Stacking fault

Last updated March 23, 2024

In crystallography, a stacking fault is a planar defect that can occur in crystalline materials.^[1]^[2] Crystalline materials form repeating patterns of layers of atoms. Errors can occur in the sequence of these layers and are known as stacking faults. Stacking faults are in a higher energy state which is quantified by the formation enthalpy per unit area called the stacking-fault energy. Stacking faults can arise during crystal growth or from plastic deformation. In addition, dislocations in low stacking-fault energy materials typically dissociate into an extended dislocation, which is a stacking fault bounded by partial dislocations.

The most common example of stacking faults is found in close-packed crystal structures. Face-centered cubic (fcc) structures differ from hexagonal close packed (hcp) structures only in stacking order: both structures have close-packed atomic planes with sixfold symmetry — the atoms form equilateral triangles. When stacking one of these layers on top of another, the atoms are not directly on top of one another. The first two layers are identical for hcp and fcc, and labelled AB. If the third layer is placed so that its atoms are directly above those of the first layer, the stacking will be ABA — this is the hcp structure, and it continues ABABABAB. However, there is another possible location for the third layer, such that its atoms are not above the first layer. Instead, it is the atoms in the fourth layer that are directly above the first layer. This produces the stacking ABCABCABC, which is in the [111] direction of a cubic crystal structure. In this context, a stacking fault is a local deviation from one of the close-packed stacking sequences to the other one. Usually, only one- two- or three-layer interruptions in the stacking sequence are referred to as stacking faults. An example for the fcc structure is the sequence ABCABABCAB.

Formation of stacking faults in FCC crystal

Stacking faults are two dimensional planar defects that can occur in crystalline materials. They can be formed during crystal growth, during plastic deformation as partial dislocations move as a result of dissociation of a perfect dislocation, or by condensation of point defects during high-rate plastic deformation.^[3] The start and finish of a stacking fault are marked by partial line dislocations such as a partial edge dislocation. Line dislocations tend to occur on the closest packed plane in the closest packed direction. For an FCC crystal, the closest packed plane is the (111) plane, which becomes the glide plane, and the closest packed direction is the [110] direction. Therefore, a perfect line dislocation in FCC has the burgers vector ½<110>, which is a translational vector.^[4]

Splitting into two partial dislocations is favorable because the energy of a line defect is proportional to the square of the burger’s vector magnitude. For example, an edge dislocation may split into two Shockley partial dislocations with burger’s vector of 1/6<112>.^[4] This direction is no longer in the closest packed direction, and because the two burger’s vectors are at 60 degrees with respect to each other in order to complete a perfect dislocation, the two partial dislocations repel each other. This repulsion is a consequence of stress fields around each partial dislocation affecting the other. The force of repulsion depends on factors such as shear modulus, burger’s vector, Poisson’s ratio, and distance between the dislocations.^[4]

As the partial dislocations repel, stacking fault is created in between. By nature of stacking fault being a defect, it has higher energy than that of a perfect crystal, so acts to attract the partial dislocations together again. When this attractive force balance the repulsive force described above, the defects are in equilibrium state.^[4]

The stacking fault energy can be determined from the width of dislocation dissociation using^[4]

SFE={G{\boldsymbol {b}}_{1}\cdot {\boldsymbol {b}}_{2} \over 2\pi d}={Gb^{2} \over 4\pi d}

where ${\boldsymbol {b}}_{1}$ and ${\boldsymbol {b}}_{2}$ are the burgers vectors and $b$ is the vector magnitude for the dissociated partial dislocations, $G$ is the shear modulus, and $d$ the distance between the partial dislocations.

Stacking faults may also be created by Frank partial dislocations with burger’s vector of 1/3<111>.^[4] There are two types of stacking faults caused by Frank partial dislocations: intrinsic and extrinsic. An intrinsic stacking fault forms by vacancy agglomeration and there is a missing plane with sequence ABCA_BA_BCA, where BA is the stacking fault.^[5] An extrinsic stacking fault is formed from interstitial agglomeration, where there is an extra plane with sequence ABCA_BAC_ABCA.^[5]

Visualizing stacking faults using electron microscopy

Stacking faults can be visualized using electron microscopy.^[6] One commonly used technique is transmission electron microscopy (TEM). The other is electron channeling contrast imaging (ECCI) in scanning electron microscope (SEM).

In an SEM, near-surface defects can be identified because backscattered electron yield differs in defect regions where the crystal is strained, and this gives rise to different contrasts in the image. In order to identify the stacking fault, it is important to recognize the exact Bragg condition for certain lattice planes in the matrix such that regions without defects will detect little backscattered electrons and thus appear dark. Meanwhile, regions with the stacking fault will not satisfy the Bragg condition and thus yield high amounts of backscattered electrons, and thus appear bright in the image. Inverting the contrast gives images where the stacking fault appears dark in the midst of a bright matrix.^[7]

In a TEM, bright field imaging is one technique used to identify the location of stacking faults. Typical image of stacking fault is dark with bright fringes near a low-angle grain boundary, sandwiched by dislocations at the end of the stacking fault. Fringes indicate that the stacking fault is at an incline with respect to the viewing plane.^[3]

Stacking faults in semiconductors

Many compound semiconductors, e.g. those combining elements from groups III and V or from groups II and VI of the periodic table, crystallize in the fcc zincblende or hcp wurtzite crystal structures. In a semiconductor crystal, the fcc and hcp phases of a given material will usually have different band gap energies. As a consequence, when the crystal phase of a stacking fault has a lower band gap than the surrounding phase, it forms a quantum well, which in photoluminescence experiments leads to light emission at lower energies (longer wavelengths) than for the bulk crystal.^[8] In the opposite case (higher band gap in the stacking fault), it constitutes an energy barrier in the band structure of the crystal that can affect the current transport in semiconductor devices.

Related Research Articles

A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect. Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization.

<span class="mw-page-title-main">Crystal structure</span> Ordered arrangement of atoms, ions, or molecules in a crystalline material

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.

A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains.

In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.

In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement. Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is

<span class="mw-page-title-main">Grain boundary</span> Interface between crystallites in a polycrystalline material

In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship.

<span class="mw-page-title-main">Crystal twinning</span> Two separate crystals sharing some of the same crystal lattice points in a symmetrical manner

Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane.

<span class="mw-page-title-main">Cottrell atmosphere</span> Concept in materials science

In materials science, the concept of the Cottrell atmosphere was introduced by A. H. Cottrell and B. A. Bilby in 1949 to explain how dislocations are pinned in some metals by boron, carbon, or nitrogen interstitials.

The stacking-fault energy (SFE) is a materials property on a very small scale. It is noted as γ_SFE in units of energy per area.

In materials science, slip is the large displacement of one part of a crystal relative to another part along crystallographic planes and directions. Slip occurs by the passage of dislocations on close/packed planes, which are planes containing the greatest number of atoms per area and in close-packed directions. Close-packed planes are known as slip or glide planes. A slip system describes the set of symmetrically identical slip planes and associated family of slip directions for which dislocation motion can easily occur and lead to plastic deformation. The magnitude and direction of slip are represented by the Burgers vector, $b$ .

In metallurgy, solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice of another element, forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms.

Diffraction topography is a imaging technique based on Bragg diffraction. Diffraction topographic images ("topographies") record the intensity profile of a beam of X-rays diffracted by a crystal. A topography thus represents a two-dimensional spatial intensity mapping of reflected X-rays, i.e. the spatial fine structure of a Laue reflection. This intensity mapping reflects the distribution of scattering power inside the crystal; topographs therefore reveal the irregularities in a non-ideal crystal lattice. X-ray diffraction topography is one variant of X-ray imaging, making use of diffraction contrast rather than absorption contrast which is usually used in radiography and computed tomography (CT). Topography is exploited to a lesser extends with neutrons, and has similarities to dark field imaging in the electron microscope community.

In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as $b$ , that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.

Dislocation creep is a deformation mechanism in crystalline materials. Dislocation creep involves the movement of dislocations through the crystal lattice of the material, in contrast to diffusion creep, in which diffusion is the dominant creep mechanism. It causes plastic deformation of the individual crystals, and thus the material itself.

An antiphase domain (APD) is a type of planar crystallographic defect in which the atoms within a region of a crystal are configured in the opposite order to those in the perfect lattice system. Throughout the entire APD, atoms sit on the sites typically occupied by atoms of a different species. For example, in an ordered AB alloy, if an A atom occupies the site usually occupied by a B atom, a type of crystallographic point defect called an antisite defect is formed. If an entire region of the crystal is translated such that every atom in a region of the plane of atoms sits on its antisite, an antiphase domain is formed. In other words, an APD is a region formed from antisite defects of a parent lattice. On either side of this domain, the lattice is still perfect, and the boundaries of the domain are referred to as antiphase boundaries. Crucially, crystals on either side of an antiphase boundary are related by a translation, rather than a reflection or an inversion.

In materials science, a partial dislocation is a decomposed form of dislocation that occurs within a crystalline material. An extended dislocation is a dislocation that has dissociated into a pair of partial dislocations. The vector sum of the Burgers vectors of the partial dislocations is the Burgers vector of the extended dislocation.

Geometrically necessary dislocations are like-signed dislocations needed to accommodate for plastic bending in a crystalline material. They are present when a material's plastic deformation is accompanied by internal plastic strain gradients. They are in contrast to statistically stored dislocations, with statistics of equal positive and negative signs, which arise during plastic flow from multiplication processes like the Frank-Read source.

In materials science, cross slip is the process by which a screw dislocation moves from one slip plane to another due to local stresses. It allows non-planar movement of screw dislocations. Non-planar movement of edge dislocations is achieved through climb.

Electron channelling contrast imaging (ECCI) is a scanning electron microscope (SEM) diffraction technique used in the study of defects in materials. These can be dislocations or stacking faults that are close to the surface of the sample, low angle grain boundaries or atomic steps. Unlike the use of transmission electron microscopy (TEM) for the investigation of dislocations, the ECCI approach has been called a rapid and non-destructive characterisation technique

Weak beam dark field (WBDF) microscopy is a type of transmission electron microscopy (TEM) dark field imaging technique that allows for the visualization of crystal defects with high resolution and contrast. Specifically, the technique is mainly used to study crystal defects such as dislocations, stacking faults, and interfaces in crystalline materials. WBDF is a valuable tool for studying the microstructure of materials, as it can provide detailed information about the nature and distribution of defects in crystals. These characteristics can have a significant impact on material properties such as strength, ductility, and corrosion resistance.

References

↑ Fine, Morris E. (1921). "Introduction to Chemical and Structural Defects in Crystalline Solids", in Treatise on Solid State Chemistry Volume 1, Springer.
↑ Hirth, J. P. & Lothe, J. (1992). Theory of dislocations (2 ed.). Krieger Pub Co. ISBN 0-89464-617-6.
1 2 Li, B.; Yan, P. F.; Sui, M. L.; Ma, E. Transmission Electron Microscopy Study of Stacking Faults and Their Interaction with Pyramidal Dislocations in Deformed Mg. Acta Materialia2010, 58 (1), 173–179. doi : 10.1016/j.actamat.2009.08.066.
1 2 3 4 5 6 Hull, D.; Bacon, D. Chapter 5. Dislocations in Face-Centered Cubic Metals. In Introduction to Dislocations; 2011; pp 85–107.
1 2 5.4.1 Partial Dislocations and Stacking Faults http://dtrinkle.matse.illinois.edu/MatSE584/kap_5/backbone/r5_4_1.html .
↑ Spence, J. C. H.; et al. (2006). "Imaging dislocation cores - the way forward". Philos. Mag. 86 (29–31): 4781. Bibcode:2006PMag...86.4781S. doi:10.1080/14786430600776322. S2CID 135976739.
↑ Weidner, A.; Glage, A.; Sperling, L.; Biermann, H. Observation of Stacking Faults in a Scanning Electron Microscope by Electron Channelling Contrast Imaging. IJMR2011, 102 (1), 3–5. doi : 10.3139/146.110448.
↑ Lähnemann, J.; Jahn, U.; Brandt, O.; Flissikowski, T.; Dogan, P.; Grahn, H.T. (2014). "Luminescence associated with stacking faults in GaN". J. Phys. D: Appl. Phys. 47 (42): 423001. arXiv: 1405.1261 . Bibcode:2014JPhD...47P3001L. doi:10.1088/0022-3727/47/42/423001. S2CID 118671207.

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[Introduction_to_Chemical_and_Structural_Defects_in_Crystalline_Solids-1] Fine, Morris E. (1921). "Introduction to Chemical and Structural Defects in Crystalline Solids", in Treatise on Solid State Chemistry Volume 1, Springer.

[Hirth-Lothe-2] Hirth, J. P. & Lothe, J. (1992). Theory of dislocations (2 ed.). Krieger Pub Co. ISBN 0-89464-617-6.

[:0-3] 1 2 Li, B.; Yan, P. F.; Sui, M. L.; Ma, E. Transmission Electron Microscopy Study of Stacking Faults and Their Interaction with Pyramidal Dislocations in Deformed Mg. Acta Materialia2010, 58 (1), 173–179. doi : 10.1016/j.actamat.2009.08.066.

[:1-4] 1 2 3 4 5 6 Hull, D.; Bacon, D. Chapter 5. Dislocations in Face-Centered Cubic Metals. In Introduction to Dislocations; 2011; pp 85–107.

[:2-5] 1 2 5.4.1 Partial Dislocations and Stacking Faults http://dtrinkle.matse.illinois.edu/MatSE584/kap_5/backbone/r5_4_1.html .

[6] Spence, J. C. H.; et al. (2006). "Imaging dislocation cores - the way forward". Philos. Mag. 86 (29–31): 4781. Bibcode:2006PMag...86.4781S. doi:10.1080/14786430600776322. S2CID 135976739.

[7] Weidner, A.; Glage, A.; Sperling, L.; Biermann, H. Observation of Stacking Faults in a Scanning Electron Microscope by Electron Channelling Contrast Imaging. IJMR2011, 102 (1), 3–5. doi : 10.3139/146.110448.

[8] Lähnemann, J.; Jahn, U.; Brandt, O.; Flissikowski, T.; Dogan, P.; Grahn, H.T. (2014). "Luminescence associated with stacking faults in GaN". J. Phys. D: Appl. Phys. 47 (42): 423001. arXiv: 1405.1261 . Bibcode:2014JPhD...47P3001L. doi:10.1088/0022-3727/47/42/423001. S2CID 118671207.

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