Ion size. Ionic and crystalline radii. Ionic radii Shannon ionic radii

The problem of ion radii is one of the central ones in theoretical chemistry, and the terms themselves "ionic radius" and " crystal radius”, characterizing the corresponding dimensions, are a consequence of the ion-covalent model of the structure. The problem of radii develops primarily within the framework of structural chemistry (crystal chemistry).

This concept found experimental confirmation after the discovery of X-ray diffraction by M. Laue (1912). The description of the diffraction effect almost coincided with the beginning of the development of the ionic model in the works of R. Kossel and M. Born. Subsequently, the diffraction of electrons, neutrons and other elementary particles was discovered, which served as the basis for the development of a number of modern methods of structural analysis (X-ray, neutron, electron diffraction, etc.). The concept of radii played a decisive role in the formation of the concept of lattice energy, the theory of closest packings, contributed to the emergence of the Magnus-Goldschmidt rules, the Goldschmidt-Fersman isomorphism rules, etc.

Back in the early 1920s. two axioms were accepted: on the portability (transferability) of ions from one structure to another and on the constancy of their sizes. It seemed quite logical to take half of the shortest internuclear distances in metals as radii (Bragg, 1920). Somewhat later (Huggins, Slater) a correlation was found between the atomic radii and distances to the maxima of the electron density of the valence electrons of the corresponding atoms.

Problem ionic radii (g yup) is somewhat more difficult. In ionic and covalent crystals, according to X-ray diffraction analysis, the following are observed: (1) a certain shift in the overlap density to a more electronegative atom, as well as (2) a minimum electron density on the bond line (the electron shells of ions at close distances should repel each other). This minimum can be considered as the area of contact between individual ions, from which the radii can be counted. However, from the structural data for internuclear distances it is impossible to find a way to determine the contribution of individual ions and, accordingly, a way to calculate the ionic radii. To do this, it is necessary to specify at least the radius of one ion or the ratio of ion radii. Therefore, already in the 1920s. a number of criteria for such a definition were proposed (Lande, Pauling, Goldschmidt, etc.) and various systems of ionic and atomic radii were created (Ahrens, Goldschmidt, Boky, Zakhariazen, Pauling) (in domestic sources, the problem is described in detail by V.I. Lebedev, V.S. Urusov and B. K. Vainshtein).

Currently, the system of ionic radii of Shannon and Pruitt is considered the most reliable, in which the ionic radius F “(r f0W F "= 1.19 A) and O 2_ (r f0W О 2- = 1.26 A) (in monographs by B. K. Vainshtein, these are called physical.) A set of radii values was obtained for all elements of the periodic system, for various oxidation states and cn, as well as for transition metal ions and for various spin states (the values of the ionic radii of transition elements for cn 6 are given in Table 3.1) This system provides an accuracy of about 0.01 A in the calculation of internuclear distances in the most ionic compounds (fluorides and oxygen salts) and allows reasonable estimates of the radii of ions for which there are no structural data. Pruitt in 1988 calculated the then unknown radii for ions d- transition metals in high oxidation states, consistent with subsequent experimental data.

Table 3.1

Some ionic radii r (according to Shannon and Pruitt) of transition elements (CH 6)

0.75LS

The end of the table. 3.1



							0.75 lls

th CC 4 ; b CC 2; LS- low spin state; HS- high-spin state.

An important property of ionic radii is that they differ by about 20% when the cn changes by two units. Approximately the same change occurs when their oxidation state changes by two units. Spin "crossover"

Ionic radius- value in Å characterizing the size of ion-cations and ion-anions; characteristic size of spherical ions, used to calculate interatomic distances in ionic compounds. The concept of ionic radius is based on the assumption that the size of ions does not depend on the composition of the molecules in which they are included. It is affected by the number of electron shells and the packing density of atoms and ions in the crystal lattice.

The size of an ion depends on many factors. With a constant charge of the ion, with an increase in the serial number (and, consequently, the charge of the nucleus), the ionic radius decreases. This is especially noticeable in the lanthanide series, where the ionic radii change monotonically from 117 pm for (La3+) to 100 pm (Lu3+) at a coordination number of 6. This effect is called lanthanide contraction.

In groups of elements, ionic radii generally increase with increasing atomic number. However, for d-elements of the fourth and fifth periods, due to lanthanide contraction, even a decrease in the ionic radius can occur (for example, from 73 pm for Zr4+ to 72 pm for Hf4+ at a coordination number of 4).

In the period, there is a noticeable decrease in the ionic radius, associated with an increase in the attraction of electrons to the nucleus with a simultaneous increase in the charge of the nucleus and the charge of the ion itself: 116 pm for Na+, 86 pm for Mg2+, 68 pm for Al3+ (coordination number 6). For the same reason, an increase in the ion charge leads to a decrease in the ionic radius for one element: Fe2+ 77 pm, Fe3+ 63 pm, Fe6+ 39 pm (coordination number 4).

Comparison of ionic radii can only be done at the same coordination number, since it affects the size of the ion due to the repulsive forces between the counterions. This is clearly seen in the example of the Ag+ ion; its ionic radius is 81, 114, and 129 pm for coordination numbers 2, 4, and 6, respectively.
The structure of an ideal ionic compound, due to the maximum attraction between unlike ions and the minimum repulsion of like ions, is largely determined by the ratio of the ionic radii of cations and anions. This can be shown by simple geometric constructions.

The ionic radius depends on many factors, such as the charge and size of the nucleus, the number of electrons in the electron shell, its density due to the Coulomb interaction. Since 1923, this concept has been understood as effective ionic radii. Goldschmidt, Ahrens, Bokiy, and others created systems of ionic radii, but all of them are qualitatively identical, namely, cations in them, as a rule, are much smaller than anions (with the exception of Rb + , Cs + , Ba 2+ and Ra 2+ in relation to O 2- and F-). For the initial radius in most systems, the size of the radius K + = 1.33 Å was taken, all the rest were calculated from the interatomic distances in heteroatomic compounds, which were considered ionic according to the chemical type. connections. In 1965 in the USA (Waber, Grower) and in 1966 in the USSR (Brattsev) the results of quantum-mechanical calculations of the sizes of ions were published, which showed that cations, indeed, have a smaller size than the corresponding atoms, and anions practically do not differ in size from the corresponding atoms. This result is consistent with the laws of the structure of electron shells and shows the erroneousness of the initial positions adopted in calculating the effective ionic radii. Orbital ionic radii are unsuitable for estimating interatomic distances; the latter are calculated on the basis of a system of ionic-atomic radii.

From consideration of the physical essence periodic law it follows that periodic changes chemical properties elements associated with the electronic structure of atoms, which, in accordance with the laws of wave mechanics, also changes periodically. All periodic changes in the chemical properties of elements, as well as changes in various properties of simple and complex substances, are associated with the properties of atomic orbitals.

The next most important conclusion, which follows from the analysis of the data given in Table 6, is the conclusion about the periodic change in the nature of the filling of external energy levels with electrons, which causes periodic changes in the chemical properties of elements and their compounds.

The atomic radius is the radius of the sphere that contains the nucleus of an atom and 95% of the density of the entire electron cloud surrounding the nucleus. This is a conditional concept, because. The electron cloud of an atom does not have a clear boundary; it allows one to judge the size of the atom.

The numerical values of the atomic radii of different chemical elements are found experimentally by analyzing the lengths of chemical bonds, i.e. the distances between the nuclei of interconnected atoms. The radii of atoms are usually expressed in nanometers (nm), 1 nm = 10–9 m, picometers (pm), 1 pm = 10–12 m or angstroms (A), 1 A = 10–10 m.

The dependence of atomic radii on the charge of the atomic nucleus Z has a periodic character. Within one period of the periodic system of chemical elements, D.I. Mendeleev, the largest value of the atomic radius of an alkali metal atom. Further, with increasing Z, the value of the radius decreases, reaches a minimum at the atom of the element of group VIIA, and then increases abruptly at the atom of an inert gas, and then even more - at the atom of the alkali metal of the next period.

Ionic radius.

The radii of ions differ from the atomic radii of the corresponding elements. The loss of electrons by atoms leads to a decrease in their effective sizes, and the addition of excess electrons leads to an increase. Therefore, the radius of a positively charged ion (cation) is always less, and the radius of a negatively charged ion (anion) is always greater than the radius of the corresponding electrically neutral atom. Thus, the radius of the potassium atom is 0.236 nm, and the radius of the K + ion is 0.133 nm; the radii of the chlorine atom and the chloride ion Cl are 0.099 and 0.181 nm, respectively. In this case, the radius of the ion differs the more from the radius of the atom, the greater the charge of the ion. For example, the radii of the chromium atom and the Cr 2+ and Cr 3+ ions are 0.127, 0.083, and 0.064 nm, respectively.

Within the main subgroup, the radii of ions of the same charge, like the radii of atoms, increase with increasing nuclear charge

Ionization energy(a measure of the manifestation of metallic properties) is the energy required to detach an electron from an atom.

(Ca 0 - Ca 2+ + 2e - - H).

The more electrons on the outer electron layer, the greater the ionization energy. As the atomic radius increases, the ionization energy decreases. This explains the decrease in metallic properties in periods from left to right and the increase in metallic properties in groups from top to bottom. Cesium (Cs) is the most active metal.

The energy of electron affinity (a measure of the manifestation of non-metallic properties) is the energy that is released as a result of the attachment of an electron to an atom (Cl 0 + 1e - -> Cl - + H). With an increase in the number of electrons on the outer electron layer, the energy of electron affinity increases, and with an increase in the radius of the atom, it decreases. This explains the increase in non-metallic properties in periods from left to right and the decrease in non-metallic properties in the main subgroups from top to bottom.

The affinity energy of an atom to an electron, or just him electron affinity(ε), is called the energy released in the process of addition electron to a free atom E in its ground state with its transformation into a negative ion E - (the affinity of an atom to an electron is numerically equal, but opposite in sign, to the ionization energy of the corresponding isolated singly charged anion).

E + e − = E − + ε

Electronegativity- chemical property of an atom, a quantitative characteristic of the ability of an atom in a molecule to attract electrons from atoms of other elements.

The strongest metallic properties are those elements whose atoms easily donate electrons. The values of their electronegativity are small (χ ≤ 1).

Non-metallic properties are especially pronounced in those elements whose atoms vigorously add electrons.

In each period of the Periodic system, the electronegativity of the elements increases with increasing serial number (from left to right), in each group of the Periodic system, the electronegativity decreases with increasing serial number (from top to bottom).

Element fluorine F has the highest, and the element cesium Cs - the smallest electronegativity among the elements of 1-6 periods.

conditional characteristics of ions used for an approximate estimate of internuclear distances in ionic crystals (See Ionic radii). Values I. r. are naturally related to the position of the elements in the periodic system of Mendeleev. I. r. are widely used in crystal chemistry (see. Crystal chemistry), making it possible to reveal the regularities in the structure of crystals of various compounds, in geochemistry (see. Geochemistry) in the study of the phenomenon of substitution of ions in geochemical processes, etc.

Several systems of values of I. are offered. These systems are usually based on the following observation: the difference between the internuclear distances A - X and B - X in ionic crystals of the composition AX and VC, where A and B are a metal, X is a non-metal, practically does not change when X is replaced by another non-metal similar to it ( for example, when replacing chlorine with bromine), if the coordination numbers of similar ions in the compared salts are the same. It follows from this that I. p. possess the property of additivity, i.e., that the experimentally determined internuclear distances can be considered as the sum of the corresponding "radii" of the ions. The division of this sum into terms is always based on more or less arbitrary assumptions. I. R. systems proposed by different authors differ mainly in the use of various initial assumptions.

The tables give I. p., corresponding to different values of the oxidizing number (see. Valence). With its values other than +1, the oxidation number does not correspond to the actual degree of ionization of atoms, and I. p. acquire an even more conventional meaning, since the bond can be largely covalent in nature. Values I. r. (in Å) for some elements (according to N.V. Belov and G.B. Bokiy): F - 1.33, Cl - 1.81, Br - 1.96, I - 2.20, O 2- 1 .36, Li + 0.68, Na - 0.98, K + 1.33, Rb + 1.49, Cs + 1.65, Be 2+ 0.34, Mg 2+ 0.74, Ca 2+ 1.04, Sr 2+ 1.20, Ba 2+ 1.38, Sc 3+ 0.83, Y 3+ 0.97, La 3+ 1.04.

V. L. Kireev.

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Because at n. y. Since it is difficult to observe molecules with ionic bonds and at the same time a large number of compounds that form ionic crystals are known, then when it comes to ionic radii, these are almost always the radii of ions in crystals. Internuclear distances in crystals have been measured by X-ray diffraction since the beginning of the 20th century, now it is an accurate and routine method, there is a huge amount of reliable data. But when determining ionic radii, the same problem arises as for covalent ones: how to divide the internuclear distance between neighboring cation and anion?

Therefore, it is necessary to use independent, usually calculated values of ionic radii for at least one ion. The assumptions underlying these calculations are generally well founded. So, in the popular system of Pauling ionic radii, the values of R K + \u003d 1.33 Å and R C l - \u003d 1.81 Å are used.

Table 18

Ionic radii, in Å

Note. Holschmidt (G) and Pauling (P) ionic radii values are from Cotton F., Wilkinson J., Modern Inorganic Chemistry; according to Shannon-Pruitt (Sh) - from the textbook by M. Kh. Karapetyants, S. I. Drakin.

There are quite a large number of systems (scales) of effective radii, including ionic ones. These scales differ in some basic assumptions. For a long time, the Goldschmidt and Pauling scales were popular in crystal chemistry and geochemistry. Known scale Bokiya, Ingold, Melvin-Hughes, Slater and others. V Lately the scale proposed by the physicists Shannon and Pruitt (1969) has become widespread, in which the boundary between ions is considered to be the point of minimum electron density on the line connecting the centers of the ions. In table. 18 shows the values of a number of ionic radii on three different scales.

When using effective ionic radii, one should understand the conditionality of these quantities. So, when comparing radii in series, it is naturally correct to use the values of the radii on any one scale, it is completely wrong to compare the values taken for different ions from different scales.

The effective radii depend on the coordination number, also for purely geometric reasons. Given in Table. 18 data refer to a crystal structure of the NaCl type, i.e. with CN = 6. Due to the geometry, to determine the radii of ions with CN 12, 8 and 4, they must be multiplied by 1.12, 1.03 and 0.94, respectively. In this case, it should be borne in mind that even for the same compound (during a polymorphic transition), a real change in the interatomic distance will include, in addition to the geometric contribution, a change associated with a change in the nature of the bond itself, i.e., the “chemical contribution”. Naturally, the problem of separating this contribution into cation and anion again arises. But these changes are usually insignificant (if the ionic bond is maintained).

The main regularities of the change in radii along the PS, discussed in Sec. 2.4 for orbital and higher for covalent radii are also valid for ionic ones. But specific values of effective ionic radii, as can be seen from Table 18, can differ significantly. It should be noted that according to the later and probably more realistic Shannon-Pruitt system, the radii of cations, as a rule, are larger, and anions are smaller than their traditional values (although isoelectronic cations are still much “smaller” than anions).

The size of ions is determined by the force of attraction of external electrons to the nucleus, while the effective charge of the nucleus is less than the true one due to screening (see Section 2.2.2). Therefore, the orbital radii of cations are smaller and anions larger than the neutral atoms from which they were formed. In table. 19 compares the orbital radii of neutral atoms and ions with the effective ionic radii according to Goldschmidt (from the textbook by Ya. Ugai). The difference in orbital radii between an atom and an ion is much greater for cations than for anions, since for the atoms listed in the table, all the electrons of the outer layer are removed during the formation of cations, and the number of layers decreases by one. This situation is also typical for many other (though not all) common cations. When, for example, an anion F is formed, the number of electron layers does not change and the radius almost does not increase.

Table 19

Comparison of orbital and effective radii

Although the comparison of two conventional values, orbital and effective radii, is conditionally doubly, it is interesting to note that the effective ionic radii (regardless of the scale used) are several times larger than the orbital radii of ions. The state of particles in real ionic crystals differs significantly from free non-interacting ions, which is understandable: in crystals, each ion is surrounded and interacts with six to eight (at least four) opposite ions. Free doubly charged (let alone multiply charged) anions do not exist at all; the state of multiply charged anions will be discussed in Sec. 5.2.

In a series of isoelectronic particles, the effective ionic radii will decrease with an increase in the positive charge of the ion (R Mg 2+< R Na + < R F - и т. п.), как и орбитальные радиусы (разумеется, сравнение корректно в пределах одной и той же шкалы).

The radii of ions with noble gas electronic configurations are much larger than those of ions with d- or f-electrons in the outer layer. For example, the radius (on the Goldschmidt scale) of K + is 1.33 Å, and Cu + from the same 4th period is 0.96 Å; for Ca 2+ and Cu 2+ the difference is 0.99 and 0.72 Å, for Rb + and Ag + 1.47 and 1.13 Å, respectively, etc. The reason is that when going from s- and p-elements to d-elements, the charge of the nucleus increases significantly while maintaining the number of electron layers, and the attraction of electrons by the nucleus increases. This effect is called d-compression ; it manifests itself most clearly for f-elements, for which it is called lanthanide compression : the ionic radius decreases in the lanthanide family from 1.15 Å for Ce 3+ to 1.00 Å for Lu 3+ (Shannon–Pruit scale). As already mentioned in sect. 4.2, a decrease in the radius leads to a greater polarizing effect and a lower polarizability. However, ions with an 18-electron shell (Zn 2+ , Cd 2+ , Hg 2+ , Ag + , etc.) have a higher polarizability compared to ions with noble gas shells. And if in crystals with noble-gas shells (NaF, MgCl 2, etc.) polarization is mainly one-sided (anions are polarized under the action of cations), then for 18-electron crystals an additional polarization effect appears due to the polarization of cations by anions, which leads to an increase in their interaction, bond strengthening, reduction of interatomic distances. For example, the Shannon–Pruitt ionic radius of Ag+ is 1.29 Å, which is comparable to 1.16 and 1.52 Å for Na+ and K+, respectively. But due to the additional polarization effect, the interatomic distances in AgCl (2.77 Å) are smaller than even in NaCl (2.81 Å). (It is worth noting that this effect can also be explained from a slightly different position - an increase in the covalent contribution to the bond for AgCl, but by and large this is the same thing.)

We recall once again that in real substances there are no monatomic ions with a charge of more than 3 units. CGSE; all the values of their radii given in the literature are calculated. For example, the effective radius of chlorine (+7) in KClO 4 is close to the value of the covalent radius (0.99 on most scales) and much larger than the ionic one (R С l 7+ = 0.26 Å according to Bokiya, 0.49 Å according to Ingold) .

There is no free proton H + in substances, the polarizing effect of which, due to its ultra-small size, would be enormous. Therefore, the proton is always localized on some molecule - for example, on water, forming a polyatomic ion H 3 O + of "normal" size.