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A multi-component lattice gas model is introduced into superionic conductors. Using the model, the ionic conductivity in superionic conductors with two kinds of mobile ions is investigated. The Hamiltonian includes a repulsive interaction term and a weak hopping term for describing the interacting-ion system. It is shown that the ionic conductivity does not vary linearly with the fraction substituted and it has the minimum at an intermediate composition. This concentration dependence of the ionic conductivity qualitatively agrees with experiments performed for (Ag x Cu 1- x ) 2 Se.

Orbitally ordered states of a Ti t 2 g -electron in Y 1- x Ca x TiO 3 (0 < x ≤0.5) have been systematically investigated by the resonant X-ray scattering (RXS) technique near the Ti K -edge. The RXS intensities at 1 s →3 d transition energy (pre-edge) reflecting the 3 d -orbital ordering markedly decrease with increasing Ca concentration toward the ferromagnetic–paramagnetic phase boundary ( x FP ∼0.15). The intensity remaining above x FP decreases gradually and almost disappears at the metal–insulator transition ( x MI ∼0.4). Namely, it is suggested that the orbital ordering is strongly suppressed toward x FP , and vanishes at x MI . The Ca concentration dependence of the Jahn–Teller distortion determined by X-ray structural analysis is consistent with the orbital state obtained by the RXS experiment.

Based on the experimental results of magnetic susceptibilities for liquid silver-polyvalent metals systems, the dielectric behaviours and thereafter the charge distributions in these systems have been derived. Concentration dependence of a compound forming effect for the charge distribution in liquid Ag–In and Ag–Sn alloys has been found to be an anomalous, while such dependence can be scarcely found in liquid Ag–Pb alloys.

High field ESR of Kagome antiferromagnets SrCr x Ga 12- x O 19 have been observed in the submillimeter wave region from 1.8 K to 265 K. The concentration dependence was observed from x =0.6 to x =8.78, and all samples showed the decrease of the resonance field and broadening of linewidth as the temperature was decreased. As the linewidth is very broad at low temperature, for instance about 7 T at 4.2 K, the measurement using high frequency was essential. The results are discussed in connection with the peculiar magnetic behaviors of the system observed by other measurements.

Dielectric, elastic and piezoelectric properties of the mixed crystals system, Na[K 1- x (NH 4 ) x ]C 4 H 4 O 6 · 4H 2 O (0.90< x

Neutron diffraction experiments have been carried out for molten CuCl–CuBr and AgBr–AgI systems along their liquidus curves. For molten CuCl–CuBr mixtures, the contraction of the interionic distance has been found. The concentration dependence of the result is consistent with that found in the magnetic susceptibilities for this system. Molten AgBr–AgI mixture shows an expansion of the interionic distance in their concentration dependence.

The dependence of the ionic conductivity on the mobile ion concentration in superionic conductors is studied by making use of the lattice gas model with a hopping term and Kubo's formula. The ionic...

The conductivity of TiO 2 -dispersed AgI was measured as a function of mole ratio of TiO 2 at 30°C and 180°C. An enhancement of the conductivity was observed at low temperature phase. A simple model is proposed, which will be useful in quantitative estimation of concentration dependence of the conductivity enhancement due to dispersed insulating particles.

The measurements of heat capacity were made for liquid Tl-Te alloys using an adiabatic scanning calorimeter over the whole concentration range. The excess heat capacity for liquid Te-rich Tl-Te alloys can be attributed to the change in the bonding configuration around Te. The concentration dependence of the heat capacity suggests that the bonding nature changes gradually with increasing Tl content and drastically changes around the composition of Tl 2 Te. The heat capacity for liquid Tl 2 Te alloys has a small temperature coefficient at temperature where a nonmetal-metal transition occurs. It means that the excess heat capacity for liquid Tl 2 Te alloy may not be due to the dissociation of the chemical complex.

It was found experimentally that the magnetic birefringence of magnetic fluid thin films obeys a Curie-Weiss like law for all kinds of magnetic fluids except for a water-based one. The birefringence can be described by θ( T , H )=θ a f ( H )/[ T - T a + f ( H )], where θ( T , H ), H and T are the phase difference, the applied field and the temperature of the film, respectively, and θ a is a positive constant. T a and f(H) are also found to be expressed empirically by T a = T 0 +κ ln c , f ( H )=1-exp [-α( c ) H ], respectively, where c is a volume fraction of the colloidal particles, T 0 , κ are positive constants and α( c ) is a function of c . Taking the empirical expression of θ into consideration, the free energy of the magnetic fluid is discussed using Landau's phase transition theory.

An experimental study of the magnetocrystalline anisotropy for Ni-Co alloys has been carried out from 0% to 64% Co concentration and also between 77 and 700 K. The concentration dependence of the magnetocrystalline anisotropy constant K 1 can be described in the form K 1 ( x )= a + b x + A exp (-α x ), a , b , α and A : constant; x : concentration of cobalt). The temperature where K 1 =0 was determined as a function of x and it was found that the diagram of K 1 in the Ni-Co alloy system could be classified into three concentration ranges. The temperature dependence of K 1 has been discussed, based on the result by Carr: K 1 ( T )= K 1 (0)(1-β T / T c )( M s ( T )/ M s (0)) n . The value of n and β were estimated as a function of x , and both n and β show an abrupt change around 8%Co where K 1 changes from negative to positive.

The magnetic properties of GdCo 2 and Gd 1- x Y x Co 2 have been observed and discussed in terms of the molecular field approximation. An appropriate set of interaction parameters reproduces the temperature dependence of the magnetization of GdCo 2 and the concentration dependence of the Curie temperature of Gd 1- x Y x Co 2 for x 0.2, suggests that the Co moment is suppressed by Y substitution and quite sensitive to magnetic environments. A stepwise anomaly in the temperature dependence of the magnetization previously reported could not be observed.

The lamellar thickness of isotactic polystyrene crystallized at high supercoolings has been studied as a function of crystallization temperature and concentration. The temperature dependence of the lamellar thickness is explained by a rough surface growth model throughout the concentration range studied. The limiting thickness is found to increase with concentration. The effects of entanglement and uncrystallized cilia on the limiting thickness are discussed.

Near-noraml reflectance spectra of CeO 2 and Ce x La 1- x Al 2 alloy system were measured at photon energies from 90 to 140 eV. The results were compared with the photoyield data on Ce x La 1- x Cu 6 alloy system paying attention to the chemical shifts of the 4 d -4 f multiplet components. It was found that the rigid wavefunction model is not consistent with the concentration dependence of the chemical shifts.

Absorption and photoluminescence (P.L.) spectra of Cr-doped CdIn 2 S 4 have been measured in visible and near infrared region. The oscillator strengths of the Cr absorption bands were found to be almost constant for all the samples having different Cr concentration. The ligand field parameters were estimated as Dq=1490 cm -1 , B=310 cm -1 and C=3500 cm -1 . It is observed that fine structures of the P.L. band include several lines concerned with nearest neighbor pair.

We report the dependence of the ultrasonic attenuation on the temperature, α( T ), in Sb doped Ge over the wide concentration ( N ) region 3.2×10 16 to 1.6×10 18 cm -3 which covers the critical concentration ( N c =1.5×10 17 cm -3 ) for the metal-insulator transition. The results can be classified as follows. In the region \(3.2\times 10^{16}{\lesssim}N{ 2×10 17 cm -3 , it is that predicted from a free electron gas model, and we obtained the intervalley scattering time τ i from α( T ). A discussion on the ultrasonic attenuation in the intermediate concentration region is given.

The molar magnetic susceptibility χ M of liquid Hg–Tl and Hg–Cs alloys was measured from room temperature to 748 K using the Fraday method. The observed χ M of liquid Hg–Tl alloys shows positive deviations from the linear concentration dependence. For liquid Hg–Cs alloys a positively enhanced tendency of χ M is found around 40 at.%Cs, though deviations from the linear law remain to be negative as a whole (“W shape”). Such a concentration dependence of χ M is discussed in terms of the nearly free electron model. Positive deviations or positively enhanced tendencies (“W shape”) of χ M in these liquid Hg alloys seem to be explained by taking into account electron-ion interactions. The temperature coefficient of χ M , or dχ M /d T , is discussed from the point of view of higher order ion-ion correlation effects recently found for some liquid mercury alloys.

Measurements of electrical resistivity (37 mK\({\leqq}T{\lesssim}780\) K for CeB 6 ), magnetoresistivity (\(H{\lesssim}100\) kOe) and Hall resistivity (\(H{\lesssim}150\) kOe, 4.2K≦ T ≦53 K) have been done for single crystalline samples of Ce x La 1- x B 6 (0.03≦ x ≦1). At very low temperatures, the T 2 law of resistivity is confirmed. A kind of universality for A /γ 2 =α is found even for magnetically ordered CeB 6 . The concentration dependence of residual resistivity shows that an interaction effect between Kondo states appears sharply around x =0.1. The interaction is weak for x

NMR signals due to Mn atoms with antiparallel moments to the host magnetization have been observed in NiFe Mn and NiMn alloys. In NiFe Mn alloys the dependence of the integrated intensities of resonance lines associated with the parallel and antiparallel moments on Fe concentration shows the critical number of Fe atoms surrounding Mn to reverse the moment of Mn to be 4∼5, which is in good agreement with the theoretical result. The magnitude of the antiparallel moment is estimated to be about 1.9 µ B . In NiMn alloys there appear three resonance lines due to two parallel and one antiparallel moments. The concentration dependence of the intensities of these three signals is measured and the origin of these signals is discussed.

The Curie temperatures and the probability distributions of the magnetic hyperfine fields of amorphous Fe–Zr–B alloys were obtained from 57 Fe Mossbauer studies. The Curie temperature depends on composition and the mean magnetic hyperfine field is fairly independent of B concentration. The Mossbauer spectra can be analyzed by assuming that the distribution of the magnetic hyperfine fields consists of two split-Gaussian distributions. From the concentration dependence of the intensity ratio between two split-Gaussian distributions and the temperature dependence of the mean hyperfine fields, it is found that some of the Fe atoms have small hyperfine fields as compared with those of majority Fe atoms and are located in low exchange fields.

The molar volume and the thermal expansion coefficient of liquid Hg–Tl and Hg–Cs alloys were measured by a picnometer method. The molar volume of liquid Hg–Tl alloys varies almost linearly with concentration, and that of liquid Hg–Cs alloys shows large negative deviations from the linear variation. The thermal expansion coefficient of liquid Hg–Cs alloys shows a slight hump in the dilute Cs concentration range. The concentration dependence of the molar volume of these liquid alloys calculated by a simple pseudopotential approach are qualitatively in good agreement with experiment.

Magnetic susceptibilities have been measured at temperatures down to 60 mK by AC Hartshorn bridge method for the potassium graphite intercalation compounds with several compositions (C 8.0 K ∼C 21.6 K) prepared by the use of HOPG. T c is nearly constant to be ∼150 mK for C 8.0 K ∼C 14.7 K, while no transition is found down to 60 mK for C 16.7 K and C 21.6 K. As the K concentration is decreased, the superconducting characteristic changes from type II to type I for the magnetic field H parallel to the layers, while it maintains type I for H perpendicular to the layers. The superconducting fluctuation above T c , the effective mass ratio and the curvature of H c2 versus T curve are investigated; all of them lead to the result that 3D character increases with the decrease of the K concentration. The constancy of T c above the critical K concentration is also discussed.

The resistive behavior of vanadium-based alloys with iron up to 8 at % or with tantalum up to 10 at %, measured from 4 K up to room temperature, changes at a few at% with increasing solute concentration: Weak scatterers, tantalum atoms, change the concentration dependence of the resistivity, whereas strong scatterers, iron ones, change not only the concentration dependence but also the temperature dependence of the resistivity. The change at a few at% is relevant to the substantial overlap of the Friedel oscillation of the conduction electron density around each solute-atom site. The resistive behavior of concentrated V-Fe alloys shows that an unknown mechanism which causes the anomalous resistive behavior such as the negative temperature coefficient of the resistivity observed in high-resistivity alloys works even at low solute concentrations above a few at %.

Magnetostriction constants of Ni–Pd alloys containing 0∼90 at% Pd were measured above 77 K with the (001) and (011) disks by means of a strain gauge technique. The higher order magnetostriction constants h 3 ∼ h 5 were found to be negligibly small in comparison with the lower order constants h 1 and h 2 . The values of h 1 and h 2 at 0 K determined by the extrapolation increase in magnitude with an increase of the Pd concentration, and reach the maximum of about -3.4×10 -4 and -1.6×10 -4 for h 1 and h 2 , respectively, around 70 at% Pd. At 0 K, the contribution of the magnetoelastic term ( K 1 ) M.E. to the effective magnetic anisotropy constant K 1 was found to be negligibly small, so that it is possible to regard K 1 as the intrinsic magnetic anisotropy constant ( K 1 ) 0 . The concentration dependence of h 1 and h 2 , and of ( K 1 ) 1 is qualitatively discussed.

The thermoelectric power of Fe–Ni alloys relative to Pt was measured up to 1050°C in the whole range of concentration. Great care was given to the phase transition of the alloys. The concentration dependence of thermoelectric power in the fcc phase at high temperatures shows a distinct anomaly around 50 at% Ni, suggesting that the alloys have the tendency to separation into two fcc phases. The so-called Invar problem is considered to be closely related to this anomaly.

The phase diagram of a random mixture of two antiferromagnets with competing spin anisotropies (A 1- x B x ) has been analyzed by extending the theory of Matsubara and Inawashiro, 1) and Oguchi and Ishikawa. 2) In the model assumed, the anisotropy energies are expressed by the anisotropic exchange interactions. According to this formulation, it has been shown that the concentration dependence of T N becomes a function of \(\mathscr{I}_{\text{PQ}}^{\eta}(\mathscr{I}_{\text{PQ}}^{\eta} \equiv (2zS_{\text{P}}(S_{\text{P}}+1)\cdot 2zS_{\text{Q}}(S_{\text{Q}}+1))^{1/2}\cdot J_{\text{PQ}}^{\eta}/3\), where P, Q=A, B; S P is a magnitude of P-spin, and J PQ η is a η component of exchange integral between P- and Q-spin). Further, the phase boundary between an AF phase and an OAF (oblique antiferromagnetic) phase at T =0 K has been shown to be determined by α(≡ S B / S A ), if \(\mathscr{I}_{\text{PQ}}^{\eta}\) are given. The obtained phase diagrams for Fe 1- x Co x Cl 2 , K 2 Mn 1- x Fe x F 4 and Fe 1- x Co x Cl 2...

Brillouin scattering spectra in the geometry x ( y , x ) y were measured in mixed crystals KDP 1- x DKDP x for x =0.04, 0.08, 0.23. 0.46 and 0.72. A spectrum consists of a broad component owing to polarization fluctuation and a phonon peak. On the assumption that polarization fluctuation is of Debye type, a relaxation time of an individual dipole is evaluated by fitting the calculated spectrum to an experimental one in a polarization fluctuation-acoustic phonon coupling system. The relaxation time increases from 0.19 ×10 -12 sec at x =0.04 to 1.03 ×10 -12 sec at x =0.72.

In the previous paper (J. Phys. Soc. Japan 29 (1970) 1073) a mechanism of one-dimensional Liesegang phenomena was investigated. The discussion was based on the assumption that sol zones are made in a discrete form and the flocculation proceeds with two steps. In the present paper this theory is revised to take reaction heat, concentration dependence of the diffusion coefficient, and the retardation of the observed flocculation into consideration. We obtained a revised time law which can explain quantitatively the experiments. The retardation seems to give the time taken for the coagulation with two steps.

Liquid Ag–Te and Cu–Te systems exhibited sharp minima in the conductivity and the susceptibility at the stoichiometric composition M 2 Te. Furthermore, liquid Cu–Te system exhibited a weak maximum in the conductivity near 15 at%Cu concentration. For liquid Au–Te system, the concentration dependence of conductivity increases gradually with increasing Au concentration and that of susceptibility has a smooth variation with Au concentration. For liquid Pd–Te system, that of conductivity exhibited a rapid increase from Te-side to Pd-side. On the basis of the Mott model, the density of states at the Fermi level E F is estimated from these experimental results of the conductivity and susceptibility. The difference in their concentration dependence among four liquid systems is characterized by the amount of the sp-d hybridization and the position of the energy level of d-state E d relative to E F .

The magnetic properties of the pseudobinary system, Pr 1- c La c Al 2 , have been investigated in order to know the combined effect of the crystal field and magnetic dilution of Pr by La in PrAl 2 . The Pr concentration dependence of the Curie temperature and magnetic moment of Pr 3+ in Pr 1- c La c Al 2 are reported and discussed in terms of the crystalline electric and molecular fields, suggesting that PrAl 2 has a bunched state as the ground state. A set of crystal field parameters in PrAl 2 is proposed to be x =0.81 and W =-0.53 meV.

The infrared absorption spectra due to the lattice vibrations and the intrinsic transitions in mixed crystals, Hg x Zn 1- x Cr 2 Se 4 have been studied for x =0∼1. Four absorption bands of fundamental lattice vibrations were observed in pure crystals for x =0 and 1, and five intense absorption bands were observed in mixed crystals. The concentration dependence of the three bands shows one-mode type behaviour, whereas that of the other two bands shows two-mode type behaviour. In addition to these bands, a few weak absorption bands were found near the two-mode type absorption bands. The concentration dependence of lattice vibration frequencies is interpreted by a simple model which takes into consideration the six force constants. The main features of the model are that the two force constants and the mass relating to the Hg site are varied continuously with the Hg concentration and that two kinds of clusters are taken into consideration. For these crystals, the positions of the fundamental absorption edges...

Hall Coefficient of single crystals of pure Zn and Zn-Cu η phase alloys were measured in the temperature range of -196°C∼100°C. Remarkable anisotropy was found not only in pure Zn but also in Zn-Cu alloys, while absolute values of the Hall coefficient decreas with Cu-concentration. The temperature dependences also depend on the direction of the magnetic field. In order to know the origin of the anisotropy, the contribution from the various parts of the Fermi surface are estimated, partly by calculation and partly by the present data. Consequently, it is suggested that the most heavily distorted part of the Fermi surface is the 1st and 2nd zone hole, and that observed concentration dependence should be interpreted in terms of the 1st and 2nd zone hole.

Concentration dependence of elastic constants for binary alloys with cubic symmetry are calculated by the lattice theory of Born and von Karman. Central forces between nearest are next-nearest neighbors and angular forces only between nearest neighbors are taken account. Atomic force constants for A-B alloys are given by the average of the atomic force constants for A-A, B-B and A-B pairs weighted by the probability of appearance for these pairs. The elastic constants are expressed by the mean atomic force constants and their concentration dependence is given by a quadratic equation of concentration, which is consistent with the experiments for Ag-Au and Cu-Ni alloys. The variation of the Debye temperatures with concentration is calculated by using the calculated elastic constants and its result is compared with the experiments.

The Hall coefficients of magnesium-cadmium alloys have been measured as a function of composition at both room temperature and 300°C with the magnetic field up to 6.5 KG. For all the compositions, the Hall coefficients are independent of magnetic field. An electronic structure of this system has been discussed with results of the lattice-spacing relations obtained by Hume-Rothery and Raynor. A relation between energy gap and concentration is discussed by comparing their results with the Hall coefficients measured by us. The present experimental results indicate that the energy gaps show a tendency to increase with the addition of cadmium to magnesium.

The hydrodynamical problem of many particles interacting in a laminar flow is discussed on the basis of Stokes approximation. Two methods of approximation are introduced in order to derive the concentration dependence of the viscosity of solutions of rigid spheres. In any case an improper integral is involved which can be evaluated to be of different values according to different ways of integration. This physically absurd result comes from Stokes approximation. A new fundamental equation is proposed for the problems in a laminar flow from an analogous reasoning given by Oseen for the case of uniform flow.

Debye temperature \(\varTheta_{\text{M}}\) and maximum lattice deviation \(\sqrt{\overline{U^{2}}}\) of Fe-Ni( fcc ) alloys are calculated in the range of 0°∼500°C using the values of Young's modulus and shear modulus previously obtained with the same specimens. The results obtained are the following: (1) In its concentration dependence, Debye temperature at the paramagnetic state \(\varTheta_{\text{Mp}}\) shows a minimum at around 40% of Ni. (2) In its concentration dependence \(\sqrt{\overline{U^{2}}}\) shows a maximum at around 40% of Ni. As T becomes higher, the concentration showing \(\sqrt{\overline{U^{2}}}\) maximum gradually moves toward the Fe-rich side. (3) The concentration dependence of resistivity at the paramagnetic state ρ p does not follow Nordheim's rule. As one of the significant factors causing this “shift” from the rule, the contribution of thermal agitation of lattice cannot be neglected.

Nisida and Horii have made detailed measurements of the concentration dependence of the far infrared absorption by Sb donors in Ge. A qualitative explanation of these observations is proposed, in which the strain produced by the donors themselves is able to account for the linewidths and asymmetry of the absorption lines in the low concentration range.

Valence of Ce in the Chevrel compound CeMo 6 S 8 was investigated by XPS and lattice constant measurements at room temperature. The concentration dependence of lattice constant in the system Ce x La 1- x Mo 6 S 8 follows the Vegard's law in a whole concentration region of Ce. The Ce 3 d and 4 d XPS spectra show strong peaks with the initial state of Ce 3+ and no peaks due to Ce 4+ . The mixing rate of Ce 4+ /Ce 3+ was estimated to be less than 2%, assuming the noise level of the XPS spectrum to be the upper limit of the Ce 4+ peaks.

Reflection and absorption spectra of InBr x I 1- x mixed crystals have been measured at 2 K by using polarized light. The lowest reflection peak shifts continuously from InI to InBr indicating the intra-cationic nature of the first exciton transition. In the absorption spectra of the mixed crystals with low iodine concentration, zero-phonon indirect exciton transition is identified and concentration dependence of its threshold energy is investigated. It is confirmed that the indirect-direct crossover occurs at the composition x =0.5.

Low temperature specific heat measurements were made for the pseudobinary Laves phase intermetallic compounds Y (Fe 1- x Co x ) 2 . The concentration dependence of the electronic specific heat coefficient γ, which shows a similar behavior to that of the bcc Fe–Co alloys, is discussed in connection with the magnetic properties of the pseudobinary system. The observed extraordinary high γ value for x =0.9, which is near the critical concentration for the onset of ferromagnetism, is probably due to the spin fluctuations.

The Curie temperatures of the system (Fe 1- x Ni x ) 2 P have been measured as a function of pressure up to 5 kbar. The pressure effect on the Curie temperature ∂ T c /∂ p is -3.46×10 -3 deg. bar -1 for Fe 2 P, and its value increases sharply with increasing x and becomes zero at about x =0.3. The pressure effect on the exchange interactions in Fe 2 P is discussed briefly according to the concentration dependence of ∂ T c /∂ p in the system (Fe 1- x Ni x ) 2 P.

The free energy, susceptibility and correlation functions for a linear chain of N +1 spins with unequal nearest-neighbor isotropic Heisenberg couplings due to two unlike spins randomly distributed on the chain are calculated explicitly in the (classical) limit of infinite spin. The temperature and concentration dependence of susceptibility are given in comparison with that for one-component systems.