*3.2. Thermal Deformations*

Figures 5 and 6 show the X-ray patterns of L-ala and L-ser, respectively, registered at various temperatures using the TRPXRD method. According to the data obtained, in the temperature range of 23–200 ◦C, L-serine and L-alanine do not undergo any polymorph transformations. Both components are exposed to thermal deformations manifested as various shifts of the peaks either towards low or high 2θ values depending on the *hkl* indices of the peaks. It should be noted that a small splitting of the unambiguously indexed peak 020 in Figure 6, which is present at lower temperatures, is most likely caused by texture effects.

**Figure 5.** X-ray patterns (2θ CoKα) of an L-ala sample obtained at various temperatures.

**Figure 6.** X-ray patterns (2θ CoKα) of an L-ser sample obtained at various temperatures.

Figure 7 presents a cutout of the temperature-resolved X-ray patterns of a sample with the L-ser/L-ala ratio of 90/10 studied in a temperature range between 25 and 210 ◦C. Initially, the sample was clearly a physical mixture of L-ser- and L-ala-rich solid solutions (as already mentioned in Figure 4). Despite a very low L-ala content, the existence of a two-phase mixture is obvious in the X-ray pattern by the presence of the 012 peak, as the most intensive peak of the L-ala phase. This peak is located close to the 020 peak of the L-ser phase (see the arrows in Figure 7). As the temperature rises, both peaks shift towards low 2θ values, with the shift of the 012 Ala peak being greater than that of the 020 Ser peak. Furthermore, the intensity of the 012 Ala peak gradually decreases until it disappears at 175 ◦C, while the intensity of the 020 Ser peak slightly increases, despite the fact that the sublimation point of L-ala (315 ◦C) significantly exceeds that of L-ser (228 ◦C). This could be a result of an increase in the isomorphic miscibility of L-ser and L-ala molecules when the temperature is close to 175 ◦C. This deems probable if one takes into account the following considerations: (1) the mixture with a similar composition of L-ser/L-ala = 93/07 was shown to form a solid solution at room temperature (see Figure 4), and (2) elevated temperatures usually cause the limits of solid solutions to widen.

**Figure 7.** Fragments of the X-ray pattern (2θ CoK<sup>α</sup> = 20–28◦) of a sample with the L-ser/L-ala ratio of 90/10 registered at different temperatures.

Figure 8 shows changes in the orthorhombic cell parameters and volume *V* of L-ala and L-ser versus temperature. As the temperature increases, the *a* parameter decreases, while the *b* and *c* parameters, as well as the *V* volume of the orthorhombic cells of L-ala and L-ser, increase. Thereby, the changes of both parameters and volume are more pronounced in the unit cell of L-ala than for L-ser. The functions plotted allowed to estimate the thermal expansion coefficients (CTE) of the volumes (αv) of the corresponding orthorhombic cells. It is to be mentioned that the <sup>α</sup><sup>v</sup> <sup>=</sup> 170.8 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦C−<sup>1</sup> obtained for L-ala almost by half exceeds the corresponding value calculated for L-ser, <sup>α</sup><sup>v</sup> <sup>=</sup> 113.2 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ◦C<sup>−</sup>1.

**Figure 8.** Changes in orthorhombic cell parameters *a*, *b*, and *c* (Å) and volume *V* (Å3) versus the temperature for (**a**) L-ala and (**b**) L-ser.

The temperature dependences of the orthorhombic cell parameters and volume *V* were approximated by polynomials of the first and second order. These data were used to calculate the parameters of the thermal deformation tensor and the coefficients of thermal expansion along the crystallographic axes of L-ala and L-ser, which are summarized in Table 2.

**Table 2.** Thermal expansion coefficients (<sup>α</sup> <sup>×</sup> 10−<sup>6</sup> ◦C<sup>−</sup>1) of the L-ala and L-ser orthorhombic crystal structures along the axes of the thermal deformation tensor: α<sup>11</sup> = α*a*, α<sup>22</sup> = α*b*, and α<sup>33</sup> = α*c*.


The data represented in this table, in turn, were used for plotting the figures of the thermal expansion coefficients (CTE) for L-ala (Figure 9) and L-ser (Figure 10). For better understanding, the figures also show projections of the figures onto the *ab*, *ac*, and *bc* planes of the corresponding crystal structures.

**Figure 9.** Projections of the figures of the thermal expansion coefficients (CTE) onto the *ab*, *ac, and bc* planes of the L-ala orthorhombic cell. The CTE figures are plotted for the temperatures of 23, 100, and 200 ◦C. Hydrogen bonds are shown as dashed lines. The projections of the orthorhombic cell are plotted using the structural data from CSD (identifier LALANINE54) [35].

An examination of the CTE figures for three different temperature conditions reveals that the thermal deformations of the crystal structures of both L-ala and L-ser are distinctly anisotropic. Both the crystal structures demonstrate a noticeable thermal expansion along the crystallographic axes *b* and *c* and a very significant negative (anomalous) thermal expansion (more precisely, contraction) in the direction of the *a* axis. The crystal structures of the amino acids L-ala and L-ser can be considered as frame structures containing relatively large cavities bound by hydrogen and Van der Waals contacts. When heated, the so-called "hinge mechanism" is realized [36,37]. Its most important feature is the synchronous change of two linear parameters of the unit cell in opposite directions with the "neutral" behavior of the third parameter and the volume. In the present case, both amino acids show a multidirectional synchronous change in the parameters *a* and *b*, as the hinges can be considered the "frames" of molecules connected by hydrogen and Van der Waals bonds. When heated, some of the atoms move away from each other, which leads to the convergence of the other part of the atoms with each other. In this case, one or another specific anisotropy is caused by the different geometries and concentrations of the hydrogen bonds of the N–H ... O and O–H ... O type in the crystal structures of the acids. At the same time, despite some similarities, the thermal deformations of L-ala and L-ser

have some individual patterns. In this connection, the differences of the two amino acid molecules with the different end groups (L-ala: CH3 group; L-ser: CH2OH group) should be mentioned.

**Figure 10.** Projections of the figures of the thermal expansion coefficients (CTE) onto the *ab*, *ac*, and *bc* planes of the L-ser orthorhombic cell. The CTE figures are plotted for the temperatures of 23, 100, and 200 ◦C. Hydrogen bonds are shown as dashed lines. The projections of the orthorhombic cell are plotted using the structural data from CSD (identifier LSERIN41) [35].

*L-alanine* (Figure 9, Table 2): For this amino acid, the rise of temperature results in a very considerable increase in the thermal expansion coefficients in the direction of the *b* axis, while they only slightly change in the *c* direction. In the *a* direction, the negative thermal expansion (contraction) coefficient increases noticeably. As a whole, the thermal deformation anisotropy increases with the elevation of temperature, but this process follows different patterns depending on the projection onto the *ab*, *ac*, and *bc* crystal planes.

In the projection onto the *ab* plane, the L-ala molecules are interconnected with the N–H ... O bonds to form chains positioned along the *a* direction. In the opposite direction (in the direction of the *b* axis), the contacts are much weaker due to their Van der Waals nature. Consequently, the maximum thermal expansion is observed along the *b* axis and the negative thermal expansion takes place along the *a* axis. As seen from the projection onto the *ac* plane, the hydrogen bonds of the N–H ... O type exist in the direction of both *a* and *c* axes, but their geometries and concentrations differ depending on the particular direction and, therefore, the hydrogen contacts have different strengths. In a virtual "competition" between the hydrogen bonds, those positioned along the *c* axis are the weakest, and so this direction is characterized by a relatively low thermal expansion, while along the *a* axis the structure contracts. The same reasoning can be followed to examine thermal expansion anisotropy in the projection onto the *bc* plane.

*L-serine* (Figure 10, Table 2): The elevation of temperature results in an increase in the thermal expansion coefficients in the direction of the *b* axis, but to a lesser extent in comparison with the L-ala molecule. Along the *c* axis, the thermal expansion coefficient becomes noticeably greater, while the negative thermal expansion coefficient in the direction of the *a* axis does not change. This is the principal difference between the thermal deformations in L-ser and L-ala. The anisotropy of the thermal deformations in L-ser can be observed to have various manifestations in the projections onto the *ab*, *ac*, and *bc* crystal planes.

In the direction of the *a* axis, the thermal expansion is negative (anomalous) due to the presence of strong hydrogen bonds of the N–H ... O and O–H ... O types along this direction. In the *bc* plane, the influence of the N–H ... O hydrogen bonds is reinforced by the Van der Waals contacts made by the methylene (CH2) groups. In the neighboring molecules, these groups are directed towards each other. As a result, the crystal structure undergoes thermal expansion in the directions of the crystallographic axes *b* and *c*. It is interesting to note that in this plane the thermal deformation anisotropy was not observed and, consequently, was not affected by alterations of temperature.
