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Partial dislocation

A partial dislocation is a linear crystallographic defect in crystalline materials where the Burgers vector does not correspond to a full lattice translation vector, unlike perfect dislocations, and is typically associated with the presence of a stacking fault.^[1] This defect arises when a perfect dislocation dissociates into two or more partial components to lower the overall elastic energy, with the partials separated by a thin region of stacking fault where the atomic planes are misaligned.^[2] Partial dislocations are fundamental to understanding plastic deformation in metals and semiconductors, as their motion governs processes like slip, twinning, and strain hardening.^[3] In face-centered cubic (FCC) crystals, such as copper and aluminum, the most common partial dislocations are Shockley partials, formed by the dissociation of a perfect dislocation with Burgers vector \frac{a}{2} \langle 110 \rangle into two partials each with \frac{a}{6} \langle 112 \rangle, where a is the lattice parameter.^[2] The equilibrium separation between these partials, known as the stacking fault width, ranges from 5 to 500 Å and is inversely proportional to the stacking fault energy (\gamma); for instance, copper exhibits a width of about 10 nm due to its low \gamma of 40–60 mJ/m², while aluminum has a narrower width of ~1.8 nm with \gamma of 180–200 mJ/m².^[2] Another type, Frank partials, result from the climb of dislocations via vacancy absorption or emission, producing sessile defects with Burgers vectors like \frac{a}{3} \langle 111 \rangle that bound extrinsic stacking faults and impede further dislocation motion.^[2] The behavior of partial dislocations significantly influences material properties, particularly in low stacking fault energy alloys where wide dissociation ribbons restrict cross-slip—the process by which dislocations move from one slip plane to another—thereby promoting planar slip and enhancing work hardening.^[4] In nanostructured metals with grain sizes below 50 nm, partial dislocations become dominant deformation carriers, enabling alternative mechanisms like twinning-induced plasticity and inverse Hall-Petch strengthening, where yield stress increases with decreasing grain size due to the emission of partials from grain boundaries.^[3] These defects also play roles in semiconductor devices, such as in silicon and CdTe, where they can introduce electrical activity or affect optoelectronic performance by bounding stacking faults.^[1]

Fundamentals

Definition and Characteristics

A partial dislocation is a type of line defect in crystalline materials characterized by a Burgers vector that is a fraction of the perfect lattice vector, meaning it is not a full translation vector of the underlying lattice.^[5] Unlike perfect dislocations, which close the Burgers circuit independently, partial dislocations leave an incomplete closure, necessitating the presence of an adjacent stacking fault to restore overall lattice periodicity and translational symmetry.^[5] This association with extended defects like stacking faults distinguishes partial dislocations as components of more complex defect structures in crystals with close-packed planes, such as face-centered cubic (FCC) lattices.^[6] At the atomic scale, partial dislocations in FCC crystals involve a partial shear displacement of atomic planes along slip directions, disrupting the ideal ABCABC stacking sequence and creating faulted regions where the local atomic arrangement deviates from the perfect crystal structure.^[6] This partial displacement typically shifts atoms by one-third or one-sixth of the lattice parameter, leading to a compressed or expanded configuration in the core region.^[2] The core structure of a partial dislocation is inherently narrow, often spanning just a few atomic distances, and its configuration influences the overall defect energetics.^[7] Key characteristics of partial dislocations include variations in mobility, with some exhibiting glissile behavior (capable of glide on defined crystallographic planes) and others being sessile (immobile without climb or other mechanisms).^[7] They typically bound intrinsic or extrinsic stacking faults, where the fault plane introduces an energy penalty due to the altered bonding.^[5] The total energy of a partial dislocation arises from two primary contributions: the elastic strain energy associated with the core distortion and the stacking fault energy of the bounded plane, often on the order of hundreds of mJ/m² for the latter in metallic systems.^[7] These features make partial dislocations critical to understanding plasticity, as perfect dislocations may dissociate into them under stress.^[5] The foundational concept of dislocations, including partials, emerged in 1934 when G.I. Taylor, E. Orowan, and M. Polanyi independently proposed them as mechanisms for low-stress plastic deformation in crystals.^[8] Detailed theoretical development of partial dislocations and their role in stacking faults was advanced by W. Shockley and W.T. Read in the early 1950s, building on experimental observations in metals.

Relation to Perfect Dislocations and Stacking Faults

In face-centered cubic (FCC) crystals, a perfect dislocation characterized by a Burgers vector \mathbf{b} = \frac{a}{2} \langle 110 \rangle dissociates into two Shockley partial dislocations with Burgers vectors \mathbf{b}_1 = \frac{a}{6} \langle 112 \rangle and \mathbf{b}_2 = \frac{a}{6} \langle 11\bar{2} \rangle, such that \mathbf{b}_1 + \mathbf{b}_2 = \mathbf{b}, separated by a narrow region of stacking fault.^[2] This dissociation reduces the total elastic energy of the system, as the shorter Burgers vectors of the partials lower the self-energy compared to the perfect dislocation, while the stacking fault introduces an additional energy cost.^[9] The process conserves the total Burgers vector, ensuring the overall lattice distortion remains equivalent to that of the original perfect dislocation.^[10] Partial dislocations cannot exist in isolation within a perfect crystal, as a single partial would generate an infinite stacking fault extending across the entire slip plane, resulting in prohibitively high energy.^[2] Instead, they occur as pairs bounding a finite stacking fault ribbon, where the partials' mutual repulsion maintains the separation against the fault's attractive tendency. The stacking fault ribbon represents a disruption in the ideal close-packed ABCABC... atomic stacking sequence of the FCC lattice, with an associated energy per unit area denoted as \gamma, the stacking fault energy.^[11] This \gamma typically ranges from tens to hundreds of mJ/m² in metals, influencing the width of the ribbon and thus the mobility of dislocations.^[12] The equilibrium spacing d between the partials arises from a force balance: the repulsive elastic force between the partials equals the attractive force exerted by the stacking fault tension \gamma per unit length. For screw dislocations, this balance yields the equilibrium spacing d = \frac{\mu b^2}{4\pi \gamma}, where \mu is the shear modulus and b is the magnitude of each partial Burgers vector (b = a / \sqrt{6}).^[13] To derive this, consider the repulsive force per unit length F_\text{rep} between two parallel partials, approximated as F_\text{rep} = \frac{\mu b^2}{2\pi d} accounting for the screw orientation, the 60° angle between Burgers vectors (via \cos 60^\circ = 1/2), and elastic constants; setting F_\text{rep} = \gamma and solving for d gives the expression. Lower \gamma values lead to wider separations, promoting extended dislocations and easier cross-slip inhibition in low stacking fault energy materials.^[2] Stacking faults bounded by partials are classified as intrinsic or extrinsic based on their atomic structure. An intrinsic stacking fault results from the removal of a single close-packed {111} plane, altering the stacking sequence from the ideal ABCABC... to ABCACABC..., where the fault plane exhibits a local ACACA... arrangement instead of ABCABC....^[13] This fault is bounded by two Shockley partials gliding on the same plane and typically has a lower energy than extrinsic faults. In contrast, an extrinsic stacking fault arises from the insertion of an extra close-packed plane, changing the sequence to ABCABACABC..., creating a local ABCABAC... region with higher energy due to greater lattice distortion.^[14] These fault types play key roles in dislocation dynamics, with intrinsic faults more commonly observed in dissociated dislocations under shear loading.^[2]

Types

Shockley Partial Dislocations

Shockley partial dislocations are a type of glissile partial dislocation prevalent in close-packed crystal structures, arising from the dissociation of perfect dislocations into two such partials separated by an intrinsic stacking fault. In face-centered cubic (FCC) lattices, their Burgers vector is \mathbf{b} = \frac{a}{6} \langle 112 \rangle, where a is the lattice constant, making it shorter than the perfect dislocation vector \frac{a}{2} \langle 110 \rangle. This vector connects the vertices to the face centers of the Thompson tetrahedron, a geometric construct representing the {111} slip planes in FCC crystals.^[2]^[9] The character of a Shockley partial dislocation—defined by the angle between its Burgers vector and line direction—classifies it as either 30° (mixed screw-edge) or 90° (pure edge), influencing its mobility and interaction energies within the crystal. These dislocations are inherently glissile, enabling them to glide on {111} close-packed planes under applied shear stress, which is essential for dislocation motion and plastic deformation. During dissociation, the leading partial precedes the trailing partial on the slip plane, with their separation governed by the balance between the repulsive elastic interaction and the attractive stacking fault energy.^[15]^[2] In FCC metals like copper and aluminum, Shockley partials dominate the active slip systems, contributing significantly to work hardening and ductility by mediating the extended core structure of dislocations. They are also observed in hexagonal close-packed (HCP) materials, where they dissociate basal plane dislocations to accommodate slip parallel to the basal {0001} planes, as seen in metals such as titanium and magnesium. Named after physicist William Bradford Shockley for his foundational theoretical predictions on dislocation dissociation in the 1940s, these partials were first experimentally confirmed through transmission electron microscopy observations of dissociated dislocations in thin foils during the mid-1950s.^[1]^[16]^[17]^[18]

Frank Partial Dislocations

Frank partial dislocations are sessile line defects in crystalline materials, particularly in face-centered cubic (FCC) structures, formed by the insertion or removal of an extra atomic half-plane parallel to the close-packed {111} planes. These dislocations were first conceptualized by F. C. Frank in 1951 as a type of partial dislocation that bounds a stacking fault resulting from such planar defects. Unlike glissile partials, Frank partials do not facilitate easy shear deformation but instead play a key role in non-conservative processes like climb, where they nucleate or expand stacking faults through atomic diffusion.^[19] The Burgers vector of a Frank partial dislocation, \mathbf{b} = \frac{a}{3} \langle 111 \rangle, where a is the lattice parameter, lies perpendicular to the {111} plane, distinguishing it from in-plane shear vectors of other partials. This out-of-plane component corresponds to the insertion (extrinsic) or removal (intrinsic) of a single (111) atomic layer, effectively creating an extrinsic or intrinsic stacking fault, respectively. The magnitude of the Burgers vector is \frac{a}{\sqrt{3}}, which is shorter than that of a perfect dislocation (\frac{a}{\sqrt{2}}), reducing the elastic energy associated with the defect.^[5]^[19] Due to their edge character and perpendicular Burgers vector, Frank partial dislocations are inherently sessile and cannot glide on their fault plane without additional mechanisms; their motion occurs primarily through climb, a diffusion-mediated process involving the absorption or emission of vacancies or interstitials. This climb enables the expansion or contraction of faulted loops bounded by Frank partials, facilitating defect rearrangement during high-temperature annealing or under irradiation. In irradiated materials, such as neutron-bombarded FCC metals, Frank partial loops form abundantly as a result of supersaturated point defects condensing into these structures, often leading to observable faulted loops via electron microscopy.^[2]^[20]^[21] Frank partials are classified into intrinsic and extrinsic types based on the nature of the fault they bound. Intrinsic Frank partials arise from the removal of a (111) plane, equivalent to a vacancy-type condensation, and are commonly associated with intrinsic stacking fault tetrahedra or loops in quenched and annealed metals. Extrinsic Frank partials, conversely, result from the insertion of an extra plane, akin to interstitial clustering, and are less stable but observed in certain irradiated or deformed alloys. These loops serve as nucleation sites for further faulting during climb, influencing long-range diffusion and defect evolution in materials under thermal or radiation stress.^[22]^[20]

Dissociation and Interactions

Energetics and Reaction Favorability

The energetics of partial dislocation formation arise from the balance between the elastic energy reduction achieved by splitting a perfect dislocation into partials with shorter Burgers vectors and the energy cost of creating the associated stacking fault. In face-centered cubic (FCC) metals, a perfect dislocation with Burgers vector \mathbf{b} = \frac{a}{2} \langle 110 \rangle dissociates into two Shockley partials with \mathbf{b}_p = \frac{a}{6} \langle 112 \rangle, reducing the elastic self-energy since the magnitude of each partial Burgers vector is |\mathbf{b}_p| = \frac{|\mathbf{b}|}{\sqrt{3}}, leading to a self-energy approximately two-thirds that of the perfect dislocation per unit length. The total energy E of the dissociated configuration is thus E = E_{\text{core}} + E_{\text{interaction}} + \gamma A, where E_{\text{core}} accounts for the core energies of the partials (typically higher than for the perfect due to the complex partial cores), E_{\text{interaction}} is the elastic interaction (repulsive for like-sign partials), \gamma is the stacking fault energy per unit area, and A = d is the fault width for unit length, with dissociation favored when this E is minimized below the perfect dislocation energy. An adaptation of the Peierls-Nabarro model estimates favorability when the partial self-energy \frac{\mu b_p^2}{4\pi} \ln\left(\frac{R}{r}\right) < \gamma d, where \mu is the shear modulus, R and r are outer and inner cutoff radii, highlighting that wide dissociation occurs only if the fault energy cost is outweighed by elastic savings over sufficient width d. The equilibrium separation d between partials is determined by balancing the repulsive elastic force F = \frac{\mu b_1 b_2}{2\pi d} (approximating collinear components for edge or screw partials) against the stacking fault tension \gamma, yielding d = \frac{\mu b_1 b_2}{2\pi \gamma}. For a typical Shockley pair, b_1 = b_2 = \frac{a}{\sqrt{6}} and the angle between Burgers vectors is 60°, so the effective interaction incorporates a cosine factor, but the approximation holds for order-of-magnitude estimates in isotropic elasticity. A representative dissociation reaction in FCC crystals is

\frac{a}{2} {{grok:render&&&type=render_inline_citation&&&citation_id=101&&&citation_type=wikipedia}} \to \frac{a}{6} {{grok:render&&&type=render_inline_citation&&&citation_id=112&&&citation_type=wikipedia}} + \frac{a}{6} [2\bar{1}1]

, where the partials repel due to their parallel edge components, stabilizing the configuration if \gamma is low enough to permit d > 2r_0 (core radius, ~1-5 nm). In materials with low \gamma, such as copper (\gamma \approx 45 mJ/m², yielding d \approx 10 nm), dissociation is thermodynamically favored and observed widely, whereas in aluminum (\gamma \approx 180–$200 mJ/m², d \approx 1.8 nm), the partials remain closely bound, effectively behaving as a perfect dislocation.^[2] This energy balance influences dislocation multiplication via mechanisms like the Frank-Read source, where bowing of a pinned perfect dislocation segment reduces stress for activation if partial dissociation lowers the total line tension, enabling easier glide and source operation in low-\gamma alloys. Recent ab initio density functional theory (DFT) calculations have refined \gamma values in FCC alloys, revealing composition-dependent variations; for instance, in concentrated alloys like CrCoNi, \gamma ranges from 20-50 mJ/m² due to local solute effects, promoting wider dissociation and altered plasticity compared to dilute systems.^[23] Post-2020 DFT studies in high-entropy alloys, such as equiatomic CrMnFeCoNi, confirm low \gamma \approx 25 mJ/m², favoring partial-mediated deformation modes, while machine learning integrations with DFT accelerate predictions for alloy design, showing \gamma tunability via entropy effects.^[24] These computations underscore that kinetic barriers, beyond pure thermodynamics, can hinder dissociation in high-\gamma materials even when energetically viable.^[23]

Lomer-Cottrell Lock Formation

The Lomer-Cottrell lock forms through the irreversible reaction of two Shockley partial dislocations gliding on intersecting {111} planes in face-centered cubic crystals. Specifically, when the leading Shockley partials from dissociated perfect dislocations on adjacent slip planes meet, they combine to produce a sessile stair-rod dislocation segment with a Burgers vector of type \frac{a}{6} \langle 110 \rangle, which lies along the intersection line of the two planes, typically a \{001\} direction. A representative reaction is:

\frac{a}{6} [\bar{1}2\bar{1}]_{(111)} + \frac{a}{6} [1\bar{1}2]_{( \bar{1}11 )} \to \frac{a}{6} {{grok:render&&&type=render_inline_citation&&&citation_id=011&&&citation_type=wikipedia}}_{(001)}

^[2] This configuration pins the reacting dislocations, preventing further glide and creating a stable junction that acts as an obstacle to subsequent dislocation motion. The stability of the Lomer-Cottrell lock arises from its sessile nature and the high energy barrier required to reverse the reaction or unlock it, often exceeding several electronvolts per atomic distance along the lock segment. Unlocking typically demands mechanisms like cross-slip of the attached screw components or absorption by other dislocations, both of which face significant activation energies that increase with applied stress. This inherent stability contributes to work hardening in stage II of the stress-strain curve, where the multiplication and immobilization of dislocations lead to a linear increase in flow stress.^[25]^[26] Solute atoms can further enhance the strength of Lomer-Cottrell locks through segregation to the dislocation cores, forming Cottrell atmospheres that pin the sessile segments and raise the unlocking energy barrier. In alloys, interstitial or substitutional solutes diffuse to the lock during deformation or aging, creating localized elastic interactions that impede junction dissociation and amplify hardening effects. Such segregation is particularly pronounced in low-stacking-fault-energy materials, where the extended cores of partials facilitate solute trapping.^[27]^[25]

Modeling and Visualization

Thompson Tetrahedron

The Thompson tetrahedron is a geometric construct used to index and visualize the slip systems and dislocation reactions in face-centered cubic (FCC) crystals, facilitating the analysis of partial dislocations and their interactions. Developed by N. Thompson in 1953, it provides a compact three-dimensional representation of the four {111} close-packed planes and associated Burgers vectors, serving as a standard tool in dislocation theory.^[28] The tetrahedron is formed with vertices labeled A, B, C, and D, each corresponding to one of the four {111} planes in the FCC lattice (e.g., plane ABC, ABD, ACD, BCD). The edges connecting these vertices represent perfect dislocations with Burgers vectors of type \frac{a}{2}\langle 110 \rangle, such as AB = \frac{a}{2}[10\bar{1}] or AC =

\frac{a}{2}{{grok:render&&&type=render_inline_citation&&&citation_id=011&&&citation_type=wikipedia}}

. The centers of the tetrahedral faces are denoted by Greek letters (α for the center of BCD, β for ACD, γ for ABD, and δ for ABC), and the face diagonals from a vertex to the opposite face center represent Shockley partial dislocations with Burgers vectors of type \frac{a}{6}\langle 112 \rangle, for example, Aδ = \frac{a}{6}[2\bar{1}1]. Additionally, connections between adjacent face centers, such as αβ = \frac{a}{6} \langle 110 \rangle, denote stair-rod partial dislocations. This notation maps the octahedral symmetry of FCC slip systems without requiring explicit coordinate axes.^[2]^[28] In usage, the tetrahedron functions as a vector diagram where Burgers vectors are labeled by their endpoints (e.g., AB for a perfect dislocation), enabling straightforward prediction of reactions through vector addition rules, such as AB + BC = AC for collinear reactions or DA + Dγ = Aγ for climb processes involving Frank partials. Such operations conserve the total Burgers vector while assessing glide (in-plane) versus climb (out-of-plane) feasibility based on the geometry. This approach simplifies the enumeration of possible partial dislocation configurations and their energetic favorability in FCC crystals.^[2]^[28] The primary advantages of the Thompson tetrahedron lie in its ability to distill the complex three-dimensional geometry of FCC dislocations into an intuitive, symmetry-preserving model, reducing the need for cumbersome crystallographic indices and aiding in the visualization of multi-plane interactions. It has become a staple in dislocation theory textbooks for its elegance in handling partial vector notations. The framework extends naturally to hexagonal close-packed (HCP) structures through analogous tetrahedral representations of basal and prismatic planes, adapting the labeling for non-cubic symmetries.^[28]

Geometric Representations

Geometric representations of partial dislocations provide essential visualizations for understanding their structure, orientation, and behavior in crystalline materials, particularly in face-centered cubic (FCC) lattices where Shockley partials predominate on {111} slip planes. These representations complement other methods like the Thompson tetrahedron by offering planar and three-dimensional views that aid in analyzing dislocation configurations without relying solely on tetrahedral geometry.^[5] Two-dimensional projections are commonly used to depict Burgers vectors of partial dislocations on {111} planes. In FCC crystals, the six possible Shockley partial Burgers vectors, each of magnitude a/\sqrt{6} where a is the lattice parameter, form a regular hexagon centered on the origin in the plane, illustrating the 60° angle between adjacent partials and facilitating the visualization of dissociation paths.^[2] This hexagonal polygon representation highlights how a perfect dislocation with Burgers vector \frac{a}{2} \langle 110 \rangle decomposes into two partials whose vectors sum vectorially to the perfect vector, as shown in simple addition diagrams.^[10] Stereographic projections further enhance these 2D views by mapping three-dimensional orientations of slip planes and directions onto a sphere, enabling the identification of active partial dislocation systems relative to applied stress or crystal orientation in techniques like transmission electron microscopy.^[29] Three-dimensional models, such as hard-sphere atomic simulations, reveal the core structures of partial dislocations by approximating atoms as impenetrable spheres packed in the lattice. For Shockley partials in FCC metals, these models show a compressed core region where atomic rows shift to accommodate the non-lattice Burgers vector, often displaying a zigzag arrangement of atoms along the dislocation line with a width influenced by the stacking fault energy.^[30] Vector addition diagrams in 3D extend the 2D projections by illustrating the spatial decomposition of perfect dislocations into partials separated by a stacking fault ribbon, emphasizing the equilibrium spacing determined by the balance of repulsion and fault energy.^[31] Advanced computational tools, including molecular dynamics (MD) simulations, provide dynamic 3D visualizations of partial dislocation cores and motion. Using software like LAMMPS, recent MD studies simulate the atomic-scale evolution of Shockley partials in FCC materials under shear, rendering core structures as displaced atomic layers with visible stacking faults and partial pair interactions, often visualized via tools like OVITO for trajectory analysis.^[32]^[33]^[34] These simulations capture transient core configurations, such as intrinsic or extrinsic faulting, that static models overlook. Recent advances include machine learning interatomic potentials, which allow for efficient simulations of complex partial dislocation interactions in larger systems.^[35] In comparison, while the Thompson tetrahedron excels at depicting multi-plane reactions involving partials via its labeled vertices and edges, 2D projections and stereographic maps are particularly suited for interpreting single-plane orientations in experimental data, and MD visualizations offer time-resolved insights into core dynamics.^[29]

Implications

Mechanical Properties and Plasticity

Partial dislocations play a pivotal role in the plastic deformation of face-centered cubic (FCC) crystals by dissociating perfect dislocations into extended configurations, where two Shockley partials are separated by a stacking fault. This extension increases the critical resolved shear stress (CRSS) required for dislocation motion, as the partials must glide in tandem, experiencing repulsive interactions that raise the lattice friction compared to undissociated dislocations.^[2] The magnitude of this CRSS elevation depends on the equilibrium separation distance, governed by the balance between repulsive elastic forces and the attractive stacking fault energy \gamma.^[2] The stacking fault energy \gamma further dictates the slip character: low \gamma (e.g., below 20 mJ/m²) results in wide partial separations (tens of nanometers), promoting planar slip as the extended dislocations resist constriction and cross-slip onto adjacent planes.^[36] Conversely, high \gamma (e.g., above 100 mJ/m²) yields narrow separations (a few nanometers), facilitating temporary constriction of partials at jogs, enabling cross-slip and leading to wavy slip traces on the surface.^[37] This transition from planar to wavy slip influences overall ductility and work-hardening rates, with planar slip often correlating to reduced dynamic recovery.^[2] In addition to slip, partial dislocations mediate deformation twinning through the sequential emission and glide of Shockley partials with identical Burgers vectors on consecutive {111} planes, progressively reorienting the lattice to form a twin boundary.^[38] This mechanism becomes prominent in low-\gamma materials under high strain rates or low temperatures, where full dislocation dissociation favors partial-mediated shear over perfect dislocation glide.^[39] Hardening arises from dislocation pile-ups against immobile partial configurations, such as Lomer-Cottrell locks formed by reactions between non-parallel partials on intersecting planes, which act as strong barriers accumulating stress.^[25] These pile-ups intensify local stresses, promoting further lock formation and contributing to stage II work hardening. The partial spacing modifies the Hall-Petch relation \sigma_y = \sigma_0 + k d^{-1/2}, where wider separations in low-\gamma regimes reduce the effectiveness of grain boundaries as barriers by altering stress concentration at pile-up tips, thus influencing the slope k.^[25] Recent molecular dynamics simulations reveal that the core structures of partial dislocations impose additional barriers to cross-slip, particularly in extended configurations, where non-planar core reconstructions under stress hinder constriction and raise activation energies for cross-slip. These core effects are significant in FCC metals like nickel, with typical barriers in the range of 0.5-3 eV.^[40] These core effects, evident in FCC metals like nickel, explain persistent planar slip even at elevated temperatures and inform mesoscale models of plasticity.^[40]

Role in Materials and Recent Observations

Partial dislocations play a critical role in the plastic deformation of materials beyond face-centered cubic (FCC) structures, influencing deformation modes in hexagonal close-packed (HCP) crystals, body-centered cubic (BCC) metals and alloys, and semiconductors. In HCP metals like magnesium, basal dislocations readily dissociate into Shockley partials due to low stacking fault energy, facilitating twinning as a primary deformation mechanism under shear stress.^[41] In BCC metals, such as iron or tungsten, partial dislocations are rare in pure forms owing to high stacking fault energies that prevent significant dissociation, but they emerge in certain alloys where solute interactions promote partial core spreading and altered glide planes.^[42]^[43] In semiconductors like silicon, 60° dislocations commonly dissociate into 30° and 90° partials on {111} planes, creating intrinsic stacking faults that impact electronic properties and device performance.^[44] Experimental observations of partial dislocations have advanced through high-resolution transmission electron microscopy (HR-TEM), which resolves core structures and stacking faults at the atomic scale, as demonstrated in studies of dissociated dislocations in deformed biotite and metallic thin films.^[45] In situ techniques further reveal dynamic behaviors; for instance, a 2025 synchrotron X-ray Laue diffraction study captured partial dislocation-mediated plastic flow in single-crystal aluminum under laser-induced shock loading, showing their nucleation and propagation at extreme strain rates exceeding 10^6 s^-1, confirming their dominance in high-velocity deformation.^[46] Computational methods, including density functional theory (DFT) and molecular dynamics (MD) simulations, have elucidated partial dislocation core structures by predicting dissociation widths and Peierls barriers with quantum accuracy.^[47] Recent 2020s findings highlight their behavior in advanced materials: in nanocrystalline magnesium, MD simulations reveal the presence of Shockley partial dislocations across grain sizes from 6 to 45 nm, contributing to deformation alongside grain boundary processes, with twinning observed primarily in larger grains (≥40 nm).^[48] In high-entropy alloys like CrMnFeCoNi, DFT-guided models reveal that chemical complexity induces jerky partial dislocation motion due to repeated solute pinning, contributing to exceptional strength-ductility balance under tensile loading.^[49] A key application of partial dislocations lies in enabling nanoscale plasticity in thin films, where their emission from surfaces or interfaces allows ultra-high strengths exceeding 1 GPa while accommodating strains up to 10% without fracture, as observed in gold and copper films via in situ nanoindentation.^[50]^[51]

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Sep 30, 2009 · □ Elegant Method- Use stereographic projection to determine the active slip system graphically. Page 9. Stereographic Projection Method. 1 ...
[30]
(PDF) Dislocations and stacking faults - ResearchGate
faults is generally called a partial dislocation. Frank (1951 b) and Frank and. Nicholas (1953) classified the various types of dislocations and stacking ...Missing: FC | Show results with:FC
[31]
[PDF] Atomistically-informed Dislocation Dynamics in fcc Crystals
Sep 9, 2006 · The Escaig stress tensor is defined as that which produces a force only upon the edge components of the Shockley partials. Once the equlibrium ...
[32]
[PDF] Atomistic simulations of dynamics of an edge dislocation and its ...
Apr 27, 2020 · Molecular dynamics (MD) simulation method is one such approach. MD simulations have been utilized widely to identify the role of dislocation ...
[33]
[PDF] Molecular Dynamics Simulation of Dislocation Plasticity Mechanism ...
Nov 10, 2020 · Molecular Dynamics Simulation of Dislocation. Plasticity ... partial dislocation segments was observed. In the particle/substrate ...
[34]
Stacking-fault mediated plasticity and strengthening in lean, rare ...
Jun 1, 2021 · The critical resolved shear-stresses corresponding to the active deformation mode were quantified by multiplying the measured yield stress with ...
[35]
High Stacking Fault Energy - an overview | ScienceDirect Topics
Those with high stacking fault energy are termed wavy slip metals because dislocations can readily cross-slip from one octahedral plane to another, leaving ...
[36]
Deformation twinning via the motion of adjacent dislocations in ... - NIH
In face-centered cubic (FCC) materials, twinning is generated by Shockley partial dislocations gliding on successive slip planes, and this deformation process ...
[37]
New Deformation Twinning Mechanism Generates Zero ...
Mar 5, 2008 · These deformation twins form by the glide of partials with the same Burgers vector on successive (111) planes. This collectively produces a net ...
[38]
Stress-dependent activation entropy in thermally activated cross-slip ...
Aug 16, 2023 · Cross-slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic ...
[39]
The Plastic Deformation Mechanisms of hcp Single Crystals ... - NIH
Feb 4, 2021 · The basal dislocation is easier to split into partials because of its lower SFE [47]. Therefore, the dissociation of basal <a> dislocation into ...
[40]
Full article: Slip planes in bcc transition metals
Nov 18, 2013 · Dislocations in bcc metals do not generally dissociate into extended partial dislocations. While dislocation reactions are not the subject ...
[41]
Predicting core structure variations and spontaneous partial kink ...
Jul 1, 2021 · Preliminary atomistic studies show that, unlike simple BCC metals, these alloys produce equilibrium (screw) dislocations spread on varying glide ...
[42]
Structure and Properties of Dislocations in Silicon - IntechOpen
For the 60° dislocation a 30° partial and a 90° partial dislocation are formed through dissociation, while the screw dislocation dissociates into two 30° ...
[43]
Evaluation of stacking faults and associated partial dislocations in ...
Nov 24, 2014 · Cs-corrected HRTEM image may greatly improve the accuracy of strain measurements because the transfer of phase information will be much smoother ...
[44]
First In Situ Observation of Partial Dislocation-Mediated Plastic Flow ...
Sep 10, 2025 · In single-crystal aluminum (Al), partial dislocations are believed to play a crucial role in plasticity under extreme loading conditions; ...
[45]
Finite-temperature screw dislocation core structures and dynamics ...
Dec 21, 2023 · We report the results of MD simulations (based on machine learning potentials of quantum mechanical accuracy) of screw dislocation core ...
[46]
Deformation nanomechanics and dislocation quantification at the ...
It is found that, during the tensile deformation of nanocrystalline Mg, the Shockley partial dislocation is the most common type and the perfect dislocation as ...
[47]
The origin of jerky dislocation motion in high-entropy alloys - Nature
Aug 15, 2022 · Dislocations in single-phase concentrated random alloys, including high-entropy alloys (HEAs), repeatedly encounter pinning during glide, resulting in jerky ...
[48]
Ultra-high strength and plasticity mediated by partial dislocations ...
Feb 1, 2021 · This study provides new perspectives on optimal defect networks for the design of high strength, deformable metallic materials.
[49]
Size effect on the deformation mechanisms of nanocrystalline ...
Oct 16, 2017 · The occurrence of grain rotation implies a deviation from the dislocation-grain boundary interaction controlled plasticity, i.e., the Hall-Petch ...