, and there was a tendency for alternating positive and negative values in strains maps without significant aggregations. In addition, strains εxx and εyy increased significantly to 26.4% and 9.2%, respectively, within the dislocation areas.

Visualizing local bending of lattice planes by extending two-azimuth synchrotron X-ray diffraction datasets to asymmetric reflection

Synchrotron X-ray rocking curve imaging (RCI) is modified to visualize local bending of lattice planes of a single crystal substrate (XR-V-LBLP). This method uses two-azimuth RCI datasets of asymmetric reflection or symmetric reflection. The analysis algorithm is described and a Python software code is provided in the Supplementary material. The two symmetrically equivalent 112¯4 datasets obtained from a GaN (0001) 4-inch wafer are reanalyzed using this software. The normal vector, reciprocal-lattice vector, of the local lattice planes, which is approximately parallel to the sample surface, is formulated as the product of two rotation matrices. This vector is written in polar coordinates using the length and two declination angles, newly introduced in this article. The spatial and probability distributions of the declination angles are also presented. The proposed method enables visualization of the local shape or orientation of the lattice planes of the entire wafer. The limits of application of the method are examined for the samples studied. The sample is found to satisfy two conditions regarding the relative d-spacing difference and the curvature of the lattice planes at all 50 adjacent μm positions.

Formation and transformation of metastable LPSO building blocks clusters in Mg-Gd-Y-Zn-Zr alloys by spinodal decomposition and heterogeneous nucleation

To study the formation and transformation mechanism of long-period stacked ordered (LPSO) structures, a systematic atomic scale analysis was conducted for the structural evolution of long-period stacked ordered (LPSO) structures in the Mg-Gd-Y-Zn-Zr alloy annealed at 300 °C∼500 °C. Various types of metastable LPSO building block clusters were found to exist in alloy structures at different temperatures, which precipitate during the solidification and homogenization process. The stability of Zn/Y clusters is explained by the first principles of density functional theory. The LPSO structure is distinguished by the arrangement of its different Zn/Y enriched LPSO structural units, which comprises local fcc stacking sequences upon a tightly packed plane. The presence of solute atoms causes local lattice distortion, thereby enabling the rearrangement of Mg atoms in the different configurations in the local lattice, and local HCP-FCC transitions occur between Mg and Zn atoms occupying the nearest neighbor positions. This finding indicates that LPSO structures can generate necessary Schockley partial dislocations on specific slip surfaces, providing direct evidence of the transition from 18R to 14H. Growth of the LPSO, devoid of any defects and non-coherent interfaces, was observed separately from other precipitated phases. As a result, the precipitation sequence of LPSO in the solidification stage was as follows: Zn/Ycluster+Mg layers→various metastable LPSO building block clusters→18R/24R LPSO; whereas the precipitation sequence of LPSO during homogenization treatment was observed to be as follows: 18R LPSO→various metastable LPSO building block clusters→14H LPSO. Of these, 14H LPSO was found to be the most thermodynamically stable structure.

Visualizing the Atomic Configuration of Carbonate Groups in a (Cu,C)Ba2 Ca3 Cu4 O11+δ Superconductor.

Carbonates (CO3 2- ) have always been known as impurities to degrade the superconductivity in cuprate high-Tc superconductors. Herein, the atomic arrangement of carbonates is directly visualized in (Cu,C)Ba2 Ca3 Cu4 O11+δ via integrated differential phase contrast (iDPC) combined with state-of-the-art scanning transmission electron microscopy. The carbon atoms replace Cu atoms in the charge-reservoir layers, contributing to the formation of carbonates through strong orbital hybridization with the surrounding oxygen atoms. Using first-principles calculations, the spatial configuration of the carbonate groups is confirmed and their influence on the local crystal lattice and electronic states is further investigated. The carbonates not only accommodate distortions by improving the flatness of the outer CuO2 layers but also reduce the density of states at the Fermi level. These two factors play competitive roles to affect the superconductivity. This study provides direct evidence of the presence of CO3 2- groups and gains an insight into the underlying mechanism of superconductivity in oxycarbonate superconductors.

Origins of epitaxial macro-terraces and macro-steps on GaN substrates

Localized lattice distortions in GaN substrates can serve as nucleation sites for epitaxial macro-steps and macro-terraces. These detrimental macro-scale features give rise to optically hazy homoepitaxial GaN surfaces. After nucleating, these macro-features grow laterally along the surface and coalesce, leading to significant coverage of the wafer surface. Dot-core GaN substrates consisting of a periodic array of cores were used as a defect-engineered system, where dislocations are intentionally concentrated at the cores. The high density of threading dislocations at the cores induced localized lattice distortions. These distortions are associated predominantly with lattice tilt on the order of hundreds of arcsec across ∼0.5 mm laterally along the wafer surface. The resulting macro-features that nucleated at these localized distorted sites were made up of macro-terraces with lengths ranging ∼30–∼150 μm and macro-step heights ranging ∼200–∼400 nm. Another source of localized distortion was threading screw dislocations or GaN nanopipes that resulted in spiral growth and hillock formation. Based on x-ray topography and optical microscopy measurements, we speculate that the coalescence of hillocks evolves into macro-terraces and macro-steps. While previous studies focused on the substrate miscut as a means to control macro-feature formation, we show that localized lattice tilt from defects is another important contributor to macro-feature formation.