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Interstitial defect
Interstitial defect
Interstitial defect
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Interstitial atoms (blue) occupy some of the spaces within a lattice of larger atoms (red)

In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure. When the atom is of the same type as those already present they are known as a self-interstitial defect. Alternatively, small atoms in some crystals may occupy interstitial sites, such as hydrogen in palladium. Interstitials can be produced by bombarding a crystal with elementary particles having energy above the displacement threshold for that crystal, but they may also exist in small concentrations in thermodynamic equilibrium. The presence of interstitial defects can modify the physical and chemical properties of a material.

History

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The idea of interstitial compounds was started in the late 1930s and they are often called Hagg phases after Gunnar Hägg.[1] Transition metals generally crystallise in either the hexagonal close packed or face centered cubic structures, both of which can be considered to be made up of layers of hexagonally close packed atoms. In both of these very similar lattices there are two sorts of interstice, or hole:

  • Two tetrahedral holes per metal atom, i.e. the hole is between four metal atoms
  • One octahedral hole per metal atom, i.e. the hole is between six metal atoms

It was suggested by early workers that:

  • the metal lattice was relatively unaffected by the interstitial atom
  • the electrical conductivity was comparable to that of the pure metal
  • there was a range of composition
  • the type of interstice occupied was determined by the size of the atom

These were not viewed as compounds, but rather as solutions, of say carbon, in the metal lattice, with a limiting upper "concentration" of the smaller atom that was determined by the number of interstices available.

Current

[edit]

A more detailed knowledge of the structures of metals, and binary and ternary phases of metals and non metals shows that:

  • generally at low concentrations of the small atom, the phase can be described as a solution, and this approximates to the historical description of an interstitial compound above.
  • at higher concentrations of the small atom, phases with different lattice structures may be present, and these may have a range of stoichiometries.

One example is the solubility of carbon in iron. The form of pure iron stable between 910 °C and 1390 °C, γ-iron, forms a solid solution with carbon termed austenite which is also known as steel.

Self-interstitials

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Self-interstitial defects are interstitial defects which contain only atoms which are the same as those already present in the lattice.

Structure of self-interstitial in some common metals. The left-hand side of each crystal type shows the perfect crystal and the right-hand side the one with a defect.

The structure of interstitial defects has been experimentally determined in some metals and semiconductors.

Contrary to what one might intuitively expect, most self-interstitials in metals with a known structure have a 'split' structure, in which two atoms share the same lattice site.[2][3] Typically the center of mass of the two atoms is at the lattice site, and they are displaced symmetrically from it along one of the principal lattice directions. For instance, in several common face-centered cubic (fcc) metals such as copper, nickel and platinum, the ground state structure of the self-interstitial is the split [100] interstitial structure, where two atoms are displaced in a positive and negative [100] direction from the lattice site. In body-centered cubic (bcc) iron the ground state interstitial structure is similarly a [110] split interstitial.

These split interstitials are often called dumbbell interstitials, because plotting the two atoms forming the interstitial with two large spheres and a thick line joining them makes the structure resemble a dumbbell weight-lifting device.

In other bcc metals than iron, the ground state structure is believed based on recent density-functional theory calculations to be the [111] crowdion interstitial,[4] which can be understood as a long chain (typically some 10–20) of atoms along the [111] lattice direction, compressed compared to the perfect lattice such that the chain contains one extra atom.

Structure of dumbbell self-interstitial in silicon. Note that the structure of the interstitial in silicon may depend on charge state and doping level of the material.

In semiconductors the situation is more complex, since defects may be charged and different charge states may have different structures. For instance, in silicon, the interstitial may either have a split [110] structure or a tetrahedral truly interstitial one.[5]

Carbon, notably in graphite and diamond, has a number of interesting self-interstitials - recently discovered using Local-density approximation-calculations is the "spiro-interestitial" in graphite, named after spiropentane, as the interstitial carbon atom is situated between two basal planes and bonded in a geometry similar to spiropentane.[6]

Impurity interstitials

[edit]

Small impurity interstitial atoms are usually on true interstitial sites between the lattice atoms. Large impurity interstitials can also be in split interstitial configurations together with a lattice atom, similar to those of the self-interstitial atom.

Effects of interstitials

[edit]

Interstitials modify the physical and chemical properties of materials.

  • Interstitial carbon atoms have a crucial role for the properties and processing of steels, in particular carbon steels.
  • Impurity interstitials can be used e.g. for storage of hydrogen in metals.
  • The crystal lattice can expand with the concentration of impurity interstitials
  • The amorphization of semiconductors such as silicon during ion irradiation is often explained by the build up of a high concentration of interstitials leading eventually to the collapse of the lattice as it becomes unstable.[7][8]
  • Creation of large amounts of interstitials in a solid can lead to a significant energy buildup, which on release can even lead to severe accidents in certain old types of nuclear reactors (Wigner effect). The high-energy states can be released by annealing.
  • At least in fcc lattice, interstitials have a large diaelastic softening effect on the material.[9]
  • It has been proposed that interstitials are related to the onset of melting and the glass transition.[10][11][12]

References

[edit]
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Interstitial defect

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An interstitial defect is a type of point defect in crystalline solids where an extra atom, either from the host material (self-interstitial) or a foreign species (impurity interstitial), occupies a non-lattice position known as an , typically a void such as an octahedral or tetrahedral hole between regular lattice atoms. This distortion of the surrounding lattice arises because the inserted atom is usually smaller than the host atoms; an interstitial defect is often formed when the solute atom size is less than about 85% of the host atom size. Interstitial defects can be categorized into several types based on their origin and configuration. Self-interstitials occur when a host atom is displaced to an adjacent , sometimes forming structures like pairs in metals. Impurity interstitials involve smaller solute atoms, such as carbon, , , or oxygen, inserted into the lattice of a host material like iron in alloys. A related defect is the , which consists of a vacancy-interstitial pair created when a host atom moves from its lattice site to a nearby interstitial position, commonly observed in ionic crystals to maintain charge neutrality. These defects play a critical role in influencing the physical, mechanical, and electrical properties of materials. In metals and alloys, interstitial impurities like carbon in iron enhance strength and hardness through by impeding motion, though they can reduce . They also facilitate atomic , affecting processes like and creep, and can introduce energy states that impact electrical conductivity or in semiconductors and solar cells. Overall, controlled interstitial defects are essential for materials with tailored performance in applications ranging from structural steels to advanced .

Fundamentals

Definition

In an ideal crystal lattice, atoms are arranged in a highly ordered, periodic structure where each atom occupies a specific lattice site defined by the unit cell , such as face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal close-packed (HCP). This perfect arrangement assumes no deviations, allowing the material to exhibit uniform properties throughout. An defect arises when an atom, either of the host material or an impurity, occupies a non-lattice site known as an interstice within the crystalline solid, thereby distorting the surrounding atomic arrangement and introducing local strain. This point defect contrasts with other types: vacancies involve the absence of an atom at a lattice site, while substitutional defects occur when a foreign atom replaces a host atom at a regular lattice position. Unlike these, defects add an extra atom to the structure without removing or replacing any existing ones, often leading to significant lattice expansion. Common interstices in crystal lattices include tetrahedral and octahedral sites, with their availability and geometry varying by structure. In FCC and HCP lattices, which are close-packed, octahedral sites are located at the midpoints of the edges and at the body center of the unit cell, surrounded by six host atoms in an octahedral coordination, while tetrahedral sites sit at positions like (1/4,1/4,1/4), coordinated by four host atoms. BCC lattices feature octahedral sites at the face centers and along the edges (midpoints) of the unit cell, and tetrahedral sites near the corners, though these are generally smaller and more distorted compared to close-packed structures. Conceptually, these sites can be visualized as voids amid the host atoms—for instance, an octahedral interstice forms a symmetric space equidistant from six neighboring atoms, allowing a smaller atom to fit with minimal initial distortion before lattice relaxation occurs.

Formation Mechanisms

Interstitial defects form through several primary mechanisms that disrupt the regular lattice arrangement in crystalline solids, forcing atoms into interstitial positions. One key process is , where high-energy particles such as or ions displace atoms from their lattice sites, creating interstitials and accompanying vacancies during the atomic displacement cascade. For instance, in nuclear materials generates self-interstitials by knocking host atoms into neighboring interstices. Another mechanism involves from high temperatures, where rapid cooling traps atoms in non-equilibrium interstitial sites that would otherwise migrate to lattice positions under slower cooling. deformation, such as during mechanical stressing, also produces interstitials by shifting atoms through shear forces in the crystal lattice. Additionally, introduces foreign or host atoms directly into interstitial sites via high-velocity bombardment, commonly used in doping. A prominent way interstitial defects arise is through Frenkel defect pair formation, where a single atom is simultaneously displaced from its lattice site to an adjacent position, generating a vacancy-interstitial pair. This process conserves the total number of atoms while distorting the local structure. The energy required for Frenkel pair formation is given by Ef=Ev+Ei+ErelE_f = E_v + E_i + E_{rel}, where EvE_v is the vacancy formation energy, EiE_i is the interstitial formation energy, and ErelE_{rel} accounts for the atomic relaxation energy around the defects. In materials like halides, this energy typically ranges from 1.5 to 3 eV per pair, making Frenkel defects more prevalent in ionic crystals with open structures. The equilibrium concentration of interstitial defects, particularly in the context of Frenkel pairs, follows a and depends strongly on . It can be expressed as ci≈exp⁡(−Ef/2kT)c_i \approx \exp(-E_f / 2 kT), where kk is Boltzmann's constant and TT is the absolute ; this approximation assumes comparable densities of lattice and interstitial sites and highlights the exponential decrease in defect density with increasing formation or decreasing . At elevated temperatures, agitation facilitates higher concentrations, often on the order of 10^{-4} to 10^{-6} in metals and ceramics near melting points. Several factors influence the formation of interstitial defects beyond the intrinsic mechanisms. Temperature plays a dominant role by modulating the available to overcome formation barriers, as seen in the exponential term of the concentration equation. Pressure affects defect stability through its impact on the of formation, Gf=Hf−TSf+PVfG_f = H_f - T S_f + P V_f, where higher pressures can suppress interstitial creation in materials with positive defect volumes. Material purity is also critical, as impurities lower the overall formation energy by providing sites or altering lattice strain, thereby increasing defect densities even in nominally pure crystals. Self-interstitials, involving host atoms, are a common outcome of these processes in elemental crystals.

Types

Self-Interstitials

Self-interstitials are point defects consisting of an extra host atom occupying an within the crystal lattice, usually generated by the displacement of a lattice atom to form a Frenkel pair alongside a vacancy. This configuration arises when the displaced atom squeezes into a void space between regular lattice positions, distorting the surrounding structure while maintaining the overall composition of the host material. In metals, the or split-interstitial configuration is prevalent, where two adjacent host atoms share a single lattice site and are displaced symmetrically into an interstitial position. In body-centered cubic (BCC) metals such as iron, the ⟨110⟩\langle 110 \rangle-oriented is the most stable form, with computational studies using embedded atom methods yielding formation energies around 4.2 eV for this in α\alpha-iron. In close-packed s like face-centered cubic (FCC) or hexagonal close-packed (HCP) metals, the crowdion configuration emerges as a stable alternative, featuring a linear displacement of atoms along a close-packed direction, such as ⟨111⟩\langle 111 \rangle, which delocalizes the extra atom over several lattice sites. These configurations minimize by aligning with the lattice , though their relative stability varies with the metal's packing and electronic . Self-interstitials generally exhibit high mobility, characterized by low migration barriers that enable rapid through the lattice. In FCC metals like , the ⟨100⟩\langle 100 \rangle dumbbell configuration migrates via a and translation mechanism with a barrier of approximately 0.08 eV, promoting efficient recombination with vacancies to annihilate the defect pair. This low barrier arises from the interstitial's ability to shift between equivalent sites with minimal energy input, often involving transient crowdion-like states, and leads to I recovery in irradiated metals where defects recombine at low temperatures. Prominent examples include self-interstitials in , where the split-⟨110⟩\langle 110 \rangle configuration dominates with a formation energy of about 3.3 eV () or 3.8 eV (generalized gradient approximation), playing a key role in processing like . In BCC iron, under relevant to nuclear materials, ⟨110⟩\langle 110 \rangle dumbbells form with energies near 4 eV, contributing to swelling and embrittlement through clustering. Unlike impurity interstitials, self-interstitials experience less severe size mismatch due to identical atomic species, resulting in more symmetric distortions.

Impurity Interstitials

Impurity interstitials refer to foreign atoms or ions, such as those introduced as dopants or contaminants, that occupy positions between the regular lattice sites of a host , typically because they are smaller in atomic size than the surrounding host atoms. These defects arise when small solute atoms fit into the interstices without significantly disrupting the overall lattice but often induce local distortions due to their mismatched size. Unlike self-interstitials, impurity interstitials introduce chemical heterogeneity, leading to unique interactions with the host lattice that can alter material properties through alloying effects. Common examples of impurity interstitials include carbon atoms in iron, where they form interstitial solid solutions in steels by occupying octahedral sites in the body-centered cubic (bcc) structure, enhancing strength but potentially causing brittleness at high concentrations. Hydrogen atoms in metals serve as another key example, diffusing rapidly through interstitial sites and contributing to by interacting with dislocations. Oxygen in represents a semiconductor case, where interstitial oxygen atoms reside near the center of Si-Si bonds, influencing electrical properties and device performance. Due to the size mismatch between the impurity and host atoms, these defects often adopt specific local configurations, such as linear dumbbell-like arrangements or planar distortions, which generate compressive and tensile strain fields extending several lattice spacings into the surrounding material. These strain fields arise from the repulsion between the smaller impurity atom and nearby host atoms, leading to lattice expansion or contraction that affects defect mobility and interactions. In bcc metals like iron, for instance, carbon prefers octahedral sites but distorts the lattice tetragonally, creating anisotropic strain. The of impurity interstitials in the host lattice is limited and governed by adaptations of the for interstitial solid solutions, particularly requiring the solute atomic radius to be less than approximately 0.59 times that of the solvent atom to allow occupation of interstitial sites without . For tetrahedral interstitial sites, which are common in close-packed structures, the ideal radius ratio is around 0.225, but the upper limit of 0.59 ensures sufficient before forming compounds or precipitates. This criterion explains the low of carbon in α-iron (maximum of about 0.02 wt% at 727°C), beyond which carbides precipitate. Formation energies for these defects vary; for example, the formation energy of interstitial carbon in α-Fe is approximately 0.41 eV, reflecting the energetic cost of inserting the atom into the lattice. Such energies influence stability and diffusion, often occurring via mechanisms like direct interstitial jumps.

Properties and Effects

Structural and Mechanical Effects

Interstitial defects introduce local distortions in the crystal lattice, often causing expansion or contraction depending on the size mismatch between the interstitial atom and the host lattice sites. These distortions generate elastic strain fields that propagate beyond the immediate vicinity of the defect, influencing the surrounding atomic arrangement. In face-centered cubic metals such as , interstitials occupy configurations like the split-<100> site, resulting in volume changes equivalent to 0.34 to 0.60 atomic volumes and significant relaxations in nearest-neighbor positions. The long-range nature of these distortions is captured by Eshelby's inclusion theory, which models point defects as dilatational inclusions undergoing a transformation within an infinite elastic medium, producing stress fields that decay as 1/r^3. This continuum approach quantifies the elastic interaction between defects and aligns with atomistic calculations showing static displacement fields that disrupt lattice and eliminate inversion centers. For dilute concentrations, the macroscopic effect on the lattice is given by Δa/a=(ci⋅ΔV)/V\Delta a / a = (c_i \cdot \Delta V) / V, where cic_i is the interstitial concentration, ΔV\Delta V is the volume change per defect, and VV is the host atomic volume; this approximation holds for isotropic expansion in cubic lattices. Mechanically, defects enhance material strength through , where the strain fields around atoms impede motion by pinning them at solute- interaction sites. In face-centered cubic alloys, such as high-entropy systems doped with carbon, this leads to a linear increase in yield strength with concentration, with strengthening coefficients up to 184 MPa per atomic percent carbon, promoting planar slip and elevated work-hardening rates. Radiation-induced clusters further contribute to hardening by acting as barriers to glide, elevating yield strength in irradiated metals; for instance, body-centered cubic alloys with massive solid solutions exhibit compressive yield strengths approaching 4.2 GPa, nearing theoretical limits while retaining substantial . In hydrogen-charged steels, interstitial hydrogen atoms exacerbate embrittlement by trapping at dislocations and grain boundaries, reducing cohesive strength and ductility through mechanisms like hydrogen-enhanced decohesion, with losses exceeding 90% in elongation for pipeline steels under tensile loading. Defect interactions amplify these effects, as interstitials trap dislocations via elastic coupling or form complexes that hinder recovery, while self-interstitial clustering can create stable aggregates that intensify local strains.

Electrical and Thermal Effects

Interstitial defects significantly influence the electrical properties of materials by acting as centers for charge carriers, thereby increasing electrical resistivity. In metals, this scattering arises from the distortion of the lattice potential around the defect sites, leading to enhanced electron-defect interactions that impede . Matthiessen's rule provides a quantitative framework for understanding this effect, stating that the total resistivity ρ\rho can be decomposed into a temperature-independent component due to defects ρi\rho_i and a temperature-dependent component ρ0\rho_0 from other sources, such that ρ=ρ0+ρi\rho = \rho_0 + \rho_i. This rule holds approximately for low defect concentrations in irradiated metals like , where electron irradiation introduces interstitials and vacancies that elevate resistivity by up to several microohm-centimeters at low temperatures. In semiconductors, interstitial impurity atoms can introduce donor or acceptor levels within the bandgap, altering carrier concentrations and enabling controlled doping. For instance, atoms occupying sites in form shallow donor levels approximately 0.03 eV below the conduction band, facilitating n-type conductivity by donating electrons to the conduction band at . These levels arise from the hybridization of the impurity's valence electrons with the host lattice, creating states that are thermally ionized, thus increasing without significantly altering the lattice structure beyond local distortions. Regarding thermal effects, interstitial defects reduce thermal conductivity primarily through enhanced , where interact with the mass and strain fluctuations induced by the extra atoms. This scattering shortens the , often by factors of 2–10 depending on defect concentration, leading to a substantial drop in lattice thermal conductivity; for example, in , thorium interstitials can reduce conductivity by over 50% at compared to the defect-free case. Additionally, the localized vibrational modes of interstitial atoms contribute to anomalies in specific , manifesting as excess contributions at low temperatures due to hindered rotations or anharmonic oscillations that excite additional . Interstitial defects also induce optical absorption by creating localized electronic states that enable transitions in the visible or spectra. These defect bands arise from the perturbation of the host material's bandgap, allowing absorption at energies corresponding to intra-defect or defect-to-band transitions; in aluminum , intrinsic interstitial defects introduce absorption peaks around 4–5 eV, influencing optoelectronic performance.

Characterization

Experimental Techniques

Transmission electron microscopy (TEM), particularly high-resolution TEM (HR-TEM), is a primary technique for directly imaging interstitial defects in crystalline materials. It allows visualization of defect clusters and associated strain fields through diffraction contrast and lattice fringe imaging, revealing atomic-scale displacements caused by self-interstitials or impurity atoms. For instance, aberration-corrected TEM has been used to observe star-like clusters of self-interstitials in electron-irradiated silicon, where defects align along specific crystallographic directions like <111> and <110>. However, TEM requires ultra-thin samples (typically 10–100 nm) to minimize multiple scattering, and high-energy electron beams can induce additional damage, limiting its application to stable defect configurations. X-ray diffraction (XRD), including synchrotron-based variants, detects interstitial defects indirectly by measuring lattice parameter shifts and peak broadening due to local strain from inserted atoms. In steels, XRD quantifies carbon interstitials by analyzing changes in the lattice expansion, where carbon occupancy in octahedral sites alters peak positions and intensities. For example, in twinning-induced plasticity () steels, XRD has revealed how interstitial carbon influences densities and strain hardening. This method is non-destructive and suitable for bulk samples but struggles with low defect concentrations, as shifts may overlap with thermal or compositional effects, requiring high-resolution setups for precise quantification. Positron annihilation spectroscopy (PAS) probes open-volume defects associated with interstitials, such as vacancy-interstitial pairs or relaxation zones around extra atoms, by measuring positron lifetimes and of annihilation radiation. In , variable-energy PAS has detected the migration and clustering of self-interstitials following , where positrons trap at sites influenced by displaced atoms, showing lifetime components indicative of interstitial-related voids. PAS excels at depth profiling with slow positron beams but is less sensitive to pure interstitials without associated vacancies, often requiring complementary techniques for unambiguous identification, and detection limits are around 10^{16} cm^{-3}. Electron paramagnetic resonance (EPR) identifies interstitial defects with unpaired electrons, such as those involving transition metals or radiation-induced centers, by detecting microwave-induced spin transitions. In irradiated , EPR has characterized tri-interstitial complexes like the B5/[I₃] center, where self-interstitials create paramagnetic states observable at low temperatures. This technique provides atomic-level structural information via hyperfine interactions but necessitates paramagnetic defects and high concentrations (>10^{16} cm^{-3}), with challenges in distinguishing overlapping signals from multiple species. Ion beam channeling, using axial alignment of MeV ions, detects interstitial displacements by measuring dechanneling yields from atoms off lattice sites. In metals like , channeling backscattering reveals self-interstitial-type defects through increased scattering from interstitial positions in open channels. This non-destructive method offers depth-resolved analysis but has limited sensitivity to single isolated interstitials, better resolving clusters or fractions above 1–5% of displaced atoms, and requires single-crystal samples. Atom probe tomography (APT) provides three-dimensional atomic-scale imaging and chemical analysis of interstitial defects, evaporating ions from a needle-shaped specimen using or voltage pulses and reconstructing their positions and identities via . It has been applied to visualize interstitial atoms and complexes, such as oxygen and interstitials in multicomponent alloys, revealing their distribution and interactions at the atomic level. APT offers sub-nanometer resolution and isotopic sensitivity, making it ideal for studying low-concentration impurities in bulk materials, but it requires specialized (e.g., milling), is sensitive to artifacts from field evaporation, and is typically limited to conductive specimens. Overall, these techniques complement each other: TEM and channeling provide for defect positions, while XRD, , EPR, and APT offer quantitative insights into concentrations and types. Limitations include resolution challenges for isolated interstitials versus aggregates, often necessitating irradiation-induced samples for enhanced visibility, as seen in self-interstitial studies.

Theoretical Approaches

Theoretical approaches to interstitial defects rely on computational and analytical models to predict their formation, migration, and interactions without direct experimentation. Atomistic simulations, such as (DFT), are widely used to calculate formation energies of interstitial defects by solving the within the local density approximation or generalized gradient approximation, providing accurate electronic structure insights for small systems like self-interstitials in semiconductors and metals. For instance, DFT computations reveal that self-interstitial formation energies in range from 3 to 5 eV, depending on the configuration and charge state, highlighting the stability of dumbbell structures over tetrahedral sites. Complementing DFT, (MD) simulations explore migration paths by evolving atomic trajectories under empirical potentials, capturing dynamic processes like interstitial diffusion in metals over picosecond timescales. In body-centered cubic (BCC) metals such as , MD reveals one-dimensional migration of small interstitial clusters along crowdion configurations, with diffusion coefficients enhanced by thermal activation. Continuum models provide a mesoscale perspective on interstitial defect behaviors, treating defects as extended sources of in an elastic medium. Elasticity theory, pioneered by Eshelby, models the strain fields around interstitials as those of an infinitesimal inclusion with a dilatational eigenstrain, yielding analytical expressions for the long-range elastic dipole tensor that governs defect-defect interactions. This approach predicts that the interaction energy between two interstitials decays as 1/r^3 at large separations r, facilitating the clustering of like defects in strained lattices. For defect evolution over longer times, kinetic (KMC) methods simulate jumps of interstitials based on Arrhenius rates derived from DFT or barriers, enabling predictions of microstructure changes under . In irradiated iron-chromium alloys, KMC demonstrates that interstitial loops grow preferentially due to one-dimensional , leading to network formation. Specific examples from DFT underscore the predictive power of these models for migration kinetics. In face-centered cubic (FCC) metals like aluminum, DFT calculations yield migration barriers typically in the range of 0.1-1 eV, with the octahedral-to-tetrahedral path exhibiting a barrier of approximately 0.3 eV for self-s under nudged elastic band optimization. Binding models, such as the embedded atom method (EAM), further refine these predictions by incorporating many-body effects into semi-empirical potentials, accurately reproducing self- formation energies in aluminum (around 2.5 eV for the split dumbbell configuration) and migration paths in MD simulations. These potentials are parameterized against DFT data, ensuring transferability across alloy compositions. In predictive applications, combined models simulate accumulation by integrating atomistic inputs into larger-scale frameworks. For example, MD-generated primary damage states—featuring Frenkel pairs with interstitial-vacancy separations of 1-5 nm—are fed into KMC to track long-term evolution, revealing that interstitials dominate swelling in metals like due to their higher mobility ( rates 10^4 times faster than vacancies at 500 K). supplements these by quantifying how strain fields bias interstitial trapping at dislocations, with binding energies up to 1 eV reducing recombination rates by 20-50% in BCC iron. Such multiscale simulations guide for nuclear applications, predicting damage thresholds where interstitial clustering exceeds 10^20 m^{-3}.

Historical Context

Early Discoveries

The recognition of point defects in crystalline solids emerged in the early through thermodynamic considerations of in crystals. In 1926, Yakov Frenkel proposed that atoms in a crystal lattice could be thermally excited to leave their regular positions, creating vacancies whose concentration follows a , thereby increasing the system's to satisfy thermodynamic stability. This foundational idea, derived from without direct experimental verification, marked the initial theoretical acknowledgment of intrinsic point defects, including the potential for positions as alternative atomic sites. A pivotal advancement occurred in 1938 when Frenkel extended his model to describe interstitial-vacancy pairs, particularly in ionic crystals like (AgCl), where an ion displaces to an , leaving a vacancy to maintain charge neutrality. Frenkel's analysis of AgCl, based on ionic conductivity data and simple kinetic models without computational aids, demonstrated that such defects could explain observed deviations from ideal lattice behavior, such as enhanced and electrical properties in non-stoichiometric crystals. This proposal shifted focus from isolated vacancies to paired defects, providing a framework for understanding lattice imperfections in materials with limited atomic mobility. Early experimental evidence for interstitial defects arose in the 1940s amid research on radiation effects in metals for nuclear applications. Studies of and fission fragment bombardment in materials like and revealed lattice swelling and increased stored energy, attributed to the creation of interstitial atoms and vacancies as Frenkel pairs displaced by atomic collisions. Frederick Seitz's theoretical models during this period quantified the displacement cascades, predicting that high-energy particles generate clusters of interstitials that cause volumetric expansion, aligning with observed macroscopic changes in irradiated metals. Confirmation of these defects solidified in the through quenching experiments on pure metals, where samples heated to high temperatures were rapidly cooled to "freeze in" thermal defects for measurement. In 1955, J. W. Kauffman and J. S. Koehler quenched wires from elevated temperatures and measured excess electrical resistivity, providing of quenched-in vacancies and, by from annealing , associated interstitials that migrate at low temperatures. These experiments validated Frenkel's thermodynamic predictions, establishing point defect concentrations on the order of 10^{-4} to 10^{-6} at melting points and highlighting interstitials' role in radiation-induced damage recovery.

Key Developments

The development of computer simulations marked a pivotal advancement in understanding interstitial defects during the 1960s and 1970s. In 1960, Gibson et al. conducted the first (MD) simulations of in , modeling the creation and evolution of interstitial atoms and vacancies in displacement cascades, which provided insights into defect dynamics under . This work laid the foundation for computational studies of defect formation and annealing processes. Concurrently, refinements in electron microscopy techniques enhanced the direct observation of interstitial defects; the weak-beam dark-field method, introduced by Cockayne, Ray, and Hirsch in 1969, allowed for high-resolution imaging of small dislocation loops and interstitial clusters by minimizing image overlap and improving contrast for defects as small as 1-2 nm. In the , theoretical models for solute gained prominence, building on earlier foundational work. Wert and Zener's model for atomic coefficients in body-centered cubic metals, which correlated energies with lattice distortions, was extensively applied and refined in studies of solute-defect interactions during this decade, influencing predictions of diffusion rates in irradiated alloys. These models highlighted the role of interstitials in enhancing solute mobility, addressing key gaps in understanding defect-mediated transport. From the 1990s onward, (DFT) enabled precise calculations of interstitial defect energies and structures. For instance, Leung et al.'s 1999 study used LDA and GGA approximations to determine formation energies and migration barriers for silicon self-interstitials, revealing the stability of configurations and resolving discrepancies in earlier empirical models. This era also saw a shift toward , with controlled interstitial doping via and annealing becoming central to engineering nanostructures; early 2000s experiments demonstrated precise incorporation of interstitial impurities like in nanowires to tune electrical properties without lattice disruption. Post-2000 advances have integrated experimental and computational tools to probe defect dynamics in real time. In-situ transmission electron microscopy (TEM) under irradiation has illuminated the evolution of interstitial loops during heavy-ion bombardment, as shown in studies of nanocrystalline metals where defect nucleation and growth occur at elevated temperatures, aiding the design of radiation-tolerant materials. Machine learning models, trained on DFT datasets, now predict interstitial formation energies and migration paths with near-ab initio accuracy, accelerating simulations of complex defect landscapes in metals and semiconductors. As of 2025, recent integrations of AI-driven simulations have further advanced predictions of interstitial defects in 2D materials for quantum computing applications. These developments have extended to applications in fusion materials, where interstitial defects influence helium clustering and embrittlement in tungsten plasma-facing components, and in quantum materials, such as 2D van der Waals systems, where engineered interstitials serve as spin qubits for quantum information processing. A key gap addressed is the evolving understanding of dynamic annealing, where interstitial-vacancy recombination during irradiation reduces stable defect populations, as quantified in 2017 simulations showing Frenkel pair diffusion as the dominant mechanism in silicon.

References

  1. https://www.sciencedirect.com/topics/materials-science/interstitial-defect
  2. https://www.princeton.edu/~maelabs/mae324/glos324/pointdefects.htm
  3. https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%253A_General_Chemistry%253A_Principles_Patterns_and_Applications_%28Averill%29/12%253A_Solids/12.04%253A_Defects_in_Crystals
  4. https://www.minaprem.com/materials-science/defects/interstitial-defect-point-defect-defects-in-solid/
  5. https://sites.chemengr.ucsb.edu/~ceweb/courses/che142242/pdfs/lecture_2_chex42.pdf
  6. https://courses.ems.psu.edu/matse81/book/export/html/2136
  7. https://web.pdx.edu/~pmoeck/phy381/lecture4.pdf
  8. https://chemistry.stackexchange.com/questions/81809/how-many-tetrahedral-and-octahedral-holes-are-there-in-a-bcc-unit-cell
  9. https://digital.library.unt.edu/ark:/67531/metadc832805/m2/1/high_res_d/1035143.pdf
  10. https://www.osti.gov/servlets/purl/1850514
  11. https://pmc.ncbi.nlm.nih.gov/articles/PMC7801622/
  12. https://dspace.lu.lv/server/api/core/bitstreams/2819d7ed-ad06-4da9-9724-ccfd9f7f4ff5/content
  13. https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1019&context=physicshardy
  14. https://bingweb.binghamton.edu/~suzuki/ThermoStatFIles/3.4%20MC%20and%20CE%20Frenkel%20%20and%20Schottky%20type%20defects.pdf
  15. https://www.uomus.edu.iq/img/lectures21/MUCLecture_2023_12543886.pdf
  16. https://www.sciencedirect.com/science/article/abs/pii/S0022311596007362
  17. https://link.aps.org/doi/10.1103/PhysRevB.87.134108
  18. https://link.aps.org/doi/10.1103/PhysRevB.73.020101
  19. https://link.aps.org/doi/10.1103/PhysRevB.55.4941
  20. https://link.aps.org/doi/10.1103/PhysRevMaterials.9.023601
  21. https://link.aps.org/doi/10.1103/PhysRevLett.83.2351
  22. https://chemed.chem.purdue.edu/genchem/topicreview/bp/materials/defects3.html
  23. https://dspace.mit.edu/bitstream/handle/1721.1/75283/3-091-fall-2004/contents/readings/notes_6.pdf
  24. https://www.colorado.edu/faculty/zunger-matter-by-design/sites/default/files/attached-files/90.pdf
  25. https://newton.ex.ac.uk/research/qsystems/jones/projects/oxygen/oxy.what.html
  26. https://pubs.aip.org/aip/jap/article/137/23/230701/3350077/Re-examination-of-important-defect-complexes-in
  27. https://www.ias.ac.in/article/fulltext/pram/060/01/0159-0166
  28. https://www.nature.com/articles/s41524-018-0068-9
  29. https://link.aps.org/doi/10.1103/PhysRevB.81.245206
  30. https://www.sciencedirect.com/science/article/abs/pii/S1359645406005581
  31. https://www.sciencedirect.com/topics/engineering/rothery-rule
  32. https://msestudent.com/interstitial-sites-size-types-applications-and-calculations/
  33. https://roymech.org/Useful_Tables/Matter/Phase_diagram.html
  34. https://link.aps.org/doi/10.1103/PhysRevB.98.064105
  35. https://nvlpubs.nist.gov/nistpubs/Legacy/MP/nbsmiscellaneouspub287.pdf
  36. https://hal.science/hal-01703022v1/document
  37. http://newmaeweb.ucsd.edu/~vlubarda/research/pdfpapers/mm-03.pdf
  38. https://www.sciencedirect.com/science/article/pii/S2772834X22000173
  39. https://www.nature.com/articles/s41467-022-28706-w
  40. https://pmc.ncbi.nlm.nih.gov/articles/PMC5171798/
  41. https://pubs.acs.org/doi/10.1021/acs.chemrev.3c00624
  42. https://link.aps.org/doi/10.1103/PhysRevB.11.2860
  43. https://bdt.semi.ac.cn/download/0.6470168434231495.pdf
  44. https://utw10370.utweb.utexas.edu/publications/P98.pdf
  45. https://link.aps.org/doi/10.1103/PhysRevMaterials.2.095001
  46. https://link.aps.org/doi/10.1103/PhysRevB.99.014207
  47. https://link.aps.org/doi/10.1103/PhysRevB.81.014105
  48. https://pubs.aip.org/aip/apm/article/13/9/091105/3361787/Optical-properties-of-intrinsic-vacancy-and
  49. https://www.researchgate.net/publication/241562166_Optical_Absorption_of_Impurities_and_Defects_in_SemiconductingCrystals
  50. https://www.researchgate.net/publication/324616800_Experimental_techniques_for_defect_characterization_of_highly_irradiated_materials_and_structures
  51. https://iopscience.iop.org/article/10.1088/0305-4608/3/2/009
  52. https://www.sciencedirect.com/science/article/abs/pii/S1359646219307031
  53. https://www.iucr.org/publ/50yearsofxraydiffraction/full-text/metallurgical-science
  54. https://pubmed.ncbi.nlm.nih.gov/17678103/
  55. https://www.sciencedirect.com/science/article/abs/pii/S0168583X98007186
  56. https://iopscience.iop.org/article/10.1088/0953-8984/21/36/364212
  57. https://www.osti.gov/servlets/purl/1495945
  58. https://www.sciencedirect.com/science/article/abs/pii/S1005030225009971
  59. https://www.nature.com/articles/s41467-020-20574-6
  60. https://www.epj-n.org/articles/epjn/full_html/2025/01/epjn20250045/epjn20250045.html
  61. https://www.annualreviews.org/doi/pdf/10.1146/annurev.ms.26.080196.000245
  62. https://www.sciencedirect.com/science/article/abs/pii/S0370157397000823
  63. https://www.jstor.org/stable/1710358
  64. https://link.aps.org/doi/10.1103/PhysRev.97.555
  65. https://www.tandfonline.com/doi/abs/10.1080/14786436908229939
  66. https://pubs.acs.org/doi/10.1021/nl025571j
  67. https://www.nature.com/articles/srep04716
  68. https://www.nature.com/articles/s41524-024-01207-8
  69. https://pubs.aip.org/aip/pop/article/12/5/058101/1016444/Fusion-materials-science-Overview-of-challenges
  70. https://www.annualreviews.org/doi/10.1146/annurev-matsci-070317-124453
  71. https://www.nature.com/articles/srep39754
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