STRUCTURE AND SOME PROPERTIES OF CRYSTAL HYDRATES

K. M. KEVROLEVA

(Presented by the scientific seminar on dielectrics)

The powerful development of industry, especially power engineering, requires the creation of new types of insulation that meet the complex of requirements imposed by the heightened demands of operation.

In order to obtain materials with any predetermined properties, it is necessary to clarify the significance and properties of the individual elements of which solid bodies consist.

There is no systematic information in the literature on the influence of water of crystallization on the electrical and mechanical properties of dielectrics, although natural crystal hydrates (mica, talc, kaolin, gypsum) are widely used as raw materials for insulating materials. A distinctive feature of crystal hydrates is the presence in their lattice of dipole elements either in the form of molecules of water of crystallization, or in the form of hydroxyl \(OH\) and hydrogen ion \(H^{+}\), if the crystals contain constitutionally bound water. The crystal form, interionic distances, the associated bond energy in the lattice of the compound, and a number of other physicochemical properties of crystal hydrates are determined by the quantity and arrangement of these polar structural elements.

Without dwelling in detail on the classification of crystal hydrates (considerable attention has been devoted to this question in the works of J. D. Bernal and Fowler [1] [2], Wells [3], Stillwell [4], Rice [5], Kapustinskii [6], and others), we note that the vitriols considered by us, \(RSO \cdot nH_{2}O\), where \(R = Mg, Zn, Fe, Ni, Co, Cu\), and \(n\) varies from 1 to 7, belong to the type of crystal hydrates in which the water molecules are bound to definite ions (coordination-bound water).

Gypsum, talc, and micas belong to the type of layered crystal hydrates; ice has a molecular lattice. A characteristic determining a number of properties of alkali-halide crystals is the energy of the crystal lattice [7]. To determine the influence of water molecules entering the lattice on the properties of a compound, it is necessary to determine how the energy of the crystal lattice changes when the number of polar elements in the crystal hydrate is increased or decreased. Crystal hydrates are complex heterogeneous compounds, an essential feature of which

is the presence in the lattice of at least two types of chemical bond: within the complex ion and between complex ions.

The vitriols considered by us have the unchanged anion \(\mathrm{SO_4}\); the covalent forces acting within the anion are so significant that the distance within the complex \(\mathrm{SO_4^{--}}\) does not change when it is surrounded by different cations. In the complex cation \([\mathrm{R(H_2O)_n}]^{++}\), forces of ion–dipole interaction act between the excess charge of the central ion and the permanent dipoles of the water molecules, weakening the surface density of the complex cation (according to J. D. Bernal [2], the charge on the surface of \(\mathrm{Mg^{2+}}\) is \(\simeq 0.27\, e/\text{\AA}^2\), the mean charge on the surface of the complex \([\mathrm{Mg(H_2O)_6}]^{++} \simeq 0.015\, e/\text{\AA}^2\)), thereby reducing the strength of the bond between the complex cation and the complex anion.

The structural formulas of crystal hydrates with an odd number of water molecules according to Kapustinskii [6] and Syrkin and Dyatkina [8] are given in Figs. 1 and 2.

Fig. 1. Structural formula of crystal hydrates of the type
\(\mathrm{RSO_4 \cdot nH_2O}\) (\(n\) is the coordination number of the cation) according to
A. F. Kapustinskii

Fig. 2. Structural formula of crystal hydrates of the type
\(\mathrm{RSO_4 \cdot nH_2O}\) (\(n\) is the coordination number of the cation) according to
Ya. K. Syrkin

According to the formulas presented, there are water molecules of two different types in crystallographic respect. According to Kapustinskii, the first water molecule, which still falls within the very considerable field

of the cation, undergoes decomposition, with OH− attaching to the cation and thereby lowering the charge density on the surface of the cation to such an extent that the subsequent water molecules arrange themselves around it only under the action of ion–dipole attraction forces. The hydrogen ion attaches to the anion. Thus, the first water molecule enters the compound constitutionally, and by this the author [6] explains the special thermal effects of its attachment.

According to Syrkin and Dyatkina (Fig. 2), the odd water molecule is connected by hydrogen bonds with the group \(\mathrm{SO}_4^{--}\) and with other water molecules. Between the water molecules in the complex cation, according to the investigations of Batsanov [9], hydrogen-bonding forces act.

We have calculated the lattice energy of crystal hydrates from Kapustinskii’s equation [10]:

\[ U_k=\frac{287.2 \sum Z_k \sum Z_a \cdot n}{(r_k+r_a)} \left(1-\frac{0.345}{r_k+r_a}\right), \]

where
\[ \begin{aligned} Z_k&\text{— charge of the cation,}\\ Z_a&\text{— charge of the anion,}\\ n&\text{— number of ions,}\\ r_k,\ r_a&\text{— radii of the anion and cation.} \end{aligned} \]

The magnitude of the interionic distance \(r_m \simeq r_k+r_a\) was determined by the method of Yatsimirskii [11], proposed by him for complex compounds. Knowing the density of the compound \(d\), its molecular weight \(M\), and the number of complex ions forming the molecule \(n\), we determine the ionic concentration \(J\) from the formula:

\[ J=\frac{1000,d\cdot n}{M}. \]

The magnitude of the interionic distance is

\[ r_m=\frac{11.85}{\sqrt[3]{J}}\ [\mathrm{A}], \]

where 11.85 is a constant factor.

The calculation data, represented graphically in Fig. 3 and in Table 1, indicate a regular increase in lattice energy as the amount of crystallization water in the compound decreases. From Figs. 4, 5, 6, and 7 it is seen that, with an increase in the number of molecules of crystallization water in the lattice of the crystal hydrate, the interionic distance, heat of formation, molecular refraction, and partial pressure increase, while the energy of the crystal lattice, ionic concentration, mass absorption coefficient of X-rays, density, and refractive index of the compound decrease. The mass absorption coefficient of X-rays for \(\mathrm{NiSO}_4\cdot7\mathrm{H}_2\mathrm{O}\) and \(\mathrm{NiSO}_4\cdot6\mathrm{H}_2\mathrm{O}\) was determined on a URS-70 K1 apparatus with a US-DD-6 type amplifier. During the measurement, the voltage on the X-ray tube was maintained at 62.5 kV, and the tube current at 10 mA. The remaining quantities shown in Figs. 4, 5, 6, and 7 are given from calculated and literature data [18].

Fig. 3. Dependence of lattice energy on the number of molecules of crystallization water in the structure of a crystal hydrate

1 — interionic distance, in Å.
2 — heat of formation, kcal.
3 — lattice energy, kcal/mol.
4 — ionic concentration.
5 — density, g/cm³.

Fig. 4. Physicochemical properties of \( \mathrm{MgSO_4 \cdot nH_2O} \) as a function of the presence in its lattice of molecules of crystallization water

Fig. 5. Molecular refraction of the crystal hydrates \( \mathrm{MgSO_4 \cdot nH_2O} \) as a function of the presence of crystallization-water molecules in the lattice.

Fig. 6. Partial pressure of the crystal hydrates \( \mathrm{MgSO_4 \cdot nH_2O} \) as a function of the presence of crystallization-water molecules in the lattice.

In the figure: \( \lg p \); \(p\) in atm.

In the figure: \( \mathrm{NiSO_4 \cdot nH_2O} \); 1—calculated curve; 2—experimental curve; \(\lambda_{\mathrm{eff}} = 0.400\) Å.
Axis labels: \(M/\rho\); \(n \cdot \mathrm{H_2O}\); number of crystallization-water molecules.

Fig. 7. Mass absorption coefficient of X-rays for crystal hydrates with different numbers of crystallization-water molecules \((\mathrm{NiSO_4 \cdot nH_2O})\).
1—calculated curve, 2—experimental curve.

Table 1

Values of the energies of the crystal lattice of crystal hydrates as a function of the number of molecules of water of crystallization

By interionic distance is meant the distance between the complex cation $[\mathrm{Ni(H_2O)_6}]^{++}$ and the complex anion $[\mathrm{SO_4}]^{--}$.

It may be assumed that a similar relation also extends to crystal hydrates of other structures.

Gypsum, talc, and micas, as mentioned above, have a layered structure. Figure 8 shows a section of the crystal structure of gypsum according to Wells [3]. The layers of CaSO₄ are connected with one another by hydrogen bonds O—H—O, which are the weakest in this structure; this also determines the good cleavage of gypsum along the layers.

Doubled and cemented layers of Si₂O₅, according to Hassel [12], are a basic structural feature of the mineral family of kaolin, talc, micas, and related platy minerals. Two silicic-oxygen tetrahedra are linked by means of an intermediate layer Mg(OH)₂; such a three-layer compound forms a “packet,” whose thickness is 6.8 Å.

The interaction within a packet is determined to a considerable extent by the forces binding silicon with oxygen in the silicate; the bond between packets is effected by weak van der Waals forces.

Part of the crystallization water entering the structure of talc is located partly within and between the packets of talc; the greater part (5.1% of a total 5.5%) enters the structure of talc constitutionally as part of (OH)₄Mg₆Si₈O₂₂ [12].

Fig. 8. Section of the crystal structure of gypsum.
O — Ca++, × — SO₄, ● — H₂O,
-·-·- cleavage line

The structural formula of talc and micas may be written in the following form:

\[ \text{talc}—\mathrm{Mg_3[Si_4O_{10}](OH)_2}, \]

\[ \text{mica phlogopite } \mathrm{KMg_3[Si_3AlO_{10}](OH)_2}, \]

\[ \text{mica muscovite } \mathrm{KAl_2[Si_3AlO_{10}](OH)_2}, \]

where \([\mathrm{Si_4O_{10}}]\) and \([\mathrm{Si_3AlO_{10}}]\) are complex anions, while \(\mathrm{Mg_3(OH)_2}\), \(\mathrm{KMg_3(OH)_2}\), and \(\mathrm{KAl_2(OH)_2}\) should be regarded as complex cations. The energy of the crystal lattice of layered crystal hydrates, according to the proposition of Acad. A. E. Fersman [14], has the following components:

1. Energy due to bonding forces within a packet.

2. Energy determined by interpacket bonds.

The second component, both in the case of gypsum (hydrogen bond), talc (van der Waals forces), and micas (weak ionic), has a small value, and in comparison with the first it may be neglected. The values of the lattice energy of gypsum are presented in Fig. 3. The relation noted earlier between \(u_{\mathrm{cr}}\) and the number of molecules of crystallization water remains valid also for layered structures. The lattice energy of talc and micas, according to our calculations, is equal to: for talc 1760 kcal/mole, phlogopite mica 2700 kcal/mole, muscovite mica 2810 kcal/mole.

The lattice energy of micas is considerably higher than the \(u_{\mathrm{cr}}\) of talc, since the complex cations and anions of the former have a higher charge. The lattice energy of muscovite is higher than the lattice energy of phlogopite, since in the cation of the latter, upon formation of muscovite mica, the ion \(\mathrm{Mg}^{++}\) is replaced by the ion \(\mathrm{Al}^{+++}\), which also has smaller linear dimensions. Both circumstances (increase in valence and decrease in radius) strengthen the bonding forces in the muscovite lattice.

Analogously to layered lattices, in molecular crystallohydrates the forces acting within molecules are more significant than those between molecules.

Fig. 9. Structure of ice.

Figure 9 shows a section of the structure of ice (the oxygen atoms are located at the nodes of a lattice similar to the wurtzite lattice, and are tetrahedrally surrounded by four hydrogen atoms).

The forces of intermolecular interaction in ice, equal, according to G. B. Bokii [15], to the sublimation energy, amount to \(12.2\ \text{kcal/mol}\); the forces of ionic bonding within the molecule, according to our calculations, are equal to \(383\ \text{kcal/mol}\). The total lattice energy of ice is \(395\ \text{kcal/mol}\). It has been established [16], [17] that the electrical and mechanical strength of alkali-halide crystals changes almost linearly with the change in the lattice energy of the compound. It is of both theoretical and practical interest to determine whether this regularity also extends to complex compounds—crystallohydrates.

Conclusions

1. The structure of crystallohydrates is determined by the number of molecules of water of crystallization and by their position in the crystal lattice. A change in the structure of a crystallohydrate leads to a change in a number of its physicochemical properties.

2. An increase in the number of molecules of water of crystallization increases the interionic distance, weakens the bonding forces in the lattice of crystallohydrates, and decreases the energy of the crystal lattice.

As the number of molecules of water of crystallization increases, the partial pressure, molecular refraction, and heat of formation of the compound increase, while the density and the mass absorption coefficient of X-rays of crystallohydrates decrease.

References

1. Bernal K. D. Fowler, R. Journ. Chem. Phys. 1, 515. 1933.
2. Bernal J. D. Uspekhi khimii, vol. 25, no. 5, 643. 1956.
3. Wells A. F. The Structure of Inorganic Substances. Moscow, 1948.
4. Stillwell, Crystall chemistry, London, 1938.
5. Rice. Electronic Structure and Chemical Bond. Izd. IL, Moscow, 1949, p. 417.
6. Kapustinskii A. F. Journal “Mineral’noe syr’e,” No. 6, 1930.
7. Vorob’ev A. A. Izv. Tomskogo politekhn. in-ta, vol. 63, 1945.

1. Syrkin Ya. K. and Dyatkina M. E. Chemical Bond and the Structure of Molecules. Moscow, 1946.
2. Blinov S. S. Bulletin of Moscow University, No. 9, 95, 1954.
3. Kapustinskii A. F. ZhOKh, issues 7–8, vol. XIII, 1949.
4. Yatsimirskii K. B. ZhOKh, issue 11, vol. XVII, 2019, 1947.
5. Gassel O. Crystal Chemistry. ONTI, Leningrad, 1936.
6. Avgustinnik A. I., Vichdergauz V. S. Proceedings of the Leningrad Technological Institute named after Lensovet, issue 20, 63, 1951.
7. Fersman A. E. Geochemistry, vol. III, 1936.
8. Bokii G. B. Introduction to Crystal Chemistry. Moscow State University Press, 1954.
9. Vorob’ev A. A. DAN SSSR, vol. 27, 934, 1940.
10. Vorob’ev A. A. Proceedings of the Tomsk Polytechnic Institute, vol. 83, 27, 1956.
11. Technical Encyclopedia. Handbook of Physical, Chemical, and Technological Quantities, vol. I, Moscow, OGIZ, 1931.

Errata