Analysis of the dopant segregation effects at the floating zone growth of large silicon crystals

A computer simulation is carried out to study the dopant concentration fields in the molten zone and in the growing crystal for the floating zone (FZ) growth of large (> 100 mm) Si crystals with the needle-eye technique and with feed/crystal rotation. The mathematical model developed in the previous work is used to calculate the shape of the molten zone and the velocity field in the melt. The influence of melt convection on the dopant concentration field is considered. The significance of the rotation scheme of the feed rod and crystal on the dopant distribution is investigated. The calculated dopant concentration directly at the growth interface is used to determine the normalized lateral resistivity distribution in the single crystal. The calculated resistivity distributions are compared with lateral spreading resistivity measurements in the single crystal.     

Floating zone growth of high-quality SrTiO3 single crystals

Strontium titanate single crystals 15–20 mm in diameter and 40–80 mm in length were grown by a floating zone method with radiation heating. Additional crystal heating just below the molten zone by an in-growth annealing furnace was applied in order to lower the temperature gradients and to achieve slower cooling of the grown crystal. The crystal perfection was studied with X-ray topography and double-crystal diffractometry. The most perfect crystals were grown in [0 0 1] direction with single grain rocking curve widths of about 30″ and subgrain misorientations of 1′–3′ over 10×10 mm² areas of the boule cross-section for both (0 0 1)-, (1 1 0)- and (1 1 1)-oriented slices. Such high-quality crystal can be grown reproducibly with starting materials of 4N grade quality.     

Crystal Growth of High‐melting Multi‐component Rare Earth‐Transition Metal Intermetallic Compounds from the Melt

The crystal growth of different classes of high melting multi‐component Rare Earth‐Transition Metal‐Compounds by vertical floating zone melting with inductive heating has been investigated. Phase diagram features of the multi‐component systems relevant for the crystallization process have been revealed. The critical zone travelling rate for RENi₂B₂C crystal growth is one order of magnitude smaller than for RE₂TMSi₃ compounds. This is attributed to different solidification modes of both classes of compounds, peritectic and congruent melting, respectively. The crystal perfection, element segregation and selected properties of the bulk crystals such as critical temperature of superconductivity were studied as function of the axis co‐ordinate. In the case of RE₂TMSi₂ plate‐like RESi or RESi₂ precipitates were detected in the single crystalline matrix. They were partially dissolved by annealing and subsequent quenching. The anisotropy of various superconducting and magnetic properties was determined at YNi₂B₂C and TbNi₂B₂C single crystalline specimens.     

Analytical bifurcation analysis of a rotor supported by floating ring bearings

Like with other types of fluid bearings, rotors supported by floating ring bearings may become unstable with increasing speed of rotation due to self-excited vibrations. In order to study the effects of the nonlinear bearing forces, within this contribution a perfectly balanced symmetric rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. A linear stability analysis about the static equilibrium position of the rotor shows that for a critical revolution speed the real part of an eigenvalue pair changes its sign. By means of a center manifold reduction it is shown that this destabilization of the steady state is due to a Hopf-bifurcation. Furthermore, the type of this bifurcation is determined as well as the existence and stability of limit-cycles. Notably it is found that depending on the parameters of the floating ring bearing subcritical as well as supercritical bifurcations may occur. Additionally, the analytical results obtained from the center manifold reduction are compared to numerical results by a continuation method. In conclusion, the influences of bearing design parameters on the stability and on the limit-cycles are discussed.     

无单元法计算钢筋混凝土筏板

对无单元法的基本理论作了介绍,并从变分原理出发推导Ｗｉｎｋｌｅｒ地基上钢筋混凝土筏板的无单元法刚度矩阵,编制了相应的计算程序,通过计算实例验证了本文方法的有效性。     

Rotating magnetic fields: Fluid flow and crystal growth applications

Rotating or alternating magnetic fields are widely used in the industrial steel casting process or in metallurgical manufacturing. For the growth of single crystals, these techniques attracted a rapidly increasing attention within the last years: a well defined melt flow leads to a more homogeneous temperature and concentration distribution in the melt and consequently improves the growth process. Rotating magnetic fields (RMF) might be used instead of crucible and/or crystal rotation avoiding mechanically induced disturbances or might be added to conventional rotation mechanisms to gain a further flow control parameter. Compared to static magnetic fields, rotating ones are distinguished by a much lower energy consumption and technical effort. Furthermore, there are no reports on detrimental effects such as the generation of thermoelectromagnetic convection or coring effects in the grown crystals. One advantage of rotating magnetic fields is the possibility to apply them even to melts with a rather low electrical conductivity like e.g. aqueous solutions. High flow velocities are already generated with moderate fields. Therefore the field strength has to be adjusted with care because otherwise undesirable Taylor vortices might be induced. In the last years, the potential of rotating magnetic fields for crystal growth processes was demonstrated for model arrangements using e.g. gallium or mercury as a test liquid as well as for a variety of growth techniques like Float Zone, Czochralski, Bridgman, or Travelling Heater Methods: Fluctuations of the heat transport due to time-dependent natural convection have could be reduced by more than an order of magnitude or the mass transport could be improved with respect to the a better radial symmetry and/or a more homogeneous microscopic segregation.     

Application of dynamic vibration absorbers in floating raft system

To improve the isolation performance of the traditional floating raft system, dynamic vibration absorber (DVA) is introduced into floating raft in this research. The mathematical models of floating raft system consisting of beams are implemented by assembling the mobility matrices of the subsystems. Then the power flow transmission characteristics of the coupled system with/without the DVAs are investigated to evaluate the vibration reduction performance of DVAs. Numerical simulations are performed to explore the influence of several parameters, such as the setting positions, damping and mass of the passive DVAs, on the vibration reduction effects of DVAs. Moreover the vibration reduction performance of the semi-active absorber adjusting its stiffness adaptively is analyzed for the case of time-varying frequency excitation. In addition, the vibration reduction effects of semi-active DVAs under multi-frequency excitation are investigated. The results show that DVAs can significantly improve the isolation performance of floating raft system.     

A novel continuous process for synthesis of carbon nanotubes using iron floating catalyst and MgO particles for CVD of methane in a fluidized bed reactor

A novel continuous process is used for production of carbon nanotubes (CNTs) by catalytic chemical vapor deposition (CVD) of methane on iron floating catalyst in situ deposited on MgO in a fluidized bed reactor. In the hot zone of the reactor, sublimed ferrocene vapors were contacted with MgO powder fluidized by methane feed to produce Fe/MgO catalyst in situ. An annular tube was used to enhance the ferrocene and MgO contacting efficiency. Multi-wall as well as single-wall CNTs was grown on the Fe/MgO catalyst while falling down the reactor. The CNTs were continuously collected at the bottom of the reactor, only when MgO powder was used. The annular tube enhanced the contacting efficiency and improved both the quality and quantity of CNTs.The SEM and TEM micrographs of the products reveal that the CNTs are mostly entangled bundles with diameters of about 10-20 nm. Raman spectra show that the CNTs have low amount of amorphous/defected carbon with I_G/I_D ratios as high as 10.2 for synthesis at 900 °C. The RBM Raman peaks indicate formation of single-walled carbon nanotubes (SWNTs) of 1.0-1.2 nm diameter.     

On the variance of random polytopes

A random polytope is the convex hull of uniformly distributed random points in a convex body K. A general lower bound on the variance of the volume and f-vector of random polytopes is proved. Also an upper bound in the case when K is a polytope is given. For polytopes, as for smooth convex bodies, the upper and lower bounds are of the same order of magnitude. The results imply a law of large numbers for the volume and f-vector of random polytopes when K is a polytope.