Вопросы:

1. Что такое дефекты кристаллической решетки?

2. Что такое твердые растворы и каковы условия образования твердых растворов замещения и внедре­ния?

3. Охарактеризуйте дефекты по Я.И.Френкелю и В. Шоттки и почему дефекты по Шоттки и Френкелю относятся к термодинамически равновесным дефектам, в чем причина их образования и какие факторы оказы­вают влияние на их концентрацию в кристаллической решетке?

4. Назовите виды линейных дефектов.

5. Что является структурным признаком наличия в кристаллической ре­шетке краевой и винтовой дислокации и их качественной и количественной харак­теристикой?

6. Опишите причины образования и свойства дислокаций, методы опреде­ления их плотности и приведите значения этой плотности в совершенных и де­формированных кристаллах.

Lecture № 5.

Theme: Defects in the crystal lattice. Classification of defects. Pointlike atomic defects in ionic crystals. Defects by Ya.I. Fraenkel and V.Shottki. Solid solutions. Linear defects (dislocations).

1. Defects of a crystal lattice.

2. Firm solutions.

3. Defects by Ya.I. Frenkel and V.Shottki.

4. Linear defects (dislocation).

Defects - distortion or infringement.

Firm solutions - homogeneous crystal phases of variable structure.

DEFECTS of a CRYSTAL LATTICE

In a lattice of an ideal crystal atoms (ions) settle down in space strictly is ordered and naturally, and электроны should be at levels with the minimal energy. In real crystals there are various distortions or infringements of this ideal arrangement of particles, which usually name by defects of a crystal lattice.

The nature of defects can be various and reaches from microlevel (electronic, nuclear) up to defects in microvolumes of substance. Depending on the size of that area disorder (area of distortions of a lattice), which is borrowed (occupied) by(with) those or other defects, they can be classified to an only geometrical attribute - "dimensions" of defect ("dimension" - number of measurements, on which the defect has macroscopic extent). On this classification the defects of a crystal lattice divide (share) on zero-dementional (dot), one, two and three-dimensional. Zero-dementional defects as a first approximation borrow (occupy) in a crystal area of distortions, commensurable on all directions with the size of atom or electron. The one-dimensional defects have extent considerably superior the size of atoms in any one direction (in other directions they zero-dementional), two demensions- in two and three-dimensional - in three directions.

Zero and the one-dimensional defects concern to microdefects or to defects of thin structure of a crystal. Zero-dementional the defects can be divided (shared) on electronic and nuclear. To electronic defects belong superfluous electrons, hole and exitons. To atomic zero-dementional to defects (fig. 9) the vacancies, impurity atoms replacing own atoms of substance in their regular rule (in lattice site), and own or impurity atoms which are taking place (displaced by) in irregular position irregular a rule(situation) in interstitial site of a lattice (of a particle, taking place in interstitial site, sometimes name interstitial site or interstitial). To one-dimensional nuclear defects concern regional and screw dislocation.

Two and the three-dimensional defects belong to macrodefects or defects of rough structure. Examples two demensions of defects are so-called mosaic structure of crystals, border of grains, the defects of packing, three-dimensional -pore, crack in a crystal, inclusion in him(it) of other phase and other infringements of integrity of a crystal.

Fig. 9. Types nuclear нульмерных of defects:

1- vacancies; 2 - impurity atom in unit of a lattice; 3 - impurity atom in interstice

The large meaning (importance), which is given to study of defects of a crystal lattice in physics of a firm body, is caused by their huge influence on properties of crystal substances. Besides the defects render often decisive influence on such processes, as growth of crystals, mass transport (diffussion) in firm bodies determining kinetics such important in technology silicates and other refractory not metal materials of processes, as powder (solid) phase of reaction, sintering, recrystallization and e. c.

As it was already marked, to nuclear zero measure or dot defects the vacancies, impurity atoms in regular units concern lattices and impurity atoms, dislocated in interstice. These the types of defects basically can meet in a lattice of crystals separately, but more often they are present at a combination with each other. Depending on it distinguish the following types nuclear zero measure of defects: firm solutions (switching defect nonstoichiometry), defects on Schottky and defects on Fraenkel

Firm solutions

By firm solutions the homogeneous crystal phases of variable structure name.

The firm solutions of the certain structure represent one crystal phase, which structure in the certain limits (in so-called area homogenicity) can change without occurrence of new phases. Distinguish some types of firm solutions (fig. 10). Two types firm solutions of replacement (firm solutions I of a sort) and firm solutions of introduction (firm solutions II of a sort) are formed at introduction in a lattice ("dissolution" in a lattice) any of crystal connection of atoms or ions of other connection. And at education of firm solutions of replacement the "own" atoms of the basic substance (matrix) are replaced on taking root atoms, and at education of firm solutions of introduction these atoms settle down in interstice of a lattice of matrix substance. The third type of firm solutions is not connected to introduction in a lattice of extraneous atoms or ions, and is caused by a deviation (rejection) in the certain limits of structure of the given connection from it(him) stoichiometric of structure. Such firm solutions are called as defects nonstoichiometry (for some of them sometimes use the name firm solutions of subtraction).

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Fig. 10. Types of firm solutions: and - replacement; - introduction; in - subtraction

The firm solutions are not any exclusive phenomenon. On the contrary, this rather characteristic condition of real substances, as does not exist of substances absolutely insoluble in each other in a firm condition. Precisely as practically there are no connections with coordination lattices, which structure always precisely would correspond (meet) stoichiometric to structure.

Firm solutions of replacement. If atoms or the ions of one substance, taking root in a lattice of other substance, replace his(its) own atoms or ions in units of a lattice, there are firm solutions of replacement.

As firm solutions of replacement such solutions are called which are formed as a result of statistical replacement of atoms or ions in structure any of crystal substance (solvents or matrixes) atoms or ions of other (dissolved) substance borrowing (occupying) as a result of it regular units of a crystal lattice.

The firm solutions of replacement (fig. 10, а) often name also by mixed crystals and isomorphic by mixes, and process of education of firm solutions of replacement name isomorphic by replacement.

At education of firm solutions of replacement basically to replace each other can both cationand anion.

Some substances can form firm solutions rather easily, for example at their joint crystallization of solutions. However more often, for example in silicate systems, educations of firm solutions need significant energy of activation, therefore their occurrence is connected to various thermal processes (heating to high temperature, melting with subsequent crystallization, hydrothermal by processes).

The quantity(amount) of extraneous atoms or ions which are taking root in structure of the basic substance, can be various. Some substances can mix up among themselves over a wide range, down to complete replacement of own atoms with atoms of other substance. In this case speak about a continuous number (line) of firm solutions, complete mixability or accomplished(perfect) isomorphism. To such substances, for example, the forming continuous firm solutions – olivines concern 2МgO·SiO2 and 2FеО-SiO2. And in structure 2FеО·SiO2 cation of iron can be completely replaced on cation of magnesium and, on the contrary, in structure 2МgO·SiO2 cation of magnesium on cation of iron (replacement such as Мg2 +-Fе2 +). Replacements quantitatively however are much more often can occur only in the certain limits, outside of which the firm solutions are not formed any more. In this case speak about the limited number(line) твер д ы х of solutions limited смешиваемости or imperfect изоморфизме (at very small solubility education of firm solutions name эндокриптией - masking).

Ability of atoms or ions to enter into structure of other substance is defined(determined), on the one hand, by individual properties of atoms or ions (size, charge, electronic structure) and, on the other hand, by features of crystal structure of substances forming firm solutions.

Firm solutions of introduction. The atoms or ions of one substance can not replace atoms or ions another, and to settle down in intervals between them (fig. 10, б). In this case there are firm solutions of introduction.

As firm solutions of introduction such solutions are called which are formed as a result of introduction of atoms or ions of one substance in free intervals (interstice) of a crystal lattice of other substance - solvent.

The typical representatives of similar firm solutions are the so-called phases of introduction - connections formed at introduction in междоузлия плотноупакованных of lattices of transitive metals of atoms неметаллов, for example of hydrogen (гидриды), nitrogen (нитриды), carbon (карбиды) and т. д. A concrete example of a phase of introduction is the steel - firm solution of introduction of carbon in a lattice of iron. The phases of introduction of variable structure often have significant areas гомогенности.

It is necessary to note, that the firm solutions of introduction as against firm solutions of replacement can be only limited, as it is usual at the certain concentration растворяющегося of a component of a pressure(voltage) in a lattice at the expense of taking root atoms become so significant, that the existence of a steady firm solution is poorly probable.

Many properties of phases of introduction, such, for example, as high hardness and тугоплавкость, exceeding these characteristics at metals, are caused strong ковалентной by communication(connection) of atoms of metal and неметалла with participation -электронов. The presence of metal internuclear communication(connection) in similar phases explains their metal shine, high electrical conductivity, ability of some of them near to temperature of absolute zero to pass in сверхпроводящее a condition.

Defects нестехиометрии. Now is established, that practically all chemical connections in a firm condition with coordination (nuclear, ионными or metal) lattices have variable structure, т. е. Find out to some extent deviations(rejection) from стехиометрического of structure expressed by the formula of this connection. The area of structures laying inside boundary meanings(importance) of infringement стехиометрического of structure, is called as area гомогенности or area нестехиометрии. Constant and constant chemical structure appropriate стехиометрической to the formula, can have only connections with molecular lattices.

The deviations(rejection) from стехиометрии are a consequence of defects of a lattice (defects нестехиометрии), which can be shown as surplus (in comparison with стехиометрическим) катионов owing to анионных of vacancies (КС1, ТhO2, СеO2, РbО, ТiO and т. д.) or as a result of presence катионов in междоузлиях of a lattice (ZnО, СdO and т. д.), surplus анионов because of presence in a lattice катионных of vacancies (FеО, NiO, FеS, ТiO and т. д.) or presence анионов in междоузлиях (UO2 and т. д.). The combinations of the specified kinds of defects in the same connection are possible(probable) also.

As нестехиометрические of connection within the limits of area гомогенности represent one phase of variable structure, they can be qualified as firm solutions. If the infringements стехиометрии are called by presence in a lattice катионных or анионных of vacancies, т. е. At lack of atoms in appropriate катионной or анионной подрешетке, such firm solutions sometimes name by firm solutions of subtraction (fig. 10, е), if these infringements are called by surplus катионов or анионов in междоузлиях, such firm solutions can be considered(examined) as firm solutions of introduction own катионов or анионов of the given connection in his(its) crystal lattice.

The occurrence нестехиометрических of connections is a consequence термодинамически of an inevitable exchange of substance of the given crystal phase with an environment, т. е. By other phases (газообразными, liquid or firm). The degree of a deviation(rejection) from стехиометрии depends first of all on a физико-chemical nature of the connection and for different connections is various. Sometimes area гомогенности (area нестехиометрии) happens rather narrow and its(her) detection is limited to unsufficient sensitivity of used methods of research. Such connections can conditionally be considered(examined) as connection not having areas гомогенности, т. е. Connections of constant structure. Them sometimes name by linear phases, as on the diagram of a condition the structure of these connections is displayed by a vertical line - ordinate of the appropriate structure.

Defects by Schottky and Fraenkel

The defects by Schottky and Fraenkel concern to the thermal equilibrium defects connected to a disorder arrangement in a lattice of a crystal of "own" particles (of atoms or ions). Such arrangement arises, if the particle leaves(abandons) the regular rule(situation) in unit of a lattice, leaving his(its) free (vacant). There are two opportunities of education of defects in a lattice at the expense of moving particles from its(her) units. One of them was postulated I. E. Fraenkel another - by V. Schottky.

The atom or ion can move from unit of a lattice, leaving there vacancy, in intersticeremoved from unit on some distance.

Such defect as pair vacancy - interstice atom (ion) is called as defect on Fraenkel (fig. 11, а). If atom (ion) leaves(abandons) unit of a lattice, leaving in him vacancy, and leaves for limits of a lattice on a surface of a crystal, completing her(it), in a lattice there are only vacancies. Such type of defect as free (vacant) units of a lattice is called as defect on Шоттки (fig. 11,6).

The basic reason of education of defects on Fraenkel and Schottky are the thermal fluctuations of atoms (ions). The average amplitude of fluctuation of atoms at usual temperatures is rather small (≈ 5... 10 % from size of the period of a lattice).

Fig. 11. The schematic image of defects on Fraenkel (а) and Schottky (б) (in - ideal lattice)

However atoms in a lattice make thermal fluctuations not strictly in coordination, therefore even in these conditions at the expense of power fluctuations one of atoms can receive from next energy, sufficient for his(its) output(exit) from unit of a lattice. Especially this process occurs at the raised(increased) temperatures, at which the amplitude of fluctuation of atoms strongly grows. Thus, any crystal which is taking place at temperature, distinct from absolute zero, will contain always certain number of the specified thermal defects.

For education of defects on Френкелю and Шоттки the certain expenses of energy (energy of activation of process of education of defect) are required, however it is accompanied by increase энтропии at the expense of increase of a degree разупорядоченности of a lattice, that causes reduction of energy Гиббса. Hence, the education of similar defects appears energetically favourable and results in increase of stability of a crystal. From here follows, that the thermal defects on Френкелю and Шоттки are equilibrium and to each temperature there corresponds(meets) their certain equilibrium concentration in a crystal.

From the given equations follows, that the equilibrium concentration of defects on Шоттки and Френкелю is экспоненциальной function of temperature and energy of activation. Increase of temperature and accordingly reduction of energy of activation result in increase of equilibrium concentration of defects.

The energy of activation of process of education of dot defects depends on their type, chemical nature of substance and his(its) structure, therefore, though at a lattice of any not molecular crystal there are simultaneously all kinds of dot defects, one of them (with smaller energy of activation) usually prevail above others. The energy of education of defects on Шоттки with other things being equal is less, than defects on Френкелю, as accommodation of atom in междоузлии requires(demands) usually significant power expenses

For example, the defects on Френкелю will arise more easy in crystals with structure having large emptiness, or then, when the sizes аниона and катиона strongly differ, as all this facilitates accommodation катионов in междоузлиях.

Defects on Френкелю in the pure state, т. е. When the number of vacancies is equal to number межузельных of atoms, can take place only in crystals стехиометрического of structure, in real crystals with coordination lattices it, as a rule, is not observed. The defects on Шоттки can arise at the expense of education both катионных, and анионных of vacancies. In ионных crystals often there is energetically to more favourable an education of pairs vacancies, т. е. The education of vacant unit on a place катиона and аниона, as thus is more easy saved an electroneutrality of a surface of a crystal and lattice as a whole. However basically it is not necessary and in real crystals equality thermal катионных and анионных of vacancies can and not be observed.

The dot nuclear defects in a crystal lattice have the certain properties. For example, the vacancies in ионных crystals act by carriers of a charge, and катионная the vacancy bears(carries) negative, and анионная - a positive charge. Certainly, actually charge in vacancy does not contain, but electrical field, arising around of it,(her,) same, what would arise, if in vacancy the charge, on meaning(importance) equal settled down, and on a mark opposite to a charge of an ion, which has left(abandoned) given unit of a lattice. Any dot defects have ability to migration (диффузии) in a crystal lattice as a result of thermal флуктуации or application to a crystal of an external electrical field. For example, катион in междоузлии can pass at the appropriate excitation in next междоузлие, vacancy мигрируют at the expense of moving the next ion to vacant unit, т. е. By a consecutive exchange of positions between ions and vacancies (at such so-called вакансионном the mechanism диффузии the moving of vacancies in one direction is equivalent to moving of ions in the friend). The dot defects can cooperate with each other, forming in the elementary case ассоциаты - defects borrowing(occupying) next кристаллографические of a position. For example, in a lattice there can be connected groups of vacancies (кластеры). The connected pairs vacancies are capable диффундировать faster, than the isolated vacancies, and threefold кластеры are even faster.

The presence in crystals of dot defects on Шоттки and Френкелю renders essential influence on many properties of crystal ph. In particular, their presence at a crystal and ability to migration cause ионную electrical conductivity and processes массопереноса (диффузии) in a crystal lattice (in бездефектном an ideal crystal the process массопереноса practically is impossible). In this connection the presence of dot defects strongly accelerates such important in technology силикатов and refractory not metal materials processes, as твердофазовые of reaction, sintering, рекристаллизацию and т. д., which speed is defined(determined) by speed диффузии of material particles. The education of defects on Шоттки results in increase of volume of a crystal (crystal as though "swells" for the bill достраивания from a surface by atoms excluded from units of a lattice) and downturn of his(its) density (education of defects on Френкелю anyway as a first approximation does not result in change of density).

Dislocation

Dislocation concern to linear defects of a lattice, т. е. To imperfections covering in a crystal area, which extent in one direction considerably surpasses the size of atoms or ions. On character of distortions of a lattice dislocation are divided in the pure state on regional (linear) and screw. In real crystals dislocation often represent a combination regional and screw dislocation Such dislocation are called mixed. dislocation are a source of internal pressure(voltage) in crystal bodies, they create even in free from external loadings a crystal a field of deformations and pressure(voltage).

One of the basic concepts of the theory dislocationis the concept of a line dislocation. As a line dislocation that imagined line in a crystal is called, along which (in its(her) small vicinity) the maximal distortions of a lattice concentrate. Actually at occurrence dislocation the crystal lattice remains undistorted everywhere, except for area directly environmental a line dislocation. The line dislocation not necessarily should be a straight line, and can have excesses, step, т. е. Any form. The feature of this line consists that she never comes to an end (breaks) in a crystal, and leaves on his(its) surface, becomes isolated on itself, forming a loop, or becomes isolated on other lines dislocation.

Line dislocation. An attribute line dislocation the presence in one part of a crystal superfluous ("torn off" or "unfinished") nuclear plane (half plane or extraplane), not having continuations in other part of a crystal (fig. 12, extraplane is specified by an arrow(pointer)).

The maximal distortions and pressure(voltage) in a lattice concentrate at presence line dislocation along edges(territory) of a superfluous nuclear plane. This zone of the maximal pressure(voltage) limited to a dashed line in a fig. 13, is called as a nucleus dislocation

Screw дислокация. An attribute screw dislocationis the transformation of parallel nuclear planes (in defectless a crystal) in a uniform nuclear plane as helicoidal of a surface (like a screw plane) and presence on a surface of a crystal original dislocation nuclear step (stepwise).

Fig. 12. Model line dislocation a Fig. 13. The circuit of formation line

in a crystal dislocation

The schematic image screw dislocation is given in a fig. 16. Its(her) formation can be imagined if mentally to make in a crystal a cut(section) (on a plane АВСD), and then at the expense of force Р to move one part of a crystal in this plane in relation to other part on one internuclear distance downwards so that one cut off edge(territory) of each nuclear plane of a lattice, perpendicular planes section, has coincided with other cut off edge(territory) underlying of a plane of a lattice. The cut off surfaces can thus be connected absolutely precisely, then it is impossible to distinguish, on what plane inside crystal the cut(section) was made.

Fig. 14. The circuit of formation screw dislocation- a Fig. 15. The schematic image nuclear of planes at screw dislocation

In other words, at presence screw dislocation nuclear planes of a lattice, as it was already marked, turn to similarity spiral of a screw surface, whence and name - screw dislocation (fig. 15).

Questions:

1. What such defects of a crystal lattice?

2. What such firm solutions and what conditions of formation of firm solutions of replacement and introduction?

3. Characterize defects on Y.E. Fraenkel and In. Schottky and why defects on Y.E. Fraenkel and In. Schottky concern to thermodynamically to equilibrium defects, in what the reason of their education and what factors render influence on their concentration in a crystal lattice?

4. Name kinds of linear defects.

5. What is a structural attribute of presence in a crystal lattice regional both screw dislocation and their qualitative and quantitative characteristic?

6. Describe the reasons of education and property dislocation, methods of definition of their density and result meanings(importance) of this density in the perfect and deformed crystals.

Lecture № 6.

Theme: The structure of crystalline silicates. The development of ideas about the structure of silicates. Features of the structure of silicates. Structural classification of silicates. Structure of borides, carbides, nitrides and silicides.

1. The structure of crystalline silicates

2. The development of ideas about the structure of silicates.

3. Features of the structure of silicates.

4. Structural classification of silicates.

5. Structure of borides, carbides, nitrides and silicides.

Structure силикатов - тетраэдр [SiO4]

Карборунд - карбид of silicon

Structure crystal силикатов

Силикаты and алюмосиликаты - most widespread minerals in terrestrial коре. They make more thirds of all minerals.

The majority natural силикатов has complex(difficult) structure and, as a rule, insolubly in water. This long time complicated an establishment of their structure. Therefore in a history of study силикатов it is possible clearly to allocate 5 stages.

The first stage is connected to only chemical study силикатов. In this перид the items of information on their structure collected. The empirical formulas силикатов entered the name as оксидов in ascending order of charge катиона. For example Na2O·Al2O3·6SiO2 - альбит, СaO·Al2O3·2SiO2 - анортит.

In a basis of classification силикатов the attitude(relation) of number of atoms of oxygen connected to silicon, to number of atoms of oxygen connected to others катионами was necessary. On this classification силикаты were divided on моно-, ди-, трисиликаты etc. So СaO·Al2O3·2SiO2 is моносиликатом, because the number of atoms of oxygen connected to silicon, is equal to number of atoms of oxygen connected with кальцием and aluminium (4). On similar accounts лейцит К2O·Al2O3·4SiO2 is дисиликатом, and альбит Na2O·Al2O3·6SiO2 - трисиликатом. Thus the substances, close on a nature, (field шпаты - альбит, ортоклаз, анортит) got in different classes, and various - in one of a class.

The second stage is connected to representation about силикатах, as about salts of hypothetical polysilicon acids - метакремниевой Н2SiO3, ортокремниевой Н4SiO4 and ортодикремниевой Н6Si2O7. However question on a structure силикатов and here remained unsolved.

The third stage in development силикатов is closely connected to a name of outstanding Russian scientist В.И.Вернадского (1863-1945г), which in 1891 has put forward idea about the special role of aluminium in силикатах, that has facilitated decoding their structures.

At the fourth stage of study силикатов was connected to successes of stereochemistry of complex connections. By analogy with четырехвалентной by platinum, which in complex connections has coordination number 6, the same coordination number attributed also to silicon. The structural formulas constructed on these principles, further have appeared incorrect.

The modern (fifth) stage of development of representations about structures силикатов is closely connected to successes рентгеноструктурного of the analysis. Leaning(basing) on rules of education ионных of crystals formulated Л.К. Полингом in 1929г., В.Л.Брегу and Ф.Махачки it was possible to decipher the first structures силикатов. Has appeared, that силикаты are not ионными crystals. A primary type of communication(connection) in силикатах is ионно-ковалентная communication(connection). Now are deciphered a structure and structure many complex(difficult) силикатов. The especially large merit in it belongs to the Soviet school кристаллографии, based акад. Н.В.Беловым.