Particle sizes often determine the type of crystal structure and are important for understanding the occurrence of many chemical reactions. The size of atoms, ions, and molecules is determined by valence electrons. The basis for understanding this issue - the patterns of changes in orbital radii - are presented in subsection. 2.4. An atom has no boundaries and its size is a relative value. Nevertheless, it is possible to characterize the size of a free atom by its orbital radius. But of practical interest are usually atoms and ions in the composition of a substance (in a molecule, polymer, liquid or solid), and not free ones. Since the states of a free and bound atom differ significantly (and, above all, their energy), the sizes must also differ.

For bonded atoms, you can also enter quantities characterizing their size. Although electron clouds of bound atoms can differ significantly from spherical ones, the sizes of atoms are usually characterized by effective (apparent) radii .

The sizes of atoms of the same element significantly depend on the composition of which chemical compound and what type of bond the atom has. For example, for hydrogen, half of the interatomic distance in the H 2 molecule is 0.74/2 = 0.37 Å, and in metallic hydrogen the radius value is 0.46 Å. Therefore, they highlight covalent, ionic, metallic and van der Waals radii . As a rule, in the concepts of effective radii, interatomic distances (more precisely, internuclear distances) are considered the sum of the radii of two neighboring atoms, taking the atoms to be incompressible balls. In the presence of reliable and accurate experimental data on interatomic distances (and such data have been available for a long time for both molecules and crystals with an accuracy of thousandths of an angstrom), one problem remains to determine the radius of each atom - how to distribute the interatomic distance between two atoms . It is clear that this problem can be solved unambiguously only by introducing additional independent data or assumptions.

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Covalent radii
The most obvious situation is with covalent radii for atoms that form nonpolar diatomic molecules. In such cases, the covalent radius is exactly half the interatomic distance

Ionic radii
Since under n. u. It is difficult to observe molecules with ionic bonds and at the same time a large number of compounds are known that form ionic crystals, then when it comes to ionic radii,

Metal radii
Determining metal radii in itself is not a problem - it is enough to measure the internuclear distance in the corresponding metal and divide in half. In table 20 are some meth

Vander Waals radii
Van der Waals radii can be determined by measuring the distances between atoms in a crystal when there is no chemical bond between them. In other words, the atoms belong to different molecules

Self-test questions
1. What are orbital and effective radii? 2. What is the difference between the radius of a pellet and an atom or ion? 3. In what cases is the covalent radius equal to half the length?

Effective atomic charges
When a chemical bond is formed, a redistribution of electron density occurs, and in the case of a polar bond, the atoms become electrically charged. These charges are called effective. They are hara

Effective charges in some ionic crystals
Substance CsF CsCl NaF NaCl LiF LiCl LiI DEO 3.3

Effective charges of atoms in oxides (according to N. S. Akhmetov)
Oxide Na2O MgO Al2O3 SiO2 P2O5 SO

Self-test questions
1. What is the effective charge of an atom? 2. Can the effective charge exceed (in absolute value) the oxidation state of an atom? 3. What is the degree of ionicity of a bond? 4. K

Valence
In general, valence characterizes the ability of the atoms of an element to form compounds containing a certain composition (certain ratios of the amounts of different elements in the compound). Often in

Self-test questions
1. Define the concepts: degree of oxidation; covalency; coordination number; steric number. 2. Determine covalency, oxidation state and CN for: H2S; H

Communication energy
The amount of energy is the most important characteristic of a bond, determining the resistance of substances to heat, lighting, mechanical stress, and reactions with other substances[†]. There are various methods

Binding energies of diatomic molecules in a gas (N. N. Pavlov)
Molecule H2 Li2 Na2 K2 F2 Cl2

Self-test questions
1. Predict the change in the energy of the C–N bond in the series Н3СNН2, Н2СНН, НННН. 2. Predict the change in binding energy in the series O2, S2, Se2

Chemical Bonding and the Periodic Table of Elements
Let us consider the regularities of the structure and properties of some simple substances and the simplest compounds, determined by the electronic structure of their atoms. The noble gas atoms (group VIIIA) are completely

Changes in interatomic distances for simple substances of group VIA
Substance Distance between atoms, Å inside molecules between molecules difference S

Additional
3. General chemistry / ed. E. M. Sokolovskaya. M.: Moscow State University Publishing House, 1989. 4. Ugai Ya. O. General chemistry. M.: Higher. school, 1984. 5. Same. General and inorganic chemistry. M..

Even before the properties of multielectron atoms were calculated quite accurately by the methods of quantum mechanics, information about their structure was obtained through the experimental study of chemical compounds, primarily crystalline ones. However, a complete coincidence of the properties of free atoms and atoms in a crystal did not occur, and it cannot be demanded. On the contrary, when an atom transitions from a free state to a bound state, all its properties naturally change. Let us consider the reasons why such a natural difference arises, as well as the properties of atoms that are discovered when studying a crystal. Their comparison with the original ones, taken as a certain level of comparison, provides a lot of meaningful information about the nature of the chemical bond and the properties of the crystal.

2. EFFECTIVE RADISI OF ATOMS AND IONS

A. Atomic radii

After the discovery of M. Laue (1912), over the next few years, dozens of crystals, mainly minerals and metals, were subjected to X-ray diffraction analysis. Having approximately a hundred values ​​of interatomic distances, V. L. Bragg was able to determine the sizes of individual atoms in a crystal already in 1920. The method for determining the radii of atoms in simple substances, for example in metals, is very simple: you need to divide the shortest interatomic distance in half. Bragg extended this method to other cases, estimating the radius of the sulfur atom to be half the interatomic S-S distance in pyrite FeS2 (rs = 2.05/2 = 1.02 Å). Then it was possible to calculate “along the chain” the radii of other atoms (Zn from ZnS, O from ZnO, etc.). In total, Bragg determined the sizes of about 40 atoms in this way, which provided the basis for a number of comparisons. Thus, it turned out that in the Bragg system the sizes of electronegative atoms (r p = 0.67; r o = 0.65; r Cl =1.05; r s =l.02 Å) are significantly smaller compared to the sizes of electropositive elements (r Na = 1.77; r Mg =l.42; r Sr =l.95 Å, etc.). This conflicted with the Kossel ionic model, according to which electrons are detached from the cation and transferred to the anion, making it larger. Thus, in a Na+ F- crystal consisting of two neon-like ions, the Na+ ion with a nuclear charge of +11 should

be smaller than the F- ion with nuclear charge + 9. Therefore, the use of the Bragg radius system as a universal one had to be abandoned for a long time.

This idea was approached many years later, when it became clear that the mechanism of chemical bond formation is the same and in all cases corresponds principle of maximum overlap electron densities of Slater-Pauling valence shells. This means that we can expect that the atomic radii should be close to the orbital radii of atoms r0, which precisely measure the distance from the nucleus to the maximum electron density of the valence shell. Indeed, the Bragg radius of the Na atom 1.77 Å is close to its orbital radius (1.71 Å), the Al radius 1.35 Å is almost equal to the orbital one (1.31 Å), the S radius is slightly larger than the orbital one (1.02 and 0.81 Å respectively). Using the results of theoretical calculations of r 0, which were completed by 1964, as well as interatomic distances measured for 1200 crystals of various types, J. Slater constructed his system of atomic radii. They turned out to be very close to the Bragg radii (the average deviation is only 0.03 Å).

According to the physical meaning of their derivation, atomic radii should be used primarily in cases where atoms are connected to each other by a covalent or metallic bond.

B. Ionic radii. Derivation of the main taxonomies of ionic radii

The distribution of electron density in essentially ionic crystals is undoubtedly different than in covalent or metallic crystals, namely, it is characterized by a shift in the overlap density to a more electronegative atom, as well as the presence of a minimum electron density along the bond line. It is logical to consider this minimum as the region of contact between individual ions and try to determine their radii as the distance from the nucleus to the specified minimum.

The usual result of X-ray diffraction analysis is the coordinates of atoms in the crystal, that is, data on interatomic distances, which must then be somehow divided into fractions of individual ions. From these experimental data one can obtain only information about the differences in the sizes of atoms or ions and the degree of their constancy within a certain group of compounds. The exception is homoatomic compounds, i.e. crystals of simple substances, for which the problem of determining the atomic radius is solved simply (see the previous section). And in

In the general case, having only the sum of experimental data on interatomic distances, it is impossible to find a way to divide them into the contributions of individual ions - ionic radii. To do this, you need to know at least the radius of one ion or the ratio of the radii of ions in at least one crystal. Therefore, in the 20s, when it became clear that the Bragg radius system did not satisfy the obvious requirements of the ionic model, criteria for such division appeared, using some theoretical or semi-empirical assumptions.

The first in time was the criterion proposed by A. Lande (1920). He suggested that in crystals with large anions and small cations there should be direct contact between the former, i.e., the cations seem to begin to “dangle” slightly in the large void between the anions. This assumption is indeed confirmed by a comparison of interatomic distances (Å), for example, in the following pairs of Mg and Mn compounds with a NaCl-type structure: MgO 2.10; MnO 2.24; ∆ = 0.14; MgS 2.60; MnS 2.61; ∆ = 0.01; MgSe 2.73; MnSe 2.73; ∆ = 0.00. From the values ​​of ∆ it follows that even for sulfides, and even more so for Mg and Mn selenides, the interatomic distances are almost the same. This means that the size of the cations ceases to affect the cell period, which is controlled only by the anion-anion distance equal to R 2 . From here it is easy to calculate the radius of the anion as half of this distance: in our example, r (S2- ) = l.83 Å, r (Se2- ) = 1.93 Å. These values ​​are quite sufficient to further derive a complete system of ionic radii from a certain set of interatomic distances.

In 1926, V. M. Goldshmidt used for these purposes the data of the Finnish scientist Vasasherna, who divided the observed interatomic distances in crystals in proportion to the refractive ratio of the electronic configuration of the ions. Vazasherna found that the radius of O2- is 1.32 Å, and the radius of F- is 1.33 Å. For Goldschmidt, this data was enough to derive a complete system of ionic radii, which was subsequently supplemented and refined several times. The most reasonable and detailed system is R. Shannon and C. Pruitt (1970) (Appendix 1-9).

Almost simultaneously with Goldschmidt and independently of him, L. Pauling (1927) developed a different approach to estimating ion radii. He suggested that in crystals such as Na+ F-, K+ Cl-, Rb+ Br-, Cs+ I-, consisting of isoelectronic ions similar to the same inert gas (Ne, Ar, Xe and Kr, respectively), the radii

cation and anion must be inversely proportional to the effective nuclear charges acting on the outer electron shells.

Rice. 48. Periodic dependence of atomic (1) and ionic (2) radii on the atomic number of the element Z.

The close agreement of all the main systems of ionic radii based on the independent criteria of Goldschmidt, Pauling and Lande turned out to be remarkable. At the end of the last century, in 1987, Pauling recalled that, for example, in 1920 Lande found a radius value of 2.14 Å for the I ion, three years later Vazasherna determined the value of this radius as 2.19 Å, and even after four years later he himself found an intermediate value of 2.16 Å for it. This coincidence could not fail to make a great impression on contemporaries and subsequent generations of scientists, as a result of which, over time, the idea arose that the concept of “ion radius” reflects some objective reality. The statement of A.E. Fersman still remains true: “...no matter how one regards the physical meaning of ion radii... they have enormous practical significance as quantities that can be easily and simply operated both in crystal chemistry and in geochemistry". Indeed, having a set of quantities of the order of hundreds - the number of chemical elements - one can approximately predict many thousands of interatomic distances, their differences or ratios. For

In crystal chemistry, this circumstance radically facilitates the analysis of experimental data and provides the possibility of condensing enormous information.

In Fig. Figure 48 shows the periodic dependence of atomic and ionic (CN = 6) radii on the atomic number of the element. One of the most characteristic features of this dependence is a decrease in the size of cations from the beginning to the end of each period. The steep drop in ion sizes from low-valent (alkali metals) to highly charged (N5+, Cr6+, etc.) is disrupted only in families of transition metals, where the decrease in radii is slower. The long-term gradual decrease in the radii of TR3+ lanthanide ions was called by V. M. Goldshmidt lanthanide compression: the radii of heavy lanthanides (Lu3+) are almost 0.2 Å less than the radii of light ones (La3+). The size of the Y3+ ion turns out to be identical to the Ho3+ radius, i.e., in geometric properties it is closer to heavy TR, which is therefore sometimes called the “yttrium” group in contrast to the lighter lanthanides of the “cerium” group.

The main significance of lanthanide compression is that period VI elements appear to be very close in size to their period V group counterparts. Thus, Hf4+ is 0.02 Å smaller than Zr4+, W6+ is 0.01 Å larger than Mo6+, Ta5+ and Nb5+ are almost the same size. This effect also brings the sizes of heavy platinoids (Os, Ir, Pt) closer to lighter ones (Ru, Rh, Pd), Au and Ag, etc. It plays a large role in the isomorphism of these elements.

Looking carefully at Fig. 48, the reader can easily notice that in most cases the course of the ionic radius curve seems to repeat a similar course of the atomic radius curve, with the former shifting downward relative to the latter. Indeed, according to J. Slater (1964), although atomic and ionic radii measure completely different things, there is no contradiction between them. By saying “various things,” he meant that atomic radii are the distances from the nucleus to the maximum overlap of electron densities of nearest neighbors, and ionic radii, on the contrary, to the minimum in electron density along the bond line. However, despite this, both series of radii are suitable for approximate determination of interatomic distances in crystals of various types, since the radii of electropositive atoms are approximately 0.85 ± 0.10 Å larger than the ionic radii of the corresponding cations, while the radii of electronegative atoms are the same amount less than their ionic radii: r at. – r cat. ≈ r an. – r at. ≈ 0.85 Å. Hence it is clear that the sum of atomic and ionic radii for

for each given pair of elements should be almost the same. For example, the sum of the ionic radii of Na+ and Cl- is 1.02+1.81 = 2.83 Å, and the sum of the atomic radii of Na

and Cl: 1.80+1.00 = 2.80 Å.

To use the ionic radius system correctly, you need to remember the following basic rules.

Firstly, as was noted long ago, the radius of the ion depends on the coordination number: the higher the coordination number, the larger the radius of the ion. If the tables give standard ion radii for CN = 6, then for other CNs approximate corrections should be introduced: increase the radius by several percent for CN > 6 and decrease it by several percent for CN< 6.

The radius of an ion greatly depends on its charge. For a cation, as the charge increases, it noticeably decreases. So, for Mn2+ it is equal to 0.97 (CN = 6), for Mn4+ - 0.68 (CN = 6),

for Mn6+ - 0.41 (CN = 4) and Mn7+ - 0.40 Å (CN = 4).

In Appendix 1-9, two series of ionic radius values ​​are indicated for transition metal ions - in high-spin (hs) and low-spin (ns) states. In Fig. 49, a and 49, b show the empirical radii of di- and trivalent 3d elements for octahedral coordination in low-spin (lower curve) and high-spin (upper curve) states.

Rice. 49. Effective ionic radii of transition elements of the IV period: a - divalent, b - trivalent, q - number of d-electrons. Empty circles refer to the high-spin state of the ion

It can be seen that the minima in the lower curves occur on Fe2+ and Co3+, respectively, i.e., on ions with six d electrons, which in the low spin state are all located in the lower orbitals. On the other hand, the maxima in the upper curves occur on Mn2+ and Fe3+, i.e., ions with five d electrons, which

Periodic properties of elements

Periodicity is expressed in the structure of the electron shell of atoms, therefore, properties that depend on the state of electrons are in good agreement with the periodic law: atomic and ionic radii, ionization energy, electron affinity, electronegativity and valence of elements. But the composition and properties of simple substances and compounds depend on the electronic structure of atoms, therefore periodicity is observed in many properties of simple substances and compounds: temperature and heat of melting and boiling, length and energy of chemical bonds, electrode potentials, standard enthalpies of formation and entropies of substances, etc. d. The periodic law covers more than 20 properties of atoms, elements, simple substances and compounds.

According to quantum mechanics, an electron can be located at any point around the nucleus of an atom, both close to it and at a considerable distance. Therefore, the boundaries of atoms are vague and indefinite. At the same time, in quantum mechanics the probability of electron distribution around the nucleus and the position of the maximum electron density for each orbital are calculated.

Orbital radius of an atom (ion)is the distance from the nucleus to the maximum electron density of the most distant outer orbital of this atom (ion).

Orbital radii (their values ​​are given in the reference book) decrease over periods, because An increase in the number of electrons in atoms (ions) is not accompanied by the appearance of new electronic layers. The electron shell of an atom or ion of each subsequent element in a period becomes denser compared to the previous one due to an increase in the charge of the nucleus and an increase in the attraction of electrons to the nucleus.

Orbital radii in groups increase because the atom (ion) of each element differs from its superior one by the appearance of a new electronic layer.

The change in orbital atomic radii for five periods is shown in Fig. 13, from which it is clear that the dependence has a “sawtooth” shape characteristic of the periodic law.

Rice. 13. Dependence of orbital radius

from the atomic number of elements of the first – fifth periods.

But during periods, the decrease in the size of atoms and ions does not occur monotonically: small “bursts” and “dips” are observed in individual elements. As a rule, the “gaps” contain elements whose electronic configuration corresponds to a state of increased stability: for example, in the third period it is magnesium (3s 2), in the fourth period it is manganese (4s 2 3d 5) and zinc (4s 2 3d 10) etc.

Note. Calculations of orbital radii have been carried out since the mid-seventies of the last century thanks to the development of electronic computing technology. Previously used effective radii of atoms and ions, which are determined from experimental data on internuclear distances in molecules and crystals. It is assumed that the atoms are incompressible balls that touch their surfaces in compounds. The effective radii determined in covalent molecules are called covalent radii, in metal crystals – metal radii, in compounds with ionic bonds – ionic radii. Effective radii differ from orbital radii, but their change with atomic number is also periodic.

EFFECTIVE ATOMIC RADIUS - see Radius is atomic.

Geological Dictionary: in 2 volumes. - M.: Nedra. Edited by K. N. Paffengoltz et al.. 1978 .

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The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which electrons orbit. The sequence of elements in Mendeleev's Periodic Table corresponds to the sequence of filling electron shells. The effective radius of the ion depends on the filling of the electron shells, but it is not equal to the radius of the outer orbit. To determine the effective radius, atoms (ions) in the crystal structure are represented as touching rigid balls, so that the distance between their centers is equal to the sum of the radii. Atomic and ionic radii are determined experimentally from X-ray measurements of interatomic distances and calculated theoretically based on quantum mechanical concepts.

The sizes of ionic radii obey the following laws:

1. Within one vertical row of the periodic table, the radii of ions with the same charge increase with increasing atomic number, since the number of electron shells, and therefore the size of the atom, increases.

2. For the same element, the ionic radius increases with increasing negative charge and decreases with increasing positive charge. The radius of the anion is greater than the radius of the cation, since the anion has an excess of electrons, and the cation has a deficiency. For example, for Fe, Fe 2+, Fe 3+ the effective radius is 0.126, 0.080 and 0.067 nm, respectively, for Si 4-, Si, Si 4+ the effective radius is 0.198, 0.118 and 0.040 nm.

3. The sizes of atoms and ions follow the periodicity of the Mendeleev system; exceptions are elements from No. 57 (lanthanum) to No. 71 (lutetium), where the radii of the atoms do not increase, but uniformly decrease (the so-called lanthanide contraction), and elements from No. 89 (actinium) onwards (the so-called actinide contraction).

The atomic radius of a chemical element depends on the coordination number. An increase in the coordination number is always accompanied by an increase in interatomic distances. In this case, the relative difference in the values ​​of atomic radii corresponding to two different coordination numbers does not depend on the type of chemical bond (provided that the type of bond in the structures with the compared coordination numbers is the same). A change in atomic radii with a change in coordination number significantly affects the magnitude of volumetric changes during polymorphic transformations. For example, when cooling iron, its transformation from a modification with a face-centered cubic lattice to a modification with a body-centered cubic lattice, which takes place at 906 o C, should be accompanied by an increase in volume by 9%, in reality the increase in volume is 0.8%. This is due to the fact that due to a change in the coordination number from 12 to 8, the atomic radius of iron decreases by 3%. That is, changes in atomic radii during polymorphic transformations largely compensate for those volumetric changes that should have occurred if the atomic radius had not changed. Atomic radii of elements can only be compared if they have the same coordination number.

Atomic (ionic) radii also depend on the type of chemical bond.

In metal bonded crystals, the atomic radius is defined as half the interatomic distance between adjacent atoms. In the case of solid solutions, metallic atomic radii change in a complex way.

The covalent radii of elements with a covalent bond are understood as half the interatomic distance between nearest atoms connected by a single covalent bond. A feature of covalent radii is their constancy in different covalent structures with the same coordination numbers. Thus, the distances in single C-C bonds in diamond and saturated hydrocarbons are the same and equal to 0.154 nm.

Ionic radii in substances with ionic bonds cannot be determined as half the sum of the distances between nearby ions. As a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions differs from spherical. There are several approaches to estimating the ionic radii. Based on these approaches, the ionic radii of elements are estimated, and then the ionic radii of other elements are determined from experimentally determined interatomic distances.

Van der Waals radii determine the effective sizes of noble gas atoms. In addition, van der Waals atomic radii are considered to be half the internuclear distance between the nearest identical atoms that are not connected to each other by a chemical bond, i.e. belonging to different molecules (for example, in molecular crystals).

When using atomic (ionic) radii in calculations and constructions, their values ​​should be taken from tables constructed according to one system.