“Thermal radiation” - Leads to equalization of body temperature. Examples of conduction: Examples of convection. Examples of radiation. Convection. Thermal conductivity in nature and technology. The proportionality coefficient is called the thermal conductivity coefficient. Thermal radiation.
“Solid State Physics” - Positively charged ions (core). The energy EF is called the Fermi energy. Levels of an isolated atom. Distance between atoms. Diagram of the band structure of a semiconductor. Splitting of levels when atoms approach each other (Pauli principle). Charge density at an arbitrary point on the surface: T.5, M: Mir, 1977, P. 123.
“Water as a solvent” - The role of water in industry, agriculture and everyday life is very large and diverse. Water is the most common substance on our planet. Application of water and solutions. Water plays a major role in the life of plants and animals. Water is a universal solvent. Physics teacher N.A. Korishonkova Water is a solvent.
“Properties of solids” - Liquid crystals. The arrangement of atoms in crystal lattices is not always correct. Diamond. The properties of crystalline substances are determined by the structure of the crystal lattice. Tourmaline crystal. Mechanical strength Thermal conductivity Electrical conductivity Optical properties. Amorphous. Defects in crystal lattices.
“Temperature and thermal equilibrium” - Lesson goal: Properties of temperature: Celsius scale. Fragment of a physics lesson in 10th grade. A measure of the average kinetic energy of molecules. Temperature. Topic: "Temperature". Kelvin scale.
“Molecular-kinetic theory” - Brownian motion is the random movement of particles. Evidence of the first position of the ICT. A chemical element is a collection of atoms of the same type. A molecule is a system of a small number of atoms connected to each other. Basic concepts of MKT. Particles of matter interact with each other. Evidence for the second position of the ICT.
Defects in crystals are divided into:
Zero-dimensional
One-dimensional
Two-dimensional
Point defects (zero-dimensional) - violation of periodicity at lattice points isolated from each other; in all three dimensions they do not exceed one or more interatomic distances (lattice parameters). Point defects are vacancies, atoms in interstices, atoms in sites of a “foreign” sublattice, impurity atoms in sites or interstices.
Vacancies– absence of an atom or ion in a crystal lattice site; Implemented or interstitial atoms or ions can be both intrinsic and impurity atoms or ions that differ from the main atoms in size or valency. Substitutional impurities replace particles of the main substance at lattice nodes.
Linear(one-dimensional) defects – The main linear defects are dislocations. The a priori concept of dislocations was first used in 1934 by Orowan and Theiler in their study of plastic deformation of crystalline materials, to explain the large difference between the practical and theoretical strength of a metal. Dislocation– these are defects in the crystal structure, which are lines along and near which the correct arrangement of atomic planes characteristic of the crystal is disrupted.
Surface defects of the crystal lattice. Surface lattice defects include stacking faults and grain boundaries.
Conclusion: All types of defects, regardless of the cause of their occurrence, lead to a violation of the equilibrium state of the lattice and increase its internal energy.
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Description of the presentation Presentation Defects in crystals on slides
Energy changes that occur during the formation of defects in a perfect crystal. The gain in entropy associated with the presence of a choice of positions is called configuration entropy and is determined by the Boltzmann formula S = k ln. W, where W is the probability of the formation of a single vacancy, proportional to the number of regular atoms forming the lattice (10 23 per 1 mole of substance).
Various types of defects in crystals: a) vacancy; b) interstitial atom; c) a small replacement defect; d) large replacement defect; e) Frenkel defect; e) Schottky defect (a pair of vacancies in the cation and anion sublattices)
The energy of displacement of an atom from its position in the lattice. Energy barrier. To move an atom from its position, activation energy is required. ΔE – defect formation energy; E * - activation energy. 1 / 1 1 E k. T sn C N e , 2/ 2 2 E k. T mn C N e Equilibrium will be established if n 1 = n 2: under equilibrium conditions, there are vacancies and interstitial atoms in the metal lattice! //Ek. T m s. N N Ce
Dislocations. Mechanical properties and reactivity of solids. 1) - metals usually turn out to be much more ductile than can be expected based on calculations. The calculated value of shear stress in metals is 10 5 - 10 6 N/cm 2, while experimentally found values for many metals do not exceed 10 - 100 N/cm 2. This indicates that there are some “weak links” in the structure of metals , thanks to which metals are deformed so easily; 2) - on the surfaces of many well-cut crystals, under a microscope or even with the naked eye, spirals along which the crystal grew are visible. Such spirals cannot form in perfect crystals; 3) - without ideas about the existence of dislocations, it would be difficult to explain such properties of metals as plasticity and fluidity. Plates of magnesium metal, for example, can be stretched, almost like rubber, to several times their original length; 4) - hardening in metals could not be explained without invoking ideas about dislocations.
Arrangement of atoms around an edge dislocation An edge dislocation is an “extra” atomic half-plane that does not pass through the entire crystal, but only through part of it. Edge dislocation projection.
Movement of an edge dislocation under the action of shear stress. If you connect points A and B, then this will be a projection of the slip plane along which dislocations move. Dislocations are characterized by the Burgers vector b. To find the magnitude and direction of b, it is necessary to describe a contour around the dislocation, mentally drawing it from atom to atom (Fig. e). In a defect-free region of the crystal, such a contour ABCD, constructed from translations to one interatomic distance in each direction, is closed: its beginning and end coincide at point A. On the contrary, contour 12345 surrounding the dislocation is not closed, since points 1 and 5 do not coincide. The magnitude of the Burgers vector is equal to the distance 1 - 5, and the direction is identical to the direction 1 - 5 (or 5 - 1). The Burgers vector of an edge dislocation is perpendicular to the dislocation line and parallel to the direction of motion of the dislocation line (or direction of shear) under the action of an applied stress.
Screw dislocation With continued shear stress, indicated by the arrows, the SS ' line and slip marks reach the back face of the crystal. To find the Burgers vector of a screw dislocation, let us again imagine contour 12345 (Fig. a) “circling” around it. Vector b is determined by the magnitude and direction of the segment 1 - 5. For a screw dislocation, it is parallel to the dislocation line SS ' (in the case of an edge dislocation, it is perpendicular) and perpendicular to the direction of movement of the dislocation, coinciding, as in the case of an edge dislocation, with the direction of shear or slip.
A dislocation line that changes the nature of the dislocation from screw to edge. Origin and movement of a dislocation loop The nature of dislocations is such that they cannot end inside the crystal: if in some place on the crystal surface a dislocation enters the crystal, this means that somewhere on another part of the surface it leaves the crystal.
Scheme of the appearance of a dislocation loop (ring) Scheme of the appearance of vacancies (b) by the annihilation of two dislocations of the opposite sign (a). In reality, direct application of an external deforming force is not necessary for the formation of dislocations. This force can be thermal stresses arising during crystallization, or, for example, similar stresses in the area of foreign inclusions in a solidifying metal ingot during cooling of the melt, etc. In real crystals, excess extraplanes can arise simultaneously in different parts of the crystal. The extraplane, and therefore the dislocations, are mobile in the crystal. This is their first important feature. The second feature of dislocations is their interaction with the formation of new dislocations, dislocation loops similar to those shown in the figures below, and even the formation of vacancies due to the annihilation of two dislocations of opposite sign.
Mechanical strength of metals. Frenkel's model. The destructive force is usually called stress and denoted by σ. According to this model, the resistance σ first increases as the shift along the x axis increases and then drops to zero as soon as the atomic planes shift by one interatomic distance a. When x>a the value of σ increases again and again falls to zero at x = 2a, etc., i.e. σ(x) is a periodic function that can be represented as σ = A sin (2 π x/a ) , for the region of small x A = G /(2π), where G is Young’s modulus. A more rigorous theory subsequently gave a refined expression σ m ax = G /30. Diagram of the shift of atomic planes (a) and the dependence of voltage on distance in the crystal (b).
Experimental and theoretical values of the shear strength of some metals. Roller model of shift of atomic planes of a crystal | F 1 + F 2 |=| F 4 + F 5 | the entire roller system is in balance. One has only to slightly change the balance of forces with a weak external influence, and the top row of rollers will move. Therefore, the movement of a dislocation, i.e., a collection of defective atoms, occurs at low loads. The theory gives σ m ax, which shifts a dislocation, in the form σ m ax = exp ( - 2 π a / [ d (1- ν) ]), where ν is Poisson's ratio (transverse elasticity), d is the distance between slip planes, and - period of the crystal lattice. Assuming a = d, ν = 0.3, we obtain the values of σ m ax in the last column of the table, from which it can be seen that they are much closer to the experimental ones.
Scheme of caterpillar movement Schemes of dislocation-type movement: a - tensile dislocation, b - compressive dislocation, c - carpet movement. “First, let’s try to drag the caterpillar along the ground. It turns out that this is not easy to do; it requires significant effort. They are due to the fact that we are trying to simultaneously lift all pairs of caterpillar legs off the ground. The caterpillar itself moves in a different mode: it tears off only one pair of legs from the surface, carries them through the air, lowers them to the ground, then repeats the same with the next pair of legs, etc., etc. After doing this all pairs of legs will be transported through the air, the entire caterpillar as a whole will move the distance by which each pair of legs alternately shifted. The caterpillar does not drag any pair of legs along the ground. That’s why it crawls easily.”
Ways to control dislocation defects. Fixation by impurities. An impurity atom interacts with a dislocation and the movement of such a dislocation, burdened with impurity atoms, turns out to be difficult. Therefore, the efficiency of dislocation pinning by impurity atoms will be determined by the interaction energy E, which in turn consists of two components: E 1 and E 2. The first component (E 1) is the energy of elastic interaction, and the second (E 2) is the energy of electrical interaction. Fixation by foreign particles. Foreign particles are microscopic inclusions of a substance different from the base metal. These particles are introduced into the metal melt and remain in the metal after it solidifies when the melt cools. In some cases, these particles enter into a chemical interaction with the base metal, and then these particles already represent an alloy. The mechanism of dislocation pinning by such particles is based on different speeds of movement of dislocations in the metal matrix and in the material of foreign particles. Fixation with inclusions of the second phase. The second phase is understood as the release (precipitates) of an excess concentration of an impurity from a metal-impurity solution compared to the equilibrium one. The separation process is called solid solution decomposition. Intertwining of dislocations. When the density of dislocations in a metal is high, they become intertwined. This is due to the fact that some dislocations begin to move along intersecting slip planes, preventing the movement of others.
Qualitative view of the solubility curve. If the crystal contained a concentration of C m at a temperature T m and was quickly cooled, then it will have a concentration of C m at low temperatures, for example, at T 1, although the equilibrium concentration should be C 1. The excess concentration ΔC = C m – C 1 should be at sufficiently long heating will drop out of the solution, because only then will the solution assume a stable equilibrium state corresponding to the minimum energy of the system A 1- x B x.
Methods for detecting dislocations a) Micrograph (obtained in a transmission electron microscope, TEM) of a Sr crystal. Ti. O 3 containing two edge dislocations (100) (marked in the figure). b) Schematic representation of an edge dislocation. c) Micrograph of the surface of a Ga crystal. As (obtained in a scanning tunneling microscope). At point C there is a screw dislocation. d) Scheme of a screw dislocation.
Visualization of dislocations using a transmission electron microscope. a) Dark lines on a bright background are dislocation lines in aluminum after 1% stretching. b) The reason for the contrast of the dislocation region - and the curvature of crystallographic planes leads to electron diffraction, which weakens the transmitted electron beam
a) Etching pits on the surface (111) of bent copper; b) on the surface (100) c) (110) recrystallized Al -0.5% Mn. Dislocations can also be made visible in a conventional optical microscope. Since the areas around the point where dislocations reach the surface are more susceptible to chemical etching, so-called etch pits are formed on the surface, which are clearly visible in an optical microscope. Their shape depends on the Miller indices of the surface.
To obtain a metal material with increased strength, it is necessary to create a large number of dislocation pinning centers, and such centers must be evenly distributed. These requirements led to the creation of superalloys. New metal functional materials. "Designing" the structure of alloys A superalloy is at least a two-phase system in which both phases differ primarily in the degree of order in the atomic structure. The superalloy exists in the Ni - Al system. In this system, an ordinary mixture can be formed, i.e., an alloy with a chaotic distribution of Ni and Al atoms. This alloy has a cubic structure, but the nodes of the cube are replaced by Ni or Al atoms randomly. This disordered alloy is called the γ phase.
Along with the γ phase in the Ni - А l system, an intermetallic compound Ni 3 А l can also be formed, also with a cubic structure, but ordered. Cuboids Ni 3 А l are called γ ‘ -phase. In the γ '-phase, Ni and A l atoms occupy the sites of the cubic lattice according to a strict law: for one aluminum atom there are three nickel atoms. Scheme of dislocation movement in an ordered crystal
C diagram of dislocation pinning by inclusions of another phase. DD – moving dislocation. To create a superalloy, nickel is melted and mixed with aluminum. When the molten mixture is cooled, the disordered γ phase first solidifies (its crystallization temperature is high), and then small-sized cuboids of the γ '-phase are formed inside it as the temperature decreases. By varying the cooling rate, it is possible to regulate the kinetics of formation, and hence the size of inclusions of the γ ‘-phase Ni 3 А l.
The next step in the development of high-strength metallic materials was the production of pure Ni 3 Al without the γ phase. A type of fine-grained mosaic structure of metal. This material is very fragile: chipping occurs along the grain boundaries of the mosaic structure. Here other types of defects are revealed, in particular the surface. Indeed, on the surface of the crystal there is a break in chemical bonds, i.e. a violation is a break in the crystal field, and this is the main reason for the formation of a defect. Dangling chemical bonds are unsaturated, and in contact they are already deformed and therefore weakened. Scheme of breaking chemical bonds on the crystal surface.
To eliminate these defects it is necessary: - either to produce a monocrystalline material that does not contain individual grains-crystallites; - or find a “buffer” in the form of impurities that would not penetrate in noticeable quantities into the volume of Ni 3 Al, but would be well adsorbed on the surface and fill vacancies. Isovalent impurities have the greatest affinity for vacancies, i.e. impurities whose atoms are in the same group of the Periodic Table as the atom removed from the crystal lattice and forming the vacancy. Superalloys Ni 3 Al and Ni 3 Al are widely used today as heat-resistant materials at temperatures up to 1000°C. Similar cobalt-based superalloys have slightly lower strength, but retain it up to a temperature of 1100°C. Further prospects are associated with the production of intermetallic compounds of Ti. Al and T i 3 A l in their pure form. Parts made from them are 40% lighter than the same parts made from nickel superalloy.
Alloys with easy deformability under load. The method for creating such metallic materials is to produce a structure with very small crystallite grains. Grains with dimensions less than 5 microns slide over each other under load without destruction. A sample consisting of such grains can withstand a relative tension Δ l / l 0 = 10 without destruction, i.e., the length of the sample increases by 1000% of the original length. This is the effect of superplasticity. It is explained by the deformation of bonds in grain contacts, i.e., a large number of surface defects. Superplastic metal can be processed almost like plasticine, giving it the desired shape, and then a part made of such material is heat treated to enlarge the grains and quickly cooled, after which the effect of superplasticity disappears, and the part is used for its intended purpose. The main difficulty in producing superplastic metals is achieving a fine grain structure.
It is convenient to obtain nickel powder by the leaching method, in which the Al - Ni alloy is crushed using Na alkali. OH leach aluminum to produce a powder with a particle diameter of about 50 nm, but these particles are so chemically active that they are used as a catalyst. The activity of the powder is explained by a large number of surface defects - broken chemical bonds that can attach electrons from adsorbed atoms and molecules. Scheme of rapid crystallization of a metal melt sprayed in a centrifuge: 1 - cooling gas; 2 - melt; 3 - melt jet; 4 - small particles; 5 - rotating disk Scheme of dynamic pressing of metal powders: 1 - projectile, 2 - powder, 3 - mold, 4 - gun barrel
Laser glazing method. The term is borrowed from porcelain (ceramic) production. Using laser radiation, a thin layer on the metal surface is melted and rapid cooling is applied at rates of the order of 10 7 K/s. The limiting case of ultra-fast hardening is the production of amorphous metals and alloys - metallic glasses.
Superconducting metals and alloys Material Al V In Nb Sn Pb Nb 3 Sn Nb 3 Ge Т с, К 1, 19 5, 4 3, 4 9, 46 3, 72 7, 18 18 21. . . 23In 1911 in Holland, Kamerlingh Onnes discovered a decrease in the resistivity of mercury at the boiling point of liquid helium (4.2 K) to zero! The transition to the superconducting state (ρ = 0) occurred abruptly at a certain critical temperature Tc. Until 1957, the phenomenon of superconductivity had no physical explanation, although the world was busy searching for more and more new superconductors. Thus, by 1987, about 500 metals and alloys with different Tc values were known. Niobium compounds had the highest Tc.
Continuous current. If an electric current is excited in a metal ring, then at normal, for example, room temperature, it quickly dies out, since the flow of current is accompanied by heat losses. At T ≈ 0 in a superconductor, the current becomes undamped. In one of the experiments, the current circulated for 2.5 years until it was stopped. Since the current flows without resistance, and the amount of heat generated by the current is Q = 0.24 I 2 Rt, then in the case of R = 0 there are simply no heat losses. There is no radiation in the superconducting ring due to quantization. But in an atom the momentum and energy of one electron are quantized (take on discrete values), and in a ring the current, i.e. the entire set of electrons, is quantized. Thus, we have an example of a cooperative phenomenon - the movement of all electrons in a solid is strictly coordinated!
Meissner effect Discovered in 1933. Its essence lies in the fact that an external magnetic field at T< Т с не проникает в толщу сверхпроводника. Экспериментально это наблюдается при Т=Т с в виде выталкивания сверхпроводника из магнитного поля, как и полагается диамагнетику. Этот эффект объясняется тем, что в поверхностном слое толщиной 0, 1 мкм внешнее магнитное поле индуцирует постоянный ток, но тепловых и излучательных потерь нет и в результате вокруг этого тока возникает постоянное незатухающее магнитное поле. Оно противоположно по направлению внешнему полю (принцип Ле-Шателье) и экранирует толщу сверхпроводника от внешнего магнитного поля. При увеличении Н до некоторого значения Н с сверхпроводимость разрушается. Значения Н с лежат в интервале 10 -2 . . . 10 -1 Т для различных сверхпроводников. http: //www. youtube. com/watch? v=bo 5XTURGMTM
If there were no Meissner effect, the conductor without resistance would behave differently. When transitioning to a state without resistance in a magnetic field, it would maintain a magnetic field and would retain it even when the external magnetic field is removed. It would be possible to demagnetize such a magnet only by increasing the temperature. This behavior, however, has not been observed experimentally.
In addition to the superconductors considered, which were called superconductors of the first kind, superconductors of the second kind were discovered (A, V. Shubnikov, 1937; A. Abrikosov, 1957). In them, an external magnetic field, upon reaching a certain H c1, penetrates into the sample, and electrons, whose velocities are directed perpendicular to H, begin to move in a circle under the influence of the Lorentz force. Vortex filaments appear. The “trunk” of the thread turns out to be a non-superconducting metal, and superconducting electrons move around it. As a result, a mixed superconductor is formed, consisting of two phases - superconducting and normal. Only when another, higher value of Hc is reached, the 2 filaments, expanding, come closer together, and the superconducting state is completely destroyed. The values of Нс2 reach 20. . . 50 T for such superconductors as Nb 3 Sn and Pb. Mo 6 O 8 respectively.
Josephson structure diagram: 1-dielectric layer; 2-superconductors The structure consists of two superconductors separated by a thin dielectric layer. This structure is located at a certain potential difference specified by the external voltage V. From the theory developed by Feynman, the expression for the current I flowing through the structure follows: I= I 0 sin [(2e. V/h)t+ φ 0 ], where I 0 = 2Kρ/ h (K is the interaction constant of both superconductors in the Josephson structure; ρ is the density of particles carrying the superconducting current). The quantity φ 0 = φ 2 - φ 1 is considered as the phase difference between the wave functions of electrons in contacting superconductors. It can be seen that even in the absence of external voltage (V = 0), a direct current flows through the contact. This is the stationary Josephson effect. If we place the Josephson structure in a magnetic field, then the magnetic flux Ф causes a change in Δ φ, and as a result we get: I= I 0 sinφ 0 cos (Ф / Ф 0), where Ф 0 is the magnetic flux quantum. The value of Ф 0 = h с/е is equal to 2.07·10 -11 T cm 2. Such a small value of Ф 0 allows the production of ultra-sensitive magnetic field meters (magnetometers) that detect weak magnetic fields from the biocurrents of the brain and heart.
The equation I= I 0 sin [(2e. V/h)t+ φ 0 ] shows that in the case of V ≠ 0 the current will oscillate with a frequency f = 2 e. V/h. Numerically, f falls into the microwave range. Thus, the Josephson contact allows you to create alternating current using a constant potential difference. This is the non-stationary Josephson effect. An alternating Josephson current, just like an ordinary current in an oscillating circuit, will emit electromagnetic waves, and this radiation is actually observed experimentally. For high-quality Josephson S - I - S contacts, the thickness of the dielectric layer I must be extremely small - no more than a few nanometers. Otherwise, the coupling constant K, which determines the current I0, is greatly reduced. But the thin insulating layer degrades over time due to the diffusion of atoms from superconducting materials. In addition, the thin layer and the significant dielectric constant of its material lead to a large electrical capacitance of the structure, which limits its practical use.
Basic qualitative ideas about the physics of the phenomenon of superconductivity. Mechanism of formation of Cooper pairs Let us consider a pair of electrons e 1 and e 2, which are repelled by the Coulomb interaction. But there is also another interaction: for example, electron e 1 attracts one of the ions I and displaces it from the equilibrium position. The I ion creates an electric field that acts on the electrons. Therefore, its displacement will affect other electrons, for example, e 2. Thus, the interaction of electrons e 1 and e 2 occurs through the crystal lattice. An electron attracts an ion, but since Z 1 > Z 2, the electron, together with the ion “coat,” has a positive charge and attracts a second electron. At T > T c, thermal motion blurs the ion “coat”. The displacement of an ion is the excitation of lattice atoms, i.e., nothing more than the birth of a phonon. During the reverse transition, a phonon is emitted and is absorbed by another electron. This means that the interaction of electrons is the exchange of phonons. As a result, the entire collective of electrons in the solid body turns out to be bound. At any given moment, an electron is more strongly connected to one of the electrons in this collective, i.e., the entire electronic collective seems to consist of electron pairs. Within a pair, electrons are bound by a certain energy. Therefore, only those influences that overcome the binding energy can affect this pair. It turns out that ordinary collisions change the energy by a very small amount, and it does not affect the electron pair. Therefore, electron pairs move in the crystal without collisions, without scattering, i.e., the current resistance is zero.
Practical application of low-temperature superconductors. Superconducting magnets, made of Nb 3 Sn superconducting alloy wire. At present, superconducting solenoids with a field of 20 T have already been built. Materials corresponding to the formula M x Mo 6 O 8, where the metal atoms M are Pb, Sn, Cu, Ag, etc., are considered promising. The highest magnetic field (approximately 4 0 T) obtained in Pb solenoid. Mo 6 O 8. The colossal sensitivity of Josephson junctions to a magnetic field served as the basis for their use in instrument making, medical equipment and electronics. SQUID is a superconducting quantum interference sensor used for magnetoencephalography. Using the Meissner effect, a number of research centers in different countries are conducting work on magnetic levitation - “floating” above the surface to create high-speed magnetic levitation trains. Induction energy storage devices in the form of a circuit with undamped current and electric power transmission lines (EPL) without losses through superconducting wires. Magnetohydrodynamic (MHD) generators with superconducting windings. They have an efficiency of converting thermal energy into electrical energy of 50%, while for all other power plants it does not exceed 35%.
Defects in the crystal structureReal metals that are used as structural
materials consist of a large number of irregularly shaped crystals. These
crystals
called
grains
or
crystals,
A
structure
polycrystalline or granular. Existing production technologies
metals do not allow obtaining them of ideal chemical purity, therefore
real metals contain impurity atoms. Impurity atoms are
one of the main sources of defects in the crystal structure. IN
Depending on their chemical purity, metals are divided into three groups:
chemically pure - content 99.9%;
high purity - content 99.99%;
ultrapure - content 99.999%.
Atoms of any impurities are sharply different in size and structure
differ from the atoms of the main component, so the force field around
such atoms are distorted. An elastic zone appears around any defects.
distortion of the crystal lattice, which is balanced by volume
crystal adjacent to a defect in the crystal structure.
inherent in all metals. These violations of the ideal structure of solids
have a significant impact on their physical, chemical,
technological and operational properties. Without use
ideas about defects in real crystals, it is impossible to study the phenomena
plastic deformation, hardening and destruction of alloys, etc. Defects
crystal structure can be conveniently classified according to their geometric
shape and size:
surface (two-dimensional) are small in only one direction and have
flat shape - these are the boundaries of grains, blocks and twins, the boundaries of domains;
point (zero-dimensional) are small in all three dimensions, their sizes are not
more than several atomic diameters are vacancies, interstitial atoms,
impurity atoms;
linear (one-dimensional) are small in two directions, and in the third
direction they are commensurate with the length of the crystal - these are dislocations, chains
vacancies and interstitial atoms;
volumetric (three-dimensional) have in all three dimensions relatively
large sizes mean large inhomogeneities, pores, cracks, etc.; Surface defects are interfaces
between individual grains or subgrains in a polycrystalline metal, to
This also includes “packing” defects in crystals.
A grain boundary is a surface on either side of which
crystal lattices differ in spatial orientation. This
the surface is a two-dimensional defect having significant dimensions in
two dimensions, and in the third - its size is comparable to the atomic. Grain boundaries
- these are areas of high dislocation density and inconsistency
structure of adjacent crystals. Atoms at grain boundaries have increased
energy compared to the atoms inside the grains and, as a consequence, more
tend to engage in various interactions and reactions. At grain boundaries
there is no ordered arrangement of atoms. At the grain boundaries during metal crystallization, they accumulate
various impurities, defects, non-metallic inclusions are formed,
oxide films. As a result, the metallic bond between the grains is broken
and the strength of the metal decreases. As a result of the broken border structure
weaken or strengthen the metal, which leads, respectively, to
intercrystalline (intergranular) or transgranular (along the grain body)
destruction. Under the influence of high temperatures, the metal tends to reduce
surface energy of grain boundaries due to grain growth and contraction
the length of their borders. When chemically exposed to grain boundaries
turn out to be more active and, as a result, corrosion destruction
begins at grain boundaries (this feature underlies microanalysis
metals in the manufacture of polished sections).
There is another source of surface distortion of the crystalline
metal structure. The metal grains are mutually misoriented into several
degrees, the fragments are misoriented by minutes, and the blocks that make up
fragment, mutually misoriented for only a few seconds. If
examine the grain at high magnification, it turns out that inside it
There are areas misoriented relative to each other at an angle of 15"...30".
This structure is called block or mosaic, and areas are called blocks
mosaics. The properties of metals will depend both on the sizes of blocks and grains, and
and on their mutual orientation. Oriented blocks are combined into larger fragments in
whose general orientation remains arbitrary, thus all grains
misoriented relative to each other. As the temperature rises
misorientation of grains increases. Thermal process causing grain division
into fragments is called polygonization.
The difference in properties depending on the direction in metals is
the name is anisotropy. Anisotropy is characteristic of all substances with
crystalline structure. The grains are located randomly in the volume, therefore
There are approximately the same number of atoms in different directions and
properties remain the same, this phenomenon is called quasi-anisotropy
(false – anisotropy). Point defects are small in three dimensions and sizes
approaching the point. One of the common defects is
vacancies, i.e. a place not occupied by an atom (Schottky defect). To replace a vacant position
node, a new atom can move, and a vacant place—a “hole”—is formed along
neighborhood. With increasing temperature, the concentration of vacancies increases. So
like atoms. located near the surface. may come to the surface
crystal. and atoms will take their place. located further from the surface.
The presence of vacancies in the lattice imparts mobility to the atoms. those. allows them
move through the process of self-diffusion and diffusion. and thus provides
influence on processes such as aging, release of secondary phases, etc.
Other point defects are dislocated atoms
(Frenkel defect), i.e. atoms of own metal leaving the node
lattice and took place somewhere in the internodes. At the same time in place
moving atom, a vacancy is formed. The concentration of such defects
small. because their formation requires a significant expenditure of energy. Any metal contains foreign impurity atoms. IN
Depending on the nature of the impurities and the conditions under which they enter the metal, they can
be dissolved in the metal or exist in the form of separate inclusions. On
properties of the metal are most influenced by foreign dissolved
impurities whose atoms can be located in the voids between atoms
base metal - interstitial atoms or at crystal lattice sites
base metal - substitution atoms. If the impurity atoms are significantly
fewer base metal atoms, then they form interstitial solutions, and if
more - then they form substitution solutions. In both cases the lattice becomes
defective and its distortions affect the properties of the metal. Linear defects are small in two dimensions, but in the third they can
reach the length of the crystal (grain). Linear defects include chains
vacancies. interstitial atoms and dislocations. Dislocations are special
type of imperfections in the crystal lattice. From the perspective of dislocation theory
strength, phase and structural transformations are considered. Dislocation
called a linear imperfection that forms a zone inside the crystal
shift Dislocation theory was first applied in the mid-thirties
20th century physicists Orowan, Polyany and Taylor to describe the process
plastic deformation of crystalline bodies. Its use allowed
explain the nature of strength and ductility of metals. Dislocation theory gave
the ability to explain the huge difference between theoretical and practical
strength of metals.
The main types of dislocations include edge and screw. Regional
a dislocation is formed if an extra
half-plane of atoms, which is called an extraplane. Her edge is 1-1
creates a linear lattice defect called an edge dislocation.
It is conventionally accepted that a dislocation is positive if it is in the upper
part of the crystal and is indicated by the sign “ ” if the dislocation is located at the bottom
parts - negative “T“. Dislocations of the same sign repel each other, and
the opposite - they attract. Under the influence of edge tension
a dislocation can move across the crystal (along the shear plane) until
will reach the grain (block) boundary. This creates a step the size of
one interatomic distance. Plastic shear is a consequence
gradual movement of dislocations in the plane
shift Propagation of slip along a plane
sliding occurs sequentially. Every
the elementary act of moving a dislocation from
one position to another is accomplished by
rupture of only one vertical atomic
plane. To move dislocations it is required
significantly less force than for hard
displacement of one part of the crystal relative to another in the shear plane. At
movement of a dislocation along the shear direction through the entire crystal
there is a displacement of its upper and lower parts by only one interatomic
distance. As a result of the movement, the dislocation comes to the surface
crystal and disappears. A sliding step remains on the surface. Screw dislocation. Formed by incomplete displacement of the crystal along
density Q. Unlike an edge dislocation, a screw dislocation
parallel to the shift vector.
Dislocations are formed during the crystallization of metals during
“collapse” of a group of vacancies, as well as in the process of plastic deformation
and phase transformations. An important characteristic of the dislocation structure
are the dislocation density. The dislocation density is understood as
total dislocation length l (cm) per unit volume V
crystal (cm3). Thus. dimension of dislocation density, cm-2. U
annealed metals - 106...108 cm-2. When cold plastic
deformation, the dislocation density increases to 1011...1012 cm-2. More
high dislocation density leads to the appearance of microcracks and
metal destruction.
Near the dislocation line, the atoms are displaced from
their places and the crystal lattice is distorted, which
causes the formation of a stress field (above the line
dislocations, the lattice is compressed, and below it is stretched).
The value of a unit displacement of planes
characterized by the Burger vector b, which
reflects both the absolute value of the shift and its
direction. Mixed dislocation. Dislocation cannot end inside
crystal without connecting to another dislocation. This follows from the fact that
a dislocation is the boundary of a shear zone, and there is always a shear zone
a closed line, and part of this line can pass along the outer
crystal surface. Therefore, the dislocation line must close
inside the crystal or end on its surface.
When the shear zone boundary (dislocation line abcdf) is formed
straight sections parallel and perpendicular to the shear vector, and
a more general case of a curved dislocation line gh. In sections av, cd and
ef is an edge dislocation, and in the sections all and de there is a screw dislocation. Separate
sections of a curved dislocation line have an edge or screw
orientation, but part of this curve is neither perpendicular nor parallel
shear vector, and in these areas there is a mixed dislocation
orientation. Plastic deformation of crystalline bodies is related to the amount
dislocations, their width, mobility, degree of interaction with defects
lattices, etc. The nature of the bond between atoms affects plasticity
crystals. Thus, in nonmetals with their rigid directional bonds
dislocations are very narrow, they require high stresses to start - in 103
times greater than for metals. Resulting in brittle fracture in non-metals
occurs earlier than the shift.
The main reason for the low strength of real metals is
the presence of dislocations and other imperfections in the structure of the material
crystalline structure. Obtaining dislocation-free crystals
leads to a sharp increase in the strength of materials.
The left branch of the curve corresponds to the creation
perfect
dislocation-free
filamentous
crystals (so-called “whiskers”), strength
which is close to theoretical. With limited
dislocation density and other distortions
crystalline
gratings
process
shift
occurs more easily the more dislocations there are
located in the bulk of the metal. One of the characteristics of a dislocation is the displacement vector - vector
Burgers. The Burgers vector is an additional vector that needs
insert into the contour described around the dislocation to close
the corresponding circuit in the lattice of an ideal crystal, open
due to the presence of dislocation. A contour drawn along a grid around the area, in
which has a dislocation will turn out to be open (Burgers contour). Gap
contour characterizes the sum of all elastic displacements of the lattice accumulated in
the area around the dislocation is the Burgers vector.
For an edge dislocation the Burgers vector is perpendicular, and for a screw dislocation
dislocation – parallel to the dislocation line. The Burgers vector is a measure
distortion of the crystal lattice due to the presence in it
dislocations. If a dislocation is introduced into the crystal by pure shear, then the vector
shift and is the Burgers vector. Burgers outline may be displaced
along the dislocation line, stretched or compressed in a direction perpendicular to
dislocation lines, while the magnitude and direction of the Burgers vector
remain constant. As stress increases, the number of dislocation sources in the
metal and their density increases. In addition to parallel dislocations
dislocations arise in different planes and directions. Dislocations
influence each other, prevent each other from mixing, their
annihilation (mutual destruction), etc. (which allowed J. Gordon to figuratively
call their interaction in the process of plastic deformation “intimate”
life of dislocations"). As the density of dislocations increases, their movement
becomes increasingly difficult, which requires an increase in the applied
load to continue deformation. As a result, the metal is strengthened, which
corresponds to the right branch of the curve.
Dislocations, along with other defects, participate in phase transitions.
transformations, recrystallization, serve as ready-made centers during precipitation
the second phase from solid solution. Along dislocations, the diffusion rate is
several orders of magnitude higher than through a crystal lattice without defects.
Dislocations serve as a place for concentration of impurity atoms, especially
interstitial impurities, as this reduces lattice distortion. If, under the influence of external forces, dislocations arise in the metal,
then the elastic properties of the metal change and the influence begins to affect
sign of initial deformation. If the metal is subjected to weak
plastic deformation by a load of the same sign, then when the sign changes
load, a decrease in resistance to initial plastic
deformations (Bauschinger effect).
Dislocations arising during primary deformation cause
the appearance of residual stresses in the metal, which, when combined with
operating voltages when the sign of the load changes, cause a decrease
yield strength. With increasing initial plastic deformations
the amount of reduction in mechanical characteristics increases.
Effect
Bauschinger
obviously
manifests itself
at
insignificant
initial
cold hardening
Short
vacation
riveted
materials
eliminates all manifestations
Bauschinger effect. Effect
is significantly weakened by
multiple
cyclical
loads
material
With
presence of small plastic
deformations of different signs. All of the above defects in the crystal structure lead to
the appearance of internal stresses. By volume, where they are
are balanced, stresses of the 1st, 2nd and 3rd kind are distinguished.
Internal stresses of the first kind are zonal stresses,
occurring between individual section zones or between individual
parts parts. These include thermal stresses that appear
with accelerated heating and cooling during welding and heat treatment.
Internal stresses of the second kind - occur inside the grain or between
neighboring grains are due to the dislocation structure of the metal.
Internal stresses of the third kind - arise inside a volume of the order
several elementary cells; the main source is point
defects.
Internal residual stresses are dangerous because
add up to the current operating voltages and can lead to
premature destruction of the structure.
Slide 1
PROPERTIES OF DEFECTS AND THEIR ENSEMBLES IN CONDENSED MATTER Radiation physics of solidsSlide 2
Contents Section 1 Types of individual elementary defects and their properties. Defects in simple substances 1.1. Classification of defects in simple substances 1.1.1. Interstitial 1.1.2. Vacancies in covalent compounds 1.1.3. Characteristics of point defects 1.1.4. Internodes in simple substances and their characteristics 1.1.5. Packaging defects 1.1.6. Disordered alloys. Impurity defects 1.1.7. Ordered alloys. Types of lattices with ordering 1.2. Equilibrium and nonequilibrium defects 1.2.1. Equilibrium concentration of point defects in simple substances 1.3. Defects in ordering alloys 1.3.1. Long-range order metric in ordering alloys 1.3.2. Short-range order metric in ordering alloys. Relationship between long-range order and the average value of short-range order in ordering alloys 1.3.3. Temperature dependence of the concentration of equilibrium substitutional defects in ordering alloys 1.3.4. Temperature dependence of the concentration of equilibrium vacancies in ordering alloys
Slide 3
Contents Section 2. Description of defects in the crystal structure within the framework of the theory of elasticity 2.1. Basic principles of continuum mechanics 2.1.1. Definitions 2.1.2. Hooke's Law 2.1.3. Hooke's law in a generalized form 2.1.4. General form of equations in absolute displacements 2.2. Displacement of atoms in a crystal lattice with point defects. Change in volume 2.3. Behavior of a defect in an external displacement field 2.4. Density of internal forces equivalent to the center of dilatation 2.5. Interaction of defects with an external elastic field 2.6. Elastic interaction of point defects 2.7. Continuous distribution of point defects in an elastic field 2.8. Crystal flow. Creep 2.9. Kinetics of pores in a crystal 2.10. Instability of a uniform distribution of point defects 2.11. Dislocations 2.12. Plastic deformation of crystals 2.13. One-dimensional dislocation model – Frenkel–Kontorova model
Slide 4
Contents Section 3. Radiation defects 3.1. Methods for CREATION OF RADIATION DEFECTS 3.1.1. Irradiation in the reactor 3.1.2. Irradiation at heavy ion accelerators 3.1.3. Irradiation in a high-voltage electron microscope 3.1.4. Main advantages and disadvantages of expressive radiation testing methods 3.2. Primary processes of interaction of particles and radiation with a solid body 3.2.1. General ideas about the processes of interaction of particles with a solid body 3.2.2. Interaction of neutrons with matter 3.2.3. Interaction of accelerated ions with matter 3.2.4. Distribution by penetration depth of embedded ions and defects created by ions 3.2.5. Interaction of electrons with matter 3.2.6. Interaction - quanta with matter 3.3. Basic conditions for the reproducibility of reactor damage phenomena during accelerator irradiation
Slide 5
Contents Section 4. Theoretical comparison of the structure of random fields of radiation defects formed during irradiation with fast particles in film samples 4.1. Cascade of atomic collisions. Individual characteristics 4.2. Random field of defects. Damage statistics 4.3. Model of sparse cascades 4.4. Model of dense cascades 4.5. Simulation parameters 4.6. Simulation relations for model spectra of PVA 4.7. Methodology for determining the temporary life of superconducting compounds 4.8. Calculation of damage field characteristics when thin films are irradiated with ions and neutrons with a spectrum close to the real TNR spectrum
Slide 6
Introduction “Physics of Real Solids” studies physical phenomena and processes caused or arising when there is a high content of defects in a solid, and tries to develop predictive theories that determine the characteristics of a solid. All areas of application and “forced” use of a solid body are, one way or another, determined by structural defects. The simplest examples: the conductivity of an ideal solid is zero; the critical current in superconductors is also zero in the absence of pinning of the system of vortices at structural defects. An important direction is the controlled introduction of impurities and defects into the matrix, as well as radiation-stimulated changes in the structure. The beginning of intensive development of this direction corresponds to the appearance of semiconductor devices. This direction can be called “Physical Technology” since the design and creation of new instruments and tools for researchers is determined by the development of a detailed physical picture of the processes and interpretation of the measured quantities. The natural reduction in the size of the objects being studied and new measurement capabilities have led to the emergence of a new direction, “Nanosystems”. The controlled introduction of impurities and defects into the matrix is also of physical interest for analyzing the applicability of certain concepts of condensed matter physics. For example, to analyze the mechanism of superconductivity in compounds with the A15, HTSC structure.
Slide 7
A number of problematic problems in the physics of condensed systems are of a fundamental nature: Prediction of the mechanical properties of real solids, including in intense radiation fields; Electrical properties and phenomena in condensed systems with a high content of defects; Mechanisms of superconductivity, including high-temperature, improvement of critical parameters of superconductors; Electronic and photonic properties of organic semiconductors and crystals
Slide 8
Slide 9
Classification of defects of simple substances. Definition: Any disturbance or distortion in the regularity of the arrangement of atoms in a crystal is considered a defect in the crystal lattice. The following types of individual defects are distinguished: Thermal motion of atoms Interstitial atoms and vacancies Impurity atoms Crystal boundary Polycrystals Dislocations Static lattice displacements near the defect
Slide 10
1. Thermal movement of atoms; deviation of atoms from the equilibrium position; This is a thermodynamically equilibrium type of defect that has a dynamic character.
Slide 11
2. Interstitial atoms and vacancies. These defects tend to be in equilibrium. The characteristic relaxation time to the equilibrium state can be quite long. Indeed, the process of diffusion of defects, which determines their distribution in a solid, is a thermally activated process; therefore, at insufficiently high temperatures, nonequilibrium states of systems of these defects often occur. A significant difference between systems of point defects is the presence of their interaction with each other (through matrix atoms), which leads, in particular, to the formation of their complexes (ensembles), condensate in the matrix, i.e. the equilibrium state of a system of point defects in most cases is inhomogeneous in space (for example, vacancies - an ensemble of vacancies - a pore).
Slide 12
3. Impurity atoms Impurities, even at low concentrations, can significantly affect the properties of the crystal, for example, they make a significant contribution to the conductivity of semiconductors. The density of atoms in condensed systems is 1022 - 1023 atoms/cm3, the concentration of defects, depending on the background of obtaining the sample, varies from 1012 - 1020 atom/cm3.
Slide 13
4. Crystal boundary This defect leads to distortions even within the matrix and to a violation of crystal symmetry in areas adjacent to the boundary. Pattern of grains in a polycrystal 5. Polycrystalline grains or crystallites with different orientations. The volume of grains is larger than the physically representative volume. The transverse grain size is about 10-3 10-6 cm. The properties of polycrystals are determined both by the crystal grains themselves and by the grain boundaries. If the grains are small and randomly oriented, then the anisotropy of properties characteristic, for example, of a single crystal, does not appear in polycrystals. If there is a certain grain orientation, then the polycrystal is textured and has anisotropy.
Slide 14
The emergence of an edge dislocation at the boundary Screw dislocation of crystal growth. Accumulation of dislocations at grain boundaries Dislocation network Screw dislocation 5. Dislocations are a nonequilibrium type of defect, i.e. their appearance is determined by the prehistory of the sample and is associated either with crystallite growth or with the action of external loads or influences. There are several types of dislocations: edge, screw, mixed. Their accumulations often form grain boundaries.
Slide 15
Depending on the dimension, the following types of defects are distinguished: 1. Point defects: Interstitial atoms and vacancies, Impurity atoms 2. Linear defects: Dislocations 3. Planar defects: Crystal boundary, Polycrystals Phenomenological characteristics of point defects: - energy of formation; - energy of migration; - dilation volume.
Slide 16
In an ideal structure of some type, the atom occupies a position corresponding to a lattice site. An extra atom for which there is no corresponding site occupies an interstitial position. There may be several such provisions for a structure. Different types of interstitial carbon atoms in the diamond lattice: a – Tetrahedral – T; b – Hexagonal –H; c – internode in the middle of the bond – M; d – Split internode (dumbbell -). internode
Slide 17
An extra atom, for which there is no corresponding site, occupies an interstitial position and disturbs the distribution of electron density inside the unit cell. Own interstitial site in diamond. Distribution of electron density in the unit cell of diamond and in the cell containing a tetrahedral interstitial carbon atom. The level of the depicted isosurfaces is the same =1.25
Slide 18
Vacancies in covalent compounds The absence of an atom at a lattice site creates a point defect such as a vacancy: Configuration of a vacancy and divacancy in diamond The pattern of displacements differs from the displacements for interstitial atoms in direction; usually the nearest environment is displaced towards an empty site. In ionic-type compounds, vacancies are formed in pairs, which is an energetically more favorable configuration for a given structure (Schottky defect). The need to maintain neutrality is reflected. This type of defects manifests itself more favorably the higher the ionicity of the bond, for example in NaCl. Note also that in YBa2Cu3O7 type HTSC the bond is observed to be partially ionic.
Slide 19
There is no atom in the corresponding site, which leads to a disturbance in the distribution of electron density inside the unit cell. Single vacancy in diamond. Distribution of electron density in an ideal unit cell of diamond and in a cell containing a single vacancy. The level of the depicted isosurfaces is the same =1.25
Slide 20
Slide 21
Model for the formation of a vacancy in simple substances The following mechanism for the formation of a vacancy can be proposed. The atom is brought to the crystal boundary, while the number of particles in the system does not change. Indeed, simply removing an atom from a crystal lattice site to infinity changes the number of particles in the system, and to calculate the thermodynamic potential of the system it will be necessary to take this fact into account. In the vicinity of the formed vacancy, relaxation of atoms will occur (red arrows in the figure). We will assume that two atoms of a substance interact with each other through a pairwise interaction potential, which does not depend on the environment of the atoms.
Slide 22
The energy of an atom located in a crystal site is equal to Esite=z1*φ(R*), where the number of nearest neighbors is of the order of z1 6 - 8, R* is the equilibrium interatomic distance, an estimate of the potential φ(R*) can be made, for example, from energy of sublimation of the substance, which gives φ(R*) ≈ 0.2 ÷ 0.3eV. Thus, the energy value of an atom at a lattice site is Esite ~ 1.6 ÷ 2.4 eV. Such energy must be expended to break bonds during the formation of a vacancy. However, the removed atom is placed on the surface, therefore, we can assume that half of the broken bonds are restored. The energy of an atom located on the surface is equal. Thus, the energy of vacancy formation Ef ≈ 0.8 ÷ 1.2 eV. Migration of vacancies Let's consider the migration of vacancies. In order for atom A to jump to the empty site where the vacancy is located, it would seem that he does not need to overcome the barrier, but this is not the case - the bonds must be broken. Calculation of vacancy formation energy
Slide 23
In addition, along the migration trajectory of the vacancy (or atom A), an energy barrier (energy lens) appears, created by nearby atoms. This is most clearly visible in a three-dimensional crystal. The number of nearest neighbors in the ABCD section is usually less than at the site, z2 = 4. If we assume that the pair potential changes weakly, then the energy barrier for vacancy migration can be estimated as Emγ ≈ 0.8 ÷ 1 eV.
Slide 24
Dilation volume of a vacancy Let ω0 be the volume per one atom of the solid. When a vacancy is formed, the surface will be distorted due to relaxation, and the volume of the crystal V will change. Estimates give approximately δV(1)= - 0.1ω0, this result was obtained based on the results of dilatation experiments associated with the introduction of many vacancies into the sample. Note that in the matrix surrounding the region of vacancy formation there is a slight increase in the density of the substance due to relaxation. In the mechanism of vacancy formation discussed above, the atom comes to the surface. The associated additional volume change is δV(2)=+ω0. Thus, the total change in the volume of the crystal is equal to: δV=δV(1) + δV(2) =+0.9ω0 Change in volume