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Solid

A solid is one of the fundamental states of matter, characterized by particles—such as atoms, molecules, or ions—that are tightly packed together and held in relatively fixed positions by strong intermolecular forces. This arrangement gives solids a definite shape and volume, distinguishing them from liquids and gases, which can flow and conform to their containers. Solids typically resist deformation, compression, and expansion under normal conditions.^[1] Solids can be classified into crystalline forms, with ordered, repeating atomic structures, or amorphous forms, lacking long-range order. Their properties, including mechanical strength, thermal conductivity, and electrical behavior, form the basis for fields like materials science, solid-state physics, and chemistry.^[2]

Definition and Basic Characteristics

Atomic and Molecular Structure

Solids represent a state of matter in which constituent particles, such as atoms, ions, or molecules, are tightly packed together with minimal vibrational motion relative to one another, conferring a definite volume and shape to the material. This rigidity arises from strong interparticle forces that restrict translational and rotational freedom, distinguishing solids from more fluid phases. The specific atomic and molecular structure of a solid is governed by the nature of the chemical bonds holding the particles together, which fall into several primary categories: ionic, covalent, metallic, van der Waals (including London dispersion forces), and hydrogen bonding. Ionic bonds, characterized by electrostatic attractions between oppositely charged ions, predominate in salts like sodium chloride (NaCl), where sodium cations and chloride anions form a stable lattice.^[3] Covalent bonds involve the sharing of electron pairs between atoms, as seen in diamond, where carbon atoms are linked in a tetrahedral network, yielding exceptional hardness.^[3] Metallic bonds feature delocalized electrons surrounding positively charged metal ions, enabling high electrical conductivity in materials like copper.^[4] Weaker van der Waals forces, arising from temporary dipoles, bind noble gas solids such as argon, while hydrogen bonds, involving partial charges on hydrogen and electronegative atoms, stabilize structures like ice.^[5] In crystalline solids, these bonded units arrange into highly ordered, repeating three-dimensional lattices that define the material's symmetry and properties. Common lattice types include the simple cubic (SC) structure with a coordination number of 6 and packing efficiency of 52%, the body-centered cubic (BCC) with coordination number 8 and 68% efficiency, the face-centered cubic (FCC) with coordination number 12 and 74% efficiency, and the hexagonal close-packed (HCP) structure, which also achieves 74% packing efficiency through its ABAB layering.^[6] These efficiencies reflect the fraction of space occupied by atoms, assuming hard-sphere models, and influence density and stability.^[7] Real solids deviate from ideal lattices due to structural defects, which occur inevitably and profoundly affect macroscopic properties. Point defects, zero-dimensional imperfections, encompass vacancies (empty lattice sites) and interstitials (atoms occupying non-lattice positions), facilitating processes like diffusion and altering electrical conductivity.^[8] Line defects, or one-dimensional dislocations, include edge and screw types that enable slip during deformation, thereby controlling plasticity and mechanical strength without fracturing the material.^[8] In contrast to crystalline solids, amorphous solids exhibit no long-range periodic order at the atomic level, instead displaying only short-range order where neighboring atoms maintain local bonding similar to that in the liquid state from which they often solidify.^[9] This disordered, isotropic arrangement results in gradual softening upon heating rather than sharp melting, as seen in glasses like silica-based materials.^[10]

Phase Distinction from Liquids and Gases

The solid phase of matter is defined by its definite shape and volume, maintained by strong intermolecular forces that predominate over thermal energy, constraining constituent particles to fixed positions within a rigid structure.^[11]^[12] This contrasts with liquids, where particles can slide past one another while retaining a fixed volume, and gases, where particles are widely separated and fill their container dynamically.^[12] In terms of particle dynamics, solids exhibit only vibrational motion, with atoms or molecules oscillating around equilibrium sites in a lattice, unlike the translational diffusion in liquids that enables flow or the rapid, random translational and rotational movements in gases.^[13]^[14] This restricted motion in solids arises from the close atomic packing that resists shear forces, distinguishing the phase from the more disordered arrangements in fluids.^[13] Thermodynamically, the solid phase is delineated by the melting point, the temperature at which solid and liquid coexist in equilibrium under a given pressure, marking the transition where thermal energy overcomes lattice stability.^[15] The slope of the solid-liquid phase boundary in a phase diagram is given by the Clausius-Clapeyron equation:

\frac{dP}{dT} = \frac{\Delta H}{T \Delta V}

where \Delta H is the enthalpy of fusion, T is the equilibrium temperature, and \Delta V is the change in molar volume between phases; for most substances, \Delta V > 0, so melting points increase with pressure.^[15] In phase diagrams, the triple point represents the unique conditions where solid, liquid, and gas phases coexist in equilibrium, serving as a reference for solid stability; for water, this occurs at 0.01°C and 611.657 Pa, below which the solid phase dominates.^[16] The critical point, by contrast, ends the liquid-gas distinction at high temperatures and pressures (e.g., 374°C and 22.064 MPa for water), but solids persist beyond this under sufficient pressure, as seen in water's multiple ice phases like ice VII, which form under gigapascal pressures and maintain solidity where liquids would otherwise prevail.^[17]^[18] Metastable solids occur when a material adopts a higher-energy configuration that is locally stable but not the global minimum, such as diamond persisting despite graphite being thermodynamically favored under ambient conditions.^[19] Supercooling phenomena, often observed in liquids but relevant to solid formation, involve cooling below the melting point without crystallization, creating a metastable supercooled state that can rapidly solidify upon nucleation; this is exemplified in water supercooled to -40°C before forming ice.^[20]^[21]

Classification of Solids

Crystalline Solids

Crystalline solids are defined by their long-range, periodic arrangement of atoms, ions, or molecules, which form repeating unit cells that extend throughout the material.^[22] This ordered structure distinguishes them from amorphous solids, which lack such periodicity.^[23] The arrangement is categorized into seven crystal systems based on symmetry and lattice parameters: triclinic, monoclinic, orthorhombic, tetragonal, trigonal (or rhombohedral), hexagonal, and cubic.^[24] In metals, crystalline solids are stabilized by metallic bonding, where valence electrons are delocalized in a "sea" around positively charged metal ions, enabling high electrical and thermal conductivity as well as ductility due to the ability of layers to slide without breaking bonds.^[25] For example, alpha-iron adopts a body-centered cubic (BCC) structure, with atoms at each corner and one in the center of the unit cell, contributing to its strength and magnetic properties.^[26] Copper, in contrast, forms a face-centered cubic (FCC) lattice, with atoms at the corners and face centers, which enhances its malleability and use in wiring.^[27] Natural minerals often exhibit crystalline structures with ionic or covalent network bonding, leading to high hardness and stability. Quartz, composed of SiO₂, crystallizes in a trigonal system with helical chains of SiO₄ tetrahedra linked by shared oxygen atoms, resulting in its piezoelectric properties.^[28] Diamond, a form of carbon, features a covalent network in a diamond cubic lattice, where each carbon atom bonds tetrahedrally to four others, making it the hardest known natural material.^[29] Crystalline semiconductors, such as silicon, possess a diamond cubic lattice structure identical to that of diamond but with a band gap of approximately 1.12 eV between the valence and conduction bands, allowing tunable electrical conductivity through doping.^[30] This ordered atomic arrangement enables the formation of precise electronic devices. A key feature of crystalline solids is the anisotropy of their properties, arising from the directional bonding and lattice orientation, which causes variations in mechanical, thermal, and electrical behaviors depending on the crystallographic direction.^[31] For instance, cleavage planes align with weak bonding directions, influencing how the material fractures.^[32]

Amorphous Solids

Amorphous solids, also known as glassy solids, are non-crystalline materials characterized by the absence of long-range atomic or molecular order, featuring only short-range order without a repeating lattice structure.^[33] In these materials, atoms or molecules are arranged in a disordered fashion similar to that in a liquid, yet they maintain rigidity due to limited mobility at low temperatures.^[34] This structural disorder distinguishes them from crystalline solids, which exhibit periodic arrangements, and results in isotropic properties and often lower packing efficiency.^[35] Common examples of amorphous solids include inorganic glasses, such as silica-based materials like soda-lime glass, which constitutes a vitreous phase in ceramics and glass ceramics used in windows and containers.^[36] Organic amorphous solids encompass non-crystalline polymers, such as polystyrene and acrylics, which form rigid yet disordered structures in applications like packaging and optical lenses.^[37] These materials are typically produced by rapid cooling of melts to suppress crystallization, preserving the liquid-like arrangement in a solid state.^[34] A defining feature of amorphous solids is the glass transition temperature, denoted as T_g, which marks the temperature at which the material's viscosity reaches approximately $10^{12} Pa·s, transitioning from a hard, glassy state to a more rubbery one without a distinct melting point.^[38] Unlike crystalline solids, this gradual transition reflects the kinetic arrest of molecular motion rather than a thermodynamic phase change.^[39] The value of T_g varies with composition; for example, it is around 1200 °C for pure silica glass but lower, near 100 °C, for polystyrene. Amorphous solids exhibit relaxation processes, where structural rearrangements occur over time to approach a lower-energy configuration, leading to physical aging that manifests as changes in density, enthalpy, and mechanical properties.^[40] During aging below T_g, the material's volume decreases and its viscosity increases, enhancing brittleness but improving dimensional stability, as observed in pharmaceutical glasses and polymers stored for extended periods.^[41] These slow, non-exponential relaxations, often spanning hours to years, arise from the broad distribution of energy barriers in the disordered structure.^[42]

Composite and Hybrid Solids

Composite and hybrid solids are engineered materials composed of two or more distinct phases or constituents with different physical or chemical properties, combined to produce enhanced overall performance that surpasses the individual components. These materials are typically multiphase systems where the phases are macroscopically separable and artificially assembled, distinguishing them from naturally occurring multiphase solids. Common examples include fiber-reinforced composites and particle-filled matrices, where the reinforcement phase provides strength or stiffness while the matrix binds the structure together.^[43]^[44] In composite materials, such as carbon fiber-reinforced polymer (CFRP) composites, high-strength carbon fibers are embedded in a polymer matrix like epoxy to achieve a high strength-to-weight ratio, making them ideal for aerospace and automotive applications. Another classic example is concrete, a composite consisting of a cement-based matrix reinforced with aggregates and often steel bars, which leverages the compressive strength of the matrix and tensile reinforcement for structural durability. These combinations exploit the complementary properties of the phases to optimize mechanical behavior.^[45]^[44] Hybrid solids, particularly in biomaterials, integrate organic and inorganic components for biological compatibility and functionality, as seen in bone, a natural nanocomposite of type I collagen fibers (about 90% organic) and hydroxyapatite nanocrystals (about 70% inorganic by weight). This hierarchical structure provides bone with a balance of flexibility from collagen and rigidity from hydroxyapatite, enabling it to withstand both compressive and tensile loads while supporting osteoconduction and remodeling. Synthetic analogs, such as collagen-hydroxyapatite scaffolds, mimic this hybrid design to promote bone regeneration in tissue engineering.^[46] Nanocomposites represent an advanced class of hybrid solids where nanoscale reinforcements, such as carbon nanotubes (CNTs) or quantum dots, are dispersed in a matrix to yield size-dependent properties. For instance, CNTs in polymer matrices enhance stiffness, strength, and fracture toughness due to their exceptional tensile strength (up to 100 GPa) and high aspect ratio, often improving matrix-dominated properties by 20-50% at low loadings (1-5 wt%). Quantum dots, semiconductor nanoparticles typically 2-10 nm in size, exhibit tunable optical properties when embedded in composites; their emission wavelength shifts with particle size due to quantum confinement, enabling applications in optoelectronics and sensors. These nanomaterials introduce synergistic effects at the interface, altering properties like thermal conductivity or luminescence beyond simple additive contributions.^[47]^[48] The synergistic effects in composites arise from interactions between phases, often modeled by the rule of mixtures for predictive purposes. For the longitudinal Young's modulus in unidirectional fiber-reinforced composites under isostrain conditions, it is given by

E_c = V_f E_f + V_m E_m

where E_c is the composite modulus, V_f and V_m are the volume fractions of the fiber and matrix (with V_f + V_m = 1), and E_f and E_m are the respective moduli of the fiber and matrix. This linear approximation assumes perfect bonding and uniform stress distribution, providing a baseline for understanding how phase fractions influence overall stiffness, though real systems may deviate due to interfacial effects.^[49]^[50]

Key Physical Properties

Mechanical Properties

Mechanical properties of solids describe their response to applied forces, encompassing deformation, strength, and failure mechanisms under various loading conditions. These properties are fundamental to materials science, as they determine a solid's suitability for structural applications, where resistance to stress without excessive distortion or rupture is essential. Solids exhibit a range of behaviors depending on their atomic structure and composition, from elastic recovery in metals to brittle shattering in ceramics.^[51] The stress-strain curve illustrates a solid's mechanical response during tensile loading, plotting engineering stress (σ, force per unit area) against strain (ε, deformation per unit length). In the elastic region, deformation is reversible, governed by Hooke's law, which states that stress is directly proportional to strain: σ = E ε, where E is the Young's modulus representing the material's stiffness.^[52] Beyond the elastic limit, plastic deformation occurs, involving permanent shape change due to dislocation movement in crystalline solids. The yield strength marks the transition to this irreversible regime, while the ultimate tensile strength indicates the maximum stress the material can withstand before necking and failure. For example, mild steel has a yield strength of approximately 250 MPa and ultimate tensile strength of 400-550 MPa.^[53]^[54] Hardness quantifies a solid's resistance to surface indentation or scratching, serving as a proxy for strength and wear resistance. Common scales include the Mohs scale, an ordinal measure primarily for minerals and ceramics (e.g., quartz at 7, diamond at 10), the Brinell scale using a steel ball indenter for softer metals (e.g., aluminum around 15-30 HB), and the Vickers scale employing a diamond pyramid for both metals and harder ceramics (e.g., steel up to 600 HV, alumina ceramics exceeding 1500 HV). Metals generally exhibit lower hardness than ceramics due to their ductility, allowing plastic flow under load, whereas ceramics' ionic or covalent bonds confer higher resistance but increased brittleness.^[55]^[56]^[57] Fracture mechanics analyzes crack propagation and failure modes in solids, distinguishing brittle failure—characterized by sudden, low-energy fracture without significant plastic deformation, as in glass—from ductile failure, where extensive yielding and necking precede rupture, typical of metals. The Griffith criterion provides a foundational model for brittle fracture, predicting the critical stress (σ_f) for crack growth in a plate with a through-thickness crack of length 2a:

\sigma_f = \sqrt{\frac{2 E \gamma}{\pi a}}

where E is Young's modulus and γ is the surface energy required to create new crack surfaces. This equation highlights how flaw size inversely affects strength, explaining why seemingly strong materials fail catastrophically from microscopic defects.^[58]^[59] Viscoelasticity combines viscous and elastic responses, prominent in polymers and composites, where deformation under load is time-dependent due to molecular chain entanglements and relaxation processes. Unlike purely elastic solids, viscoelastic materials show creep (gradual strain increase under constant stress) and stress relaxation (decreasing stress under fixed strain), with behavior modeled by elements like springs (elastic) and dashpots (viscous) in series or parallel. In polymer-matrix composites, this property enhances energy dissipation for damping applications but requires careful consideration for long-term structural integrity.^[60]^[61]^[62] Under sustained or cyclic loads, solids can fail through fatigue or creep, distinct from monotonic loading. Fatigue involves progressive crack initiation and growth under repeated stress cycles below the yield strength, leading to sudden fracture after many cycles (e.g., 10^6 cycles for high-cycle fatigue in alloys). Creep, conversely, is time-dependent plastic deformation under constant stress, particularly at elevated temperatures, progressing through primary (decreasing rate), secondary (steady-state), and tertiary (accelerating to rupture) stages, as observed in turbine blades. These mechanisms underscore the importance of load duration and cycling in design.^[63]^[64]

Thermal Properties

Thermal properties of solids describe how these materials conduct, store, and respond to heat, influencing their behavior under temperature variations. Thermal conductivity, denoted by k, quantifies the ability of a solid to transfer heat and is governed by Fourier's law, which states that the heat flux \mathbf{q} is proportional to the negative gradient of temperature: \mathbf{q} = -k \nabla T.^[65] In metals, heat conduction is primarily electron-mediated, where free electrons carry thermal energy efficiently, leading to high k values often exceeding 100 W/m·K at room temperature.^[66] Conversely, in insulators and semiconductors, phonon-mediated conduction dominates, involving lattice vibrations that scatter more readily, resulting in lower k typically below 10 W/m·K.^[67] Specific heat capacity, often C_p at constant pressure or C_v at constant volume, measures the heat required to raise the temperature of a unit mass of solid by one degree. The Debye model explains low-temperature behavior, predicting C_v \propto T^3 due to the freezing out of low-frequency phonon modes as temperature decreases.^[68] At high temperatures, the Dulong-Petit law applies, stating that C_v \approx 3R per mole of atoms, where R is the gas constant, reflecting the equipartition of energy among vibrational degrees of freedom.^[69] This high-temperature limit, approximately 25 J/mol·K, holds for many elemental solids like copper and diamond above room temperature.^[70] Thermal expansion characterizes the dimensional changes in solids with temperature, quantified by the linear coefficient \alpha, defined as \alpha = \frac{1}{L} \frac{dL}{dT}, where L is length. The volumetric coefficient \beta relates as \beta = 3\alpha for isotropic materials, though crystals often exhibit anisotropy, with \alpha varying by direction due to lattice symmetry—for instance, up to 50% differences along principal axes in hexagonal crystals.^[71]^[72] Values of \alpha range from low (e.g., 0.5 × 10^{-6} K^{-1} for invar alloys) to high (e.g., 25 × 10^{-6} K^{-1} for aluminum).^[73] Melting in solids involves absorbing the latent heat of fusion to overcome intermolecular forces, transitioning from ordered lattice to disordered liquid without temperature change; typical values are around 100-400 kJ/kg for metals like iron (247 kJ/kg). Sublimation, the direct solid-to-gas transition, requires the latent heat of sublimation, which equals the sum of fusion and vaporization heats, such as 571 kJ/kg for dry ice (CO₂).^[74]^[75] These latent heats determine the energy barriers for phase changes, affecting processes like metallurgy and freeze-drying. Certain solids, particularly metallic alloys and compounds, exhibit superconductivity below a critical transition temperature T_c, where electrical resistance vanishes and thermal properties shift dramatically, including a jump in specific heat at T_c. Conventional superconductors have T_c up to about 23 K, as in niobium-tin alloys, while high-temperature cuprates reach above 90 K under ambient pressure. This thermal threshold arises from electron-phonon interactions forming Cooper pairs, enabling zero thermal resistivity in the superconducting state.^[76]^[77]

Electrical and Magnetic Properties

The electrical properties of solids are fundamentally described by band theory, which arises from the quantum mechanical treatment of electrons in a periodic lattice potential. In this framework, the allowed energy levels for electrons form continuous bands: the valence band, filled with electrons at absolute zero, and the conduction band, which is empty or partially filled. The region between these bands, known as the band gap E_g, determines the material's conductivity. Insulators possess a large band gap (E_g > 5 eV), preventing electron excitation from the valence to the conduction band under typical conditions, resulting in negligible conductivity. Semiconductors have a smaller band gap ($0.1 < E_g < 3 eV), allowing thermal or optical excitation of electrons across the gap, while conductors (metals) feature overlapping bands or a partially filled conduction band with no significant gap, enabling free electron movement. The Fermi level, the highest occupied energy at absolute zero, lies within the conduction band for conductors, in the band gap for insulators and semiconductors, and influences charge carrier availability. The density of states, denoting the number of electronic states per energy interval, varies across bands and is crucial for understanding carrier populations in these materials.^[78]^[79] Electrical conductivity \sigma in solids, particularly metals, is modeled by the Drude theory, which treats electrons as a classical gas scattered by lattice ions. The conductivity is given by \sigma = n e \mu, where n is the carrier density (number of free electrons per unit volume), e is the elementary charge, and \mu is the electron mobility, defined as the drift velocity per unit electric field. In metals, n is on the order of $10^{28} to $10^{29} m^{-3}, leading to high \sigma values around $10^7 S/m at room temperature, though mobility \mu decreases with temperature due to increased scattering. This model explains Ohm's law in solids but overestimates specific heat; quantum refinements, like the Sommerfeld model, address such limitations while retaining the core expression for \sigma.^[80]^[81] Semiconductors exhibit tunable conductivity through doping, the intentional introduction of impurities to alter carrier density. In n-type doping, donor atoms (e.g., phosphorus in silicon) add extra electrons to the conduction band, increasing electron concentration n while keeping hole density low. Conversely, p-type doping with acceptors (e.g., boron in silicon) creates vacancies in the valence band, generating holes as majority carriers. The Hall effect provides a method to identify carrier type and measure properties: applying a magnetic field perpendicular to current flow induces a transverse voltage proportional to the carrier charge sign and density, with negative Hall coefficient for n-type (electron-dominated) and positive for p-type (hole-dominated) materials. This effect confirms, for instance, that electrons are the primary carriers in n-type germanium with doping densities around $10^{16} cm^{-3}.^[82]^[83] Magnetic properties of solids stem from atomic magnetic moments due to electron spin and orbital motion, leading to distinct behaviors under applied fields. Diamagnetism occurs in all materials as a weak, induced repulsion from the field, arising from Lenz's law-like orbital currents that oppose the field, with susceptibility \chi \approx -10^{-5}. Paramagnetism appears in materials with unpaired electrons, where thermal disorder aligns moments weakly with the field (\chi > 0, small), following Curie's law \chi \propto 1/T. These effects are present in insulators and semiconductors without cooperative interactions.^[84]^[85] Ferromagnetism represents a strong, spontaneous alignment of moments below the Curie temperature T_C, resulting from exchange interactions that favor parallel spins in lattice sites. In ferromagnets like iron, magnetic domains—regions of uniform magnetization—form to minimize demagnetizing fields, with domain walls allowing reorientation under external fields for hysteresis. Iron, a body-centered cubic metal, exhibits ferromagnetism up to T_C = 1043 K, with saturation magnetization around 1.7 T due to its five unpaired d-electrons per atom. Above T_C, thermal agitation disrupts alignment, transitioning the material to paramagnetism.^[86]^[84] Certain non-centrosymmetric crystals display piezoelectricity, an electromechanical coupling where mechanical strain induces electric polarization, or vice versa. The piezoelectric coefficient d quantifies this, defined as d = strain/voltage, linking applied voltage to generated strain in actuators or stress to voltage in sensors. This effect requires a lack of inversion symmetry in the crystal structure, as in quartz or barium titanate, enabling charge separation under deformation. Applications rely on d values up to $500 pm/V in lead zirconate titanate ceramics.^[87]^[88]

Optical and Other Properties

Optical Properties

Optical properties of solids describe their interaction with electromagnetic radiation, particularly in the visible, ultraviolet (UV), and infrared (IR) regions, governing phenomena such as refraction, absorption, reflection, and emission of light. The refractive index n, defined as the ratio of the speed of light in vacuum to that in the material, quantifies how much light bends upon entering a solid and varies with wavelength, leading to dispersion. In solids like glass or crystals, dispersion causes white light to separate into colors, as shorter wavelengths (e.g., blue) experience higher n than longer ones (e.g., red).^[89] Refraction in solids follows Snell's law, n_1 \sin \theta_1 = n_2 \sin \theta_2, where n_1 and n_2 are the refractive indices of the incident and transmitting media, and \theta_1, \theta_2 are the angles of incidence and refraction, respectively; this law applies to interfaces involving solids, enabling applications in lenses and prisms.^[90] Absorption and transmission in solids occur when photons are captured by electrons, converting light energy into heat or other forms, with transmission being the fraction of light that passes through. The Beer-Lambert law models this attenuation: I = I_0 e^{-\alpha x}, where I is the transmitted intensity, I_0 the incident intensity, \alpha the absorption coefficient, and x the path length; in solids, \alpha depends on material composition and wavelength.^[91] Chromophores—specific molecular groups or defects within the solid—act as primary absorbers, responsible for color in materials like dyes embedded in polymers or impurities in crystals, where they excite electrons to higher energy states upon photon absorption.^[92] Reflection at solid surfaces follows Fresnel equations, but in anisotropic crystals, it couples with birefringence, where the refractive index differs for light polarized in different directions, splitting a single beam into two orthogonally polarized rays with distinct velocities. Calcite (CaCO₃), a classic uniaxial crystal, exhibits strong negative birefringence (\Delta n \approx 0.17), producing double images of objects viewed through it due to the ordinary ray (o-ray) following Snell's law and the extraordinary ray (e-ray) deviating based on its angle to the optic axis.^[93] This property arises from the non-cubic lattice structure, enabling polarization-dependent reflection and refraction essential for optical isolators and waveplates. Luminescence in solids involves light emission following excitation, with fluorescence occurring via rapid radiative decay (nanoseconds) from singlet excited states and phosphorescence from slower triplet states (milliseconds to seconds), often at room temperature in doped or organic solids. In crystalline hosts like ZnS or organic matrices, persistent phosphorescence persists after excitation ceases due to trapped charges, while fluorescence dominates in wide-bandgap semiconductors.^[94] These processes enable applications in displays and sensors, with efficiency influenced by host-guest interactions in solid matrices.^[95] Opto-electronic effects in semiconductors link light absorption to electrical changes, notably photoconductivity, where illumination generates electron-hole pairs that increase conductivity; in materials like GaN, this is quantified by persistent photoconductivity lasting seconds due to defect trapping.^[96] Light-emitting diodes (LEDs) exploit the reverse: injecting carriers into p-n junctions of direct-bandgap semiconductors like AlGaInP or InGaN recombines them, emitting photons at energies matching the bandgap (E_g \approx 1.8-3.1 eV for visible light).^[97] Band structure plays a key role, as direct bandgaps in these solids allow efficient momentum-conserving recombination, unlike indirect gaps in silicon.^[98]

Chemical and Surface Properties

The chemical stability of solids, particularly metallic ones, is closely tied to their oxidation states and position in the reactivity series. Metals exhibit varying oxidation states depending on their electron configuration and bonding environment, with transition metals often displaying multiple stable states that influence their resistance to oxidation or reduction. For instance, heavier transition metals like ruthenium and osmium tend to form stable higher oxidation states, such as +8 in tetroxides, enhancing their chemical inertness under oxidative conditions.^[99] The reactivity series ranks metals by their tendency to lose electrons and form positive ions, with highly reactive metals like lithium and potassium at the top, readily undergoing oxidation in air or water, while noble metals like gold remain stable due to low reactivity.^[100] This series predicts displacement reactions and overall stability, where metals higher in the series displace those below them from compounds, reflecting inherent thermodynamic favorability for oxidation.^[100] Corrosion in solids, especially metals, proceeds via electrochemical mechanisms involving anodic and cathodic reactions at the surface. In anodic regions, metal atoms oxidize to ions (e.g., Fe → Fe²⁺ + 2e⁻), releasing electrons that drive cathodic reactions such as hydrogen evolution or oxygen reduction (e.g., O₂ + 4H⁺ + 4e⁻ → 2H₂O) in acidic or neutral environments.^[101] Passivation enhances corrosion resistance by forming a thin, protective oxide layer, as seen in stainless steels where chromium content above 12% promotes a stable Cr₂O₃ film that inhibits further anodic dissolution.^[102] This layer acts as a barrier, reducing the exchange current density and shifting the corrosion potential to more noble values, thereby minimizing uniform or pitting corrosion in chloride-containing media.^[102] Surface energy in solids quantifies the excess free energy per unit area due to unbalanced intermolecular forces at the interface, driving phenomena like adsorption and wetting.^[103] Adsorption of gases or solutes on solid surfaces lowers this energy, with the Langmuir isotherm modeling monolayer coverage under equilibrium conditions. The fractional surface coverage θ is given by

\theta = \frac{K P}{1 + K P}

where K is the adsorption equilibrium constant and P is the partial pressure of the adsorbate; this assumes uniform sites with no lateral interactions, predicting saturation at high pressures.^[104] Such adsorption is crucial for surface modification and reactivity, as it influences the energetics of subsequent chemical processes. Solid surfaces facilitate heterogeneous catalysis by providing active sites for reactant adsorption and reaction, exemplified by the Haber-Bosch process for ammonia synthesis. In this process, N₂ and H₂ adsorb dissociatively on iron-based catalysts promoted with potassium and alumina, forming surface intermediates like adsorbed nitrogen atoms that recombine with hydrogen to yield NH₃, enabling high-pressure, high-temperature conversion of atmospheric nitrogen.^[105] The solid catalyst's surface defects and electronic structure lower the activation barrier for N≡N bond cleavage, a rate-limiting step, achieving industrial yields through optimized adsorption thermodynamics.^[105] Solubility of solids refers to the maximum concentration of solute in equilibrium with undissolved solid, governed by temperature and solvent interactions, while dissolution kinetics describe the rate of this process. For many solids, solubility increases with temperature if dissolution is endothermic, as higher thermal energy overcomes lattice binding.^[106] Kinetics often follow a shrinking-core model for spherical particles, where the rate is limited by either surface reaction or diffusion through a boundary layer, expressed as proportional to surface area and undersaturation.^[107] Aggregation of particles can reduce effective surface area, slowing dissolution and altering bioavailability in applications like pharmaceuticals.^[107]

Formation and Synthesis

Natural Formation Processes

Natural solids form through a variety of geological and biological processes that have shaped Earth's crust and biosphere over billions of years. The planet's solid crust originated approximately 4.5 billion years ago during the accretion of planetesimals in the early solar nebula, where gravitational collapse of dust and gas led to the differentiation into core, mantle, and crust as the proto-Earth cooled from a molten state.^[108]^[109] This foundational event set the stage for subsequent natural formation mechanisms, primarily driven by thermal, pressure, and chemical dynamics in the lithosphere and hydrosphere. Igneous processes represent one primary pathway for solid formation, occurring when molten magma cools and solidifies to produce crystalline rocks. As magma ascends or resides within the Earth's crust, it undergoes progressive crystallization, with high-temperature minerals forming first, followed by lower-temperature ones as the melt temperature drops below 1300°C.^[110]^[111] For instance, mafic magmas rich in iron and magnesium yield rocks like basalt upon rapid cooling at the surface, incorporating minerals such as olivine and pyroxene that define their dark, dense composition.^[112]^[113] Slower cooling in plutonic environments produces coarser-grained equivalents like gabbro, allowing larger crystal growth.^[110] Sedimentary formation involves the accumulation, compaction, and lithification of particles or chemical precipitates at or near Earth's surface, often in aquatic environments. Chemical precipitation occurs when dissolved minerals supersaturate and crystallize from water, as seen in evaporite deposits or biogenic sources.^[114] A prominent example is limestone, formed primarily from the compaction of calcium carbonate (CaCO₃) shells and skeletal remains of marine organisms, which accumulate as sediment and harden over time through diagenetic processes.^[115]^[116] Clastic sediments, derived from weathered rock fragments, further compact under burial pressure to form sandstones or shales, contributing to vast layered sequences that record environmental histories.^[117] Metamorphic transformations alter pre-existing rocks into new solids under elevated temperatures and pressures without melting, typically in tectonic settings like subduction zones or mountain belts. These conditions, exceeding 200°C and 300 MPa, induce recrystallization and mineral reconfiguration, enhancing density and altering textures.^[118]^[119] For example, limestone subjected to such metamorphism recrystallizes into marble, where calcite grains grow larger and interlock, often preserving faint fossils but losing original porosity.^[120] This process exemplifies how regional or contact metamorphism recycles crustal materials, forming durable solids like schist or gneiss from diverse protoliths.^[121] Biological processes contribute to natural solid formation through biomineralization, where organisms synthesize minerals to construct structural components like shells and bones. In marine invertebrates such as mollusks, calcium carbonate precipitates within organic matrices to form aragonite or calcite shells, providing protection and support via controlled nucleation and growth.^[122] In vertebrates, bone mineralization involves the deposition of hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂) crystals along collagen fibrils, creating a composite solid that balances rigidity and toughness.^[123] These biogenic solids, often incorporating amorphous precursors that transform into crystalline phases, integrate into sedimentary cycles upon organism death, influencing global carbon and nutrient dynamics.^[124] Crystal structures in these minerals, such as the rhombohedral lattice of calcite, underpin their mechanical properties.^[114]

Artificial Synthesis Methods

Artificial synthesis methods enable the controlled production of solids with precise microstructures, compositions, and properties, distinguishing them from naturally occurring formations by allowing tailoring for specific applications in electronics, aerospace, and beyond. These techniques, developed primarily in the 20th century, leverage thermodynamic and kinetic principles to assemble atoms, molecules, or particles into ordered solid structures under laboratory or industrial conditions. Unlike natural mineralization processes that occur over geological timescales, artificial methods accelerate synthesis to hours or days, often mimicking crystal growth seen in minerals but with enhanced purity and uniformity. The Czochralski process, invented in 1915 by Jan Czochralski, is a cornerstone for growing single-crystal ingots of semiconductors such as silicon, which forms the basis for integrated circuits. In this method, a seed crystal is dipped into a molten material contained in a crucible and slowly pulled upward while rotating, allowing the melt to solidify around the seed and form a cylindrical boule with diameters up to 300 mm and lengths exceeding 2 meters. This technique produces dislocation densities as low as 10^3 cm⁻², critical for high-performance electronics, and accounts for over 90% of global silicon wafer production. Powder metallurgy involves compacting and sintering fine metal powders to create dense alloys and composites, offering advantages in shaping complex geometries and incorporating hard inclusions like carbides. The process begins with atomization or milling to produce powders with particle sizes typically 10-100 μm, followed by cold pressing at pressures of 200-800 MPa to form green compacts, and then sintering at temperatures 70-90% of the melting point (e.g., 1100-1300°C for iron-based alloys) to achieve densities up to 99% of theoretical via diffusion-driven necking and grain growth. This method is widely used for tool steels and superalloys, enabling properties like tensile strengths over 1000 MPa in nickel-based components for turbine blades. Chemical vapor deposition (CVD) deposits thin films of solids from gaseous precursors onto substrates, ideal for coatings with atomic-level control. In thermal CVD, reactants like methane and hydrogen are heated to 800-1000°C, decomposing to form diamond films with growth rates of 1-10 μm/hour and hardness matching natural diamond (Knoop hardness ~70 GPa). Variants such as plasma-enhanced CVD lower temperatures to 200-400°C for semiconductor applications, producing silicon carbide films for high-temperature electronics with thermal conductivities up to 490 W/m·K. This technique has revolutionized synthetic diamond production since the 1980s, yielding gem-quality crystals indistinguishable from natural ones. The sol-gel process synthesizes ceramics and glasses through hydrolysis and condensation of metal alkoxides in solution, forming gels that are dried and calcined into monolithic solids. Starting with precursors like tetraethyl orthosilicate (TEOS) for silica, the sol phase evolves into a gel network via reactions such as Si(OR)₄ + 2H₂O → SiO₂ + 4ROH, followed by aging, drying at 100-200°C, and sintering at 500-1200°C to densify the structure. This method produces optically transparent glasses with porosities controllable from 0-90% and is pivotal for bioactive glasses in medical implants, achieving bioactivity indices where 90% surface coverage by hydroxyapatite occurs within 7 days in simulated body fluid. Additive manufacturing, or 3D printing, fabricates solid composites layer-by-layer from digital models, emerging in the 1980s with stereolithography and expanding to metals and polymers by the 2010s. Techniques like selective laser melting fuse metal powders (e.g., titanium alloys) with laser powers of 200-500 W, achieving resolutions down to 20 μm and mechanical properties rivaling wrought materials, such as yield strengths of 900 MPa in Ti-6Al-4V parts. This enables rapid prototyping of intricate lattice structures for lightweight aerospace components, reducing material waste by up to 90% compared to subtractive methods.

Applications and Fields of Study

Materials Science and Engineering

Materials science and engineering is an interdisciplinary field that leverages the inherent properties of solid materials to design, process, and manufacture advanced substances optimized for specific applications. At its core lies the structure-property-processing-performance (PSPP) paradigm, which establishes causal relationships among these elements: processing techniques dictate the material's microstructure (structure), which in turn governs its mechanical, thermal, and other properties, ultimately determining its real-world performance under load or environmental stress. This framework, often visualized as a tetrahedron, enables systematic innovation by allowing engineers to predict and tailor material behavior through controlled variations in composition and fabrication methods.^[125] In alloy design, a cornerstone of the field, engineers exploit the PSPP relationships to create high-performance metals by adjusting elemental compositions and heat treatments. A landmark achievement occurred in the 1910s when British metallurgist Harry Brearley developed the first modern stainless steel by incorporating about 12.8% chromium into molten iron, enhancing corrosion resistance while maintaining strength; this innovation, initially aimed at improving rifle barrel durability, transformed industries from cutlery to construction by preventing oxidation in harsh environments. Subsequent steel variants, such as those with added nickel for austenitic structures, further exemplify how targeted alloying refines properties like ductility and weldability to meet engineering demands.^[126] Polymer engineering similarly applies PSPP principles to organic solids, distinguishing between thermoplastics—which soften reversibly upon heating due to linear or branched chain structures, enabling efficient molding and recycling—and thermosets, which form rigid, cross-linked networks during curing for superior heat resistance and dimensional stability but complicate end-of-life processing. Thermoplastics like polyethylene dominate packaging and automotive parts for their processability, while thermosets such as epoxy resins excel in aerospace composites; however, recycling thermosets remains challenging, often requiring energy-intensive chemical breakdown to recover monomers and avoid landfill accumulation. These distinctions guide material selection, balancing performance with lifecycle sustainability.^[127] Failure analysis is a critical practice in materials engineering, employing techniques like fractography and metallography to diagnose root causes of structural breakdowns and prevent recurrence. For instance, the 1967 collapse of the Silver Bridge in West Virginia, which claimed 46 lives, was traced to stress corrosion cracking in a high-stress eyebar chain link of the suspension bridge, exacerbated by hydrogen embrittlement and undetected fatigue over decades of service; this incident spurred rigorous standards for non-destructive testing and corrosion monitoring in civil infrastructure. Such analyses not only reveal vulnerabilities in material-environment interactions but also inform PSPP-based redesigns, enhancing safety in bridges, aircraft, and pipelines.^[128] Sustainability drives contemporary materials engineering toward eco-friendly solids that minimize environmental impact throughout their lifecycle, with biodegradable polymers emerging as key solutions to plastic pollution. Derived from renewable sources like corn starch or sugarcane, polymers such as polylactic acid (PLA) exhibit tunable mechanical properties comparable to petroleum-based alternatives while fully degrading via microbial action in industrial composting facilities, reducing microplastic persistence in ecosystems. Research highlights their integration into packaging and biomedical applications, where they achieve up to 90% biodegradation within months under optimal conditions, fostering a circular economy by replacing non-degradable thermosets and thermoplastics.^[129]

Solid-State Physics and Chemistry

Solid-state physics applies quantum mechanics to the behavior of electrons and atoms within crystalline lattices, providing the foundational understanding of electronic and vibrational properties in solids. In periodic lattices, electrons do not behave as free particles but are influenced by the periodic potential of the atomic array, leading to the formation of energy bands that determine electrical conductivity and other properties. A key principle in this field is the Bloch theorem, which describes the wavefunctions of electrons in such potentials.^[130] The Bloch theorem, formulated by Felix Bloch in 1928, states that the eigenfunctions of an electron in a periodic potential can be expressed as a plane wave modulated by a periodic function with the same periodicity as the lattice. Mathematically, this is given by

\psi_{\mathbf{k}}(\mathbf{r}) = u_{\mathbf{k}}(\mathbf{r}) e^{i \mathbf{k} \cdot \mathbf{r}},

where u_{\mathbf{k}}(\mathbf{r}) is periodic, \mathbf{k} is the wavevector in the Brillouin zone, and \mathbf{r} is the position vector. This form implies that electrons propagate as Bloch waves, enabling the band structure theory that explains insulators, semiconductors, and metals. The theorem's implications extend to nearly free electron models and tight-binding approximations, which approximate the periodic potential to compute band gaps and densities of states.^[131] Lattice vibrations in solids are quantized as phonons, which are collective excitations arising from the harmonic oscillations of atoms around their equilibrium positions in the lattice. These vibrations follow dispersion relations that relate phonon frequency \omega to wavevector \mathbf{q}, often linear at long wavelengths (\omega = v_s q, where v_s is the speed of sound) and more complex near zone boundaries due to interactions. Phonons contribute significantly to the specific heat of solids; at high temperatures, the classical Dulong-Petit law predicts a constant value, but quantum effects dominate at low temperatures. Albert Einstein's 1907 model treated vibrations as independent harmonic oscillators, yielding a specific heat C_V = 3Nk_B ( \theta_E / T )^2 e^{-\theta_E / T} / (e^{-\theta_E / T} - 1)^2, where \theta_E is the Einstein temperature, which underestimates low-temperature behavior. Peter Debye's 1912 refinement modeled the lattice as a continuum of acoustic modes up to a cutoff frequency, producing C_V \propto T^3 at low T, aligning closely with experiments for many materials.^[132] Solid-state chemistry focuses on the synthesis and properties of extended solid structures, emphasizing the design and preparation of new compounds with tailored compositions and phases. Methods such as solid-state reactions, where precursors are heated to promote diffusion and reaction, enable the formation of inorganic materials like perovskites or superconductors, often requiring high temperatures to overcome kinetic barriers. This field integrates thermodynamics and kinetics to predict stable phases and reaction pathways, facilitating the discovery of novel materials with unique electronic or magnetic properties.^[133] Phase diagrams in solid-state chemistry map the equilibrium phases of binary systems as functions of temperature, composition, and pressure, guiding the synthesis of intermetallic compounds or alloys. For binary systems, common features include eutectic points where liquid solidifies into two phases, peritectic reactions forming a new solid from liquid and solid, and solid solutions with varying solubility limits. These diagrams, constructed from experimental data like thermal analysis or X-ray diffraction, reveal phase boundaries and invariant reactions, such as in the Cu-Ni system exhibiting complete solid solubility or the Pb-Sn system showing a eutectic at 61.9% Sn.^[134] Defects in solids, including vacancies, interstitials, and dislocations, play a crucial role in atomic diffusion, which governs processes like sintering and doping. Diffusion occurs via random atomic jumps mediated by these defects, described phenomenologically by Fick's laws; the first law states that the flux \mathbf{J} is proportional to the concentration gradient, \mathbf{J} = -D \nabla C, where D is the diffusion coefficient and C is concentration. The second law, \partial C / \partial t = D \nabla^2 C, predicts how concentration profiles evolve over time. Formulated by Adolf Fick in 1855, these laws apply to both self-diffusion in pure solids and impurity diffusion, with activation energies reflecting defect formation and migration barriers.^[135] A pivotal historical milestone in solid-state physics was the derivation of Bragg's law in 1913 by William Henry Bragg and William Lawrence Bragg, which established X-ray diffraction as a probe for atomic structure. The law relates the wavelength \lambda of X-rays to the spacing d of crystal planes and scattering angle \theta via n \lambda = 2 d \sin \theta, where n is an integer order, enabling the determination of lattice parameters from diffraction patterns. This breakthrough, building on Max von Laue's 1912 experiments, founded X-ray crystallography and confirmed the wave nature of X-rays while revealing atomic arrangements in solids like NaCl.^[136]

Emerging Applications in Technology

In electronics, the development of transistors using doped semiconductors marked a pivotal advancement, enabling the miniaturization and efficiency of modern devices. In 1947, John Bardeen and Walter Brattain at Bell Laboratories demonstrated the first point-contact transistor, a semiconductor amplifier that amplified electrical signals, which William Shockley subsequently refined into the junction transistor for practical use.^[137] This innovation laid the foundation for integrated circuits, independently conceived by Jack Kilby at Texas Instruments in 1958 and Robert Noyce at Fairchild Semiconductor in 1959, allowing multiple transistors to be fabricated on a single semiconductor chip and revolutionizing computing and consumer electronics.^[138]^[139] In the energy sector, solid-state batteries represent a promising evolution of lithium-ion technology, replacing flammable liquid electrolytes with solid ones to enhance safety and energy density. Post-2010 advancements have focused on materials like sulfide-based and oxide-based solid electrolytes, achieving ionic conductivities approaching those of liquids while improving stability and cycle life; for instance, developments in garnet-type Li7La3Zr2O12 electrolytes have enabled prototypes with energy densities exceeding 300 Wh/kg.^[140]^[141] QuantumScape demonstrated over 1000 charging cycles with more than 95% capacity retention in prototypes by 2023, while Solid Power shipped first A-sample EV cells for automotive qualification in late 2023. As of 2025, QuantumScape has begun shipping Cobra-based B1 battery samples and entered baseline production for its separator process, advancing toward commercialization by 2026.^[142]^[143] Nanotechnology applications of solids, particularly graphene and other two-dimensional (2D) materials, have opened avenues for flexible electronics due to their exceptional mechanical strength and conductivity. Graphene, isolated in 2004 by Andre Geim and Konstantin Novoselov, earned the 2010 Nobel Prize in Physics for revealing its two-dimensional structure and properties, including high electron mobility and flexibility, making it ideal for bendable circuits and displays.^[144] In flexible electronics, graphene-based composites serve as transparent electrodes in organic light-emitting diodes (OLEDs) and touch sensors, with prototypes achieving bending radii under 1 mm without performance degradation; extensions to 2D materials like transition metal dichalcogenides further enable stretchable wearables and foldable screens.^[145]^[146] In biomedicine, solid biomaterials facilitate advanced implants and targeted drug delivery systems, leveraging biocompatibility to integrate with human tissues. Polymeric biomaterials, such as poly(lactic-co-glycolic acid) (PLGA), are used in resorbable implants for orthopedic applications, providing mechanical support while degrading over time to avoid secondary surgeries; these have shown success in bone regeneration scaffolds with over 90% tissue integration in clinical trials.^[147] For drug delivery, nanoparticle-embedded biomaterials enable controlled release, as in titanium implants coated with hydroxyapatite for localized antibiotic delivery, which can reduce postoperative infection risk; recent hydrogel-based systems further allow on-demand release via external stimuli like ultrasound.^[148] Quantum computing harnesses solid-state qubits in superconducting materials to perform computations unattainable by classical systems, with rapid progress in scalability and error correction. Superconducting qubits, fabricated from materials like niobium and aluminum, operate at cryogenic temperatures to maintain quantum coherence; IBM's 2023 milestones include the Heron processor with 133 qubits achieving error rates below 0.1% per gate and the demonstration of utility-scale algorithms outperforming supercomputers in error-mitigated simulations.^[149] The 1,121-qubit Condor processor, also unveiled in 2023, advances toward fault-tolerant systems, enabling applications in materials simulation and optimization problems.^[150]^[151] As of November 2025, IBM has introduced the Nighthawk processor with 120 qubits and enhanced connectivity for 30% more computational complexity at low error rates, alongside the experimental Loon processor paving the way for fault-tolerant quantum computing by 2029.^[152]

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Heat capacity estimation of complex materials for energy technologies
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[PDF] Thermal Expansion - Rice University
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[PDF] High pressure thermal expansion - SE
Feb 11, 2014 · 2.1 Thermal expansion coefficient based on a linear elastic Hookian solid ... and the volumetric, thermal expansion coefficient, β β ≡. 1 ν. ∂ν.
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[PDF] Idaho National Laboratory
Mean linear thermal expansion coefficient for polycrystalline β-Zr (α in units of ... The thermal expansion of single crystals of α-Np is anisotropic.
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14.3 Phase Change and Latent Heat – College Physics chapters 1-17
In the case of direct solid-vapor transitions, the energy required is given by the equation Q = m L s , where L s is the heat of sublimation, which is the ...
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Phase Changes - Chembook
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Superconductivity - HyperPhysics
Several materials exhibit superconducting phase transitions at low temperatures. The highest critical temperature was about 23 K until the discovery in 1986 ...
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Superconductivity is the property of certain materials to conduct direct current (DC) electricity without energy loss when they are cooled below a critical ...
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A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials.Missing: density authoritative sources
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Drude model - Open Solid State Notes
From solving this equation in the steady state, we found the Drude conductivity σ = n e 2 τ m \sigma = \frac{ne^2\tau}{m} σ=mne2τ. Discuss if its scaling with ...
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Semiconductor p-type doping creates new energy levels just above the valence band. The Hall effect can be used to determine charge, drift velocity, and charge ...
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Magnetic Susceptibilities of Paramagnetic and Diamagnetic Materials at 20°C ; Iron oxide (FeO). 720 ; Iron amonium alum. 66 ; Uranium. 40 ; Platinum. 26 ; Tungsten ...
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Piezoelectricity - Engineering LibreTexts
Jul 5, 2021 · Piezoelectricity is the effect of mechanical strain and electric fields on a material; mechanical strain on piezoelectric materials will produce a polarity in ...
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[PDF] 1 Fundamentals of Piezoelectricity - Wiley-VCH
The g-constants are calculated from the piezoelectric charge (strain) constant (d) and relative permittivity (𝜀) from the equation: g = d. 𝜀. (Vm∕N). (1.9).
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[PDF] TIE-29: Refractive Index and Dispersion
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[PDF] Basic Geometrical Optics
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[PDF] Two Photon Absorption in Chromophore Doped Solid Matrices
Two-photon absorption (TPA) offers the advantage of very high transmission at ... The Beer-Lambert law can be derived from an approximation for the absorption.
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Optimizing the optical properties of large chromophore aggregates and molecular solids for applications in photovoltaics and nonlinear optics is an ...
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Principles of Birefringence | Nikon's MicroscopyU
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Jun 21, 2017 · Biluminescent organic emitters show simultaneous fluorescence and phosphorescence at room temperature.
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23.1 General Trends among the Transition Metals
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Sedimentary Rocks
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