Jiro Kakinoki

Intensity of X-ray Diffraction by an One-Dimensionally Disordered Crystal (1) General derivation in cases of the "Reichweite" S=0 and 1

The present paper shows the calculation of the intensity of X-rays diffracted by a one-dimensionally, disordered crystal by the matrix method of Hendricks and Teller and has two purposes; the one is to make clear the relation between the above mentioned matrix method and the difference equation method used by Wilson and Jagodzinski, and the other is to rearrange the results obtained by Hendricks and Teller by introducing the general intensity equation from a rather simple and intuitive standpoint, assuming a finite number N of layers. The obtaind result for the former is \(\overline{S_{j}S^{*}_{j+n}}\)=Spur VFP n . For the latter case, it is concluded that the matrix φ containing the phase shift exp (- i ϕ s ) is not a general matrix but a diagonal one, and the assumption of a finite number N of layers gives rise to a higher term in addition to the normal diffuse term and this higher term becomes the Laue function in special cases and can hardly be neglected at and near a special point and also when N is ...

Intensity of X-ray Diffraction by a One-dimensionally Disordered Crystal (II) General Derivation in the Case of the Correlation Range s≥2.

The general intensity equation for X-rays diffracted by a one-dimensionally disordered crystal i.e. \(I{=}N\text{Spur}\ \textbf{\itshape V}\textbf{\itshape F}+\sum\limits_{n{=}1}^{N-1}(N-n)\text{Spur}\ \textbf{\itshape V}\textbf{\itshape F}\textbf{\itshape Q}^{n}+\text{conj.}\) which was derived for the correlation range s =1 was found to be valid for any s -value by modifying slightly the elements of the matrices. \(\overline{S_{j}S_{j+n^{*}}}\) as used by Wilson and Jagodzinski was shown to be equal to Spur V F P n for any s -value. In our present method, layer form factors are refered to single layers and the preceding ( s -1) layers are used only to classify them into r l subgroups where r is the number of the kinds of layers and l that of combinations of ( s -1) preceeding layers. This method which we call the “antecedent” one is found to be equivalent to another one as used by Hendricks and Teller in which each layer form factor is taken over the whole s layers hence there are R = r l different laye...

Ordered Alloys of Gold-Palladium System. I. Electron Diffraction Study of Evaporated Au3Pd Films

Evaporated single crystal films of gold-palladium alloys were studied by electron diffraction, compositions of the alloys widely ranging from 10 to 60 atomic per cent palladium. An ordered phase with the Cu 3 Au type structure was found to exist in the region of composition around 25 atomic per cent palladium. The order-disorder transformation seems to occur at about 850°C in the films of this composition range.

Intensity of X-ray Diffraction by a One-dimensionally Disordered Crystal (III) The Close-packed Structure.

The general intensity equation for X-rays diffracted by a one-dimensionally disordered crystal with any value of the correlation range s i.e. \(I{=}N\text{Spur}\ \textbf{\itshape V}\textbf{\itshape F}+\sum\limits_{n{=}1}^{N-1}(N-n)\text{Spur}\ \textbf{\itshape V}\textbf{\itshape F}\textbf{\itshape Q}^{n}+\text{conj.}\) was applied to the case of the close-packed structure. The obtained result is

Ordered Alloys of the Gold-Palladium System. II. Electron Diffraction Study on Evaporated AuPd3 Films

Gold-palladium alloys, ranging around AuPd 3 in composition, were studied by electron diffraction using evaporated single crystal films, and a superlattice AuPd 3 was found. The temperature of order-disorder transformation was estimated at about 780°C for the alloy with a composition of about 80 at. % palladium. The electron diffraction pattern of the ordered alloy AuPd 3 showed that the intensities of the superlattice reflections were extremely weak, though they were sharp. The results mean that the degree of order is of a very reduced value. This special nature of the ordered alloy AuPd 3 is discussed by comparing to other ordered alloys of the noble metal-palladium systems.