If in the construction of the crystal atoms or molecules are

the principle of packing, it would seem, must occur in nature

crystals only in hexagonal prisms and cubes. Crystals of this form

really very common. Hexagonal close-packed

corresponds, for example, the form of crystals of zinc, magnesium, cadmium. Cubic

dense packaging of the shape of the crystals of copper, aluminum, silver,

gold and other metals.

But these two forms of diversity of the world of crystals does not

limited.

The existence of crystal forms that do not conform to the principle

closest packing of spheres of equal size can have different causes.

First, the crystal can be built in compliance with the principle of

packing, but the atoms of different sizes or of molecules having

a form very different from spherical (Fig. 2). Oxygen atoms and

Hydrogen has a spherical shape. When connecting one atom of oxygen and

two hydrogen atoms are mutual penetration of their electronic

shells. Therefore, the water molecule has a shape significantly different from

spherical. Solidification of water close packing of its molecules can not

implemented in the same way as the packaging of equal balls.

In - the second, the difference of packing of atoms or molecules of the densest can

be explained by the existence of stronger links between them

certain areas. In the case of atomic crystal orientation

relationships determined by the structure of the outer electron shells of the atoms,

molecular crystals - molecular structure.

Understand the device crystals, using only the volume

models of their structure, it is difficult. In this connection is often used

method of representing the structure of crystals with spatial

the crystal lattice. It is a spatial grid

nodes coincide with the position of the centers of atoms (molecules) in the crystal.

These models are reviewed thoroughly, but it can not learn anything about

the shape and size of the particles making up the crystals.

At the heart of the crystal lattice is the unit cell - a figure

smallest size, serial transfer which to build

the whole crystal. For unique characteristics of the cell to specify the size

its edges a, b and c and angles (, (and (between them. length of one of

edges is called the lattice constant, and the entire set of six

values that define the cell - cell parameters.

Figure 3 shows how you can build up all the space by

Addition of unit cells.

It is important to note that most of the atoms, and for many

types of crystal lattice and each atom does not belong to one

unit cell, and is simultaneously a member of several neighboring

elementary cells. Consider, for example, the unit cell of the crystal

rock salt.

Per unit cell of the crystal of rock salt, from which,

transfer in space can build the whole crystal must be accepted

part of the crystal shown in Fig. It should be noted that from

ions located at the vertices of the cell, it owns only one-eighth

one of them, of the ions located on the edges of the cell, it owns one

four each, from the ions located on the sides, the share of each of the two

neighboring unit cells accounting for half of the ion.

We count the number of sodium ions and chloride ions the number included in the

one unit cell of rock salt. Cell belongs entirely to one

chloride ion in the center of the cell, and one quarter of each of the 12

ions located on the edges of the cell. Total chlorine ions in a single cell

1 +12 * 1/4 = 4. Sodium ions in the unit cell, six halves on the faces and

vosmushek eight at the corners, with 6 * 1/2 * 8 1/8 = 4.

A comparison of the unit cells of different types of crystal lattices

can be carried out by various parameters, including the often used

atomic radius, packing density and the number of atoms in the unit

cell. The atomic radius is defined as half the distance between the centers

nearest neighboring atoms in the crystal.

Fraction of the volume occupied by the atoms in the unit cell, called

packing density.

Classification of crystals and an explanation of their physical properties

are possible only on the basis of a study of symmetry. The doctrine of

symmetry is the basis of all crystallography.

To quantify the degree of symmetry are the elements

symmetry - axes, planes, and a center of symmetry. Axis of symmetry is called

imaginary line, you turn around a 360 ° crystal (or pound) a few times combined with itself. These alignments

called the order of the axis.

Symmetry plane is called a plane cutting the crystal into two

parts, each of which is a mirror image of each other.

The plane of symmetry as it acts as a two-way mirror

(Fig. 4). The number of planes of symmetry may be different. For example, a cube

there are nine, and in any form of snowflakes - six.

A center of symmetry is called a point within a crystal, in which the

intersect all the axes of symmetry.

Each crystal is characterized by a certain combination of elements

symmetry. Given that the number of elements of symmetry is small, the problem

find all the possible forms of crystals is not hopeless.

Prominent Russian crystallographer Evgraf S. Fedorov found that the

nature can only have 230 different crystal lattices

having axes of symmetry of the second, third, fourth and sixth order.

In other words, the crystals may be in the form of various prisms and pyramids,

base on which lie only a right triangle, the square,

parallelogram and hexagon.

Fedorov is the founder of Crystal - a science

engaged in determining the chemical composition of the crystals by

study of the shape of faces and measure the angles between them.

Crystal-chemical analysis in comparison with the chemical usually takes less

time and does not lead to the destruction of the sample.

Many contemporaries Fedorov not only did not believe in the existence of

lattices, and even questioned the existence of atoms. The first

experimental proof of the validity of conclusions were Fedorova

obtained in 1912 by the German physicist E. Laue. His method

determine the atomic or molecular structure of the bodies with the help of X

rays is called X-ray analysis. Results of the study

crystal structure using X-ray analysis showed

the reality of all the calculated ES Fedorov crystalline

lattices. The theory of this method is too complex, so it can be

consider the school physics course.

Visual representation of the internal structure of the crystals gives a new

wonderful tool for studying the structure of crystals - Ion

microprojector, invented in 1951, similar to the device microprojector

device CRT TV (puc.5). In a glass bottle

is investigated crystal metal as a fine needle 1

10-5-10-6 cm in diameter against the needle tip is fluorescent

Screen 2, capable of light when bombarded by fast particles. After

thorough vacuuming of the cylinder is injected a small amount of

helium. Between the needle and the screen voltage is applied to approximately 30 000.

When the helium atoms collide with the tip of a positively charged

needles, they are detached one electron, and they become

positive ions. Most often collide with helium atoms are

protruding parts of a tip - "with protruding" from the grid

individual metal, atoms or groups of atoms. Therefore, the ionization of helium in the

generally occurs around these projections. Of each projection of the ion-atom

ion flies direct toward the negatively charged cathode 3. At

hit the screen they call it glow, creating up to 107 times larger

image of the surface of the tip. The dotted line of the bright points in a photo -

this image the edges of steps atomic layers, while they themselves are bright points -

individual atoms at the vertices of the stairs. The whole picture is good passes

periodicity and symmetry of the arrangement of atoms in the crystal.

The process of crystal growth.

No one saw the crystal nucleus is formed in solution or

melt. One can suggest that the randomly moving atoms

or molecules are randomly located in such a manner as

corresponds to the crystal lattice. If the solution is not saturated or

melt temperature above the crystallization temperature, the embryos

formed and then dissolved or destroyed by thermal motion. In

supersaturated solution or melt, cooled to a temperature below

crystallization temperature, the rate of growth exceeds the rate of embryo

destruction.

This would seem a reasonable assumption is inconsistent with the

the results of practice. Calculations show that the fetus will be stable and

will rise if the number of molecules on the surface is much smaller than the number of

internal molecules. Theoretical evaluation of the edge of the nucleus gives

of about 1 * 10-8 m, ie, equal to several tens of interatomic

distances. To the extent that minimum stable nuclei contained

several thousand atoms. Clearly, the probability of a collision of such a large

the number of atoms is negligible. However, suppose that the germ somehow

yet formed, and find out what conditions are necessary to ensure that it does not dissolve, and began to grow.

In the formation of the embryo produce heat. Atoms formed

the crystal lattice of the embryo transfer part of its energy to neighboring

atoms of the melt, which began to move faster. Atoms nearest

surrounding the embryo until then be able to "settle" on it, until they have delivered

excess energy to more distant atoms. Thus, the growth of the embryo

will occur in the event that provide permanent removal of heat from

melt.

How then are deposited on the surface of the nucleus atoms?

Before

believed that the crystal growth occurs layer by layer. First ends

construction of a single layer, then starts laying, and so on

resulting faces increasing layer by layer, moving parallel to itself