Том 2. Электромагнетизм и материя

Грядущая великая эра пробуждения человеческого разума принесет с собой метод понимания качественного содержания уравнений. Сегодня еще мы не способны на это. Сегодня мы не можем увидеть в уравнениях потока воды такие вещи, как спиральное строение турбулентности, которую мы видим между вращающимися цилиндрами. Сегодня мы не можем сказать с уверенностью, содержит ли уравнение Шредингера и лягушек, и композиторов, и даже мораль или там ничего похожего и быть не может. Мы не можем сказать, требуется ли что-либо сверх уравнения, вроде каких-то богов, или нет. Поэтому каждый из нас может иметь на этот счет свое особое мнение.

ПРИЛОЖЕНИЕ (к главе 30)

A dynamical model of a crystal structure [62]

by sir Lawrence Bragg, F.R.S. and J. F. Nye Cavendish Laboratory, University of Cambridge

(Received 9 January 1947—Read 19 June 1947) [Plates 8 to 21]

The crystal structure of a metal is represented by an assemblage of bubbles, a millimetre or less in diameter, floating on the surface of a soap solution. The bubbles are blown from a fine pipette beneath the surface with a constant air pressure, and are remarkably uniform in size. They are held together by surface tension, either in a single layer on the surface or in a threedimensional mass. An assemblage may contain hundreds of thousands of bubbles and persists for an hour or more. The assemblages show structures which have been supposed to exist in metals, and simulate effects which have been observed, such as grain boundaries, dislocations and other types of fault, slip, recrystallization, annealing, and strains due to 'foreign' atoms.

1. The bubble model

Models of crystal structure have been described from time to time in which the atoms are represented by small floating or suspended magnets, or by circular disks floating on a water surface and held together by the forces of capillary attraction. These models have certain disadvantages; for instance, in the case of floating objects in contact, frictional forces impede their free relative movement. A more serious disadvantage is that the number of components is limited, for a large number of components is required in order to approach the state of affairs in a real crystal. The present paper describes the behaviour of a model in which the atoms are represented by small bubbles from 2.0 to 0.1 mm. in diameter floating on the surface of a soap solution. These small bubbles are sufficiently persistent for experiments lasting an hour or more, they slide past each other without friction, and they can be produced in large numbers. Some of the illustrations in this paper were taken from assemblages of bubbles numbering 100,000 or more. The model most nearly represents the behaviour of a metal structure, because the bubbles are of one type only and are held together by a general capillary attraction, which represents the binding force of the free electrons in the metal. A brief description of the model has been given in the Journal of Scientific Instruments (Bragg 1942b).

figure 1. Apparatus for producing rafts of bubbles.

2. Method of formation

The bubbles are blown from a fine orifice, beneath the surface of a soap solution. We have had the best results with a solution the formula of which was given to us by Mr. Green of the Royal Institution. 15-2 c.c. of oleic acid (pure redistilled) is well shaken in 50 c.c. of distilled water. This is mixed thoroughly with 73c.с. of 10% solution of tri-ethanolamine and the mixture made up to 200 c.c. To this is added 164 c.c. of pure glycerine. It is left to stand and the clear liquid is drawn off from below. In some experiments this was diluted in three times its volume of water to reduce viscosity. The orifice of the jet is about 5 mm. below the surface. A constant air pressure of 50 to 200cm. of water is supplied by means of two Winchester flasks. Normally the bubbles are remarkably uniform in size. Occasionally they issue in an irregular manner, but this can be corrected by a change of jet or of pressure. Unwanted bubbles can easily be destroyed by playing a small flame over the surface. Figure 1 shows the apparatus. We have found it of advantage to blacken the bottom of the vessel, because details of structure, such as grain boundaries and dislocations, then show up more clearly.