Vol. 22, No. 1 (1966)
1966, 126 (1): 1-16. doi: 10.7498/aps.22.1
The idea of free energy has been used in the discussion of physical conditions for the formation of colloidal particles. The formulas for critical concentration of impurity atoms and donor atoms and for critical values of crystal nuclei are deduced and discussed under the assumption that all the crystal nuclei have the same size. It is pointed out that there is a critical temperature for the transformation of colloidal particles into impurities of semiconductor or F-centres of alkali halides. The characteristics of surfaces of free energy and the sufficient condition of the formation of colloidal particles are also discussed in this paper.
1966, 126 (1): 17-28. doi: 10.7498/aps.22.17
In this paper the characteristics of the concentration of donor atoms in ionic crystal with colloidal particles are discussed. It is shown that the concentration of donor atoms is independent of the concentration of impurity. At the late period of growth of colloidal particles, the concentration of donor atoms can be approximately represented by the critical concentration of impurity. At that period the "equilibrium" between donor atoms and colloidal particles does not imply that the free energy of the system is located at its minimum point, and it implies that the free energy of the system decreases slowly. From the point of view of diffusion of impurity atoms the physical picture of the growth of colloidal particles is described, and the growth speed of colloidal particle is discussed.The critical states and parameters Eβ, β for KC1, KBr, KI, and NaCl are discussed quantitatively, and the thermal coagulation and the optical coagulation are discussed qualitatively.It is pointed out that all discussions can be applied in the atomic crystals and alloys after some corrections.
It was well known that the effective mass approximation cannot be used to calculate the deep impurity levels in semiconductors. Starting from the band wave functions and making use of the idea of pseudo-potential, we proved that, the impurity states are the approximate solutions of an equivalent Schr?dinger equation, which contains not only the usual term of the long range Coulomb potential, but also a short range one. For the shallow level impurities this short range force gives rise to the so called "valley-orbit" splitting, while for deep level impurities it cannot be taken as perturbation. It is essentially different for different impurities.The effect of this short range force on the bond states was discussed. It was shown that, when this part is so strong that it alone can give rise to resonance scattering or bond state of electron, the bond energy does strongly depend on it, and rapidly increases as it increases. At the same time the wave function also shrinks largely. It was proved that the matrix elements between valence and conduction bands of this part of potential can be replaced approximately by an equivalent intraband repulsive interaction and the influence of interband interaction is important when the bond energy is nearly equal to the forbidden band width. It also may be the cause of the fact that many impurities can capture electron and hole simultaneously.Furthermore, we carried out numerical calculation for a simple model and analysed in detail all the above mentioned effects. Finally the energy levels of Cu, Ag, Au in Ge were discussed with the help of this simple model.
FURTHER EXPERIMENTS ON THE DISLOCATION INTERNAL FRICTION PEAKS WITH ANOMALOUS AMPLITUDE EFFECTIN Al-0.5% Cu ALLOY AND THE DISLOCATION KINK ATMOSPHERE MODEL
1966, 126 (1): 71-82. doi: 10.7498/aps.22.71
Conditions for the appearance of the anomalous dislocation damping peaks in Al-0.5% Cu alloy were further studied with a low frequency torsion pendulum. Experimental results showed that a suitable amount of cold working is necessary for a fully annealed specimen but not for specimens quenched from an elevated temperature.Previously observed internal friction peaks versus strain aging time and versus temperature which exhibit an anomalous amplitude effect were elucidated qualitatively by the simple dislocation atmosphere model. However, in making quantitative explanations, this simple model meets the following difficulties: (i) Under the action of the alternating stress used in internal friction measurements, the distance that the atmosphere of solute atoms can be dragged along with the dislocation is too small, (ii) For the atmosphere to catch up with the dislocation, the diffusion coefficient of the solute atoms constituting the atmosphere has to be many orders of magnitude larger than the ordinary value, (iii) The critical stress necessary to move the dislocation dragging the atmosphere along with a critical speed as calculated theoretically is several hundred times greater than the observed value.A modified dislocation atmosphere model in which the solute atoms are assumed to diffuse along dislocation kinks was proposed. This model takes into account the above mentioned difficulties and can explain the experimental results obtained in a qualitative manner. The basic assumption of this model is that in order to be able to observe the anomalous internal friction phenomena, a certain number of kinks must exist on the dislocation line. Such kinks can be formed through cold working or quenching the specimens from an elevated temperature. The motion of a dislocation line in a direction perpendicular to itself can be achieved through the sidewise motion of the kinks along the dislocation line. It is assumed that atmospheres of solute atoms are formed only on the straight portions at the ends of the kink, and not on the kinks themselves. In the process of the to and fro sidewise motion of the kinks, a to and fro short range diffusion of the solute atoms segregated at the ends of the kinks can carry out along the dislocation pipe. The diffusion coefficient for diffusion along a dislocation pipe is known to be much greater than that for the diffusion in the regular crystal lattice.
1966, 126 (1): 83-93. doi: 10.7498/aps.22.83
Some experimental investigations on the pressure dependence of resistivity and Hall coefficient of n- and p-type InSb samples with different doping (for n-type 5×1013-2.3×1018 cm-3; for p-type 2.6×1014-6.0×1017 cm-3) up to 12,500 kg/cm2 are given. A brief account of the pressure variation of the energy gap, carrier concentration, electron and hole mobilities, and also some preliminary discussion on the scattering mechanism of hole are presented.
SECOND ORDER PHASE TRANSFORMATION OF MAGNETIC CRYSTALS AND MAGNETIC STRUCTURE OF METALS OF THE LANTHANUM SERIES
1966, 126 (1): 94-110. doi: 10.7498/aps.22.94
The stability conditions in the Landau theory of second order phase transformation are discussed. It is shown that the restrictions imposed by Lifshitz on the change of type of symmetry are not necessary. As a consequence, the second order transformation at the Neél point of metals of the Lanthanum series such as dysprosium, which was thus far regarded as a problem that could not be treated on the basis of the Landau theory, is amenable to theoretical treatment. The linear relationship to temperature of the pitch of the helical spin structure of dysprosium is explained. In the meantime, a new method for the analysis of spin structure is developed employing the theory of space group representation and the minimum conditions of the thermodynamic potential. The results obtained by the application of this method to the magnetic structure of metals of the Lanthanum series are in agreement with the results of neutron diffraction experiments.