Measurements on X-ray photographs of cylindrical specimens of different absorption and thickness taken in a camera without eccentricity show that the absorption error in the apparent unit-cell dimension a is proportional to cos2θ/sinθ + cos2θ/θ. The plot of a against ½(cos2θ/sinθ + cos2θ/θ) is linear down to θ = 30° for all four specimens used. The extrapolated values for a are in good agreement, and this extrapolation function is accordingly recommended in the case of data from well constructed cameras. Other extrapolation functions are also considered, and the effect of various sources of error discussed. A table of ½(cos2θ/sinθ + cos2θ/θ) is given.
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J E Lennard-Jones 1931 Proc. Phys. Soc. 43 461
J B Nelson and D P Riley 1945 Proc. Phys. Soc. 57 160
N F Mott and R Peierls 1937 Proc. Phys. Soc. 49 72
F R N Nabarro 1947 Proc. Phys. Soc. 59 256
The properties of dislocations are calculated by an approximate method due to Peierls. The width of a dislocation is small, displacements comparable with the interatomic distance being confined to a few atoms. The shear stress required to move a dislocation in an otherwise perfect lattice is of the order of a thousandth of the "theoretical" shear strength. The energy and effective mass of a single dislocation increase logarithmically with the size of the specimen. A pair of dislocations of opposite sign in the same glide plane cannot be in stable equilibrium unless they are separated by a distance of the order of 10 000 lattice spacings. If an external shear stress is applied there is a critical separation of the pair of dislocations at which they are in unstable equilibrium. The energy of this unstable state is the activation energy for the formation of a pair of dislocations. It depends on the external shear, and for practical stresses is of the order of 7 electron volts per atomic plane.
The size and energy of dislocations in real crystals are unlikely to differ greatly from those calculated: the stress required to move a dislocation and the critical separation of two dislocations may be seriously in error.
R Peierls 1940 Proc. Phys. Soc. 52 34
Calculations are made of the size of a dislocation and of the critical shear stress for its motion.
G F J Garlick and A F Gibson 1948 Proc. Phys. Soc. 60 574
Phosphorescence and thermoluminescence emission from photoconducting impurity activated phosphors have been satisfactorily explained by the storage of electrons, freed from luminescence centres or other atoms of the solid, in metastable energy levels known as electron traps. Electrons escaping from these traps give rise to emission when they recombine with luminescence centres but there is a probability that they may be retrapped in empty electron traps before their final recombination with centres. The present theoretical and experimental studies attempt to determine the extent to which retrapping does occur and what effects it will have in modifying the phosphorescence and thermoluminescence characteristics. Theoretical treatment shows that there are marked differences in these characteristics for conditions when the retrapping process is present and for those when it is negligible. Experimental investigations of the characteristics of specimens of zinc sulphide, zinc silicate and strontium silicate phosphors indicate that, except under special conditions, retrapping of electrons is negligible. These results together with other work can be explained theoretically if it is assumed that electron traps operative in the luminescence process are spatially associated with the immediate neighbourhood of the luminescence centres formed by activating impurities. This new concept is also supported by the relations found between the luminescence characteristics and the dielectric changes in phosphors of the zinc sulphide type.
R F Bishop et al 1945 Proc. Phys. Soc. 57 147
A discussion is given of the indentation of ductile materials by cylindrical punches with conical heads. On the experimental side, experiments have been made with work-hardened and with annealed copper, with penetrations up to nine times the diameter of the punch. It is found that the load rises towards a maximum value which is not approached until the base of the cone has travelled four to five diameters into the copper block. Denoting this maximum load by p0A, where A is the area of the cross-section of the punch, it is found that p0 for a lubricated punch is about twice the hardness, or five times the yield stress, of the work-hardened material. A theoretical method is given for calculating p0, as follows: the pressures pc and p8 required to enlarge a cylindrical and a spherical hole in a material showing any kind of strain hardening can be calculated. It is plausible to assume that p0 should be between pc and p8, and since p8 is only slightly greater than pc, an approximate theoretical estimate of p0 is obtained. This is in good agreement with experiment. In the light of these results a qualitative discussion is given of hardness testing, and it is shown both on experimental and on theoretical grounds that with lubricated cones and work-hardened materials the hardness, i.e. load/indentation area, will not depend much on the angle of the cone unless this is less than 10°.
J H de Boer and E J W Verwey 1937 Proc. Phys. Soc. 49 59
Attention is drawn to a class of semi-conductors or insulators with incompletely filled 3d bands. Their lack of conductivity, if the number of electrons per atom is an integer, is explained by the circumstance that a moving electron will have a large probability of being withdrawn to the initial atom, if only the potential barriers to be penetrated are sufficiently high to reduce the frequency of transition below a certain limit. This inhibiting factor disappears, if for ions of equal electronic levels the number of electrons per atom differs from an integer. In the case of NiO this condition is fulfilled if an electron is brought by thermal excitation from the lattice 3d band into the somewhat raised and less occupied levels a, a' (figure 1); these levels belong to Ni ions adjacent to a vacant Ni lattice point introduced by the deviations from stoichiometry, and two of these Ni ions are at the absolute zero Ni3+ ions. An analogous conduction mechanism holds for non-stoichiometric Cu2O, with a completely filled 3d band (figure 2).
Photoconductivity is generally observed with substances with completely filled zones and never with substances of the NiO type. A tentative explanation is given for this fact on the basis of the model of figure 1 and figure 2.
In non-stoechiometric ZnO vacant oxygen lattice points are assumed (figure 3); in that case the calculation of the lattice levels shows that at the lattice holes one Zn2+ is converted into Zn, whereas in the lattice the additional electrons form Zn+ ions, as will be the case after thermal transitions of the electrons belonging to these Zn atoms into the lattice 4s band.
E Orowan 1940 Proc. Phys. Soc. 52 8
A discussion is given of the rate of flow in metal single crystals. Flow is believed to be due to the presence of dislocations; the rate of production and rate of movement of dislocations are treated.
C N Davies 1945 Proc. Phys. Soc. 57 259
For calculation of terminal velocities it is convenient to express the Reynolds' number, Re, of a moving sphere as a function of the dimensionless group ψRe2, where ψ is the drag coefficient. The following equations have been fitted by the method of least squares to critically selected data from a number of experimenters:
Re = ψRe2/24 -0.00023363(ψRe2)2 + 0.0000020154(ψRe2)3 - 0.0000000069105(ψRe2)4 for Re<4 or ψRe2<140. This tends to Stokes' law for low values ofRe. It is specially suited to calculation of the sedimentation of air-borne particles. The upper limit corresponds to a sphere weighing 1.5 μg. falling in the normal atmosphere, that is, one having a diameter of 142 μ for unit density.
logRe=-1.29536+0.986 (logψRe2)-0.046677 (logψRe2)2+0.0011235 (logψRe2)3 for 3<Re<10,000 or 100<ψRe2<4.5.107.
Correction for slip in gases should be applied to Stokes' law by the following expression, based on the best results available:
1 + l/a[1.257 + 0.400exp(-1.10a/l)],
where the mean free path l is given by η/0.499σc.
This conveniently transforms to the following for the sedimentation of particles in air at pressure p cm. mercury
1 + l/pa[6.32.10-4 + 2.01.10-4exp(-2190ap)]
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R E Belin 1948 Proc. Phys. Soc. 61 571
Corrections to 1948 Proc. Phys. Soc. 60 381.
R B R-Shersby-Harvie 1948 Proc. Phys. Soc. 61 571
Corrections to 1948 Proc. Phys. Soc. 61 255.
F K Goward and J J Wilkins 1948 Proc. Phys. Soc. 61 580
Mary P Lord 1948 Proc. Phys. Soc. 61 489
A critical survey of previous work on the measurement of fixation eye movements shows that none of it has satisfied all the conditions: (i) possibility of detection of movements of magnitude one minute of arc; (ii) little interference with the natural state of the eye; (iii) satisfactory treatment of the head movement problem.
A technique which more nearly meets these requirements is described. Photoelectric recording of the movements of an ultraviolet beam reflected from the surface of the cornea enables the first and second conditions to be satisfied. The reflected beam is divided into two parts, one of which falls on a horizontal straight edge, the other on a vertical straight edge. In each case more or less of the radiation passes the straight edge as the eye moves, and is focused on an electron multiplier phototube. The output of each multiplier is amplified and fed to a cathode-ray oscillograph, the time-base of which is suppressed. The oscillograph beams are thus arranged to give vertical traces only, and these are photographed simultaneously on a continuously moving film travelling in the horizontal direction. The eye movements can be deduced from the two records on the film. In an attempt to meet the third requirement the subject is placed in the prone position, in which the movements of the ultraviolet beam due to head movements are smaller than for other positions of the subject.
No attempt at analysis of the observations has yet been made.