(1. Rule of phases. 2. Concepts of phase equilibrium diagrams. 3. The rule of segments. 4. State diagramIIIkind)
1. Rule of phases
When the temperature or concentration of components changes, the system (alloy) can be in different states. In the process of transition from one state to another, phase transformations occur in it - new phases appear or existing phases disappear.
The possibility of changing the state of the system, i.e., the number and chemical composition of the phases, is determined by its variance - number of degrees of freedom.
Definition. The number of degrees of freedom of a system is the number of external (temperature, pressure) and internal (concentration) factors that can be changed without changing the number of phases of the system.
Phase rule equation ( Gibbs law) for a system at constant pressure formed by several components has the form
C \u003d K - F + 1, (3.1)
where C is the number of degrees of freedom (variance of the system); K is the number of components; Ф is the number of phases.
Since the number of degrees of freedom is always greater than or equal to zero, i.e. C 0, then the condition is satisfied between the number of components and phases
Ф K + 1, (3.2)
establishing the maximum possible number of equilibrium phases in alloys.
2. Concepts of equilibrium phase diagrams
Phase diagrams of equilibrium ( state diagrams) are used in the study of the structure of alloys, the choice of modes of their heat treatment, etc.
The equilibrium phase diagram shows which phases exist under given conditions (concentration of components and temperature) in equilibrium conditions. The diagram can be used to determine the state of aggregation, the number and chemical composition of the phases, as well as the structural-phase state of the alloy, depending on the temperature and concentration of its constituent components.
The phase equilibrium diagram is a “graph”, on the abscissa of which the concentration of components is plotted (the total content of components in any alloy is 100%), and on the ordinate is the temperature. The extreme points (left and right) on the x-axis of the diagram correspond to the pure components. Any other point on this axis corresponds to a certain concentration of alloy components.
For example, for a two-component alloy (Fig. 3.1), the point A corresponds to pure, i.e. containing 100%, component A, point IN- pure component B, point C - alloy containing 75% A and 25% B, point D - an alloy containing 75% B and 25% A. The concentration axis indicates the change in the content of one of the components (in Fig. 3.1 - component B).
Rice. 3.1 - Coordinates of the phase equilibrium diagram
To construct phase diagrams, alloys of various compositions are examined at different temperatures. The traditional method of constructing diagrams is the method of thermal analysis, which allows obtaining cooling curves of alloys in the coordinates "temperature - time" - cooling curves(alloys).
The alloys are cooled at a very low rate, i.e., under conditions close to equilibrium.
The construction of cooling diagrams is performed in the following sequence:
in the coordinates "temperature - concentration" draw vertical lines corresponding to the alloys of the studied compositions (the smaller the concentration step, the more accurate the diagram);
cooling curves are built for these alloys;
on vertical lines, dots indicate the temperature at which the temperature changes state of aggregation or structure alloys;
points of identical transformations of different alloys are connected by lines that limit the areas of identical states of the system.
We performed such constructions in laboratory work No. 1 when constructing the “zinc-tin” state diagram (“Zn – sn»).
The appearance of the diagram depends on how the components in the solid and liquid states interact with each other.
The simplest diagrams are binary (double or two-component) systems ( multicomponent systems can be reduced to them at fixed values of "redundant" components), the main types of which include state diagrams for alloys, which are in solid state(at normal temperature):
a) mechanical mixtures of pure components (I kind);
b) alloys with unlimited solubility of components (type II);
c) alloys with limited solubility of components (III kind);
d) alloys with the formation of a chemical compound (IV kind).
In the lecture, we will consider the construction of phase equilibrium diagrams using the example of a phase diagram of the third kind - an alloy with limited solubility of components (other types of diagrams are considered in laboratory work).
But first we will discuss what is important for the analysis of such diagrams segment rule(lever).
Introduction
1. Types of phase diagrams
2. Systems of importance in microelectronics
3. Solid solubility
4. Phase transitions
Literature
Introduction
Phase diagrams are an integral part of any discussion of the properties of materials when it comes to the interaction of different materials. Phase diagrams are especially important in microelectronics, because for the manufacture of leads and passivating layers, a large set of different materials must be used there. In the production of integrated circuits, silicon is in close contact with various metals; we will pay special attention to those phase diagrams in which silicon appears as one of the components.
This essay discusses what types of phase diagrams are, the concept of phase transition, solid solubility, the most important systems of substances for microelectronics.
1. Types of phase diagrams
Single-phase state diagrams are graphs that, depending on pressure, volume and temperature, depict the phase state of only one material. It is usually not customary to draw a three-dimensional graph on a two-dimensional plane - they depict its projection onto the temperature-pressure plane. An example of a single-phase state diagram is given in fig. 1.
Rice. 1. Single phase state diagram
The diagram clearly delineates the areas in which the material can exist in only one phase state - as a solid, liquid or gas. Along the demarcated lines, a substance can have two phase states (two phases) in context with each other. Any of the combinations takes place: solid - liquid, solid - vapor, liquid - vapor. At the point of intersection of the lines of the diagram, the so-called triple point, all three phases can exist simultaneously. Moreover, this is possible at a single temperature, so the triple point serves as a good temperature reference point. Typically, the reference point is the triple point of water (for example, in precision measurements using thermocouples, where the reference junction is in contact with the ice-water-steam system).
The dual phase diagram (dual system state diagram) represents the state of a system with two components. In such diagrams, the temperature is plotted along the ordinate axis, and the percentage of the mixture components is plotted along the abscissa axis (usually it is either a percentage of the total mass (wt.%), or a percentage of the total number of atoms (at.%)). The pressure is usually assumed to be 1 atm. If liquid and solid phases are considered, the volume measurement is neglected. On fig. 2. shows a typical two-phase state diagram for components A and B using weight or atomic percent.
Rice. 2. Two-phase state diagram
The letter denotes the phase of substance A with solute B, denotes the phase of substance B with substance A dissolved in it, and + denotes a mixture of these phases. The letter (from liquid - liquid) means the liquid phase, and L+ and L+ mean the liquid phase plus phase or respectively. Lines separating phases, i.e. lines on which different phases of a substance can exist, have the following names: solidus - a line on which phases or simultaneously exist with phases L + and L + , respectively; solvus is a line on which phases and + or and + simultaneously coexist, and liquidus is a line on which phase L and phase L+ or L+ simultaneously exist.
The intersection point of two liquidus lines is often the lowest melting point for all possible combinations of substances A and B and is called the eutectic point. A mixture with a ratio of components at the eutectic point is called a eutectic mixture (or simply a eutectic).
Let us consider how the transition of a mixture from a liquid state (melt) to a solid one occurs and how the phase diagram helps to predict the equilibrium composition of all phases existing at a given temperature. Let's turn to Fig. 3.
Rice. 3. Two-phase state diagram showing curing processes
Let us assume that at the beginning the mixture had the composition C M at the temperature T 1 , at the temperature from T 1 to T 2 there is a liquid phase, and at the temperature T 2 the phases L and simultaneously exist. The composition of the L phase present is C M, the composition of the phase is C 1 . With a further decrease in temperature to T 3, the composition of the liquid changes along the liquidus curve, and the composition of the phase changes along the solidus curve until it intersects with the isotherm (horizontal line) T 3 . Now the composition of the phase L is C L , and the composition of the phase is C 2 . It should be noted that the composition C 2 must have not only the substance that has passed into the phase at at the temperature T 3 , but also all the substance that has passed into the phase at a higher temperature must have the composition C 2 . This alignment of compositions must occur by solid-state diffusion of component A into the existing phase , so that by the time the temperature T 3 is reached, all the substance in the phase will have the composition C 2 . A further decrease in temperature brings us to the eutectic point. In it, the phases and exist simultaneously with the liquid phase. At lower temperatures, only the and phases exist. A mixture of phases and of composition C E with aggregates with initial composition C 3 is formed. Then, keeping this mixture for a long time at a temperature below the eutectic, you can get a solid. The resulting solid body will consist of two phases. The composition of each of the phases can be determined at the point of intersection of the isotherm with the corresponding solvus line.
It has just been shown how to determine the composition of each of the phases present. Now consider the problem of determining the amount of substance in each phase. To avoid confusion, in Fig. 4. Once again a simple two-phase diagram is shown. Suppose that at temperature T 1 the composition of the melt is C M (meaning component B), then at T 2 phase L has composition CL, and phase will have composition C s . Let M L be the mass of a substance in the solid state, and M S be the mass of the substance in the solid state. The condition of conservation of the total mass leads to the following equation
(M L + M S)C M = M L C L + M S C S .
Rice. 4. Level rule
It reflects the fact that the total mass of a substance at a temperature T 1, multiplied by the percentage B, is the total mass of a substance B. It is equal to the sum of the masses of a substance B that exists in liquid and solid phases at a temperature T 2 . Solving this equation, we get
. (1)
This expression is known as the "level rule". Using this rule, knowing the initial composition of the melt and its total mass, it is possible to determine the masses of both phases and the amount of substance B in any phase for any part of the two-phase diagram. In the same way, one can calculate
On fig. 5. shows another example of melt solidification. Decrease in temperature from T 1 to T 2 leads to mixing of phases L and with the composition C M and C , respectively. With further cooling, the composition L changes along the liquidus, and the composition - along the solidus, as described earlier. When the temperature T 3 is reached, the composition will become equal to C M, and, as follows from the level rule, at a temperature lower than T 3, the liquid phase cannot exist. At a temperature lower than T 4 , the phases and exist as aggregates of the phases and . For example, at a temperature T 5 the aggregates of the phase will have a composition determined by the intersection of the T 5 isotherm and the solvus . The composition is determined similarly - by the intersection of the isotherm and the solvus .
Rice. 5. Two-phase diagram and solidification process amount of substance A present in any of the phases
The regions of the two-phase diagram, hitherto called and , are regions of solid solubility: A and B are dissolved in the region . The maximum amount of A that can be dissolved in B at a given temperature depends on the temperature. At or above the eutectic temperature, rapid fusion of A and B can take place. If the resulting alloy is cooled rapidly, then the A atoms can be "trapped" in the B lattice. But if the solid solubility at room temperature is much lower (this indicates that that at this temperature the considered approach is not very suitable), then strong stresses can arise in the alloy, which significantly affect its properties (in the presence of significant stresses, supersaturated solid solutions arise, and the system is not in an equilibrium state, and the diagram provides information only about equilibrium states ). Sometimes, such an effect is desirable, for example, when hardening steel by hardening to obtain martensite. But in microelectronics, its result will be devastating. Therefore, doping, i.e., adding additives to silicon before diffusion, is carried out at elevated temperatures in such a way as to prevent damage to the surface due to excessive alloying. If the amount of the dopant in the substrate is higher than the solid solubility limit at any temperature, then a second phase appears and the deformation associated with it.
2. Systems of substances that are important in microelectronics
There are a number of materials that are completely soluble in each other. An example is a system of two such important substances for microelectronics as silicon and germanium. The silicon-germanium system is shown in fig. 6.
Rice. 6. System silicon - germanium
The diagram does not have a eutectic point. Such a diagram is called isomorphic. For two elements to be isomorphic, they must obey the Hume-Rothery rules, i.e. have a difference in the values of atomic radii by no more than 15%, the same probability, the same crystal lattice and, in addition, approximately the same electronegativity (the electronegativity of an atom is its inherent family to attract or capture extra electrons, with covalent bonds). The Cu-Ni, Au-Pt, and Ag-Pd systems are also isomorphic.
The Pb–Sn system serves as a good example of a simple binary system with significant, albeit limited, solid solubility. The phase diagram of the states of this system is shown in fig. 7. The point of intersection of solidus and solvus is called the boundary solubility, the value of the boundary solubility of both tin in lead and lead in tin will be large. This system is important for microelectronics due to the widespread use of tin-lead solders. Their two-phase diagram of this system shows how changing the composition of the alloy changes its melting point. When several consecutive solderings are required during the manufacture of a microcircuit, a solder with a lower melting point is used for each subsequent soldering. This is done so that the solderings made earlier do not flow.
Rice. 7. Phase diagram of the states of the lead-tin system
For the production of microcircuits, the properties of the Au-Si system are also important, since the eutectic temperature of this system is extremely low compared to the melting points of pure gold or pure silicon (Fig. 9). The solubilities of gold in silicon and silicon in gold are too small to be displayed in a conventional phase diagram. Due to the low eutectic temperature, it is advantageous to install chips on gold substrates, holders or boards with gold pads, using the Au-Si eutectic reaction as the main welding (or soldering) mechanism. For soldering silicon crystals, gold containing a few percent germanium is also used.
Combinations of elements that form chemical compounds have more complex state diagrams. They can be broken down into two (or more) simpler diagrams, each referring to a specific pair of connections, or a connection and elements. For example, AuAl 2 is formed when 33% (atomic percentage) of gold is combined with aluminum at a temperature of less than 1060 ° (Fig. 2.10). To the left of this line, AuAl 2 and a pure aluminum phase coexist. Compounds like AuAl 2 are called intermetallic and are formed at the appropriate stoichiometric ratio of the two elements. Intermetallic compounds are characterized by a high melting point, a complex crystal structure, and, in addition, are hard and brittle.
The phase diagram of states Au - Al can be divided into two or more diagrams, for example, an Al - AuAl 2 diagram and an AuAl 2 - Au diagram.
Rice. 8. Aluminum-silicon system
Diagram of the Au–Al system shown in fig. 2.10 is extremely important in microelectronics, since gold wires are usually connected to an aluminum metallization layer located on top of silicon. Several important intermetallic compounds are listed here: AuAl 2 , Au 2 Al, Au 5 Al 2 and Au 4 Al. All of them can be present in conductors of Au-Al bonds.
Rice. 9. Gold-silicon system
Rice. 10. Gold - aluminum system
3. Solid solubility
The limiting solubility of most dopants in silicon is extremely low and is not really the maximum solubility. On fig. 11 shows a typical solidus curve for a silicon-free impurity. Note that the solubility increases with temperature up to a certain value, and then decreases to zero at the melting temperature of silicon. Such a curve is called a retrograde solubility curve. An improved version of this diagram in the vicinity of the melting point of silicon is shown in Fig. 12.
Rice. 11 Retrograde solubility of silicon
Rice. 12 Typical silicon phase diagram
If the composition of the silicon melt is equal to C M in percent of the solute mass, then the silicon will solidify with a solute content of kC M , where k is the segregation coefficient (k=C S /C L). When the concentration in the solid reaches the value of C M at freezing, the concentration in the liquid solution will be equal to C M /k, since the ratio of the concentrations in the liquid and solid screens must be equal to k. The slope of the solidus line is therefore
,
and the liquidus slope is
.
The ratio of the liquidus and solidus slopes turns out to be equal to the segregation coefficient
. (2)
4. Phase transitions
Transitions from one phase state to another when the system parameters change.
Phase transitions of the first kind (evaporation, condensation, melting, crystallization, transitions from one crystal modification to another).
The crystalline state of substances is classified according to seven syngonies (triclinic, monoclinic, rhombic, tetragonal, trigonal or rhombus ...., hexagonal, cubic), while the arrangement of atoms in these syngonies is characterized by 14 types of lattices (Bravais lattice). The degree of packing of atoms in these lattices is different:
Simple cubic f = 0.52
Volume centered cubic f = 0.68
FCC f = 0.74
Hexagonal close packing f = 0.74
A very important conclusion follows from these data: during polymorphic transformations (a change in the type of crystal lattice), there is a change in volume and, consequently, in the physicochemical properties of materials.
In transitions of the first kind, two phases coexist at the transition point.
A B
a) the transition is carried out at a certain temperature T per
b) during the transition, the first derivatives of energy change abruptly: enthalpy, entropy, volume (hence, density)
Phase transitions of the second kind
During transitions of the second kind, the first derivatives of the free energy, enthalpy, entropy, volume, and density change monotonically.
Barium titanate – cubic structure –> tetragonal typical piezoelectric.
MnO is an antiferromagnet at 117 K goes into the paramagnetic phase.
1. According to the classification of phase transformations proposed in 1933 by Eripresit, transformations are subdivided into transformations (transitions) of the first and second kind.
Transitions of the first kind are characterized by the fact that the first derivatives of the thermodynamic potential with respect to temperature and pressure change stepwise
here S is entropy, V is volume
Since the thermodynamic potential during the phase transition changes continuously is determined by the expression
then the energy U must also change abruptly. Because
then the heat of transition
is equal to the product of temperature and the difference in the entropy of the phases, i.e., an abrupt change or absorption of heat.
The continuous change of the thermodynamic potential is important. The functions (Т) and (Т) do not change the features near the phase transition point, while there are minima of the thermodynamic potential on both sides of the phase transition point.
This feature explains the possibility of overheating or supercooling of the phases in the case of phase transitions in the system.
Let us determine the relationship between the jumps of the thermodynamic functions and . After differentiation with respect to temperature, the relation Function (Р, Т) = (Р, Т), taking into account the expression for S, V and q, we obtain
This is the well-known Clausis formula. It allows you to determine the change in pressure of phases in equilibrium with a change in temperature or a change in the transition temperature between two phases with a change in pressure. An abrupt change in volume leads to the absence of a definite connection between the structure and the system of phases that are transformed during a first-order phase transition, which therefore change abruptly.
Typical for phase transitions of the first kind are transitions between aggregate states of matter, allotropic transformations, and many phase transformations in multicomponent materials.
The fundamental difference between second-order phase transitions and first-order phase transitions is as follows: second-order transitions are characterized by both the continuity of the change in the thermodynamic potential and the continuity of the change in the derivatives of the thermodynamic potential.
Chemical equilibrium
Thermodynamic function - a state function that determines the change in thermodynamic potentials with a change in the number of particles in the system. In other words, there is a function that determines the direction and limit of the spontaneous transition of a component from one phase to another under appropriate transformations and conditions (T, P, V, S, n i).
Thermodynamic potentials are related to each other by the following relationships
Amount of substance in grams; - the amount of substance in moles;
M is the molecular weight of the corresponding substance.
For the theory of solid solutions, on which all microelectronic devices operate, the method of chemical potentials developed by Gibbs is of great importance. Chemical equilibrium can be determined using chemical potentials.
The chemical potential is characterized by the energy per 1 atom
Chemical potential; G is the Gibbs energy;
N o - Avogadro's number, N A - L \u003d mol -1
i.e. (P, T) = (P, T)
Both curves characterize a monotonic decrease with temperature, determining the value of the phase entropy
Phase diagrams are an integral part of the discussion of material properties when it comes to the interaction of different materials.
Single-phase state diagrams depict the phase state of only one material.
The dual phase diagram (dual system state diagram) represents the state of a system with two components.
Combinations of elements that form chemical compounds have more complex state diagrams.
Literature
1. Ormont BF Introduction to physical chemistry and crystal chemistry of semiconductors. - M .: Higher school, 1973.
2. Physical metallurgy / Edited by Kahn R., vol. 2. Phase transformations. Metallography. – M.: Mir, 1968.
3. Yu.M. Tairov, V.F. Tsvetkov "Technology of semiconductor and dielectric materials", - M .: Higher school, 1990.
4. "Workshop on semiconductors and semiconductor devices", /Ed. Shalimova K.V. - M .: Higher school, 1968.
Consider P− T− X diagrams for binary systems. Intensive study work P− T− X state diagrams have shown that the use of high pressures (tens and hundreds of thousands of atmospheres) in some cases leads to a change in the type of state diagram, to a sharp change in the temperatures of phase and polymorphic transformations, to the appearance of new phases that are absent in a given system at atmospheric pressure. So, for example, a diagram with unlimited solubility in the solid state at high temperatures and the decomposition of a solid solution α into two solid solutions α1 + α2 at low temperatures can gradually turn into a diagram with a eutectic with increasing pressure (see Fig. 4.18, A). On fig. 4.18, b shows the phase diagram of the Ga–P system in which the GaP semiconductor compound is formed. Depending on the pressure, this compound may melt congruently or incongruently. Accordingly, the appearance of the double diagram also changes. T− X on various isobaric sections triple P− T− X diagrams.
In practice, volume P− T− X charts are very rare. Usually phase transformations in three-dimensional P− T− X ana charts
Rice. 4.18. A- P− T− X diagram; b- P− T− X state diagram
Ga–P systems with congruently and incongruently melting GaP compound in
pressure dependent.
lyse using their projections on the plane P− T, T− X And P− X, as well as various sections at constant values of temperature or pressure (see Fig. 4.18, A).
Note that when analyzing phase transformations in a system, one should distinguish between P− T− X phase diagrams in which the dissociation pressure P dis9 little and P in the phase diagram is the external pressure and in which the dissociation pressure is high and P- This P dis. In systems whose components have a low dissociation pressure and in which the maximum melting point of the mixture is below the lowest boiling point (there are no volatile components in the system), the role of the gas phase in phase transformations can be neglected. If the dissociation pressure of any of the components is high (the system contains highly volatile components), then the composition of the gas phase must be taken into account at temperatures both above and below the liquidus.
Let us consider in more detail the phase diagrams P dis − T− X high
dissociation pressure (phase diagrams with volatile components). It should be noted that attention to them has increased due to the increased role of compounds containing volatile components in semiconductor electronics. For example, these include IIIBV compounds containing volatile components of phosphorus and arsenic, AIIBVI compounds containing mercury, AIVBVI containing sulfur, etc.
All semiconductor compounds have a more or less extended region of homogeneity, that is, they are able to dissolve in themselves
9 P dis - equilibrium pressure for the given conditions of dissociation of all phases in equilibrium. If there is one volatile component in the system P dis is the equilibrium dissociation pressure of the highly volatile component of the system.
any of the components in excess of the stoichiometric composition, or a third component.
Any deviation from the stoichiometric composition affects the electrical properties (see Chap. 3). Therefore, in order to reproducibly obtain crystals containing a volatile component with desired properties, it is also necessary to reproducibly obtain compounds of a given composition.
However, the volatility of one of the components of the compound leads to a deviation from the stoichiometric composition due to the formation of vacancies - anionic or cationic - depending on which component's dissociation pressure is higher, and, accordingly, an excess of the other component. As already discussed in Chap. 3, vacancies in a number of compounds can create acceptor or donor levels, thereby affecting the physical properties.
The energy of formation of vacancies in positions A and B is practically never the same; therefore, the concentration of anionic and cationic vacancies is also different, and the homogeneity region of the compound turns out to be asymmetric with respect to the stoichiometric composition. Correspondingly, for practically all compounds, the maximum melting temperature does not correspond to an alloy of stoichiometric composition.10
A change in the composition of a compound due to volatility can be prevented by growing it from a melt or solution at an external pressure of the volatile component equal to the dissociation pressure at the growth temperature. This condition is chosen using P dis − T– X diagrams.
The dissociation pressure of a highly volatile component in alloys strongly depends on its composition, usually decreasing with a decrease in the concentration of this component, as, for example, for the In–As system (the dissociation pressure of arsenic decreases by almost four orders of magnitude with a decrease in the concentration of arsenic in the range from 100 to 20 % ). As a result, the dissociation pressure of the volatile component in the compound is much less than the dissociation pressure over the pure component at the same temperature.
This circumstance is used in the two-temperature scheme for obtaining this compound. Two temperature zones are created in one furnace.
10However, for compounds, in particular AIII BV , with a narrow region of homogeneity and most compounds, in particular AIV BVI , with an average width of the region of homogeneity, the concept of congruently melting compounds is used, since the deviations of the actual melting point of a compound from the melting point of a stoichiometric compound are insignificant .
Rice. 4.19. P dis − T section P dis − T− X state diagrams of the Pb–S system. 1 -
three-phase line; 2 - PS 2 pure sulfur over PbS+S2; 3 - PS 2 over PbS+Pb.
One has a temperature T 1 equal to the crystallization temperature of the compound. Here is placed the container with the melt. In the second zone, the pure volatile component of the compound, As, is placed. Temperature T 2 in the second zone is maintained equal to the temperature at which the dissociation pressure of the volatile component in its pure form is equal to the dissociation pressure of this component in the compound at a temperature T 1. As a result, in the first zone, the vapor pressure of the volatile component above the compound is equal to its partial dissociation pressure in the compound, which prevents the volatilization of this component from the melt and ensures the crystallization of the compound of a given composition.
On fig. 4.19 is given P− T projection of the Pb–S phase diagram.
The solid line shows the line of three-phase equilibrium of the solid, liquid, and gaseous phases, which limits the region of stability of the solid compound; dotted line - isoconcentration lines within the region of homogeneity. Isoconcentration lines show compositions with an equal deviation from stoichiometry (same compositions) towards an excess of lead (conductivity n-type) or in the direction of excess sulfur (conductivity p-type), equilibrium at given values of temperature and sulfur vapor pressure. Line n= p corresponds to temperature and pressure values PS 2 , at which the solid phase has a strictly stoichiometric composition. It crosses the three-phase line at a temperature which is the melting point of the stoichiometric compound. or towards excess sulfur (conductivity p-type).
As can be seen from fig. 4.19, the melting point of a compound of stoichiometric composition is below the maximum melting point that an alloy with an excess of lead has compared to the formula composition. One can see a sharp dependence of the crystal composition on the partial vapor pressure of the volatile component. At high temperatures, all curves corresponding to different compositions approach the line n= p. As the temperature decreases, the difference between the equilibrium pressures corresponding to different compositions increases. This explains the difficulty of obtaining an alloy of a given composition directly during crystallization, which takes place at high temperatures. Since the partial pressure curves for different compositions are close, small random deviations in the vapor pressure of the volatile component can lead to a noticeable change in the composition of the solid phase.
If the crystal after growth is subjected to prolonged annealing at lower temperatures and such a pressure that the isoconcentration lines for different compositions diverge sharply, then the composition of the crystal can be brought to the specified value. This is often used in practice.
) — graphic representation of the states of a thermodynamic system in the space of the main state parameters - temperature T, pressure p and composition x.
Description
Phase diagrams make it possible to find out which phases (i.e., homogeneous subsystems that differ in structure and / or properties from others) can be present in a given system under given conditions and composition. For complex systems consisting of many phases and components, the construction of phase diagrams from experimental data and thermodynamic simulation data is the most important way to predict the behavior during various processes. An analysis of the relative position of the fields, the surfaces and lines separating them, as well as the junction points of the latter, makes it possible to unambiguously and clearly determine the conditions for phase equilibria, the appearance of new phases and chemical compounds in the system, the formation and decomposition of liquid and solid solutions, etc.
State diagrams are used in materials science, metallurgy, oil refining, chemical technology (in particular, in the development of methods for separating substances), the production of electronic equipment and microelectronics, etc. With their help, the conditions for the industrial synthesis of substances are selected, the direction of the processes associated with phase transitions is determined, and selection of heat treatment modes, search for optimal phase compositions, etc.
Phase diagrams of one-component systems are depicted on a plane in coordinates p–T. They contain fields corresponding to the existence of one or another phase of the substance (gaseous, liquid, various solid modifications), separated by lines of phase equilibrium, along which the coexistence of adjacent phases is possible. The places where three different lines of phase equilibrium converge form the so-called triple points, in which three phases can coexist. This is the maximum number of phases that can coexist in equilibrium in one-component systems.
The number of phases present at a given point in the phase diagram is determined by the Gibbs phase rule and is n + 2 – f, Where n- the number of components, i.e. those substances, the amount of which in the system can change independently of the others, the number 2 corresponds to pressure and temperature (thus, n+ 2 is the number of parameters specifying the state of the system, and f- the number of degrees of freedom, i.e. the number of those generalized forces (pressure, temperature, chemical potentials of the components) that can be independently varied within certain limits without changing the equilibrium phase composition.
For example, inside the fields of a one-component phase diagram, where there is a single phase, pressure and temperature can be independently varied, and the triple point is the so-called invariant equilibrium point.
In addition, metastable phases can be depicted on the phase diagram of a single-component system, i.e., phases that are not equilibrium, but capable of existing in a certain range of parameters for a long time due to kinetic stability, as well as a critical point - a point on the liquid–gas equilibrium line , after which the abrupt difference in the properties of these phases disappears, and the concept of a phase transition loses its meaning.
In addition to temperature and pressure, other parameters of the state of the system can be considered, for example, the magnetic field strength ( H). Then the phase diagram becomes multidimensional and its various sections are considered, for example H–T, and in the phase rule, the number 2 changes to the corresponding number of generalized forces (fields).
Phase diagrams of multicomponent systems are also multidimensional. It is convenient to study their plane sections, such as temperature-composition and pressure-composition. For isobaric-isothermal sections of phase diagrams of three-component systems, which describe the dependence of the phase composition of the system only on its component composition, the so-called Gibbs triangles are used.
The general provisions discussed above are also applicable to multicomponent phase diagrams. An example of isobaric ( T–x) of the cross sections of the two-component phase diagram is shown in fig. The fields of such diagrams can correspond to one or two coexisting phases, including the melt of components, solid phases of pure components or their compounds of intermediate composition, phases of solid solutions.
The phase ratio in the field corresponding to two phases is determined according to the lever rule - it is inversely proportional to the ratio of the horizontal distances to the phase equilibrium lines limiting the field, and the coordinates of the intersection of the horizontal with these lines determine the component composition of the coexisting phases.
Among the important elements T–x the cross sections of two-component diagrams, the liquidus line should be mentioned, above which only the liquid phase is present; solidus line, below which only the solid phase is present, eutectic points (points of congruent melting), common to solidus and liquidus (at the break of the latter), and peritectic points (points of incongruent melting, i.e. melting with partial decomposition of the solid phase) on the curve liquidus, in which a liquid phase and two solid phases can coexist, as well as the corresponding horizontal lines of eutectic and peritectic transformations.
For phases consisting of nanosized particles, there may be a dependence of physical properties on size; therefore, the phase diagram is sometimes filled with a dispersion scale.
Illustrations
Authors
- Goldt Ilya Valerievich
- Ioffe Ilya Naftolyevich
Sources
- Anosov V. Ya., Pogodin S. A. Basic principles of physical and chemical analysis. - M.–L.: Publishing House of the Academy of Sciences of the USSR, 1947. - 876 p.
- Chemical encyclopedia. - M.: Soviet Encyclopedia, 1988.
A phase is a thermodynamic equilibrium state of a substance that differs in physical properties from other possible equilibrium states of the same substance. The transition of a substance from one phase to another - a phase transition - is always associated with qualitative changes in the properties of the body. An example of phase transitions can serve as changes in the state of aggregation. But the concept of "phase transition" is wider, because it also includes the transition of a substance from one modification to another while maintaining the state of aggregation (polymorphism), for example, the transformation of diamond into graphite.
There are two types of phase transitions:
Phase transition of the 1st kind - is accompanied by the absorption or release of heat, a change in volume and proceeds at a constant temperature. Examples: melting, crystallization, evaporation, sublimation (sublimation), etc.
Phase transitions of the 2nd kind - proceed without the release or absorption of heat, while maintaining the value of the volume, but with an abrupt change in heat capacity. Examples: the transition of ferromagnetic minerals at certain pressures and temperatures to a paramagnetic state (iron, nickel); the transition of some metals and alloys at a temperature close to 0 0 K into the superconducting state (ρ = 0 Ohm∙m), etc.
For a chemically homogeneous substance, the concept of a phase coincides with the concept of an aggregate state. Let us consider phase transformations for such a system, using the state diagram for clarity. On it, in the coordinates p and T, the dependence between the temperatures of phase transitions and pressure is set. These dependences in the form of curves of evaporation (EI), melting (OP) and sublimation (OS) form the state diagram.
The intersection point O of the curves determines the conditions (T and p values) under which all three aggregate states of a substance are in thermodynamic equilibrium.
For this reason it is called the triple point. For example, the triple point of water is one of the reference points of the Celsius temperature scale (0 0 C). As follows from the Clausius-Clapeyron equation, the nature of the T = f (p) dependence for the solid-liquid transition (OP curves) can be different: the course of this dependence is shown in Fig. 2a. For substances that reduce the volume upon transition to the liquid phase, the dependence has the form shown in Fig. 2b.
The evaporation curve ends with a critical point - TO. As can be seen from the diagram, there is the possibility of a continuous transition of the liquid into the gaseous phase without crossing the evaporation curve, i.e. without the phase transformations inherent in such a transition.
At a pressure less than p tr.tchk. , the substance can exist only in two phases: solid and gaseous. Moreover, at temperatures below T tr.tchk. , a transition from a solid state to a gas is possible, bypassing the liquid phase. This process is called sublimation or sublimation. Specific heat of sublimation
τ sub \u003d λ pl + r use
SOLID BODIES.
A solid is a state of aggregation of a substance, which is characterized by the presence of significant forces of intermolecular interaction, stability of shape and volume. The thermal motion of particles of a solid body is a small-amplitude fluctuations around the equilibrium positions. There are crystalline and amorphous structures of solids.
A characteristic feature of the microstructure of crystals is the spatial periodicity of their internal electric fields and the repeatability in the arrangement of crystal-forming particles - atoms, ions and molecules (long-range order). Particles alternate in a certain order along straight lines, which are called nodal. In any flat section of a crystal, two intersecting systems of such lines form a set of absolutely identical parallelograms, which tightly, without gaps, cover the section plane. In space, the intersection of three non-coplanar systems of such lines forms a spatial grid that divides the crystal into a set of completely identical parallelepipeds. The points of intersection of the lines forming the crystal lattice are called nodes. Distances between nodes along some direction are called translations or lattice periods. A parallelepiped built on three non-coplanar translations is called an elementary cell or lattice repeatability parallelepiped. The most important geometric property of crystal lattices is the symmetry in the arrangement of particles with respect to certain directions and planes. For this reason, although there are several ways to choose a unit cell for a given crystal structure, choose it so that it corresponds to the symmetry of the lattice.
There are two signs by which crystals are classified: a) crystallographic - according to the geometry of the crystal lattice and b) physical - according to the nature of the interaction of particles located at the nodes of the crystal lattice and their nature.
The geometry of crystal lattices and their elementary cells is determined by the number of symmetry elements used in the construction of this lattice. The number of possible types of symmetry is limited. Russian crystallographer E.S. Fedorov (1853 - 1919) showed that there are only 230 possible combinations of symmetry elements, which, through parallel translation, reflection and rotation, provide a dense, i.e. without gaps and slots packing elementary cells in space. Bravais showed that there are only 14 types of lattices, which differ in the form of translational symmetry. There are primitive (simple), base-centered, volume-centered and face-centered Bravais lattices. According to the shape of the cell, depending on the angles between its faces α, β and γ and the ratio between the length of the ribs a, b And With these 14 types of lattices form seven crystal systems (sygonies): cubic, hexagonal, tetragonal, trigonal or rhombohedral, rhombic, monoclinic and trigonal.
According to the nature of the interaction of particles located at the nodes of the crystal lattice and their nature, crystals are divided into four types: ionic, atomic, metallic and molecular.
Ionic - at the nodes of the crystal lattice there are ions of opposite signs; the interaction is due to electrostatic forces of attraction (ionic or heteropolar bond).
Atomic - neutral atoms are located at the nodes of the crystal lattice, held at the nodes by homeopolar, or covalent bonds.
Metallic - positive metal ions are located at the nodes of the crystal lattice; free electrons form the so-called electron gas, which ensures the bonding of ions.
Molecular - neutral molecules are located at the nodes of the crystal lattice, the forces of interaction between which are due to a slight displacement of the electron cloud of the atom (polarization or van der Waals forces).
Crystalline bodies can be divided into two groups: single crystals and polycrystals. For single crystals, a single crystal lattice is observed in the volume of the entire body. And although the external shape of single crystals of the same type may be different, the angles between the corresponding faces will always be the same. A characteristic feature of single crystals is the anisotropy of mechanical, thermal, electrical, optical, and other properties.
Single crystals are often found in the natural state in nature. For example, most minerals are crystal, emeralds, rubies. At present, for industrial purposes, many single crystals are grown artificially from solutions and melts - rubies, germanium, silicon, gallium arsenide.
One and the same chemical element can form several crystal structures that differ in geometry. This phenomenon is called polymorphism. For example, carbon is graphite and diamond; ice five modifications, etc.
The correct external faceting and anisotropy of properties, as a rule, do not appear for crystalline bodies. This is because crystalline solids usually consist of many randomly oriented small crystals. Such solids are called polycrystalline. This is due to the mechanism of crystallization: when the conditions necessary for this process are reached, crystallization centers simultaneously appear in many places of the initial phase. The nucleated crystals are located and oriented with respect to each other completely randomly. For this reason, at the end of the process, we get a solid body in the form of a conglomerate of intergrown small crystals - crystallites.
DEFECTS IN CRYSTALS.
Real crystals have a number of violations of the ideal structure, which are called crystal defects:
a) point defects
Schottky defects (nodes not occupied by particles);
Frenkel defects (displacement of particles from nodes to interstitials);
impurities (implanted foreign atoms);
b) linear - dislocations edge and screw local violations in the regularity of the arrangement of particles, due to the incompleteness of individual atomic planes, or in the sequence of their building;
c) planar - boundaries between mirrors, rows of linear dislocations.
AMORPHOUS SOLID BODIES.
Amorphous solids in many of their properties and mainly in microstructure should be considered as highly supercooled liquids with a very high viscosity coefficient. From an energetic point of view, the difference between crystalline and amorphous solids is clearly seen in the process of solidification and melting. Crystalline bodies have a melting point - the temperature when a substance stably exists in two phases - solid and liquid (Fig. 1). The transition of a solid molecule into a liquid means that it acquires an additional three degrees of freedom of translational motion. That. unit mass of a substance at T pl. in the liquid phase has a greater internal energy than the same mass in the solid phase. In addition, the distance between particles changes. Therefore, in general, the amount of heat required to convert a unit mass of a crystal into a liquid will be:
λ \u003d (U W -U k) + P (V W -V k),
where λ is the specific heat of melting (crystallization), (U f -U k) is the difference between the internal energies of the liquid and crystalline phases, P is the external pressure, (V f -V k) is the difference in specific volumes. According to the Klaiperon-Clausius equation, the melting point depends on pressure:
.
It can be seen that if (V W -V k)> 0, then 
> 0, i.e. with increasing pressure, the melting point rises. If the volume of the substance decreases during melting (V W -V k)<
0 (вода, висмут), то рост давления приводит
к понижению Т пл.
Amorphous bodies have no heat of fusion. Heating leads to a gradual increase in the rate of thermal motion and a decrease in viscosity. There is an inflection point on the process graph, which is conventionally called the softening point.
