They cause irregularities in the lattice, propagating over distances of the order of several periods.
In addition to point defects, there are defects concentrated near some lines. They are called linear defects or dislocations... Defects of this type violate the correct alternation of crystal planes.
The simplest types of dislocations are marginal and helical dislocation.
Edge dislocation is caused by an extra crystalline half-plane inserted between two adjacent layers of atoms (Fig. 2). A screw dislocation can be represented as a result of a crystal cut along a half-plane and the subsequent displacement of lattice parts lying on opposite sides of the cut towards each other by one period (Fig. 3).
Defects have a strong effect on the physical properties of crystals, including their strength.
The initially existing dislocation moves along the crystal under the action of the stresses created in the crystal. The dislocation movement is impeded by the presence of other defects in the crystal, for example, the presence of impurity atoms. Dislocations are also slowed down when they cross each other. An increase in the density of dislocations and an increase in the concentration of impurities leads to a strong deceleration of dislocations and the termination of their motion. As a result, the strength of the material increases. So, for example, an increase in the strength of iron is achieved by dissolving carbon atoms in it (steel).
Plastic deformation is accompanied by the destruction of the crystal lattice and the formation of a large number of defects that impede the movement of dislocations. This explains the hardening of materials during cold working.
Diffusion is the process of transferring matter or energy from an area of high concentration to an area of low concentration. Diffusion is a process at the molecular level and is determined by the random nature of the movement of individual molecules. Diffusion in crystals is a process by which atoms can move from one site to another. Field ion microscopy is a method of direct observation of the crystal lattice of metals and alloys with atomic resolution.
Diffusion processes in solids noticeably depend on the structure of a given crystal and on defects in the crystal structure. Defects, appearing in matter, either facilitate atomic movements, or impede them, working as traps for migrating atoms.
DIFFUSION IS THE PROCESS OF RANDOM WALKING Fick's first law: The frequency of atomic jumps: n = n 0 e - Q / kT, where Q is the diffusion activation energy, k is the Boltzmann constant, n 0 is a constant. The diffusion coefficient D depends on the crystal temperature according to the Arrhenius law: D = D 0 e - Q / kT The diffusion activation energy depends both on the formation energy of a particular defect E f and on the activation energy of its migration E m: Q = E f + E m ...
ATOMIC MECHANISMS OF DIFFUSION Mechanism of exchange of atoms in places; ring mechanism; mechanism of direct movement of atoms through interstices; mechanism for indirect movement of the interstitial configuration; crowdion mechanism; vacancy mechanism; divacancy mechanism; dislocation diffusion mechanisms; mechanisms of diffusion along grain boundaries in polycrystals.
VACANCY MECHANISMS The activation energy of migration by the vacancy mechanism for metals such as copper, silver, iron, etc. is approximately eV (the energy of vacancy formation is of the same order of magnitude). The simplest vacancy cluster is the union of two vacancies - divacancy (2V). The energy required for this movement is often less than one vacancy.
INTERSTITLE MECHANISMS The appearance of interstitial atoms in crystals can be caused by the method of preparation or operation of the material. Interstitial atoms can be divided in crystals into intrinsic and impurity (foreign) interstitial atoms. Foreign (impurity) atoms also in most cases form dumbbells with their own atoms, but they are called mixed. An abundance of interstitial configurations gives rise to an abundance of migration mechanisms using interstitial atoms.
The vacancy should be attracted to the compression region above the extreme atomic row of the extra half-plane, and the interstitial atom should be attracted to the expansion region located below the half-plane. The simplest dislocations represent a defect in the form of an incomplete atomic half-plane inside the crystal.
Diffusion over defect sites in crystals has specific features. First of all, it proceeds more easily than diffusion through defect-free mechanisms. But its sources are not unlimited: the concentration of defects in the process of diffusion almost always decreases due to the annihilation of opposite defects, the escape of defects to the so-called sinks. But if the concentration of defects is high, their role in diffusion increases so much that it leads to the so-called accelerated diffusion, accelerated phase-structural transformations in materials, accelerated creep of materials under load, etc. effects.
CONCLUSIONS The list of migration mechanisms along defect sites in crystals is constantly being updated as more and more in-depth study of defects in the crystal structure of a substance. The inclusion of a particular mechanism in the diffusion process depends on many conditions: on the mobility of a given defect, its concentration, crystal temperature, and other factors.
Slide 1
Solid state physics. Part 2.
Real crystals (just like "real guys") are perfect crystals that grow in the wrong places.
Slide 2
Crystal Growth You know, of course, that water (at normal pressure) freezes at 0 °. If the temperature drops, then exactly at 0 ° the water will begin to freeze, turn into ice crystals. Until all the water freezes, its temperature will not drop further. If, on the contrary, the ice crystal is heated to 0 °, it will remain unchanged. As soon as the temperature reaches 0 °, the crystal will immediately begin to melt. No matter how much we heat further, the temperature of the ice will not rise until all the ice has melted. Only when the entire crystal, having melted, turns into water (in other words, until the structure of all particles disintegrates), the temperature of the water can begin to rise. Any crystalline substance melts and crystallizes at a strictly defined melting point: iron - at 1530 °, tin - at 232 °, quartz - at 1713 °, mercury - at minus 38 °. Non-crystalline solids do not have a constant melting point (and hence the crystallization temperature); when heated, they gradually soften.
Slide 3
Crystal Growth Methods One of them is the cooling of a saturated hot solution. At each temperature, no more than a certain amount of a substance can dissolve in a given amount of solvent (for example, in water). If the solution is cooled slowly, little nuclei are formed, and gradually overgrowing from all sides, they turn into beautiful crystals of regular shape. On rapid cooling, many embryos are formed, and the particles from the solution will "fall" onto the surface of the growing crystals, like peas from a torn bag; Of course, correct crystals will not work out in this case, because the particles in the solution may simply not have time to "settle" on the surface of the crystal in their proper place. Another method of obtaining crystals is the gradual removal of water from a saturated solution. The "extra" substance crystallizes in this case. And in this case, the slower the water evaporates, the better the crystals are obtained.
Slide 4
The third method is growing crystals from molten substances while slowly cooling the liquid. For all methods, the best results are obtained if a seed is used - a small crystal of the correct shape, which is placed in a solution or melt. In this way, for example, ruby crystals are obtained. Cultivation of crystals of precious stones is carried out very slowly, sometimes for years. If you accelerate crystallization, then instead of one crystal you get a lot of small ones. This method can only be carried out in special devices. Currently, more than half of the technically important crystals are grown from melt. One of the most widely used industrial methods for the preparation of semiconductor and other single crystals is the Czochralski method. Designed in 1918. The starting material (charge) is loaded into a refractory crucible and heated to a molten state. Then a seed crystal in the form of a thin rod with a diameter of several mm is placed in a cooled crystal holder and immersed in the melt
Slide 5
Jan Czochralski (1885 - 1953) - Polish chemist, inventor of the currently widely known method of growing single crystals from a melt by pulling them up from the free surface, later named after him. According to some reports, Czochralski discovered his famous method in 1916 when he accidentally dropped his pen into a crucible with molten tin. Pulling the handle out of the crucible, he found that a thin thread of frozen tin was trailing behind the metal nib. Replacing the nib of the pen with a microscopic piece of metal, Czochralski made sure that the metal thread formed in this way has a monocrystalline structure. In the experiments carried out by Czochralski, single crystals of about one millimeter in diameter and up to 150 cm in length were obtained.
Slide 6
Crystal defects In describing the structure of crystals, we have so far used their ideal models. The difference between real crystals and ideal ones is that real crystals do not have the correct crystal lattice. They always contain violations of strict periodicity in the arrangement of atoms. These violations are called defects in crystals. Defects are formed during the growth of crystals under the influence of thermal motion of molecules, mechanical influences, irradiation by particle flows, due to the presence of impurities, etc. Crystal defects are called any violation of the translational symmetry of the crystal - the ideal periodicity of the crystal lattice. There are several types of defects in terms of dimension. Namely, there are zero-dimensional (point), one-dimensional (linear), two-dimensional (plane) and three-dimensional (volume) defects.
Slide 7
Zero-dimensional (or point) crystal defects include all defects that are associated with the displacement or replacement of a small group of atoms (intrinsic point defects), as well as with impurities. They arise during heating, doping, during crystal growth, and as a result of radiation exposure. They can also be introduced as a result of implantation. The properties of such defects and the mechanisms of their formation are the best studied, including motion, interaction, annihilation, and evaporation. Defects, called point defects, arise when one of the atoms of the crystal lattice is replaced by an impurity atom (a), an atom is inserted between the lattice sites (b), or as a result of the formation of vacancies - the absence of an atom in one of the lattice sites (c).
Slide 8
Substitutional impurities, replacing the particles of the basic substance at the lattice sites, are incorporated into the lattice the easier, the closer the atomic (ionic) radii of the impurity and basic substance. The interstitial impurities occupy the interstices and, moreover, the easier, the larger the volume of space between the atoms. Introduced can be either intrinsic or impurity atoms or ions that differ from the main atoms in size or valence. If a foreign atom is in a site, then this is a substitutional defect, if in an interstice, then it is an interstitial atom. The equilibrium positions occupied by interstitial atoms depend on the material and type of the lattice. The neighboring atoms in the nodes of the crystal lattice are slightly displaced, causing a slight deformation. Jobs are the most important type of point defects; they accelerate all processes associated with the movement of atoms: diffusion, sintering of powders, etc. In technically pure metals, point defects increase the electrical resistance, and have almost no effect on the mechanical properties. Only at high concentrations of defects in irradiated metals does the plasticity decrease and other properties noticeably change.
Slide 9
How can pinpoint defects appear? According to the basic principles of statistical physics, even in the case when the average kinetic energy of atoms is very small, there will always be a certain number of atoms with a higher energy, sufficient for an atom to escape from a crystal lattice site. Moving around the crystal and giving part of its energy to other atoms, such an atom can be located in interstices. The aggregate of an atom in an interstice and a vacancy is called a Frenkel defect (or a Frenkel pair). The vacancy and the interstitial atom are linked by significant elastic forces.
Frenkel defects easily arise in crystals containing significant interatomic voids. An example of such crystals are substances with a diamond or rock salt structure.
Slide 10
Schottky point defects are mainly found in close-packed crystals, where the formation of interstitial atoms is difficult or energetically disadvantageous. Some atoms from the near-surface layer, as a result of thermal motion, can escape from the crystal to the surface (Fig.). The vacancy in the vacant node can then migrate into the bulk of the crystal. The formation of Schottky defects reduces the density of the crystal, since its volume grows at a constant mass, while during the formation of Frenkel defects, the density remains unchanged, since the volume of the entire body does not change.
Walter Hermann Schottky (1886 - 1976) - the famous German physicist, in 1915 invented an electron tube with a screening grid and in 1919 a tetrode. In 1938 Schottky formulated a theory predicting the Schottky effect now used in Schottky diodes.
Slide 11
Thus, being a far from perfect, ordered and somewhat monotonic sequence of alternating positive and negative ions, real crystals contain a wide range of interesting point defects, which, as we will see, can strongly affect many of their properties. As we have already said, these are intrinsic defects, the concentration of which depends on temperature, and, in addition, improper, impurity defects, which are either randomly present or added deliberately during crystal growth. All these defects can be considered quasiparticles. Like real particles in a vacuum, they can move and interact over long distances to form more complex structures.
Slide 12
Crystalline transfer processes It is often mistakenly believed that common alkali halide compounds such as sodium chloride and potassium chloride are insulators, but in reality they are relatively good conductors, this is especially true at elevated temperatures. The fact of the existence of conductivity, as well as the fact that both self-diffusion and diffusion of impurity ions proceed quite easily in ionic solids, serve as irrefutable evidence of the presence of point defects in them. Many of these materials do not have electronic conductivity - measurements show that conductivity is due to ion migration. However, without the existence of vacancies or implanted atoms, the movement of ions in such a classical ionic conductor is impossible: this would require too much energy. Due to defects and their movements (Fig.), The process of ion movement turns into an exchange of places between the ion and the defect; in this case, the amount of required energy decreases.
Slide 13
Diffusion (Latin diffusio - spreading, spreading, dispersing, interaction) is the process of mutual penetration of molecules of one substance between the molecules of another, leading to spontaneous equalization of their concentrations throughout the occupied volume. In some situations, one of the substances already has an equalized concentration and they speak of the diffusion of one substance in another. In this case, the transfer of matter occurs from an area with a high concentration to an area with a low concentration (along the concentration gradient). In crystals, both intrinsic lattice atoms (self-diffusion or homodiffusion) and atoms of other chemical elements dissolved in the substance (impurity or heterodiffusion), as well as point defects in the crystal structure - interstitial atoms and vacancies, can diffuse.
Slide 14
Diffusion is a process at the molecular level and is determined by the random nature of the movement of individual molecules. The diffusion rate is therefore proportional to the average molecular velocity. If in a mixture of gases the mass of one molecule is four times greater than the other, then such a molecule moves twice as slow as compared to its movement in a pure gas. Accordingly, its diffusion rate is also lower. This difference in diffusion rates of light and heavy molecules is used to separate substances with different molecular weights. Isotope separation is an example. If a gas containing two isotopes is passed through a porous membrane, the lighter isotopes penetrate the membrane faster than the heavier ones. For better separation, the process is carried out in several stages. This process was widely used for the separation of uranium isotopes (separation of 235U from the main mass of 238U). (Currently, the centrifugation method is used to separate uranium isotopes, in which the gas containing uranium is brought into a very rapid rotation and, due to the difference in the mass of the molecules, the isotopes are separated, which are then converted back into the metal.)
Slide 15
Diffusion phenomenologically obeys Fick's laws. Fick's 1st law establishes proportionality of the diffusion flux of particles to the gradient of their concentration; Fick's second law describes the change in concentration due to diffusion. The phenomenon of diffusion was first investigated by the Würzburg scientist A. Fick using the example of salt solutions. Fick, through careful research, showed that free diffusion of saline solutions occurs according to laws completely analogous to the laws of heat propagation in solids.
Slide 16
Diffusion in crystals Certain general crystallographic features of the diffusion process are quite obvious if we take into account the geometry of the crystal. First of all, diffusion is almost always carried out gradually, and the length of the elementary "steps" is of the order of one atomic diameter, that is, several angstroms. Atoms move by jumping from one position in the lattice to another. Together, these elementary jumps provide the movement of atoms over long distances. Let us find out what is the mechanism of individual atomic jumps. There are several possible schemes: the movement of vacancies, the movement of interstitial atoms, or some way of mutual exchange of places between atoms (Fig).
Atomic displacements that lead to diffusion: a - motion of vacancies; b - motion of interstitial atoms; c - exchange of places of two atoms; d - ring exchange of places of four atoms
Slide 17
Based on the concept of point defects in crystals, Frenkel proposed two main diffusion mechanisms in solids: vacancy (Fig, a: an atom moves, exchanging places with a vacancy) and interstitial (Fig, b: an atom moves through interstices). Small (in size) impurity atoms move in the second way, and in the first - all the others: this is the most common diffusion mechanism.
Yakov Ilyich Frenkel (1894 - 1952) - Soviet scientist, theoretical physicist, one of the founders of solid state physics. From 1921 until the end of his life, Frenkel worked at the Leningrad Physics and Technology Institute. Since 1922, Frenkel has published a new book literally every year. He became the author of the first course in theoretical physics in the USSR.
Slide 18
Dislocations A dislocation is a linear defect in the crystal lattice of a solid, which is the presence of an "extra" atomic half-plane. The simplest visual model of an edge dislocation is a book with a part torn off from one of the inner pages. Then, if the pages of the book are likened to atomic planes, then the edge of the torn part of the page simulates the line of dislocation. A distinction is made between screw and edge dislocations.
Slide 19
For a dislocation to form in an ideal crystal, it is necessary to make a shift in some part of the slip plane
The dislocation density varies widely and depends on the state of the material. After careful annealing, the dislocation density is low; in crystals with a strongly deformed crystal lattice, the dislocation density reaches very high values.
Slide 20
The dislocation density largely determines the plasticity and strength of the material. If the density is less than a certain value, then the resistance to deformation increases sharply, and the strength approaches the theoretical one. Thus, an increase in strength is achieved by creating a metal with a defect-free structure, and also, on the other hand, by an increase in the density of dislocations, which impedes their movement.
Slide 21
During plastic deformation, one part of the crystal moves relative to the other under the action of shear stresses. When the loads are removed, the shift remains, i.e. plastic deformation occurs. The application of a shear stress leads to the displacement of the edge dislocation, and the displacement of its axis by one translation means a change in the half-plane that forms the dislocation at a given moment. The movement of an edge dislocation through the entire crystal will lead to a shift of a part of the crystal by one interatomic distance. This results in plastic deformation of the crystal (Fig.), I.e., parts of the crystal are displaced relative to each other by one translation.
A metal in a stressed state, for any type of loading, always experiences normal and tangential stresses. The growth of normal and shear stresses leads to different consequences. The growth of normal stresses leads to brittle fracture. Shear stresses cause plastic deformation.
Slide 22
An increase in strength is achieved by creating a metal with a defect-free structure, as well as an increase in the density of dislocations, which impedes their movement. At present, crystals without defects have been created - whiskers up to 2 mm long, 0.5 ... 20 µm thick - "whiskers" with a strength close to theoretical. Dislocations affect not only the strength and ductility, but also other properties of crystals. With an increase in the density of dislocations, their optical properties change, and the electrical resistance of the metal increases. Dislocations increase the average rate of diffusion in the crystal, accelerate aging and other processes, and reduce chemical resistance; therefore, as a result of treating the crystal surface with special substances, pits are formed at the points of dislocation exit.
Slide 23
Epitaxy is a regular growth of one crystalline material on another (from the Greek επι - on and ταξισ - ordering), that is, the oriented growth of one crystal on the surface of another (substrate). The minimum energy is consumed if the crystal grows along a screw dislocation.
Slide 24
Thank you for the attention!
- Size: 2.2 Mbytes
- Number of slides: 37
Description of the presentation Presentation Defects in crystals by slides
Energy changes occurring during the formation of defects in a perfect crystal. The gain in entropy associated with the presence of a choice of positions is called configurational entropy and is determined by the Boltzmann formula S = k ln. W, where W is the probability of a single vacancy formation, proportional to the number of regular atoms forming a lattice (10 23 per 1 mol of substance).
Various types of defects in crystals: a) vacancy; b) an interstitial atom; c) a small defect of substitution; d) large substitution defect; e) Frenkel defect; f) Schottky defect (a pair of vacancies in the cationic and anionic sublattices)
Energy of displacement of an atom from its place in the lattice. Energy barrier. To move an atom from the position it occupies, an activation energy is required. ΔЕ is the energy of defect formation; 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, vacancies and interstitial atoms are present in the metal lattice! / / E k. T m s. N N Ce
Dislocation. Mechanical properties and reactivity of solids. 1) - metals are usually much more ductile than can be expected on the basis of calculations. The calculated magnitude of shear stresses in metals is 10 5 - 10 6 N / cm 2, while the 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) - spirals are visible on the surfaces of many crystals with a good faceting under a microscope or even with the naked eye, along which the crystal growth took place. 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 metallic magnesium, for example, can be, almost like rubber, stretched several times in comparison with the original length; 4) - work hardening in metals could not be explained without invoking the concept of 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 a part of it. Edge dislocation projection.
Displacement of an edge dislocation under the action of shear stress. If we connect points A and B, then this will be the projection of the slip plane along which the 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, built from translations at one interatomic distance in each direction, is closed: its beginning and end coincide at point A. On the contrary, the 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 to the direction of shear) under the action of the applied stress.
Screw dislocation With continued exposure to shear stress, shown by arrows, the SS 'line and slip traces reach the back face of the crystal. To find the Burgers vector of a screw dislocation, we again imagine a contour 12345 (Fig. A), "going around" it. Vector b is determined by the size and direction of the segment 1 - 5. At a screw dislocation, it is parallel to the dislocation line SS '(in the case of an edge perpendicular) and perpendicular to the direction of motion of the dislocation, coinciding, as in the case of an edge dislocation, with the direction of shear or slip.
Dislocation line that changes the character of the dislocation from screw to edge. The origin and motion of a dislocation loop The nature of dislocations is such that they cannot end inside the crystal: if in some place of the crystal surface a dislocation enters the crystal, this means that somewhere in another part of the surface it leaves the crystal.
Diagram of the emergence of a dislocation loop (ring). Diagram of the emergence of vacancies (b) by annihilation of two dislocations of opposite sign (a). In fact, the direct application of an external deforming force for the formation of dislocations is not necessary. Such a force can be thermal stresses arising during crystallization, or, for example, similar stresses in the region of foreign inclusions in a solidifying metal ingot when the melt is cooled, etc. In real crystals, excess extraplanes can appear simultaneously in different parts of the crystal. The extraplane, and hence 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 presented below, and even with the formation of vacancies due to the annihilation of two dislocations of opposite sign.
Mechanical strength of metals. Frenkel's model. The breaking force is usually called stress and denoted by σ. According to this model, the resistance σ first increases with an increase in the shear along the x axis and then drops to zero as soon as the atomic planes move by one interatomic distance a. For x> a, the value of σ rises again and again drops 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 х A = G / (2π), where G is Young's modulus. A more rigorous theory later gave a refined expression σ m ax = G / 30. Scheme of displacement of atomic planes (a) and dependence of voltage on distance in a crystal (b).
Experimental and theoretical values of the shear strength of some metals. Roller model of the 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 by a weak external influence, and the upper row of rollers will move. Therefore, the movement of a dislocation, i.e., a set of defective atoms, occurs at low loads. The theory gives σ m ax, shearing the dislocation, in the form - the 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.
Track displacement scheme Dislocation type displacement schemes: a - tensile dislocation, b - compressive dislocation, c - carpet displacement. “First, let's try to drag the caterpillar along the ground. It turns out that it is not easy to do this; it requires significant efforts. 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, transfers them through the air, lowers them to the ground, then repeats the same with the next pair of legs, etc., etc. After this all pairs of legs will be transferred through the air, the entire caterpillar as a whole will move the distance by which each of the pairs of legs was alternately displaced. The caterpillar does not drag any of the pairs of legs along the ground. That is why it crawls easily. "
Ways of managing dislocation defects. Fixing with impurities. An impurity atom interacts with a dislocation, and the displacement of such a dislocation, burdened by impurity atoms, turns out to be hindered. Therefore, the efficiency of pinning dislocations 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. Fixing by foreign particles. Foreign particles are microscopic inclusions of a substance that differs from the base metal. These particles are introduced into the metal melt and remain in the metal after it solidifies when the melt is cooled. In some cases, these particles enter into chemical interaction with the base metal, and then these particles are already an alloy. The mechanism of dislocation pinning by such particles is based on different rates of dislocation movement in the metal matrix and in the material of foreign particles. Securing by inclusions of the second phase. The second phase is understood as the precipitation (precipitates) of an excess (in comparison with the equilibrium) concentration of an impurity from a metal-impurity solution. The separation process is called solid solution decomposition. Interlacing of dislocations. At a high density of dislocations in the metal, their interlacing occurs. This is due to the fact that some dislocations begin to move along intersecting slip planes, preventing the advance of others.
Qualitative form of the solubility curve. If the crystal contained a concentration of C m at the 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 With a sufficiently long heating to fall out of the solution, because only in this case the solution will take on a stable equilibrium state corresponding to the minimum energy of the А 1 - x В x system.
Dislocation detection methods a) Micrograph (obtained in transmission electron microscope, TEM) of the 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 Ga crystal surface. As (obtained in a scanning tunneling microscope). At point C, there is a screw dislocation. d) Diagram of a screw dislocation.
Visualization of dislocations using a transmission electron microscope. a) Dark lines on a bright background - dislocation lines in aluminum after 1% stretching. b) The reason for the contrast of the dislocation region - and the curvature of the crystallographic planes leads to electron diffraction, which weakens the transmitted electron beam
a) Etching pits on the (111) surface of curved copper; b) on the (100) surface c) (110) recrystallized Al -0.5% Mn. Dislocations can also be made visible in a conventional optical microscope. Since the regions around the point where dislocations emerge onto the surface are more susceptible to chemical etching, so-called etching pits form on the surface, which are clearly visible in an optical microscope. Their shape depends on the Miller indices of the surface.
To obtain a metallic material with increased strength, it is necessary to create a large number of dislocation pinning centers, and such centers should be evenly distributed. These requirements have led to the development of superalloys. New metallic 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. Superalloy exists in the Ni - Al system. In this system, an ordinary mixture can form, i.e., an alloy with a chaotic distribution of Ni and Al atoms. This alloy has a cubic structure, but the cube nodes are replaced by Ni or Al atoms, randomly. This disordered alloy is called the γ-phase.
Along with the γ - phase in the Ni - Al system, an intermetallic compound Ni 3 Al can also form with a cubic structure, but ordered. Cuboids Ni 3 А l are called γ ’-phase. In the γ ’-phase, the Ni and Al atoms occupy the sites of the cubic lattice according to a strict law: there are three nickel atoms per aluminum atom. Diagram of dislocation movement in an ordered crystal
C scheme of dislocation pinning by inclusions of another phase. DD is a moving dislocation. To obtain a superalloy, nickel is melted and mixed with aluminum. When the molten mixture is cooled, the disordered γ 'phase solidifies first (its crystallization temperature is high), and then, with a decrease in temperature, small cuboids of the γ' phase are formed inside it. 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 to obtain pure Ni 3 Al without the γ-phase. View of a fine-grained mosaic metal structure. This material is very fragile: chipping occurs along the grain boundaries of the mosaic structure. Here, other types of defects come to light, in particular the surface. Indeed, on the surface of the crystal there is a breakage of chemical bonds, that is, a breakdown is a breakage of 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 single-crystal material that does not contain individual grains-crystallites; - either find a "buffer" in the form of impurities that would not penetrate in noticeable amounts into the bulk of Ni 3 Al, but would adsorb well on the surface and fill vacancies. The greatest affinity for vacancies is possessed by isovalent impurities, i.e., impurities whose atoms are in the same group of the Periodic Table as the atom removed from the crystal lattice and formed a vacancy. Superalloys Ni 3 Al and Ni 3 Al are widely used today as refractory materials at temperatures up to 1000 ° C. Similar cobalt-based superalloys have a slightly lower strength, but retain it up to a temperature of 1100 ° C. Further prospects are associated with the preparation of Ti intermetallic compounds. Al and T i 3 A l in 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 the fabrication of a structure with very small crystallite grains. Grains having a size of less than 5 microns, under load, slide over each other without destruction. A sample consisting of such grains withstands the relative tension Δ l / l 0 = 10 without fracture, ie, the sample length increases by 1000% of the original length. This is the effect of superplasticity. It is explained by deformation of bonds in grain contacts, i.e., by 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 a material is heat treated to coarse grains and quickly cooled, after which the effect of superplasticity disappears and the part is used for its intended purpose. The main difficulty in obtaining superplastic metals is the achievement of a fine grain structure.
Nickel powder is conveniently obtained by the leaching method, in which the Al - Ni alloy is crushed using an alkali Na. OH leach aluminum and get 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 - dangling chemical bonds capable of attaching electrons from adsorbed atoms and molecules. Scheme of rapid crystallization of a metal melt sprayed on a centrifuge: 1 - cooling gas; 2 - melt; 3 - stream of melt; 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. With the help of laser radiation, a thin layer is melted on the metal surface and rapid cooling is applied at rates of the order of 10 7 K / s. The limiting case of ultrafast 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.. ... In 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 T c. Until 1957, the phenomenon of superconductivity had no physical explanation, although the world was busy looking for more and more superconductors. So, by 1987, about 500 metals and alloys with different values of Тс were known. Niobium compounds had the maximum T c.
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, the current in the superconductor 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 released by the current is Q = 0, 24 I 2 Rt, then in the case R = 0 there are simply no heat losses. There is no radiation in the superconducting ring due to quantization. But in the atom, the momentum and energy of one electron are quantized (take on discrete values), and in the ring - the current, that is, the entire set of electrons. 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 is that the 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 it were not for the Meissner effect, a conductor without resistance would behave differently. Upon transition to a state without resistance in a magnetic field, it would retain the magnetic field and would hold it even when the external magnetic field was removed. Such a magnet could be demagnetized only by increasing the temperature. This behavior, however, has not been observed experimentally.
In addition to the considered superconductors, which were called superconductors of the first kind, superconductors of the second kind were discovered (A, V. Shubnikov, 1937; A. Abrikosov, 1957). In them, the external magnetic field, upon reaching a certain H c1, penetrates into the sample, and the electrons, whose velocities are directed perpendicular to H, under the influence of the Lorentz force, begin to move in a circle. Vortex filaments appear. The "trunk" of the filament is obtained by 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 H c 2 is reached, the filaments, expanding, approach each other, and the superconducting state is completely destroyed. The H c2 values reach 20.. ... 50 T for superconductors such as Nb 3 Sn and Pb. Mo 6 O 8, respectively.
Josephson structure diagram: 1-dielectric interlayer; 2-superconductors The structure consists of two superconductors separated by a dielectric thin layer. This structure is found at a certain potential difference specified by an 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 = 2Кρ / h (К is the constant of interaction 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 of the wave functions of electrons in contacting superconductors. It can be seen that even in the absence of an external voltage (V = 0), a direct current flows through the contact. This is the stationary Josephson effect. If you 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 quantum of the magnetic flux. The value of Ф 0 = h s / e is equal to 2, 07 · 10 -11 T · cm 2. Such a small value of Ф 0 makes it possible to manufacture supersensitive magnetic field meters (magnetometers), which record 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 junction allows you to create an alternating current using a constant potential difference. This is the non-stationary Josephson effect. The alternating Josephson current, just like an ordinary current in an oscillatory circuit, will emit electromagnetic waves, and this radiation is indeed observed experimentally. For high-quality Josephson S - I - S contacts, the thickness of the dielectric layer I should be extremely small - no more than a few nanometers. Otherwise, the coupling constant K, which determines the current I 0, is greatly reduced. But the thin insulating layer degrades over time due to the diffusion of atoms from superconducting materials. In addition, a thin layer and a significant dielectric constant of its material leads to a high electrical capacity of the structure, which limits its practical use.
Basic qualitative ideas about the physics of the phenomenon of superconductivity. The mechanism of formation of Cooper pairs 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, an electron e 1 attracts one of the ions I and displaces it from the equilibrium position. Ion I creates an electric field that acts on electrons. Therefore, its displacement will affect other electrons, for example, e 2. Thus, there is an interaction of electrons e 1 and e 2 through the crystal lattice. The electron attracts the ion, but since Z 1> Z 2, the electron, together with the ionic "coat", has a positive charge and attracts the second electron. At T> T c, the thermal motion erodes the ionic "coat". The displacement of the ion is the excitation of the atoms of the lattice, that is, it is nothing more than the production of a phonon. In the reverse transition, a phonon is emitted and absorbed by another electron. This means that the interaction of electrons is an exchange of phonons. As a result, the entire collective of electrons in the solid is bound. At any given moment, the electron is more strongly bound to one of the electrons in this collective, that is, the entire electronic collective, as it were, consists of electron pairs. Within a pair, electrons are bound by a certain energy. Therefore, only those influences that overcome the bond energy can affect this pair. It turns out that ordinary collisions change the energy by a very small amount, and it has no effect on the electron pair. Therefore, electron pairs move in the crystal without collisions, without scattering, that is, the resistance to the current 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 largest magnetic field (approximately 4 0 T) obtained in a solenoid from Pb. Mo 6 O 8. The colossal sensitivity of Josephson junctions to the magnetic field served as the basis for their application 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 working on magnetic levitation - "hovering" over the surface to create high-speed trains on a magnetic suspension. Induction energy storage in the form of a continuous-current circuit and a power transmission line (PTL) without losses through superconducting wires. Magnetohydrodynamic (MHD) generators with superconducting windings. They have an efficiency of conversion of thermal energy into electrical energy of 50%, while in all other power plants it does not exceed 35%.
Defects in crystals are subdivided into:
Zero-dimensional
One-dimensional
Two-dimensional
Point defects (zero-dimensional) - violation of the periodicity at isolated from each other points of the lattice; in all three dimensions, they do not exceed one or more interatomic distances (lattice parameters). Point defects are vacancies, atoms in interstices, atoms in the sites of a "foreign" sublattice, impurity atoms in sites or interstices.
Vacancies- the absence of an atom or ion in a crystal lattice site; Introduced or interstitial atoms or ions can be either intrinsic or impurity atoms or ions that differ from the main atoms in size or valence. Substitution impurities replace the particles of the main substance at the lattice sites.
Linear(one-dimensional) defects - The main linear defects are dislocations. The a priori concept of dislocations was first used in 1934 by Orowan and Teyler 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 of the crystal structure, which are lines, along and near which the correct arrangement of atomic planes characteristic of a crystal is violated.
Surface defects of the crystal lattice. Surface lattice defects include stacking faults and grain boundaries.
Output: 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.
