The Influence of the Difference of Orientation of Two Crystals on the Mechanical Effect of their Boundary

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120 W. C. Price and W. M. Evans

Ley and Arends 1932 Z. phys. Chem. B, 17, 177 219.

Mulliken, R. S. 1935 a J-Chem. Phys. 3, 506-14.

— 19356 J. Chem. Phys. 3, 565-73.

— I935c d. Chem. Phys. 3, 514r-17.

Noyes, W. Albert 1935 «/. Chem. Phys. 3, 430-2.

— 1937 J. Phys- Chem. 41, 81-9.

Pauling and Sherman 1933 J • Chem. Phys. 1, 606-17.

Price, W. C. 1935® ^ Chem. Phys. 3, 256—9.

— 19356 Phys. Rev. 47, 444—52.

— 1936 a J . Chem. Phys. 4, 539-51.

— 19366 J. Chem. Phys. 4, 147-53.

Robertson, J. M. and Woodward, I. 1936 J- Chem. Soc. pp. 1817-24.

Scheibe, Povenz and Lindstrom 1933 Chem. B, 20, 283.

The Influence of the Difference of Orientation of Two Crystals on the Mechanical Effect

of their Boundary

By Bruce Chalm ers, B.Sc., Ph.D.

{Communicated by E. N . da C. Andrade, F.R.S.—Received 28 May 1937)

1— Introduction

The influence of the crystal boundaries on the mechanical properties of metals has long been recognized, and various theories have been advanced regarding the structure of the boundary region between adjacent crystals.

Since in general the lattices of two neighbouring crystals growing from independently formed nuclei will not register, there must be some modifi

cation of the lattices where they join. The two principal theories as to the nature of this modification are {a) that a structureless or amorphous layer of a thickness of at least some tens of atoms occupies the space between crystals, and (6) that the atoms are arranged on a transitional lattice joining one crystal to another.* There are two ways of distinguishing between these theories. In the first place, the amorphous theory regards the atoms of the boundary layer as being disposed at random, whereas the transitional theory considers each atom as having a calculable position; and secondly, the structure and properties of the amorphous layer should be independent of

* A review and bibliography of the theories of the crystal boundary has recently been compiled by Bucknall (1936) which makes further references here unnecessary.

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the relative orientations of the axes of the bounding crystals, while a tran sitional lattice should vary in its structure and properties according to the angle through which the transition is made.

That the second of these criteria can be applied has already been indicated by the author (Chalmers 1937). A number of specimens of tin of cylindrical form, some consisting of a few crystals with longitudinal boundaries, were subjected to tensile tests, and the results showed th at the different behaviour of different specimens could only be accounted for by the hypothesis that the effect of a crystal boundary depends on the difference of orientation of the crystals.

In the experiments to be described cylindrical specimens consisting of two crystals, separated by a longitudinal boundary, were subjected to a simple tensile test. The crystals were orientated similarly with respect to the axis of the cylindrical specimen, so th at rotation through an angle A about this axis of the specimen would bring one into coincidence with the other. This ensures th at the resolved shear stresses on all equivalent planes, and hence necessarily on equivalent glide planes, were the same with a given load in all experiments. Everything thus being fixed except the angle A , which varied from specimen to specimen, the variation of critical stress with A was investigated, the meaning attached to critical stress being defined in the paper. The results are discussed in terms of the boundary structure.

2— Ex pe r im e n t a l Te c h n iq u e

The experimental work consisted in (a) preparing cylindrical specimens of tin, each specimen consisting of two crystals with a longitudinal boundary, (6) determining the orientations of the two crystals of each specimen, and (c) applying a tensile test to determine the characteristic stress for each specimen.

(a) Preparation of “Bicrystal ” Specimens

The specimens were all made from the same ingot of “ Chempur”

tin (analysis, tin 99-98%, copper 0-00132%, antimony 0-00118%, lead 0-00585 %, iron 0-00055 %, bismuth 0-00352 %, arsenic 0-00005 %, nickel 0-00003 %, silver 0-00018 %, zinc, cobalt and sulphur, nil) by the following method.

Glass tubes of internal diameter 3-5 mm. were filled with tin for a length of 10-15 cm. by suction from a crucible containing molten tin, and the specimens prepared by a modification of the “ moving furnace” method (Andrade and Roscoe 1937) in which the specimen tube is fixed horizontally

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122 Bruce Chalmers

and a heating coil is moved slowly along, melting the specimen locally so that it refreezes progressively from one end. The introduction of two seed crystals of smaller diameter and of the required orientations into the tube at the end from which crystallization starts, so that the ends of the seeds are melted when in contact with the molten end of the specimen, causes crystallization to commence with two orientations, the lattices meeting at a boundary which is roughly a diameter of the cross-section. If the rates of crystal growth of both parts are equal, then the crystals extend along the whole specimen in such a way that the boundary between them is a plane containing the axis of the cylinder.

To ensure that the crystal lattices are all similarly orientated with respect to the axis of the specimen, not only for the two crystals comprising one specimen, but from specimen to specimen, the following orientation of all the seeds was adopted. The 001 axis was arranged to be perpendicular, and the 101 axis to be at 45°, to the axis of the specimen. This symmetry about the axis ensures that the resolved shear stress shall be the same on corre

sponding planes in different cases, but leaves the angle A between the 001 axis of the two crystals constituting a given specimen under control.

The angle A was adjusted to any desired value by manipulating the seed crystals so that their 001 axes were at the required angle before they were brought into contact with the molten meniscus from which crystallization of the specimen started.

When the orientations of the two seeds with respect to the specimen axis are different, then in general the boundary is not a diametrical plane but becomes a plane inclined to the specimen axis. This is receiving further investigation.

A single seed instead of two was used when it was required to prepare a single crystal of the same orientation.

(b) Measurement of Orientation

The optical reflexion method previously described (Chalmers 1935) was used for the determination of the orientations. The specimen, after etching with ferric chloride solution, was mounted on the axis of a goniometer, and a beam of slightly converging light directed radially on to it. The reflexion spots were viewed on a screen, and the positions of the goniometer circle were observed at which the 001 spot of each crystal was at a given position on the screen. The difference of the two angles gave the angle between the 001 axes of the two crystals. The identification of the 001 spot was carried out by using the method detailed in the paper to which reference has been made (Chalmers 1935).

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(c) Tensile Test

By means of preliminary experiments it was found th at a very simple tensile test would serve to determine a characteristic property of each specimen. An extensometer was constructed in which a load could be applied in units of 50 g. with a leverage of 5, and for a gauge length of 2 cm. the extension was measured with a magnification of about 250 by means of an optical lever.

As the load is increased from zero, no extension is observed until the stress reaches a value characteristic of the specimen, after which the extension continues rapidly if the stress is further increased. In order to estimate rather more accurately the minimum stress th at causes a measur

able extension, a definite value (0-2 mm. on the scale) was chosen as defining

■5 0 05

1 0 0 0 1150

Load in g.

Fig. 1

the minimum observable extension, and a curve was plotted of extension and load, the load being applied at a fixed rate. A typical curve is shown in fig. 1. Interpolation between A and B indicates the load th at would produce the extension indicated by CD. No claim for great accuracy is made for this method of determining the standard stress, but it is probably accurate to ± 20 g., which is shown by the results to be adequate for the present purpose. Since the specimens were all prepared in glass tubes of the same size, the stress can be taken as proportional to the load applied.

Reference to the results obtained with a precision extensometer on a similar specimen prepared accidentally in an investigation on single crystals shows th at microplasticity does not occur with such specimens (Chalmers 1936), and th at the flow increases very rapidly when the critical stress has been exceeded; hence the values obtained here are slightly greater than, but related to, the minimum stresses th at cause flow to occur.

3— Experim ental Results

The experimental results can best be exhibited in the form of a graph, fig. 2, relating the angle A between the 001 axes of the two crystals, with the

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load required to produce the minimum observable extension. It will be observed that the points fall roughly on a straight line and the point for zero angle (i.e. a single crystal) is on the same line. I Further, it has been found that the direction of the boundary plane with respect to’ the axes has no influence on the mechanical property under consideration, different specimens with the same angle A but different positions of the boundary giving the same results within the limits imposed by the experimental method.

0° 10° 20° 303 4(T 50s 60 70 Qo 90

Angle A Fig. 2

4— Disc u ssio n

Before discussing the implications of the results described above it may be useful to consider certain features of the experimental procedure. It will have been observed that the crystal boundary concerned is always longitudinal, and therefore parallel to the direction of application of stress.

The boundary is effective over the whole gauge length but is not solely responsible for any part of the extension. The effect of the boundary may be (a) to introduce a thin layer having mechanical properties of its own, differing from those of the crystals and (b) to modify the stress-strain pro

perties of the crystals.

This method of preparation of the specimens, i.e. direction of crystalli

zation parallel to the boundary, should ensure that the boundary resembles

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th at formed in the usual way in a perfectly pure metal, i.e. should be free from the impurities segregated by eutectic solidification. Application of mercury shows th at preferential diffusion takes place along this kind of boundary as it does along ordinary ones (Chalmers 1937, p. 298), showing th at the diffusion of mercury does not depend on the presence of eutectic impurities. Another feature of the experimental technique is th at every crystal was similarly oriented with respect to the stress, and so under a given stress all the specimens would stretch by the same amount if it were not for the effect of the boundaries. The experiments deal, therefore, with the effect of the boundary in modifying the stress-strain relations of the crystals, and with the mechanical properties of the boundary layer itself.

The results show th at the critical stress as defined above varies from the

value for a single crystal for A = 0° to a maximum for A = 90°, the greatest possible angle.

The effect of the boundary, considered as super-imposed on a single

crystal, varies from zero at A = 0° to a maximum for A = 90°, the variation being approximately linear. On account of the lack of precision in the

determination of the critical load, however, too much significance must not be attached to the actual form of the curve obtained in fig. 2. A linear relationship between load and angle is unlikely to be a true representation of the effect, and it is hoped th at more refined measurements will reveal the function of the angle with which the load varies linearly.

I t follows th at if the boundary structure is independent of , as the amor

phous theory requires, the boundary itself makes no contribution to the mechanical property under test, and the change is entirely due to the effect of the two lattices on each other, tending to prevent extension for a large angle A more than for a small angle. Since the two crystals should stretch equally, there is no reason why each should tend to prevent the other extending.

The possible lateral distortion at the boundary th at may accompany glide would vary according to the direction of the boundary relatively to the crystal axes; and since the direction of the boundary has been found to be of no significance it follows th at the mutual prevention of this lateral distortion cannot be the cause of the change of mechanical properties with the angle A . In any case, if the boundary were symmetrically disposed between the axes of the two crystals the lateral distortion should be the same for both crystal faces at the boundary, which should then not hinder glide for large angles A more than for small ones. The same criticism also applies to the adsorbed layer theory, which is therefore also rendered un

tenable.

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On the other hand, if the boundary is regarded as a transition zone between one lattice and the other, the hindrance to glide of each lattice may be controlled by the amount of transition between the two lattices, a violent

transition (. A large) being more effective in preventing glide than a slight transition (A small), which is in agreement with the experimental results.

A modification of the transitional lattice theory (Hargreaves and Hills 1929) suggests that two lattices may share some atoms if the inclination of the lattices happens to have certain values deduced from geometrical considerations; such a theory is not supported by the present experiments, as it should give small stresses for certain intermediate angles between 0°

and 90°, which were not observed.

It would seem that the result obtained for tin is probably of general application, since the behaviour of tin under stress is very similar to that of other metals at temperatures similarly related to the melting-point, so the conclusion is that the effect of crystal boundaries in determining the mechanical properties of a crystal aggregate depends entirely on the angles between the axes of neighbouring crystals, and that this constitutes strong- evidence for the transitional lattice boundary theory.

In conclusion, the author wishes to express his indebtedness to Professor E. N. da C. Andrade, F.R.S., for the encouraging interest he has taken in this work; to the International Tin Research and Development Council for a grant and to its Director, Mr. D. J. Macnaughtan, F.Inst.P., for his personal interest; and to the Governors and Principal of the Sir John Cass Technical Institute for the provision of facilities.

Summary

The effect of the boundary between the crystallites in a metal specimen on the mechanical behaviour is of fundamental importance for the under

standing of the strength of polycrystalline metals. The investigation deals with a particularly simple case, in which the effect of a single boundary can be measured. The specimens tested consist of two crystals with a longi

tudinal boundary prepared so that the orientation of the lattices of the two crystals with respect to the direction of the stress is the same in all cases, while the angle between the two lattices varies from specimen to specimen.

The results show that the critical tension varies regularly with the angle between the two crystals, being a minimum when the two lattices are similarly orientated (i.e. for single crystals) and a maximum when the two

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lattices are at right angles. I t is concluded th at the boundary has no inherent strength, and th at the results are best explained as the effect of a transitional lattice. The evidence is against the existence of an “ amorphous layer” or “ inter-crystalline cem ent” .

Re f e r e n c e s

Andrade, E. N. da C. and Roscoe, R. 1937 Proc. Phys. Soc. 49, 152-77.

Bucknall, E. H. 1936 “ Metal Industry”, pp. 311-16, 369-73, and 396-9.

Chalmers, B. 1935 Proc. Phys. Soc. 47, 733-45.

— 1936 Proc. Roy. Soc. A, 156, 427-43.

— x937 J • Inst. Met. 61 (in the Press).

Hargreaves, F. and Hills, R. J. 1929 J. Inst. Met. 41, 257-83.

Scattering of Slow Neutrons

By M. Go l d h a b e r, Ph.D., Magdalene College, Cambridge, a n d

G. H. Br ig g s, Ph.D., University of Sydney

{Communicated by Lord Rutherford, O.M., F .R .S .—

Received 9 June 1937)

In tr o d u c t io n

The absorption and scattering of slow neutrons have been studied by various methods. In their first survey, Amaldi, D ’Agostino, Fermi, Ponte- corvo, Rasetti and Segre (1935) investigated the absorption of slow neutrons by different elements inside a paraffin block. The number of slow neutrons present was determined by the radioactivity produced by neutron capture in an indicator (e.g. silver). The values for the absorption coefficients which they obtained with this arrangement can be regarded as a measure of the “ tru e ” absorption of slow neutrons. Later, Dunning, Pegram, Fink and Mitchell (1935) measured the “ to ta l” cross-sections, i.e. the sum of the cross-sections for true absorption and for elastic scattering,* using a fairly well-defined beam of slow neutrons, and a lithium-coated ionization chamber as indicator. Recently, Griffiths and Szilard (1937) have deter

* For brevity we shall refer to the process of “ scattering plus true absorption”

simply as “ absorption” when no ambiguity can arise.