Ionic crystals are compounds with a predominant ionic nature of the chemical bond, which is based on the electrostatic interaction between charged ions. Typical representatives of ionic crystals are alkali metal halides, for example, with a structure such as NaCl and CaCl.
When crystals like rock salt (NaCl) are formed, halogen atoms (F, Cl, Br, I), which have a high electron affinity, capture valence electrons of alkali metals (Li, Na, K, Rb, I), which have low ionization potentials, while positive and negative ions are formed, the electron shells of which are similar to the spherically symmetric filled s 2 p 6 shells of the nearest inert gases (for example, the N + shell is similar to the Ne shell, and the Cl shell is similar to the Ar shell). As a result of the Coulomb attraction of anions and cations, the six outer p-orbitals overlap and a lattice of the NaCl type is formed, the symmetry of which and the coordination number of 6 correspond to the six valence bonds of each atom with its neighbors (Fig. 3.4). It is significant that when the p-orbitals overlap, there is a decrease in the nominal charges (+1 for Na and -1 for Cl) on the ions to small real values due to a shift in the electron density in six bonds from the anion to the cation, so that the real charge of the atoms in the compound It turns out, for example, that for Na it is equal to +0.92e, and for Cl- the negative charge also becomes less than -1e.
A decrease in the nominal charges of atoms to real values in compounds indicates that even when the most electronegative electropositive elements interact, compounds are formed in which the bond is not purely ionic.
Rice. 3.4. Ionic mechanism of formation of interatomic bonds in structures likeNaCl. Arrows indicate the directions of electron density shift
According to the described mechanism, not only alkali metal halides are formed, but also nitrides and carbides of transition metals, most of which have a NaCl type structure.
Due to the fact that the ionic bond is non-directional and unsaturated, ionic crystals are characterized by large coordination numbers. The main structural features of ionic crystals are well described on the basis of the principle of dense packing of spheres of certain radii. Thus, in the NaCl structure, large Cl anions form a cubic close packing, in which all octahedral voids are occupied by smaller Na cations. These are the structures of KCl, RbCl and many other compounds.
Ionic crystals include most dielectrics with high electrical resistivity values. The electrical conductivity of ionic crystals at room temperature is more than twenty orders of magnitude less than the electrical conductivity of metals. Electrical conductivity in ionic crystals is carried out mainly by ions. Most ionic crystals are transparent in the visible region of the electromagnetic spectrum.
In ionic crystals, attraction is mainly due to the Coulomb interaction between charged ions. - In addition to the attraction between oppositely charged ions, there is also repulsion, caused, on the one hand, by the repulsion of like charges, on the other, by the action of the Pauli exclusion principle, since each ion has stable electronic configurations of inert gases with filled shells. From the point of view of the above, in a simple model of an ionic crystal, it can be assumed that the ions are hard, impenetrable charged spheres, although in reality, under the influence of the electric fields of neighboring ions, the spherically symmetrical shape of the ions is somewhat disrupted as a result of polarization.
Under conditions where both attractive and repulsive forces exist simultaneously, the stability of ionic crystals is explained by the fact that the distance between unlike charges is less than between like charges. Therefore, the forces of attraction prevail over the forces of repulsion.
Again, as in the case of molecular crystals, when calculating the cohesion energy of ionic crystals, one can proceed from the usual classical concepts, assuming that the ions are located at the nodes of the crystal lattice (equilibrium positions), their kinetic energy is negligible and the forces acting between the ions are central .
Stasenko A., Brook Y. Ionic crystals, Young’s modulus and planetary masses // Quantum. - 2004. - No. 6. - P. 9-13.
By special agreement with the editorial board and editors of the journal "Kvant"
Once upon a time there lived a Little Prince. He lived on a planet that was slightly larger than himself...
The little prince described everything to me in detail, and I drew this planet.
Antoine de Saint-Exupery. A little prince
What atoms are planets made of?
Have you ever thought about how different planets differ from each other? Of course, in mass and size, you say. This is correct; the masses and radii of planets largely determine their other characteristics. Well, from the atoms of what chemical elements are planets built? Astrophysicists say that from different ones. But in the Solar System, and indeed in the Universe in general, atoms of different elements are not present in equal quantities. It is known, for example, that the relative content (by mass) of hydrogen, helium and all other elements is determined by the ratios 0.73:0.25:0.02.
The planets of our solar system are also built differently. The largest of them are Jupiter and Saturn (their masses are, respectively, 318 and 95 times the mass of the Earth M h) - mainly consist of hydrogen and helium. True, both hydrogen and helium in these planets are not in a gaseous state, but in a solid or liquid state, and the average densities of these planets are much higher than the density of planetary atmospheres or, for example, gases, with which we usually experiment when studying gas laws in physics workshop . The planets Uranus and Neptune have masses, respectively, 15 and 17 times greater than that of the Earth, and they consist mainly of ice, solid methane ( CH 4 ) and ammonia ( NH 3 ) in the metallic phase. Note that as the mass of the planets decreases (if you “move” along the mass scale from the giant planets), the average mass numbers of the atoms from which these planets are built increase. Is this a coincidence? It seems that no - the same statement turns out to be true with further “movement” along the mass scale. The terrestrial planets (Mercury, Venus, Mars) do not exceed the Earth in mass, and the characteristic element for them (and for the Earth) is iron. In addition, they contain many silicates (for example, silicon dioxide SiO2 ). The trend is completely clear - the greater the mass of the planet, the lower the average mass numbers of the atoms of which it consists. A rather natural question arises - is it possible to say that there is some kind of connection between the masses of the planets and the masses of the atoms from which they are built?
Of course, it would be wrong to say that the masses of atomic nuclei depend on the mass of the planet. The atoms of each chemical element are arranged exactly the same not only on different planets, but in general in any place in the Universe. But the connection between the masses of those atoms from which the planets are actually “built” and the masses of the planets themselves really exists. And this is exactly what we will talk about next.
We will discuss a very simple model. But “very often a simplified model sheds more light on how the nature of a phenomenon actually works than any number of calculations.” ab initio for various specific cases, which, even if correct, often contain so many details that they conceal rather than clarify the truth.” These words belong to the Nobel Prize laureate in physics, one of the greatest theoretical physicists of our time, F. Anderson.
Surprisingly, the planets of our solar system, as it turns out, are not so far from the model discussed below. And yet, we must already warn readers here against the too formal application of those simple formulas that we will write out further, to real planets. All estimates that we make are valid only in order of magnitude. We will use qualitative considerations and the dimensional method for estimates and will not worry about those numerical coefficients that arise during more accurate calculations. This approach is justified if the numerical coefficients in the formulas are of the order of unity. But exactly this situation arises in physics and astrophysics quite often (although, of course, not always). There are more serious reasons for this, but we will not discuss them here, but simply accept without proof that dimensionless coefficients will not spoil (at least qualitatively) our conclusions.
On the way to our main goal - establishing a connection between the masses of planets and their chemical composition - we will take a short excursion into solid state physics and calculate the energy of an ionic crystal and its Young's modulus. Ultimately, these calculations will help us understand the planets.
Ionic crystals and Young's modulus
Let us first consider a model of an ionic crystal similar to a table salt crystal NaCl , but differs from the latter in that the atoms have approximately the same masses. This is different from the crystal NaCl not very important for further reasoning, but it will make our calculations somewhat easier. We can neglect the mass of electrons compared to the mass of atomic nuclei.
Let the crystal density ρ , and the mass numbers of the atoms that make it up are A 1 ≈ A 2 ≈ A. The masses of nucleons - protons and neutrons, which make up the nuclei, differ very slightly; we will not take into account the differences between them here. Under these assumptions, we can assume that the mass of each atom is approximately equal to the mass of the atomic nucleus
\(~m \approx Am_p,\)
Where m p is the mass of the nucleon. If a unit volume contains only n atoms, then their total mass is equal to density:
\(~nm = \rho.\)
It is convenient for us to rewrite this simple formula in another way. For the estimates we are about to make, we can consider our model crystal to be cubic. This means that the atoms “sit” in the corners of an elementary cube - a cell of a crystal lattice. Let us denote the length of the edge of this cube by the letter A. By its very meaning, the magnitude n directly related to A\[~na^3 = 1\], therefore
\(~\rho = \frac(m)(a^3).\)
This formula is interesting in that the right side includes m And a- the values are “microscopic”, on the left there is a completely “macroscopic” value - the density of the crystal.
Our crystal lattice is built from alternating positive and negative ions. For simplicity, the charge of each ion will be considered equal to the charge of the electron with the corresponding sign, i.e. ± e. The forces acting on each ion are ordinary Coulomb forces. If we only had two ions and they were at a distance a from each other, then the potential energy of their interaction would be the value \(~\sim \frac(e^2)(\varepsilon_0 a)\), where ε 0 is the electrical constant, and the "~" symbol means we wrote the estimate in order of magnitude. The interaction energy of two ions is a very important and useful characteristic for assessments. But there are, of course, much more than two particles in a crystal. If we assume that the average distance between particles is 2·10 -10 m, then it is easy to calculate that there will be about 10 23 particles in 1 cm 3.
People often talk about the electrostatic energy density of the system of ions that form a crystal. The word "density" is used here because it refers to the energy per unit volume. In other words, this quantity is the sum of the potential interaction energies of all pairs of ions in a unit volume. But it is difficult to accurately calculate such a sum; we cannot do this here, because for this we would need to take into account the interaction of a large number of particles located at different distances from each other. You can, however, act by analogy with the formula for crystal density.
Let us first note that the energy density we are interested in is w has the dimension J/m 3, and the dimension of the potential energy of a pair of ions is \(~\left[ \frac(e^2)(\varepsilon_0 a) \right]\) = J. The symbol [...]- denotes the dimension of the quantity , in parentheses. Let us now divide the “microscopic” quantity \(~\frac(e^2)(\varepsilon_0 a)\) by another, also “microscopic” - a 3 , and we will obtain a quantity that has the dimension of energy density. One might think that this is precisely the assessment for w.
These considerations, of course, are not a strict proof that the electrostatic energy density of the system of ions forming the crystal is equal to \(~\frac(e^2)(\varepsilon_0 a^4)\). However, an exact calculation for an ionic crystal leads to the formula
\(~w = \alpha n \frac(e^2)(\varepsilon_0 a) = \alpha \frac(e^2)(\varepsilon_0 a^4),\)
which differs from the estimate we obtain only by a numerical factor α ~ 1.
The elastic properties of a substance are determined, of course, by interatomic interactions. The most important characteristic of such properties is, as we know, Young’s modulus E. We are accustomed to defining it from Hooke's law as the stress at which the relative linear deformation of the body \(~\frac(\Delta l)(l)\) is equal to unity, or, in other words, the corresponding length changes by half. But the value of E does not at all depend on whether we know Hooke’s law and whether it is actually fulfilled. Let's pay attention to the dimension of the elastic modulus: N/m 2 = J/m 3. One can therefore interpret E and as some characteristic energy density.
To make this more clear, let's give two other examples. The first refers to a conventional parallel-plate capacitor. If you place charges on its plates ± q, then an electrostatic field will exist inside the capacitor, and the plates themselves will be attracted to each other. Let the area of each plate S, and the distance between them d. You can calculate the force of attraction between the plates and divide it by S, find the “characteristic pressure”. Or you can calculate the energy contained in the capacitor and divide it by the volume SD, find the energy density. In both cases, the value obtained is \(~\frac(\sigma^2)(2 \varepsilon_0)\), where \(~\sigma = \frac qS\) is the surface density of charges on the plates. “Characteristic pressure” and energy density turn out to be the same in this case not only in dimensions, but also numerically.
The second example is the determination of the coefficient of surface tension of a liquid. This coefficient can be defined as the force per unit length (for example, for a stretched soap film), or it can be considered the surface energy density. And in this case, the same value is defined in “power” and “energy” languages.
Let us return, however, to the ionic crystal. The energy characteristic of an ionic crystal is electrostatic energy; the elastic properties of the crystal are determined by the electrical interactions of its constituent particles. Therefore we can assume that w ~ E. Here we again assume without proof that the proportionality coefficient for these quantities is of the order of unity. So we learned evaluate the value of Young's modulus for an ionic crystal:
\(~E \sim w \sim \frac(e^2)(\varepsilon_0 a^4) \approx \frac(\rho)(m) \frac(e^2)(\varepsilon_0 \left(\frac( m)(\rho) \right)^(\frac 13)) = e^2 m^(-\frac 43) \rho^(\frac 43) \varepsilon_0^(-1).\)
From this formula it immediately follows that w- value limited from above. While it exists ionic lattice, the distance between the ions in any case cannot be less than the size of the atoms (ions). If this were not so, the electron shells of neighboring ions would overlap, the electrons would be shared, and instead of an ionic crystal we would have a metal.
On the other hand, for an ionic crystal the value w is also limited from below. This can be understood with the following example. Let us imagine that a force deforming it is applied to a crystal rod. If this force is large enough, the rod will collapse. The stress generated during failure is equal to the “breaking” force divided by the cross-sectional area of the rod perpendicular to this force. This voltage, let's denote it p pr is called the tensile strength, and it is always less than Young's modulus. The last statement is at least plausible. As we have already said, a voltage equal to Young’s modulus formally leads to a change in the length of the sample under study by half. (It should, however, also be said that Hooke’s law cannot be used for sufficiently large deformations, in general, but the qualitative conclusions that interest us are still preserved even without Hooke’s law.) From experience we know that stretching or compressing something It is practically impossible to double a crystal - it will break long before that. Let it now R- characteristic pressure due to external influence on the crystal. We can say that one of the conditions for the existence of a crystal structure is the fulfillment of the inequalities
\(~w > p_(pr) > p.\)
Another obvious condition is that the temperature of the crystal be less than the melting point of the crystal lattice.
Another question arises here. If Young's modulus is defined as a voltage that doubles the length of the rod, then what about a crystal that has the shape of a sphere or cube and is deformed simultaneously from all sides? In this case, it makes more sense to talk about a relative change not of some length, but volume crystal \(~\frac(\Delta V)(V)\), and Hooke’s law at small deformations can be written in the form
\(~\frac pK = \frac(\Delta V)(V).\)
This formula is very similar to the one we write for the case of tension (or compression) of a rod\[~\frac pE = \frac(\Delta l)(l)\], but Young's modulus E is now replaced by a comprehensive compression module TO. Module TO can also be interpreted as a characteristic energy density.
Ionic crystal planet
Let us now move on to our main task. Consider a hypothetical planet built from almost identical atoms forming a crystal lattice. For the planet to be entirely crystalline, in any case, it is necessary that the pressure in the center of the planet (it is, of course, maximum there!) does not exceed the value w.
Pressure at the center of a planet with mass M and radius R can be estimated by the formula
\(~p \sim G \frac(M^2)(R^4),\)
Where G- gravitational constant. This formula can be obtained from dimensional considerations. Let us remind you how this is done.
Suppose that the pressure at the center of the planet can depend on the mass of the planet M, its radius R and gravitational constant G, and write the formula
\(~p \sim G^xM^yR^z.\)
Numbers X, at, z not yet known. Let us write down the dimensions of the parameters included in this formula: [ R] = kg m -1 s -2 , [ G] = m 3 kg -1 s -2 , [ M] = kg, [ R] = m. Comparing the dimensions of the left and right sides of the formula, we get
Kg m -1 s -2 = m 3x kg -x s -2x kg y m z .
In order for equality to be fair, it is necessary that the numbers X, at, z satisfied the following system of equations:
\(~\left\(\begin(matrix) 1 = -x + y, \\ -1 = 3x + z, \\ -2 = -2x. \end(matrix) \right.\)
From here X = 1, at = 2, z= -4 and we get our formula for pressure.
On the other hand, this formula can be understood this way. Gravitational energy of a ball with mass M and radius R should be of the order of \(~\frac(GM^2)(R)\), but we get the density of gravitational energy if we divide the energy by the volume of the ball V ~ R 3. Just as the elastic moduli can be interpreted as the density of electrostatic energy, the density of gravitational energy can be considered to be of the same order of magnitude as the pressure at the center of the gravitating ball.
Let us emphasize once again that we are not talking about the identity of pressure and energy density (this would be simply an incorrect statement!), but about their equality in order of magnitude.
The condition for the existence of an ionic crystal in the center of our hypothetical planet is as follows:
\(~G\frac(M^2)(R^4)< w \sim e^2 m^{-\frac 43} \rho^{\frac 43} \varepsilon_0^{-1}.\)
And, of course, a fully crystalline planet only exists if it is relatively cold, in other words - the temperature at the center of the planet should not be very close to the melting point. Otherwise, the planet would have a liquid core - the crystal would melt. Let us again take into account that \(~\rho \sim \frac(M)(R^3)\) and \(~m \approx Am_p\), then our inequality can be rewritten as follows:
\(~A< \left(\frac{e^2}{\varepsilon_0 G m_p M} \right)^{\frac 43} \left(\frac{M}{m_p} \right)^{\frac 14}.\)
From this it is already clearly clear that the assumptions that the planet entirely crystalline, and its density in the center is of the order of the average density, lead us to restrictions on the masses of atoms, of which such planets can be built.
The assumption that the average density of a planet coincides in order of magnitude with the density at its center is completely natural and quite reasonable in those cases when the matter in the center of the planet is not compressed “too much.” But if the compression were very great, the ionic crystal would no longer exist anyway. If an ionic-crystalline planet has the same radius and mass as the Earth, then the densities of matter in the center and near the surface do not differ so much - only three times. Therefore, in order of magnitude, the average density is indeed the same as the density near the center of the planet. The same is true for not very accurate estimates for other planets and stars.
Limitations on the maximum masses of atoms from which entirely crystalline planets can be built are thus determined by the parameters of the planets themselves. For the simplest model of a continuous ionic-crystalline planet, we obtained
\(~A_(max) = \operatorname(const) \cdot M^(-\frac 12).\)
Let us now draw a graph of the function M(A max) (see picture). This graph, strictly speaking, only applies to our hypothetical situation, where the planets are built from ionic crystals and do not have any significant liquid cores. Let us recall the beginning of the article, where we talked about what elements or compounds are characteristic of real planets. Let us assume that the planets of the “Solar System” (quotes distinguish hypothetical planets from real ones with approximately the same masses!) are ionic-crystalline. If we accept that the average mass number for the “terrestrial planets” is about 60, for “Uranus” and “Neptune” about 16, and for “Jupiter” and “Saturn” 2-4, then the corresponding “points” fit quite well "on our schedule. On the horizontal axis on it we plotted the average value of L for the “planets”, and on the vertical axis we plotted the masses of ionic-crystalline planets in units of Earth mass.
a) Dependence of the relative mass of a hypothetical planet on the mass number of atoms; b) too, but on a logarithmic scale
But this, of course, does not mean at all that real planets do not have liquid cores; such cores probably exist. However, crystalline structures also exist on planets. And the fact that real planets, at least qualitatively, are similar to model planets allows us to assert that we have actually “caught” and understood the pattern of the existence of a connection between the masses of the planets and the masses of the atoms of the main part of the planet’s constituent matter.
Let us add in conclusion that arguments similar to those given in this article can also be carried out for those cases when the planets are not ionic-crystalline, but metallic. Metallicity means that in a crystal (or in a liquid) there are ions and “free” electrons, separated from “their” atoms under high pressure. In this case, they say that the gravitational compression is “counteracted” by the pressure of the electron gas; the balance of the corresponding forces (pressures) ensures the possibility of the existence of stable planets. The principle of calculation leading to the establishment of a connection between the masses of the planets and the characteristics of their constituent atoms remains the same, but the calculations themselves become more complicated, and we will not present them here. For those who wish to do such calculations on their own, let us inform you that the pressure of electron gas in metals is equal in order of magnitude to \(~\frac(\hbar^2)(m_e) n_e^(\frac 53)\), where \(~ \hbar\) ≈ 10 -34 J s - Planck’s constant, m e = 10 -30 kg is the mass of the electron, and n e is the number of electrons per unit volume.
The ions that make up ionic crystals are held together by electrostatic forces. Therefore, the structure of the crystal lattice of ionic crystals should ensure their electrical neutrality.
In Fig. 3.24-3.27 schematically depict the most important types of crystal lattices of ionic crystals and provide detailed information about them. Each type of ion in the ionic lattice has its own coordination number. Thus, in the crystal lattice of cesium chloride (Fig. 3.24), each Cs+ ion is surrounded by eight Cl" ions and, therefore, has a coordination number of 8. Similarly, each Cl- ion is surrounded by eight Cs+ ions, i.e., also has a coordination number of 8. Therefore It is believed that the crystal lattice of cesium chloride has a coordination of 8: 8. The crystal lattice of sodium chloride has a coordination of 6: 6 (Fig. 3.25).Note that in each case the electrical neutrality of the crystal is maintained.
The coordination and type of crystal structure of ionic lattices are determined mainly by the following two factors: the ratio of the number of cations to the number of anions and the ratio of the radii of cations and anions.
G centered cubic or octahedral
Rice. 3.25. Crystal structure of sodium chloride (rock salt).
The ratio of the number of cations to the number of anions in the crystal lattices of cesium chloride (CsCl), sodium chloride (NaCl) and zinc blende (zinc sulfide ZnS) is 1:1. Therefore, they are classified as stoichiometric type AB. Fluorite (calcium fluoride CaF2) belongs to the AB2 stoichiometric type. A detailed discussion of stoichiometry is provided in Chap. 4.
The ratio of the ionic radius of the cation (A) to the ionic radius of the anion (B) is called the ionic radius ratio rJrB. In general, the greater the ratio of ionic radii, the greater the coordination number of the lattice (Table 3.8).
Table 3.8. Dependence of coordination on the ratio of ionic radii
Coordination Ionic radius ratio
Rice. 3.26. Crystal structure of zinc blende.
As a rule, it is easier to consider the structure of ionic crystals as if they consist of two parts - anionic and cationic. For example, the structure of cesium chloride can be thought of as consisting of a cubic cationic structure and a cubic anionic structure. Together they form two interpenetrating (nested) structures that form a single body-centered cubic structure (Fig. 3.24). A structure such as sodium chloride, or rock salt, also consists of two cubic structures—one cationic and the other anionic. Together they form two nested cubic structures that form a single face-centered cubic structure. The cations and anions in this structure have an octahedral environment with a 6:6 coordination (Fig. 3.25).
The zinc blende type structure has a face-centered cubic lattice(Fig. 3.26). You can think of it as if the cations form a cubic structure and the anions have a tetrahedral structure inside the cube. But if we consider the anions as a cubic structure, then the cations have a tetrahedral arrangement in it.
The structure of fluorite (Fig. 3.27) differs from those discussed above in that it has the stoichiometric type AB2, as well as two different coordination numbers - 8 and 4. Each Ca2+ ion is surrounded by eight F- ions, and each F- ion is surrounded by four Ca2 + ions. . The structure of fluorite can be imagined as a face-centered cubic cationic lattice, inside which there is a tetrahedral arrangement of anions. You can imagine it in another way: as a body-centered cubic lattice, in which the cations are located in the center of the cubic cell.
Face-centered cubic and body-centered cubic
All compounds discussed in this section are assumed to be purely ionic. The ions in them are considered as solid spheres with strictly defined radii. However, as stated in Sect. 2.1, many compounds are partly ionic and partly covalent in nature. As a result, ionic compounds with a marked covalent character cannot fully obey the general rules outlined in this section.
In complex crystals consisting of elements of different valencies, the formation of an ionic type of bond is possible. Such crystals are called ionic.
When atoms come closer and valence energy bands overlap between elements, electrons are redistributed. An electropositive element loses valence electrons, turning into a positive ion, and an electronegative element gains it, thereby completing its valence band to a stable configuration, like that of inert gases. Thus, ions are located at the nodes of the ionic crystal.
A representative of this group is an oxide crystal whose lattice consists of negatively charged oxygen ions and positively charged iron ions.
The redistribution of valence electrons during an ionic bond occurs between the atoms of one molecule (one iron atom and one oxygen atom).
For covalent crystals, the coordination number K, the crystalline number, and the possible lattice type are determined by the valence of the element. For ionic crystals, the coordination number is determined by the ratio of the radii of the metallic and nonmetallic ions, since each ion tends to attract as many ions of the opposite sign as possible. The ions in the lattice are arranged like balls of different diameters.
The radius of the nonmetallic ion is greater than the radius of the metallic ion, and therefore metallic ions fill the pores in the crystal lattice formed by the nonmetallic ions. In ionic crystals the coordination number
determines the number of ions of the opposite sign that surround a given ion.
The values given below for the ratio of the radius of a metal to the radius of a non-metal and the corresponding coordination numbers follow from the geometry of the packing of spheres of different diameters.
For the coordination number will be equal to 6, since the indicated ratio is 0.54. In Fig. Figure 1.14 shows the crystal lattice. Oxygen ions form an fcc lattice, iron ions occupy pores in it. Each iron ion is surrounded by six oxygen ions, and, conversely, each oxygen ion is surrounded by six iron ions. In connection with this, in ionic crystals it is impossible to isolate a pair of ions that could be considered a molecule. During evaporation, such a crystal disintegrates into molecules.
When heated, the ratio of ionic radii can change, since the ionic radius of a nonmetal increases more rapidly than the radius of a metal ion. This leads to a change in the type of crystal structure, i.e., to polymorphism. For example, when an oxide is heated, the spinel crystal lattice changes to a rhombohedral lattice (see section 14.2),
Rice. 1.14. Crystal lattice a - diagram; b - spatial image
The binding energy of an ionic crystal is close in magnitude to the binding energy of covalent crystals and exceeds the binding energy of metallic and, especially, molecular crystals. In this regard, ionic crystals have a high melting and evaporation temperature, a high elastic modulus and low coefficients of compressibility and linear expansion.
The filling of energy bands due to the redistribution of electrons makes ionic crystals semiconductors or dielectrics.
