Introduction

Crystalline bodies are an ode to the varieties of minerals.

Called crystalline solids, physical properties

not the same in different directions, but in the same parallel

directions.

The family of crystalline solids consists of two groups - single crystals

and polycrystals. First sometimes have geometrically regular foreign

form, and the latter, like the amorphous bodies, have no inherent in this

some form of substance. But in contrast to the amorphous structure

polycrystals heterogeneous granular. They are a set of

fused with each other randomly oriented small crystals -

crystallites. Polycrystalline structure of cast iron, for example, can

discover, if we consider the model with a magnifying glass on a break.

By the size of the crystals vary. Many of them can be seen

only through a microscope. But there are giant crystals weighing several

tons.

Crystal structure

Variety of crystals form very large. Crystals can

have from four to several hundred faces. But they have

remarkable property - no matter what size, shape and number of faces

one and the same crystal, all planar faces intersect with each other

at specific angles. The angles between corresponding faces are always

same. Crystals of rock salt, for example, can take the form of a cube,

parallelepiped, prism, or a more complex form of the body, but always their faces

intersect at right angles. Facets of quartz are irregularly

hexagons, but the angles between the faces are always the same - 120 °.

Law of constant angles, opened in 1669 by Nicholas Dane

Walls, is the most important law of the science of crystals - crystallography.

Measuring the angles between the faces of crystals is very

practical importance, since the results of these measurements in many

cases can be reliably determined the nature of the mineral. The simplest

instrument for measuring the angles of crystals is applied goniometer.

Application can only be applied goniometer for the study of large

crystals, small and accuracy of measurements made with it.

Distinguish, for example, crystals of calcite and nitrate, are similar in shape and

with angles between corresponding faces is 101 ° 55 'of the first and

102 ° 41,5 'in the second, using a goniometer application very difficult. So

in vitro measurements of the angles between the faces of the crystal is usually

performed using more sophisticated and accurate instruments.

Crystals of regular geometric forms found in nature

rare. The combined effect of these adverse factors, such as fluctuations

temperature close surroundings adjacent solids, do not allow

growing crystal acquire its characteristic shape. In addition,

much of the crystals that had in the past perfect

faceting, managed to lose it by water, wind, friction on the other

solids. So, many rounded transparent grains that can be found in

the sand are quartz crystals, who lost faces in

result of prolonged friction with each other.

There are several ways to find out whether

solid crystal. The simplest, but very little use for

use, has been opened as a result of casual observation at the end of XVIII

a. French scientist Rennes Haüy accidentally dropped one of its crystals

collection. Having examined the crystal shards, he noticed that many of them

are smaller versions of the original sample.

A remarkable property of many crystals give the crushing

pieces like the shape of the original crystal, allowed to express Haüy

the hypothesis that all the crystals are composed of tightly packed rows of small,

invisible under a microscope, the particles having a substance inherent right

geometry. The variety of geometric shapes Haüy not explained

only a different form of "building blocks" of which they are composed, and

different ways of installations.

Hypothesis Haüy properly reflect essence of the phenomenon - the orderly and

dense arrangement of the structural elements of crystals, but she did not answer

on a number of critical issues. There is a limit to the preservation of the form?

If there is, what is the smallest "brick"?

Are atoms and molecules form polyhedra?

In the XVIII century. English scientist Robert Hooke and the Dutch scientist

Christian Huygens drew attention to the possibility of constructing a regular

polyhedra of tightly stacked balls. They suggested that

crystals are built of spherical particles - atoms and molecules. External

crystal form according to this hypothesis are the result of peculiarities

close packing of atoms or molecules. Independently of them to the same conclusion

came in 1748, the great Russian scientist Mikhail Lomonosov.

When the dense packing of spheres in one flat layer each ball

is surrounded by six other balls whose centers form

regular hexagon. If laying the second layer to keep the wells between

balls of the first layer, the second layer will be the same as the first, only

shifted relative to it in space.

Laying of the third layer of spheres can be done in two ways

(Fig. 1). In the first method, the balls of the third layer are placed in the wells,

located just above the balls of the first layer and the third layer is the exact

copy of the first. In the subsequent repetition of stacking layers in this way

a structure called a hexagonal close-packed

structure. In the second method the balls of the third layer are placed in the wells, not

located directly above the first layer of balls. In this method of packaging

a structure known as a cubic close-packed structure.

Both packages provide the degree of filling of 74%. No other way

arrangement of balls in space without any deformation greater

the filling volume does not.

When laying the balls row by row manner hexagonal close

packaging can get the right hexagonal prism, the second method

packing leads to the possibility of building a cube of balls.