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Recollections of solid state physic solid state physics. Work on the Ising model, and on Bethe' s approximation to ordering in alloys, presumably counts as statistical mechanics rather than solid state theory My only other excursion into problems of solids was rather accidental Orowan, who knew much about dislocations had conceived a model to describe the force on a dislocation as it moves through the lattice. He found the mathematics trouble some, and suggested that I look at it. It was easy enough to formulate the equations for his model, but they led to a nonlinear integral equation. I knew nothing of integral equations, let alone nonlinear ones, and was ready to give up. It was clear physically that the solution to the equation had to be a function that approached a constant value for large positive argument and the same value with opposite sign for large negative argument. In other words the behaviour was similar to an arctan Just for amusement I inserted an arctan into the equation, and to my great amaze- ment it turned out to be the solution. 28)In the remaining algebra I managed to lose a factor 2, which appears in a large exponent. This error was corrected many years later by Nabarro (29)I thought this result should be published by Orowa ho had invented the physics, or at most as a joint paper But he refused, and I did not think the paper important enough to make an issue of it. I had presented it to a meeting in Bristol where, I believe, Orowan was not present. If I had foreseen what rings this small pebble would cause in the pond of dislocation physics I might have insisted, though this would have landed Orowan with a share of the respon sibility for the disastrous factor 2, which makes the 'Peierls-Nabarro force' quite negligible for most purposes REFERENCEs (1)S feld,A.1928z.,Phy8.47,1,43; Eckart,C.1928Z,Phy8.47,38 (2) Pauli1926z.Phy8.41,81 (3)Bloch, F. 1928 Z. Phys. 52, 555. (4)McCrea, W.H. 1928 Proc. Camb. Phil. Soc. 24, 438. 5)Peierls, R. 1929 2. Phys. 53, 255 (6)Peierls, R. 1929 Phys. Z.10, 273 (7)Pauli, W. 1925 Verh. dt. phys. Ges.(3)6,10. 8)Peierls, R. 1929 Annln Phy/8. 3, 1055 9) Berman, R. 1951 Proc. R. Soc. Lond. A 208, 90: 1953 Phil Mag. Suppl. 2, 103. (10)Peierls, R. 1930 AnnIn Phys, 4, 12 (11)Brillouin, L. 1931 Annus Phys. 17, 88; Die Quantenstatistik(Berlin: Springer (12)Peierls, E. 1930 AnnIn Phy/8. 5, 24 (13)Peierls, R. 1932 AnnIn Phys. 12, 154 14)Kaveh, M,& wiser M. 1971 Phys. Rev. Lett. 26, 635; 1972 Phys. Rev. Lett. 29, 1874. (15)Kretschmann, E. 1934 Z, Phys. 87, 518 16)P (17)Peierls, R. 1934 Helu. phys. Acta 7, Suppl. no. 2, p. 24. (18)Peierls, R. 1933 4nnln Phys. 13, 905 19) Peierls, R. 1930 In Leipziger v 7. hirz )Peierls, R, 1931 Annin Phy8, 10, 97 21) Peierls, R. 1933 Z. Phys. 80, 703 22)Jones, H. 1934 Proc. R. Soc. Lond. A. 147, 39 (23) Peierls,R.19332.Phy8.81,18Recollections of solid state physics 37 solid state physics. Work on the Ising model, and on Bethe's approximation to ordering in alloys, presumably counts as statistical mechanics rather than solid state theory. My only other excursion into problems of solids was rather accidental. Orowan, who knew much about dislocations, had conceived a model to describe the force on a dislocation as it moves through the lattice. He found the mathematics trouble￾some, and suggested that I look at it. It was easy enough to formulate the equations for his model, but they led to a nonlinear integral equation. I knew nothing of integral equations, let alone nonlinear ones, and was ready to give up. It was clear physically that the solution to the equation had to be a function that approached a constant value for large positive argument and the same value with opposite sign for large negative argument. In other words the behaviour was similar to an arctan. Just for amusement I inserted an arctan into/the equation, and to my great amaze￾ment it turned out to be the solution.(28) In the remaining algebra I managed to lose a factor 2, which appears in a large exponent. This error was corrected many years later by Nabarro.(29) I thought this result should be published by Orowan, who had invented the physics, or at most as a joint paper. But he refused, and I did not think the paper important enough to make an issue of it. I had presented it to a meeting in Bristol where, I believe, Orowan was not present. If I had foreseen what rings this small pebble would cause in the pond of dislocation physics I might have insisted, though this would have landed Orowan with a share of the respon￾sibility for the disastrous factor 2, which makes the 'Peierls-Nabarro force' quite negligible for most purposes. REFERENCES (1) Sommerfeld, A. 1928 Z. Phys. 47, 1,43; Eckart, C. 1928 Z. Phys. 47, 38. (2) Pauli 1926 Z. Phys. 41, 81. (3) Bloch, F. 1928 Z. Phys. 52, 555. (4) McCrea, W. H. 1928 Proo. Camb. Phil. Soo. 24, 438. (5) Peierls, R. 1929 Z. Phys. 53, 255. . (6) Peierls, R. 1929 Phys. Z. 10, 273. (7) Pauli, W. 1925 Verh. dt. phys. Ges. (3) 6, 10. (8) Peierls, R. 1929 Armln pn,ys. 3, 1055. (9) Berman, R. 1951 Proo. R. Soo. Lond. A 208,90; 1953 Phil. Mag. Suppl. 2,103. (10) Peierls, R. 1930 Annln Phys. 4, 121. (11) Brillouin, L. 1931 Annls Phys. 17,88; Die Quantenstatistik (Berlin: Springer). (12) Peierls, E. 1930 Annln Phys. 5, 244. (13) Peierls, R. 1932 Annln Phys. 12, 154. (14) Kaveh, M. & Wiser, M. 1971 Phys. Rev. Lett. 26, 635; 1972 Phys. Rev. Lett. 29, 1874. (15) Kretschmann, E. 1934 Z. Phys. 87, 518. (16) Peierls, R. 1934 Z. Phys. 88, 786. (17) Peierls, R. 1934 Helv. phys. Acta 7, Suppl. no. 2, p. 24. (18) Peierls, R. 1933 Annln Phys. 13, 905. (19) Peierls, R. 1930 In Leipziger Vortrage, p. 7. Hirzel. (20) Peierls, R. 1931 Annln Phys. 10,97. (21) Peierls, R. 1933 Z. Phys. 80, 703. (22) Jones, H. 1934 Proo. R. Soo. Lond. A 147, 396. (23) Peierls, R. 1933Z. Phys. 81, 186
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