Stacking Fault Layer Research Articles

Microstructure evolution and shearing behaviour of δꞌ/θꞌ/δꞌ precipitates in an aged Al-Cu-Li-Mg aluminium alloy

We report here on the microstructure evolution and the strengthening behaviour of the δꞌ/θꞌ/δꞌ precipitates in the aged Al-Cu-Li-Mg aluminium alloy by atomic high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and in-situ TEM compression straining. On the chosen zone axis, atomic HAADF-STEM images reveal the in-situ microstructure evolution of the δꞌ/θꞌ/δꞌ precipitates. A monolayer GP(θꞌ) zone, grown on the (001)Al plane, evolves from the Cu-rich region. After the transformation of the GP(θꞌ) zone to θꞌ phase, the boundaries of the θꞌ phase are coated with the δꞌ phases, forming a matured δꞌ/θꞌ/δꞌ precipitate. Additionally, the growth of δꞌ phases on the two sides of θꞌ is not affected by the inclined boundaries of θꞌ and the hard impingement of the thin T1 precipitate. During the in-situ TEM compression straining on the peak-aged nanopillar, the deviated slip band structures and the large displacement bursts are presumably associated with the dislocation-precipitate interaction of the T1 and δꞌ/θꞌ/δꞌ precipitates. Furthermore, evidence from atomic HAADF-STEM images shows that dislocations can cut the δꞌ/θꞌ/δꞌ precipitate, producing the stacking fault layers within the θꞌ phase of the sheared δꞌ/θꞌ/δꞌ precipitate.

HR-STEM investigation of atomic lattice defects in different types of η precipitates in creep-age forming Al–Zn–Mg–Cu aluminium alloy

High-resolution (HR) high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) has revealed the atomic lattice defects in different types of η precipitates in the Al–Zn–Mg–Cu aluminium alloy subjected to creep-age forming treatment (with a constant stress lower than its room-temperature yield strength during ageing). Along the zone axes of [110] Al //[2 1 ‾ 1 ‾ 0]η of η 1 and η 12 , [112] Al //[2 1 ‾ 1 ‾ 0]η of η 2 and [100] Al //[2 1 ‾ 1 ‾ 0]η of η 13 , atomic projections of (2 1 ‾ 1 ‾ 0)η have been investigated. In those types of η, elongated hexagonal lattice defects (labelled as Type I defects) can be found; they are apparently related to local disorder in atomic stackings. Furthermore, in η 12 , elongated hexagonal lattice defects with a much higher aspect ratio (labelled as Type II defects) are uniquely observed. These atomic lattice defects are presumably pertinent to the lattice accommodation in the course of creep-age forming. Additionally, in η 1 and η 12 , the features of a Penrose tiling defect connecting with Type I defects are observed, and these complex defects obviously affect the growth direction of the precipitate, resulting in a nearly spherical morphology. Alternatively, several entirely-passed faulted layers in a new type of precipitate, η 14 , consequently bring about a new orientation relationship: (51 3 ‾ ) Al //(0001)η 14 and [112] Al //[2 1 ‾ 1 ‾ 0]η 14 . Moreover, in an atomic STEM image of η 14 , the significant Z-contrast gradient adjacent to the transformation front of η 14 elucidates the Zn/Cu diffusion from the matrix to the precipitate along {1 1 ‾ 1 ‾ } Al planes at the interface. • Along the [2110]η zone axis, the edge-on atomic configurations of η 1 , η 2 , η 12 , η 13 and η 14 precipitates have been investigated to explore their atomic lattice defects. • Within the spherical-like morphologies of η 1 and η 12 , Penrose tiling features jointed with elongated hexagonal lattice defects were identified. • In η 12 precipitates, two types of elongated hexagonal lattice defects of different sizes were found. • Differently-oriented elongated hexagonal lattice defects presumably affect the local stackings, bringing about differently-oriented types of η precipitates. • In the newly-typed η 14 precipitate, some entirely-passed stacking fault layers presumably cause a new specific orientation relationship with respect to the Al matrix.

Uncovering the internal structure of five-fold twinned nanowires through 3D electron diffraction mapping**Project supported by the National Natural Science Foundation of China (Grant Nos. 51201015 and U1532262).

Five-fold twinned nanostructures are intrinsically strained or relaxed by extended defects to satisfy the space-filling requirement. Although both of metallic and semiconductor five-fold twinned nanostructures show inhomogeneity in their cross-sectional strain distribution, the evident strain concentration at twin boundaries in the semiconductor systems has been found in contrast to the metallic systems. Naturally, a problem is raised how the chemical bonding characteristics of various five-fold twinned nanosystems affects their strain-relieving defect structures. Here using three-dimensional (3D) electron diffraction mapping methodology, the intrinsic strain and the strain-relieving defects in a pentagonal Ag nanowire and a star-shaped boron carbide nanowire, both of them have basically equal radial twin-plane width about 30 nm, are non-destructively characterized. The non-uniform strain and defect distribution between the five single crystalline segments are found in both of the five-fold twinned nanowires. Diffraction intensity fine structure analysis for the boron carbide five-fold twinned nanowire indicates the presence of high-density of planar defects which are responsible for the accommodation of the intrinsic angular excess. However, for the Ag five-fold twinned nanowire, the star-disclination strain field is still present, although is partially relieved by the formation of localized stacking fault layers accompanied by partial dislocations. Energetic analysis suggests that the variety in the strain-relaxation ways for the two types of five-fold twinned nanowires could be ascribed to the large difference in shear modulus between the soft noble metal Ag and the superhard covalent compound boron carbide.

Enhanced ductility of III-V covalent semiconductors from electrons and holes

Covalent semiconductors exhibit low ductility arising from the resistance of the strong chemical bonds to deformation slip. It is important to soften these strong covalent bonds to improve the ductility of covalent semiconductors for their extended engineering applications. Here, we demonstrate from quantum mechanics simulations that the free carriers, including electrons and holes, can significantly weaken the strong covalent bonds of III-V covalent semiconductors, resulting in the modified general stacking fault energy surface and enhanced ductility. Furthermore, we establish the relationship between the carrier density and the energy barriers of deformation slip, in which the increased carrier concentration leads to an increased tendency of dislocation nucleation and higher ductility. The physical origin of this phenomenon arises from the contributions of extra carriers to the formation of new weak bonds at stacking fault layers along the slip plane, decreasing the energy barrier of deformation slip. Our results indicate that free electrons and holes play an important role in the mechanical properties of covalent semiconductors at high carrier concentrations. This provides the theoretical foundation to tune the mechanical properties of covalent semiconductors using injected carriers.

Non-destructive detection of cross-sectional strain and defect structure in an individual Ag five-fold twinned nanowire by 3D electron diffraction mapping

Coherent x-ray diffraction investigations on Ag five-fold twinned nanowires (FTNWs) have drawn controversial conclusions concerning whether the intrinsic 7.35° angular gap could be compensated homogeneously through phase transformation or inhomogeneously by forming disclination strain field. In those studies, the x-ray techniques only provided an ensemble average of the structural information from all the Ag nanowires. Here, using three-dimensional (3D) electron diffraction mapping approach, we non-destructively explore the cross-sectional strain and the related strain-relief defect structures of an individual Ag FTNW with diameter about 30 nm. The quantitative analysis of the fine structure of intensity distribution combining with kinematic electron diffraction simulation confirms that for such a Ag FTNW, the intrinsic 7.35° angular deficiency results in an inhomogeneous strain field within each single crystalline segment consistent with the disclination model of stress-relief. Moreover, the five crystalline segments are found to be strained differently. Modeling analysis in combination with system energy calculation further indicates that the elastic strain energy within some crystalline segments, could be partially relieved by the creation of stacking fault layers near the twin boundaries. Our study demonstrates that 3D electron diffraction mapping is a powerful tool for the cross-sectional strain analysis of complex 1D nanostructures.

First-principles prediction of the stacking fault energy of gold at finite temperature

The intrinsic stacking fault energy (ISFE) γ is a material parameter fundamental to the discussion of plastic deformation mechanisms in metals. Here, we scrutinize the temperature dependence of the ISFE of Au through accurate first-principles derived Helmholtz free energies employing both the super cell approach and the axial Ising model (AIM). A significant decrease of the ISFE with temperature, −(36–39) % from 0 to 890 K depending on the treatment of thermal expansion, is revealed, which matches the estimate based on the experimental temperature coefficient dγ/dT closely. We make evident that this decrease predominantly originates from the excess vibrational entropy at the stacking fault layer, although the contribution arising from the static lattice expansion compensates it by approximately 60%. Electronic excitations are found to be of minor importance for the ISFE change with temperature. We show that the Debye model in combination with the AIM captures the correct sign but significantly underestimates the magnitude of the vibrational contribution to γ(T). The hexagonal close-packed (hcp) and double hcp structures are established as metastable phases of Au. Our results demonstrate that quantitative agreement with experiments can be obtained if all relevant temperature-induced excitations are considered in first-principles modeling and that the temperature dependence of the ISFE is substantial enough to be taken into account in crystal plasticity modeling.

Modeling Dislocation‐Stacking Fault Interaction Using Molecular Dynamics

AbstractIn a number of fcc materials such as copper or aluminum, as well as more complex materials such as twinning induced plasticity (TWIP) steels, the interaction between dislocations and other defects such as stacking faults or twins plays an important role in the hardening behavior of such materials. Interactions of dislocation and twin or stacking fault layers have been studied in this work using molecular dynamics. Depending on the material and the loading conditions, possible interaction modes include (i) penetration of the dislocation into the faulted layer, (ii) reduction of the faulted layer after interaction, (iii) growth of the faulted layer after interaction. Such studies up to this point have been performed without temperature control near zero K (0 to 2 K). In this work, we extend the previous studies to higher temperature with the help of two methods, both based on molecular dynamics (MD) modeling. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Clustering of Zn6Y9 and its Predominant Role in Long Period Stacking Order Phases in Mg-Zn-Y Alloys: A First-Principles Study

The local structures of Zn and Y in the long period stacking order (LPSO) phase in Mg-Zn-Y system were investigated by first principles calculations in details. The clustering of Zn and Y atoms ranging from single stacking fault layer to four consecutive layers was explicitly demonstrated. The calculations indicate that Zn and Y atoms prefer clustering in the form of Zn6Y9 embedding in ABCA-type building block to the random or ordered arrangements of Zn and Y atoms being enriched in two stacking fault layers. The cluster of Zn6Y9 can be regarded as the ideal stoichiometric component of LPSO and it plays a predominant role in the LPSO phases. The formation of LPSO phases is highly associated with the Zn6Y9 cluster and its derivatives.

Theoretical Investigation on Microstructure of the Novel 24R-Type LPSO Phase in Mg<sub>97</sub>Zn<sub>1</sub>Y<sub>2</sub> Alloy

The first-principles calculation based on density functional theory has been carried out to study the microstructural feature of the novel 24R-type long period stacking ordered structure in Mg97Zn1Y2alloy. The lattice positions of the Y and Zn atoms are determined theoretically, it is shown that the additive atoms are firstly enriched in the stacking fault layers at the two ends, a small amount are distributed in the interior stacking fault layers of the structure. And the arrangement of these Y and Zn atoms trends to be along the diagonal line of the unit cell. The structural stability is analyzed and the electronic density of state is discussed as well as.

First-principles investigation of the effect of carbon on the stacking fault energy of Fe–C alloys

The intrinsic stacking fault energy (SFE) is a critical parameter that defines the type of plasticity mechanisms in austenitic high-Mn steels. We have performed ab initio investigations to study the effect of interstitial carbon atoms on the SFE of face-centred cubic (fcc) Fe–C alloys. Simulating the stacking fault explicitly, we observe a strong dependence of the SFE on the position of carbon atoms with respect to the stacking-fault layer and the carbon concentration. To determine the SFE for realistic carbon distributions we consider two scenarios, assuming (i) an equilibration of the carbon atoms in response to the stacking fault formation and (ii) a homogeneous distribution of the C atoms when creating the stacking fault (i.e. diffusion is suppressed). This distinction allows us to interpret two sets of apparently contradicting experimental data sets, where some find an almost negligible dependence on the carbon concentration while others report a large carbon dependence. In particular, our results for the second scenario show a significant increase in the SFE as a function of carbon concentration. These trends are consistently found for the explicit calculations as well as for the computationally much more efficient axial next-nearest-neighbour Ising approach. They will be decisive for the selection of specific plasticity mechanisms in steels (such as twin formation, martensitic transformations and dislocation gliding).

Effects of stacking fault on the diffraction intensities of β-FeSi 2

β-FeSi 2 was synthesized by heating mixtures of Si and Fe powder sealed with Na metal and Ar gas in a stainless tube. Diffuse streaks elongated along the a axis were observed in the electron diffraction (ED) patterns of β-FeSi 2 prepared at 873 K in the Na melt. No streaks appeared on the spots indexed by k + l = 2 n ( n: integer), which indicated existence of stacking faults caused by a slip system of (1 0 0)[0 1 1]/2. The powder X-ray diffraction (XRD) patterns of the samples prepared at 873 K for 48 h in the Na melt and at 1173 K for 24 h under reduced Na vapor pressure were analyzed by the Rietveld method with a statistical split-site model based on the stacking fault structure. The powder X-ray diffraction patterns of the samples prepared at 873 K for 48 h in the Na melt and at 1173 K for 24 h in Na vapor which evaporated from a mixture of Na and Si were analyzed by the Rietveld method with a statistical split-site model based on the stacking fault structure. The ratios of the normal stacking layer and stacking fault layer of the samples prepared at 873 and 1173 K were estimated to be 0.95:0.05 and 0.84:0.16, respectively. Main features of the observed powder X-ray diffraction patterns were well reproduced by the calculation based on a general recursion method for calculating diffracted intensities from crystals containing stacking fault.

Interactions between point defects and edge dislocations in copper

Molecular dynamics with an embedded atom potential are used to investigate the interaction between one, two or up to six interstitials and split edge dislocations in copper. Interstitials were trapped at the core of a partial dislocation and also the stacking fault (extended) layer connecting two partial dislocations in copper. The trapped interstitials were a split <1 1 0> crowdion type just below the slip plane. Interstitials trapped by a pair of partial dislocations are oriented in the directions perpendicular to the Burgers vector of the partial dislocations. Interstitials trapped at the extended layer were oriented in the direction parallel to the Burgers vector of the complete edge dislocation. The displacements of atoms surrounding the interstitials that are trapped at the extended stacking fault layer are in (1 1 1) planes.

Electronic structures of natural quantum‐dot system; Si stacking‐fault tetrahedron

Electronic structures of the Si stacking-fault tetrahedron (SFT) are studied, by using the first-principles calculations. It is shown that the electron and hole states of bulk Si are localized around the SFT faces, the SFT ridges, and the SFT apexes. This feature occurs due to the unique atomic geometries in these structures, such as stacking-fault layers, dimer bonds, and the Si-dome structures. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

First-principles study on crystal and electronic structures of stacking-fault tetrahedra in epitaxialized Si films

Atomic and electronic structures of the ridgeline and the apex of stacking-fault tetrahedron (SFT) defect in Si films are studied by using the first-principles calculations. It is shown that the electron and hole states of bulk Si are localized around the SFT faces, the SFT ridges, and the SFT apexes. This feature occurs due to the unique atomic geometries in these SFT structures, such as stacking-fault layers, dimer bonds, and the Si-dome structures.

Si(111)−(7×7)surface probed by reflection high-energy positron diffraction

We report the observation of reflection high-energy positron diffraction from a $7\ifmmode\times\else\texttimes\fi{}7$ reconstructed Si(111) surface with a well-collimated 20-kV positron beam. The diffraction pattern clearly exhibited the (1/7)--(3/7) order Laue zones in addition to the zeroth and first Laue zones. From the dynamical calculation of the rocking curve in the total reflection region, the vertical position of adatom layer was determined to be 1.52 \AA{} relative to the stacking fault layer. This value is greater than that predicted in the first-principles study suggesting a significant outward relaxation of adatoms.

Growth of nanoscale Ge magic islands on Si( [formula omitted])-7 × 7 substrate

We reported a formation of uniform nanoscale Ge islands, which shows rounded shape having a diameter of 3.8 nm, on a Si(1 1 1)-7 × 7 substrate as a template. The rearrangement process of stacking-fault layer in the 7 × 7 reconstructed structure is a rate determinant process, when the growing layer covers the substrate. The lateral growth of Ge island is hindered by the stacking-fault layer and the hindrance restricts the size distribution of Ge islands, so called “magic islands”. We observed the nanoscale Ge magic islands formed at the temperature of 300–360 °C. The some characteristic peaks in the size distribution suggest that the step energy for the Ge islands is smaller than that of Si island. From the temperature dependence of the size distribution, we estimate that the amount of the activation energy of the rearrangement is 2.1 eV. The value is slightly smaller than that for the homo-epitaxial case.

Dynamic change in the surface and layer structures during epitaxial growth of Si on aSi(111)−7×7surface

In order to investigate the dynamic process during growth of a Si layer on the $\mathrm{Si}(111)\ensuremath{-}7\ifmmode\times\else\texttimes\fi{}7$ surface held at 380 \ifmmode^\circ\else\textdegree\fi{}C, the rocking curve of reflection high-energy electron diffraction (RHEED) is continuously measured at 0.5\ifmmode^\circ\else\textdegree\fi{} to 6\ifmmode^\circ\else\textdegree\fi{} at intervals of 0.05\ifmmode^\circ\else\textdegree\fi{} to the glancing angle of the incident electron beam which takes 18 sec. At the initial growth stage, the multilayer islands are grown on the native $7\ifmmode\times\else\texttimes\fi{}7$ surface with broader Bragg peaks in the rocking curve than those from the native surface. The sharpness of the Bragg peak is subsequently recovered after the thickness of the Si layer reaches 3 BL $(1\mathrm{B}\mathrm{L}=0.31\mathrm{}\mathrm{nm}),$ at which the growth transforms to layer-by-layer growth. The comparison of the measured rocking curve with the calculated one based on the dynamical theory of RHEED intensity is also performed by optimizing each atomic position in the growing layer so as to minimize the difference between both curves. The space of the double layer of the (111) plane in the multilayer islands expands and is restored to the normal spacing after the growth mode transforms to the layer-by-layer mode. The broadening of the Bragg peaks at the initial growth stage relates to the rearrangement process of a stacking-fault layer in the $7\ifmmode\times\else\texttimes\fi{}7$ structure on the substrate surface.

Observation of Initial Growth Stage of Amorphous Si Film Deposited on 7×7 Superlattice Surface of Si(111) by Low-Energy Electron Diffraction

The intensities of low-energy electron diffraction (LEED) were measured from Si films with various thicknesses (d) which had been deposited on a 7×7 reconstructed surface of Si(111) substrates maintained at 170°C. The intensity profile from Si films at d>60 Å gives a feature showing the formation of an amorphous phase. From ultrathin Si films with 5 Å<d<60 Å, two peaks were observed clearly at positions which correspond to the (0, 0) and (1, 0) rods in the Si(111) surface. This suggests that the Si film in the vicinity of the Si(111) substrate comprises interface layers with the some ordered structure. Some discussion is given on the interface layers, which are composed of two epitaxially grown grains. A normal stacking sequence of the diamond structure is formed in one grain and the reversed stacking sequence grows at the stacking fault layer on the preserved 7×7 structure in another grain.

RHEED intensity analysis of Li/Si(111) structures

In order to study surface reconstruction processes by Li adsorption on a Si(111) surface, RHEED intensity rocking curves for several coverages of Li atoms are analyzed by dynamical calculations. The rocking curves are measured for a one-beam condition and [112] incidence. On adsorption at room temperature the RHEED pattern gradually changes into a δ7×7 pattern. The best-fit model for this adsorption process is as follows: The backbonds of more than 0.2 ML (1 ML= 7.9×1014 atoms/cm2) of Si adatoms in DAS (dimer-adatom-stacking fault) structure are cut off by adsorption of 0.2 ML of Li atoms. Then Si adatoms bonded with Li atoms are formed at on-top sites of a stacking-fault layer. For further deposition Li atoms adsorb at both the adatoms and the stacking-fault layer atoms. The surface normal position of the Li atoms adsorbed at the adatom site changes with the coverage. After annealing 1 ML adsorbed surface at 300°C, a √3×√3 Li structure is observed. A structure model in which Li atoms adsorbed above 1.60 Å from a bulk-like Si(111) surface is proposed for this structure from analysis of the rocking curves.

Structural Analysis of Adsorption Processes on Silicon by Rheed

ABSTRACTOn the basis of results of surface structure analyses by reflection high-energy electron diffraction(RHEED) with dynamical calculations, adsorption processes on Si(111) surface are discussed. On adsorption processes on Si(111)7×7 surface at room temperature, adatom bonds of the dimer-adatom-stacking-fault(DAS) structure are broken by adsorbed atoms and the structure changes into other 7×7 one called δ7×7. At the transition into the δ7×7 structure the dimer-stacking-fault(DSF) frame work is preserved. From rocking curve analyses during adsorption of Li and Si, back bonds of the adatoms of ])AS structure are cut off in the initial stage of the adsorption at about 0.2 monolayer coverage of the adsorbates. Metal adsorbed δ7×7 structures axe unstable and changes into structure by heating at about 300 °C with dissolution of the stacking fault layer into the normal stacking arrangement. During homoepitaxial growth of Si on Si(111)7×7 surface at about 300 °C, a new metastable surface structure is foundby RHEEDdynamical analysis. This structure is concluded as pyramidal cluster structure formed on the DSF frame work. It is discussed that formation of metastable structure promotes transition to from the 7×7, and promotes successive epitaxial growth accompanied with stacking fault dissolution at the DSF frame work.