RU119504U1 - FLOOR NANO-SCALE MODEL OF CRYSTAL STRUCTURE OF SUBSTANCE - Google Patents

Abstract

 1. A model of the crystalline structure of a substance containing volumetric elements in the form of bodies of revolution, simulating particles of a simulated crystalline structure, representing atoms or ions, in compliance with the relative location of these volumetric elements, corresponding to the relative location of these particles, characterized in that these volumetric elements are placed on several parallel parallel to each other flat transparent plates of constant thickness, mounted horizontally one above the other, each of of the elements has the shape of a body of revolution around an axis normal to the surface of the flat transparent plate on which it is placed, and it is made and installed in such a way that it has a part located on one side of the median plane of the specified plate and a symmetrical part located on the other side of this plane, while at least one of these plates contains volume elements that simulate these particles located in the same crystallographic plane of the crystal lattice crystalline structure, and the number of these plates and the volumetric elements placed on them is such that the combination of the latter imitates at least one unit cell of the simulated crystalline structure. ! 2. The model according to claim 1, characterized in that each of these volumetric elements is made in the form of two identical spherical segments mounted symmetrically with respect to each other on both sides of the specified plates on which this volumetric element is placed, and facing its own flat side to her

Description

The utility model relates to educational visual aids intended for demonstration purposes, as well as scientific instruments designed to visualize the spatial structure or structure of crystalline substances during research, the purpose of which is a comparative analysis of the crystalline structures of existing substances and the creation of new substances with a crystalline structure, namely, to a device representing a model of such a structure.

There are various approaches to the constructive implementation of models of the crystalline structure of matter. With all the variety of models, they can be divided into two main groups: “open” and “closed” (see: Deane C. Smith. Bibliography on Molecular and Crystal Structure Models. US department of commerce. National bureau of standards. National Bureau of Standards Monograph 14. Issued May 20, 1960 [1]).

In “closed” models, elements that are usually spheres (sometimes truncated) or polyhedra imitating atoms or ions forming a crystal fill the space almost completely, i.e. placed in such a way that they are touched along the boundaries of the surfaces or along the planes of sections (sections).

The relative position of the elements is fixed in various ways, for example, by giving their surface adhesive properties (see Japan Patent Application No. 2005-292392 [2], publ. 20.10.2005) or by installing miniature magnets in them (see China Patent No. 201812427 [3 ], publ. 04/27/2011). Models of this type may have specific technological advantages, however, they have insufficient visibility precisely because of their congestion, the "closed" nature, the inability to observe and measure the distances between ions or atoms. They are mainly intended to illustrate the type of crystal lattice, the crystal structure, the nature of the packing of particles in a crystal, however, in doing so, they distort either the sizes of atoms (ions), or the distances between these atoms (ions), or both .

“Open” models primarily include ball-rod models (see, for example, V. Potapov. Stereochemistry. Moscow, Chemistry Publishing House, 1988, pp. 10-11 [4]; UK patent No. 1144851 , published on March 12, 1969 [5]).

In these models, elements imitating atoms or ions forming a crystal have such dimensions and are placed at such distances from each other that they can freely observe their relative position and measure the distances between them and the angles between the lines connecting them. This fact is an important advantage of the "open" type models. Designs of models of this type are also very diverse. The most common models are those containing elements in the form of balls simulating atoms or ions forming a crystal, and rod elements oriented in accordance with the geometry of the crystal lattice connecting these balls, which allows the volume structure of the crystal to be displayed.

However, in both user and technological terms, such models are not convenient enough. To preserve the correct display of the mutual arrangement of atoms when using the model, mechanical fixation of the model is necessary, eliminating the possibility of rotation around the rod bonds. Therefore, the assembly of spatial bar structures in compliance with the correct relative positioning of the elements is extremely time-consuming.

The production of such models is difficult to carry out, even if it is necessary to replicate a model of the same crystal. However, such models are most common. For these reasons, they often go on sale unassembled, in the form of a set of balls and rods, with the assembly entrusted to the user. A very difficult task is to make holes in the balls into which the ends of the connecting rods are to be inserted, since in each ball it may be necessary to make several holes oriented in space at certain angles to each other. Known inventions specifically dedicated to means for making such holes (see, for example, the aforementioned patent [5], which describes a device for providing acceptable accuracy in making holes in balls oriented in the required manner).

To the models of the "open" type can also be attributed the device according to Japanese patent No. 2642910 [6] (publ. 08/20/1997). This device has several frames located on vertical racks at different levels with the ability to adjust the position in height. On the frame, in turn, are installed, with the possibility of changing the horizontal position, rails with longitudinal slots. In the latter, there are installed, with the possibility of movement, parts for attaching elements that mimic the particles making up the crystal. In the aggregate, the listed parts of the device’s design and the possibilities of movement that they have, with a sufficient number of these parts, make it possible to install any element that imitates the particle contained in the crystal in almost any position in the space limited by the dimensions of the model. Moreover, the above-mentioned elements installed in the slots of the rails are provided with an additional possibility of adjusting the location in height, i.e. at different distances from the rail, an element that simulates a particle contained in a crystal. This eliminates the need for fewer frames mounted on uprights. In this model, when performing elements simulating particles forming a crystal in the form of balls, there is no problem of making holes in the balls that are oriented relative to each other in a certain way. Nevertheless, as can be seen from the above, the design of the device is very complex, it is also not very suitable for replicating models in assembled form.

A more convenient model described in US patent No. 4014110 (publ. 03/29/1977) [7]. In this model, volume elements in the form of balls imitating atoms or ions are placed on vertical rods mounted on the base. The number of rods and the geometry of their mutual arrangement are selected so that they can be used to place several balls at different heights that simulate the atoms or ions of a crystal of a particular substance. Moreover, such a model is also suitable for illustrating the dense packing of particles in a crystal, although it loses the advantage of clarity because it becomes “closed”. The problem of making holes in the balls, oriented relative to each other in a certain way, is absent in this model, as in the previous one, since it is sufficient to have a single diametrical hole in each ball, and at the same time it is structurally much simpler than the previous one.

The disadvantages of this model include the fact of the presence of rods that obscure the atomic crystal structure and give the impression of the presence of some special vertical bonds between atoms (ions) in the crystal structure. In addition, it is impossible to simulate structures with relatively small interatomic distances in the horizontal projection plane, when the radius of the ball mounted on the rod is greater than the distance to the neighboring rod, which, in this case, will turn from a technological element into an unremovable noise. And in the case when you need to place balls of significantly different sizes on the same vertical line, a rod whose thickness should be less than the diameter of the smallest ball may be too thin to have sufficient rigidity and stability when placing all the balls on it on this vertical. To overcome such situations, it may be necessary to use different scales to display the interatomic distances and sizes of atoms, i.e. violation of the adequacy of the model. Obvious and technological difficulties associated with the need to accurately secure each ball individually at a given height.

This known model is closest to the proposed one.

The technical solution for the proposed utility model is aimed at achieving a technical result, which consists in providing greater manufacturability and higher accuracy of positioning of elements imitating particles (atoms, ions) that make up the crystalline structure, as well as in eliminating the situations noted above in which it is impossible to observe the same scale for the sizes of atoms (ions) and the distances between them. Below, when revealing the essence of the device according to the proposed utility model and considering its specific implementation, other types of technical result will be named.

The model of the crystalline structure of the substance according to the proposed utility model, as well as the indicated closest device to it according to the patent [7], contains volume elements in the form of bodies of revolution simulating particles of the simulated crystal structure, which are atoms or ions, observing the relative arrangement of these elements, corresponding to the relative location of these particles in the simulated crystal.

To achieve the above technical result in the device according to the proposed utility model, in contrast to the closest known device, volumetric elements simulating particles of a simulated crystalline structure are placed on several flat transparent plates of constant thickness parallel to each other. The latter are mounted horizontally one above the other, i.e. volumetric elements are placed on several "floors". These elements are in the form of bodies of revolution about an axis normal to the surfaces of a flat transparent plate. Moreover, they are made and placed in such a way that each of them has a part located on one side of the median plane of the flat transparent plate on which it is placed, and a symmetric part located on the other side of the specified plane. (As you know, the median plane of a plate of constant thickness is a plane at equal distances from the upper and lower surfaces of the plate and dividing its thickness in half. See: Great Soviet Encyclopedia, 3rd edition, M., Sovetskaya Encyclopedia, 1975, v.19, p.637 [8]). In addition, at least one of the plates contains volume elements imitating these particles (atoms or ions), the centers of which belong to the same crystallographic plane of the simulated crystal structure, and the number of these plates and volume elements placed on them is such that a combination of the latter imitates at least one unit cell of a simulated crystal.

The design of the device according to the proposed utility model, which involves the use of several parallel flat transparent plates mounted horizontally one above the other, eliminates the need to individually install each of the three-dimensional elements imitating the particles forming the crystal at the same height, since the same the plate can be placed several of these elements. This feature is interconnected with a feature that characterizes the orientation of the axis of rotation of the generatrix of the volumetric elements, which are bodies of revolution, and the presence of each of the volumetric elements of two parts made and located symmetrically on both sides of the median plane of a flat transparent plate, and also with a sign according to which at least volumetric elements imitating particles, the centers of which belong to the same crystallographic plane of the modeled structure, are placed on one of the plates. Due to the indicated embodiment of volumetric elements, the geometric centers of all elements placed on the same plate are in its median plane, and this plane corresponds to the crystallographic plane of the simulated structure. In real crystal structures, there are usually several crystallographic planes parallel to each other, and to each such plane belong the centers of several particles forming a crystal. Therefore, compliance with the requirements corresponding to the indicated features ensures the correct display in the model of the actual relative arrangement of particles (atoms or ions) and at the same time helps to reduce the total number of plates and, thereby, ensure a more technological model. At the same time, this increases the physical content of the model, because it turns flat transparent plates, which are structural elements of the model, into means for displaying real crystallographic planes, and in the case of modeling crystal structures having a pronounced layered structure, the presence of flat plates in the proposed model is even more increases its visibility. Volumetric elements belonging to the same plate can easily be placed with high accuracy in the right places using preliminary coordinate marking of the plate, which can be easily automated, and when the plates are installed at a certain distance from each other, the accuracy of the relative position of several volumetric elements in the third spatial coordinate. The implementation of volumetric elements in the form of bodies of revolution (not necessarily spherical) allows you to diversify their shape and use this opportunity in specific cases to display atoms (ions) of different types, to display in the same volumetric element several different values of the radius of an atom (ion) defined taking into account the coordination number of a given atom (ion) in a specific simulated crystalline structure according to various existing systems, and other purposes. As for the feature, according to which the number of plates and the volumetric elements placed on them is sufficient to ensure the display of at least one unit cell of the simulated crystal, it is necessary for the model to realize its purpose. At the same time, the proposed design allows, in view of the noted simplicity of the manufacturing and assembly technology, to easily simulate an arbitrary number of unit cells and, thereby, visually display the frequency of their spatial arrangement in a single crystal.

In the proposed scale model, a convenient choice of scale is possible, which makes it possible to visually display nanoscale crystal structures. So, if you select a scale of 10 ⁸ : 1, at which ten centimeters in the model corresponds to one nanometer in the real structure, then, for example, in the model of a carbon nanotube of chirality (5, 5), the centers of five volume elements imitating carbon atoms will be located on an imaginary circles with a diameter of the order of 7 cm at equal angular distances (72 °) at distances between these elements of the order of 1.4 cm.

In the particular case, the particles forming the crystal can be imitated by balls. Also, the particles forming the crystal can be simulated by ellipsoids so that the semiaxes of different lengths of the ellipsoids correspond to different values of the radii of the simulated atoms. For example, one half-axis can be chosen corresponding to the Van der Waals radius, and the other to the covalent radius, which further increases the visibility and physical content of the model. The two semi-axes of the ellipsoid can also correspond to the radii of the atom (ion) due to different electron clouds.

Volumetric elements in the form of balls or ellipsoids of revolution can be installed in the holes of flat plates (for example, on glue). In both cases, the median plane of the plate is a plane of symmetry for these elements.

Volumetric elements both in the above and in other cases can be made composite. So, for example, instead of using balls or ellipsoids installed in the holes of the plate, the volumetric elements can be made, respectively, in the form of two spherical segments or segments of an ellipsoid attached to the plate, i.e. mounted symmetrically on both sides of the plate and facing it with its flat side. At the same time, they are parts of the volumetric element of the model that are symmetrical with respect to the median plane of the plate, and the geometric center of the composite body, which is the volumetric element in this case, is in the indicated median plane.

Each of the volume elements imitating particles forming a crystal can be made in the form of such a body of revolution, the generatrix of which has several maxima located at different distances from the axis of rotation. These distances can be selected corresponding to various known values of the radius of the atom (ion) modeled by the volume element. Moreover, the values of the mentioned maxima themselves can be used to display additional information about atoms (ions), for example, to characterize the frequency of use (citation rating, link rating) for the marked radius related to one or another known system of atomic (ionic) radii. The described implementation of the model is preferable when it is necessary to simultaneously display a series of values of the radius of atoms (ions) determined in accordance with different systems of crystallographic radii, since there are a large number of such systems (see, for example: L.T. Bugaenko, S.M. Ryabykh, AL Bugaenko, An almost complete system of average ionic crystallographic radii and its use for determining ionization potentials, Vestnik Mosk. Unta, Ser.2. Chemistry. 2008. V. 49. No. 6, p.363-384 [ 9]).

The model can be performed in such a way that all volume elements that simulate the same particles of the simulated crystal structure with the equality of their coordination numbers have the shape of the same body of revolution, different from volume elements that simulate other particles of the simulated crystal structure.

In the proposed model, volumetric elements simulating particles forming a simulated crystal can be colored. Moreover, all volume elements imitating the same particles of a simulated crystalline structure have the same color, different from the color of volume elements imitating other particles of this structure. The presence of this possibility (as well as the possibility of giving volumetric elements a non-spherical shape) allows, in cases where some atoms (ions) of the modeled crystal structure to be close in size, to exclude the possibility of mistaken identification of elements imitating atoms (ions) of different types. It is possible to give each volumetric element of the model color one of the spectral lines of its high-temperature radiation, or the color that the substance, atoms or ion of which this volumetric element imitates, in particular, volumetric elements that model metal atoms (ions) can be made of this the metal itself or from another material, but with a coating of this metal. This additionally increases the visibility of the model and facilitates the identification of volumetric elements and the establishment of correspondence between them and the particles forming the simulated crystal.

Flat transparent plates can be made with holes for uprights. In this case, adjacent plates are separated from each other by bushings put on the racks, and to exclude the possibility of moving these plates relative to each other and the racks, the position of the outer plates is fixed. In addition, the plates can be mounted and held on racks at the required distance from each other using clamps, clamping bolts or any other means of fixation, since all these means are equivalent in terms of the technical result provided by the proposed model.

In addition, in any of the above and in other cases, the proposed model can be performed with a base on which the racks are vertically mounted. Flat transparent plates are fixed on racks with their edges. In particular, the fixing can be carried out by means of grooves made in the struts into which the edges of the flat transparent plates are inserted. Moreover, the proposed model has at least two racks, between which are specified flat plates. Each of them is made with two edges parallel to each other, and the grooves in two racks of each pair are made symmetrically with respect to each other. With this embodiment, it is easier to replace one plate with another, with a different set and different arrangement of volumetric elements.

The proposed utility model is illustrated by drawings, on which:

- figure 1 - image of the proposed design model of the crystalline structure, in which volumetric elements that simulate heterogeneous particles of the crystalline structure are represented by balls corresponding to the simulated particle size;

- figure 2 is a traditional schematic representation of the structure of a rock salt crystal;

- on figa, 3b - the implementation of the volumetric element that simulates the particle contained in the crystal, in the form of two identical spherical segments mounted symmetrically with respect to each other on different sides of the plate;

- figure 4 - the implementation of volumetric elements that simulate the particles contained in the crystal, in the form of balls placed in the holes of a flat transparent plate;

- on figa, 5b - the implementation of volumetric elements simulating heterogeneous particles of a crystalline structure, in the form of bodies of revolution of different shapes and colors, placed in the holes of a flat transparent plate, and in the form of two identical parts of such bodies mounted symmetrically with respect to each other to a friend on opposite sides of the plate;

- on figa, 6b - the implementation of the volumetric element simulating the particle contained in the crystal, in the form of an ellipsoid of revolution and in the form of two identical segments of such an ellipsoid, mounted symmetrically with respect to each other on different sides of the plate;

- Fig.7 - the implementation of the volumetric element that simulates the particle contained in the crystal, in the form of a body of revolution, the generatrix of which has several maxima located from the axis of rotation at distances corresponding to different values of the particle radius of the modeled structure;

- on Fig - the possible implementation of the fixation of flat plates using grooves in the racks, which include the edges of the plates;

- figure 9 - the execution of the groove to limit the possibility of horizontal movement of the plate;

- figure 10 - the implementation of the auxiliary technological holes in the plate.

In the case shown in FIG. 1, volumetric elements imitating particles forming a crystal are made in the form of balls 1 and are placed on flat transparent plates 2 having a constant thickness. The plates 2, parallel to each other, are located one above the other and are fixed on the posts 3 at different heights. In this case, the distances between the median planes of the plates are proportional to the distances between the crystallographic planes. The plates 2 can be made, for example, of plexiglass, carbon fiber or any other transparent material, preferably less brittle and harder, resistant to possible damage and scratches. For the manufacture of balls, you can use metal or make balls with the appropriate metal coating on metal or non-metal; wood; plastic painted in appropriate colors with metallic paint - for modeling metal atoms (ions); opaque plastic, painted in appropriate colors - when modeling non-metal atoms (ions); transparent plastic, tinted in appropriate colors - when modeling the atoms (ions) of gases.

The distances between the plates 2 are determined by the length of the bushings 4 placed between them, worn on the posts 3. The entire system of plates and bushings is prevented from moving the nut 5 with washers screwed on the posts 3 and pressing the upper plate to the sleeve located below it. Legs 6 and 7 are installed under the bottom plate. Since in the case shown in FIG. 1, the model is made with only two legs, two of the four legs (position 6) are screwed onto the lower ends of the legs, and the other two legs (position 7) are independently mounted 8 to the bottom plate 2, simultaneously playing the role of the base.

The model of FIG. 1 corresponds to a unit cell of a NaCl rock salt crystal, the traditional schematic representation of which is shown in FIG. 2. Atoms (ions) of chlorine correspond to lighter balls, and atoms (ions) of sodium correspond to darker balls. Volume elements imitating chlorine and sodium atoms (ions) differ in size (the first are larger), and the ratio between the sizes of these volume elements is the same as between the sizes of chlorine and sodium atoms (ions) in the simulated crystal (in the corresponding selected system of values of ionic radii).

The sequence of construction of the proposed model of the crystal structure can be explained on the example of the model of the crystal structure of NaCl, illustrated in figure 1 and figure 2. The NaCl crystal has a cubic face-centered crystal lattice, at the nodes of which Na ⁺ and Cl ions are located ^- with a cube edge (unit cell parameter) a = 0.564 nm (WL Bragg. The structure of some crystals asindicated by their diffraction of X-rays. Proc. Royal Soc. London, A, 89, 1914, p. 248 [10]). On a model scale, this is 56.4 mm, i.e. model scale - 10 ⁸ : 1. In this case, to simulate one unit (cubic) cell of the NaCl crystal structure, at the vertices of the cube, built on transparent plates, and at the centers of its faces there are volume elements that model Cl ^- ions, and at the midpoints of the edges of the cube and at its very center, volume elements simulating Na ⁺ ions (RDShannon. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallographica. Section A, volume 32, number 5, 1976, p., pp. 752-753 [11]).

In this case, three flat transparent plates were selected for displaying the following NaCl crystallographic planes in the model: plate No. 1 — planes of the lower face of the cube; plate No. 2 — planes of its average horizontal section (i.e., a plane parallel to the lower and upper faces of the cube and passing through its center); plate No. 3 - the upper face of the cube. The plates were made in the form of square sheets of transparent plexiglass. The dimensions of these sheets were calculated as follows: (56.4 mm + 2r + 2d) × (56.4 mm + 2r + 2d), where 56.4 mm × 56.4 mm are the unit cell sizes calculated from the position of the ion centers, d is the width of the technological fields necessary for attaching Plexiglas sheets and applying the required inscriptions (in this example, d was 20 mm), and r = 16.7 mm is the radius of a volume element imitating Cl ^- ion, the radius of which is taken according to Shannon and Previtt (see [11], p. 752, and also: RDShannon, CTPrewitt. Effective ionic radii in oxides and fluorides. Acta Crystallographica Section B-Volume 25, Issue 5 - May, 1969 pp. 925-946 [12]).

Then, in the centers of sheets for plates No. 1, No. 2, and No. 3, having dimensions of 130 mm × 130 mm in accordance with the calculation, the squares were marked 56.4 mm × 56.4 mm, and also marked with the points of the apex of these squares, the middle their parties and centers. These points correspond to the centers of volume elements depicting Na ⁺ and Cl ^- ions.

After that, at each marking point (in the vertices, in the middle of the sides and in the center of the squares), technological holes were drilled for fastening volumetric elements in each of the three sheets of plexiglass, and in all four corners of each square at a distance of 10 mm from its edges there were holes for fixing racks.

In addition, sleeves 4 were made, put on racks 3 for fixing manufactured plates with volumetric elements fixed to them so that the distances between the median planes of the plates corresponded to the distances between the crystallographic planes mentioned above. These distances are equal to half the length, a / 2, of the edge of the simulated cubic unit cell a = 0.564 nm, which is 28.2 mm on the model scale. Therefore, the lengths of these bushings are equal to this size minus the thickness of the used plexiglass (in this case, 2 mm), i.e. 26.2 mm.

Volumetric elements depicting ions were made each of two hemispheres 1.1 and 1.2 (figa) of its radius: 11.6 mm for Na ⁺ ions and 16.7 mm for Cl ^- ions truncated on the flat side by an amount equal to half the thickness of the used plexiglass - 1 mm, with technological holes for the pins for connecting these truncated hemispheres (spherical segments) with each other.

Further, the volumetric elements - two ball segments 1.1, 1.2, on one and the other side of the plates 2 (plexiglass sheets) were fixed on pins 26 (figa) in the holes drilled in the plates: on sheets for plates No. 1 and No. 3 - volumetric elements imitating Cl ^- ions at the vertices of the square and in its center, and volumetric elements imitating Na ⁺ ions - at the midpoints of the sides of the square; on sheet for plate No. 2, on the contrary, volume elements imitating Na ⁺ ions are at the vertices of the square and in its center, and volume elements imitating Cl ^- ions are in the middle of the sides of the square. In the manufacture and installation of volumetric elements described, the geometric center of the composite body, which is each of these elements, is located at point 30 lying in the median plane 29 of the plate 2.

Along with the described connection with the help of a pin, parts 1.1, 1.2 of the composite volumetric element can also be connected using a threaded connection or stud, or snap elements, made on the side of the flat surfaces of the parts 1.1 and 1.2 outside one of them and inside the other. It is also possible to fix these parts symmetrically one another on both surfaces of the plate using glue applied to the contacting surfaces of the segments and the plate (figb).

After assembling the model, the position of the upper plate was fixed with nuts 5 (Fig. 1), and the bottom plate with parts with threaded holes that act as legs 6 for mounting the model on a flat surface. As a result, all the plates, worn with their corner holes on the uprights 3, turned out to be sandwiched between the legs, nuts and bushings 4 without the possibility of moving relative to each other and the uprights. (In Fig. 1, in contrast to the description of the model building process, only two racks 3 are used, and two of the four legs have independent fastening to the bottom plate).

For almost all known crystalline structures, there is the initial data on their sizes necessary for the design of the model (see, for example, International Tables for Crystallography. Vol AG. Kluwer Academic Publishers, for the International Union of Crystallography. 2001-2005 [13]) . For new crystal structures, such data can be obtained by x-ray diffraction analysis.

In the general case, when designing a model and calculating the coordinates of volumetric elements modeling atoms, one should take the coordinates of each atom (ion) of the simulated unit cell in a coordinate system built on a spatial (in the general case, non-orthogonal) basis of three elementary translation vectors, determine the coordinates of these vectors in a new, rectangular, coordinate system of the model and calculate in this new, rectangular system, the coordinates of the geometric centers of all volume elements imitating atoms (ions).

In the particular case of the model illustrated in Fig. 4, each ball 1 imitating one of the particles forming the crystal is placed in the hole of a flat transparent plate 2 and fixed with glue 12. The same figure shows the hole 11 into which the ball is not yet set.

On figa, where it is supposed to use the same method of attaching volumetric elements, as in figure 4, it is shown that as a visually perceptible signs to display the differences between atoms (ions) of different types can be used the shape of bodies of revolution, which is given volumetric elements imitating particles forming a crystal, and / or color of volumetric elements. Fig. 5a shows a volumetric element 1 of a spherical shape, a volumetric element in the form of a cylinder 14, and a volumetric element in the form of identical cones 15 attached to each other by the bases. Fig. 5b illustrates the possibility of performing non-spherical rotation bodies similar to those shown in Fig. 5a from two identical parts (14.1 and 14.2; 15.1 and 15.2) and their installation symmetrically to each other on two sides of the plate, for example, with glue applied on the contact surfaces of the plates and these parts.

As already noted above, when revealing the essence of a utility model, the various characteristic sizes of the body of revolution, in the form of which the volume element of the model is made, can display different values of the radii of real atoms (ions): ionic, van der Waals, covalent others. FIG. 6a volume element 21 has the shape of an ellipsoid of revolution. In this case, one of these dimensions is the size r of the horizontal, minor axis (simultaneously being the radius of the largest horizontal section of the ellipsoid of revolution), and the other is the size S of the vertical, major axis. The ellipsoid 21 can be made not only monolithic, as shown in figa, but also consisting of the upper and lower segments 21.1 and 21.2 (fig.6b) mounted on the plate 2 similarly to the spherical segments in Fig.36.

The characteristic size of the monolithic volumetric elements shown in Fig. 4, Fig. 5a, Fig. 6a, - the size comparable with the radius of the simulated particle, is the radius of these elements in the section passing through their geometric center and lying in the median plane of the plate 2. For composite volumetric elements similar to those shown in figures 3a, 3b, 5b, 6b, as such a size, you can take their radius in cross sections touching the surfaces of the plate 2.

A volumetric element imitating an ion or atom, made in the form of a body of revolution, can also have a more complex shape. For example, the generatrix of a composite volumetric element, the upper half of which 25 is shown in Fig. 7, is curve 31 having several maxima 32 located at different distances r ₁ , r ₂ , r ₃ from the axis of rotation (in the case illustrated in Fig. 7, this axis is oriented vertically). Each of these radii corresponds to its value of the radius of the atom (ion) imitated by this element. At the same time, the height of each of the maxima 32 can also be an informative sign, for example, as already mentioned above when revealing the essence of the utility model, to characterize the frequency of use (citation rating, link rating) for the marked radius related to one or another known atomic (ionic) system radii. Two identical bodies of revolution 25, which are half of the volumetric element of the model, are mounted symmetrically to each other on different sides of the plate and are connected to each other like spherical segments in figa or glued to the plate 2, like spherical segments in fig.3b or identical parts of the bodies of another forms on figb, figb.

In a certain sense, universal plates can be created with a detailed coordinate grid, for example, square or honeycomb hexagonal (for hexagonal crystal structures), plates in which holes for pins or other means for connecting the upper and lower parts of volume elements are located periodically and with a small step, for example, several millimeters, which corresponds to several hundredths of a nanometer in a real structure. A size range of bushings dividing and fixing transparent plates imitating crystallographic planes can also be made in the same increments of a few millimeters. Volumetric elements of the model can also be made that simulate the atoms (ions) of the most common chemical elements, or even all elements of the Periodic Table of Elements of D. I. Mendeleev.

The assembly of the proposed model can be simplified if instead of the sleeves 4 (Fig. 1) separating and fixing flat transparent plates, grooves made in the racks will be used. With this embodiment (Fig. 8), the position of the transparent plates 2 on the posts 33 is fixed by installing these plates in the grooves 40 into which the plates are inserted with their parallel edges. In this case, the model must have at least one pair of racks (they must be more massive than the racks 3 in figure 1), and the grooves of one rack of each pair must be symmetrical with the grooves of the other rack. Racks 33 are installed on the base 42. The lower parts of the racks 33 form legs 6. To ensure the accuracy of the horizontal plate installation, an additional rack 45 can be installed on the base (it may not have grooves), which acts as a stop for other edges of the plates that are not inserted into grooves of paired racks 33. Owing to the presence of such an abutment, all plates can easily be installed under each other in the required manner. If the number of pairs of racks with grooves is two or more, then the grooves in one of the extreme pairs of racks can be made not end-to-end, but blind with the possibility of stopping the plates in the back wall 44 of the groove (see the fragment shown in Fig. 9). In this case, an additional rack 45 is not necessary.

The number of grooves can be performed "with a margin", based on the upcoming assembly of different models. Then the model, having slightly lost (or not lost at all) in the accuracy of positioning of volume elements, will acquire the property of mobility of elements, multivariance, simplicity and speed of assembly of models of various crystal structures with known or calculated coordinates of volume elements.

In the design and manufacture of the model, it is possible that a volume element in the form of a ball imitating an atom or ion has a radius value that is greater than the distance to the nearest plate. So, in Fig. 10, spherical volumetric elements 1 on the model scale have a radius not exceeding the distance between the median planes 29 of adjacent plates 2. However, the radius of the volumetric element - ball 61 located on the lower plate 2 is greater than the distance from its median plane to the median plane the nearest plate above. In this case, in this closest plate adjacent to the one on which the ball 61 is placed, it is necessary to make an auxiliary technological hole 62, which will include the part of the ball 61 exceeding the distance between the plates.

It should be noted that in the closest model according to the patent [7] in the case when the adjacent rod prevents the placement of the required diameter on the vertical rod of the ball, this interfering rod, on which other elements are mounted, would have to be destroyed (either removed or moved) , or resort to the choice of different scales for the sizes of volumetric elements and the distances between them with respect to the corresponding sizes in a real structure, violating the adequacy of the model in any of these cases. Similarly, the device according to the proposed utility model is free from problems with ensuring acceptable stiffness and stability of the rod if it is necessary to place balls of significantly different diameters on it, the solution of which in the model according to the patent [7] can also lead to a violation of adequacy.

The proposed model of the crystal structure of a substance allows you to visualize, demonstrate and analyze different crystalline structures, evaluate their proximity or affinity, the possibilities and forms of their mutual penetration or substitution (both from the point of view of proximity of the sizes of atoms (ions), and from the point of view of meromorphic criteria - proximity values of interatomic (interionic) distances of compared crystalline structures), to carry out physical modeling of new structures.

In all the described and other special cases of the implementation of the device according to the proposed utility model technically equivalent and ensuring the achievement of a useful model of the technical result is the replacement of volumetric elements (represented by bodies of revolution) approximating their polyhedra, for example, cylinders - prisms, pairs of cones having a common base - pairs of pyramids balls, including those from which the spherical segments are isolated, with polyhedra (preferably regular or semi-regular, in particular Archimedean or Catalone bodies), etc. symmetric with varying degrees of symmetry bodies.

A design identical to that described above can also be used to model molecules with an equivalent, from the point of view of the achieved technical result, replacement of the sign “crystal structure of a substance” with the sign “structure of a molecule of a substance”, a sign “crystallographic plane” with a sign “distinguished plane in the architecture of the molecule” (for example, the plane of a cyclic element in a chemical compound) and the sign "unit cell" with the sign "molecule".

Information sources

1. Deane C. Smith. Bibliography on Molecular and Crystal Structure Models. U.S. department of commerce. National bureau of standards. National Bureau of Standards Monograph 14. Issued May 20, 1960.

2. Japanese Patent Application No. 2005-292392, publ. 10/20/2005.

3. Patent of the People's Republic of China No. 201812427, publ. 04/27/2011.

4. V.M. Potapov. Stereochemistry. Moscow, ed. "Chemistry", 1988, pp. 10-11.

5. British patent No. 1144851, publ. 03/12/1969.

6. Japanese Patent No. 2642910, publ. 08/20/1997.

7. US Patent No. 4014110, publ. 03/29/1977.

8. The Great Soviet Encyclopedia, 3rd edition, M., Ed. "Soviet Encyclopedia", 1975, v.19, p.637.

9. L.T. Bugaenko, S.M. Ryabykh, A.L. Bugaenko. An almost complete system of average ionic crystallographic radii and its use for determining ionization potentials. News. Mosk. University. Ser. 2. Chemistry. 2008.V. 49. No. 6, p. 363-384.

10. W. L. Bragg. The structure of some crystals asindicated by their diffraction of X-rays. Proc. Royal Soc. London, A, 89, 1914, p. 248.

11. R. D. Shannon. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallographica, Section A, volume 32, number 5, 1976, p.p.751-767.

12. R. D. Shannon, C. T. Prewitt Effective ionic radii in oxides and fluorides. Acta Crystallographica Section B - Volume 25, Issue 5 - May 1969, pp. 925-946.

13. International Tables for Crystallography. Vol.A-G. Kluwer Academic Publishers, for the International Union of Crystallography, 2001-2005.

Claims (10)

1. A model of the crystalline structure of a substance containing volumetric elements in the form of bodies of revolution, simulating particles of a simulated crystalline structure, representing atoms or ions, observing the relative location of these volumetric elements, corresponding to the relative location of these particles, characterized in that these volumetric elements are placed on several parallel parallel to each other flat transparent plates of constant thickness, mounted horizontally one above the other, each of of the elements has the shape of a body of revolution around an axis normal to the surface of the flat transparent plate on which it is placed, and it is made and installed in such a way that it has a part located on one side of the median plane of the specified plate and a symmetrical part located on the other side of this plane, while at least one of these plates contains volumetric elements that simulate these particles located in the same crystallographic plane of the crystal lattice crystalline structure, and the number of these plates and the volumetric elements placed on them is such that the combination of the latter imitates at least one unit cell of the simulated crystalline structure. 2. The model according to claim 1, characterized in that each of these volumetric elements is made in the form of two identical spherical segments mounted symmetrically with respect to each other on both sides of the said plates on which this volumetric element is placed and facing its own flat side to her. 3. The model according to claim 1, characterized in that each of these volumetric elements is made in the form of a ball mounted in an opening made in accordance with the size of this ball in that of said plates on which this volumetric element is placed. 4. The model according to claim 1, characterized in that each of the indicated volumetric elements is an ellipsoid of revolution, the size of each of the semiaxes of which corresponds to the radius of the atom or ion of the modeled crystal structure simulated by this volumetric element according to one of the systems of values of such radii. 5. The model according to claim 1, characterized in that the generatrix of the body of revolution in the form of which the volume element is made is a curve with several maxima located at different distances from the axis of rotation, each of these distances corresponding to the radius of the atom imitated by this volume element or ion in one of the systems of values of such radii. 6. The model according to claim 1, characterized in that all volume elements that simulate the same particles of the simulated crystal structure have the same shape, different compared to volume elements that simulate other particles of the simulated crystal structure. 7. A model according to any one of claims 1 to 6, characterized in that said flat transparent plates are made with holes for vertical struts, while adjacent plates are separated from each other by bushings put on the racks, and to exclude the possibility of moving these plates relative to each other and racks the position of the upper and lower plates is fixed. 8. The model according to claim 7, characterized in that said volumetric elements are colored, while all volumetric elements imitating the same particles of a simulated crystalline structure have the same color, different compared to volumetric elements imitating other particles of a simulated crystalline structure. 9. The model according to any one of claims 1 to 6, characterized in that it is made with a base on which racks are vertically mounted, on which said flat transparent plates are fixed by means of grooves made in said racks, into which the edges of flat transparent plates are inserted, wherein said model has at least one pair of said racks, between which said plates are installed, each of them is made with two edges parallel to each other, and the grooves in two racks of each such pair are made symmetrically with respect to to each other. 10. The model according to claim 9, characterized in that said volumetric elements are colored, while all volumetric elements imitating the same particles of a simulated crystalline structure have the same color, different compared to volumetric elements imitating other particles of a simulated crystalline structure.