Flux Methods

The flux method is a well-known method used for single crystal growth. It has not been applied to the synthesis of fine powders because usually high temperature heating is necessary to obtain molten salts. However, the modified flux method has been reported for the preparation of fine particles of Ce., Pr, 02 solid solutions. In the preparation of the powders by the flux method, molten salts of alkali metal hydroxides, nitrates, and chlorides are used as solvents. The use of molten salts. 

The precursors, cerium(IV) ammonium nitrate (NH4)2Ce(N03)3 and praseodymium(III) nitrate Pr(NO3)3-6H20, are added in a 1 1 weight ratio to the molten salts at 673 - 873 K, and the melt is maintained for 15 - 120 min. After the melt is quenched to room temperature, the reaction products are washed with water and then dried at 393 K. Well-crystallized Cei.,Pr,(02 (x = 0 - 10) powders with very fine size (10 - 20 nm), narrow size distribution, and a clearly spherical shape are obtained. 

The reactants are dissolved in an inert material with a low melting point (flux) where they mix intimately and react. If a low cooling rate is used, large crystals 

The dynamic method presented above is based on the assumption that the heat effect generated in the calorimeter proper in part accumulates in the calorimetric vessel, and in part is transferred to the calorimetric shield. When excellent heat transfer occurs between the calorimeter proper and the shield (as in conduction microcalorimeters), it can be assumed that the quantity of heat accumulated is extremely small. This assumption is the basis of the flux method. The amount of heat transferred between the calorimeter proper and the shield is then directly proportional to the temperature difference. Thus, the course ofA(t) obtained from the measurement resembles that of P(t), and its value is determined on the basis of the second term on the left-hand side of Eq. (3.61)  

The modulating method is based on the measurement of the temperature oscillations of a sample heated by oscillating heat power. Under isoperibol conditions, this method is called AC calorimetry [213-215]. The first AC calorimetry experiments were performed in 1962 by 

Kraftmacher [213], who measured the heat capacities of metals in the high-temperature region. 

Reading et al. [216, 217] proposed a method in which a DSC is used. In this case, the response of the calorimeter as a Mnear system would be a superposition oftwo input functions 1) the ramp function [Eq. (2.49)] generated in the calorimetric shield and 2) the periodic function generated in the sample. When the periodic function is sinusoidal [Eq. (2.53], 

Temperature-modulated differential scanning calorimetry is a new analytical technique used to obtain information on the heat capacity in the range close to the phase transformation. It is a method applied in many instraments, e.g. as the Modulated DSC (MDSC ) of TA Instm- 

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Den Otter, W.K., Briels, W.J. The reactive flux method applied to complex reactions using the unstable normal mode as a reaction coordinate. J. Chem. Phys. 106 (1997) 1-15. 

Aluminum-containing compounds LUAIB4, YbAlB4 (YCrB4 type) as well as Yb2AlB5 (Y2ReBg type) are prepared from A1 flux methods A1 in these compounds behaves as a transition metal. ... 

Borides have been prepared as single crystals by making use of gas-phase, liquid-phase and flux methods, depending on the thermal stability of the boride and on the required size and perfection of the single crystals. 

Formation of Borides 6.7.4. Crystal Growth of Borides 6.7.4.S. Flux Methods... 

Table 1. Growth Cond[tions of Some Boride Single Crystals Obtained by the Flux Method... 

The preparation of some polychalcogenide solids can be achieved at 200-450 °C by molten salt (flux) methods. The reaction of tin with alkali metal sulfides in the presence of Ss at 200-450 °C gives a variety of alkali metal tin sulfides depending on the ratio of the starting materials, the reaction temperature, and the alkah metals (Scheme 30) [90]. These alkali metal tin sul-... 

This method emplosrs a molten flux which dissolves the material and re-deposits it upon a seleeted substrate. That is, the molten flux acts as a transport medium. The temperature of the flux can be varied to suit the material and to promote high solubility of the solute material in the molten solvent. One example is YIG", yttrium iron garnet, i.e.- Y3FesOi2 -This material is used in the Electronics Industry as single crystals for microwave generating devices. It can be grown via the molten flux method. 

Astronomical Observatory, were used to carry out the calculations of theoretical equivalent widths of lines, synthetic spectra and a set of plane parallel, line-blanketed, flux constant LTE model atmospheres. The effective temperatures of the stars were determined from photometry, the infrared flux method and corrected, if needed, in order to achieve the LTE excitation balance in the iron abundance results. The gravities were found by forcing Fe I and Fe II to yield the same iron abundances. The microturbulent velocities were determined by forcing Fe I line abundances to be independent of the equivalent width. For more details on the method of analysis and atomic data see Tautvaisiene et al. (2001). 

In the DTA measurement, an exothermic reaction is plotted as a positive thermal event, while an endothermic reaction is usually displayed as a negative event. Unfortunately, the use of power-compensation DSC results in endothermic reactions being displayed as positive events, a situation which is counter to IUPAC recommendations [38]. When the heat-flux method is used to detect the thermal phenomena, the signs of the DSC events concur with those obtained using DTA, and also agree with the IUPAC recommendations. 

In the review by Kanatzidis et al. (2005), the preparation by the tin-flux method is mentioned also for several ternary phosphides and polyphosphides of rare-earth and transition metals. Typically the components (R metal, T metal, P and Sn in an atomic ratio of about 1 4 20 50) in sealed silica tubes were slowly heated, to avoid violent reactions, up to 800°C, annealed at that temperature for 1 week and slowly (2 K/h) cooled to ambient temperature. The tin-rich matrix was dissolved in diluted hydrochloric acid. The authors described the preparation of compounds corresponding for instance to the formula MeT4P12 (Me = heavy rare-earth metals and Th and U, T = Fe, Ru, etc.) and to the series of phases MeT2P2 (Me is a lanthanide or an actinide and T a late transition metal) having a structure related to the BaAl4 or ThCr2Si2 types. 

Because of the nonuniform shape of the bottleneck tubules (Fig. 15B), it is difficult to extract an i.d. using the gas-flux method [71]. All bottleneck membranes were plated a pH 12 bath for a duration of 8 hours, t Quinine was excited at = 308 nm and detected at X = 403 nm. 

Kato, H., Kudo, A. 1999a. Photocatalytic decomposition of pure water into Hj and Oj overStTajO, prepared by a flux method. Chem Lett 11 1207-1208. 

From a practical point of view, integrating trajectories for times which are of the order of eP is very expensive. When the reduced barrier height is sufficiently large, then solution of the Fokker-Planck equation also becomes numerically very difficult. It is for this reason, that the reactive flux method, described below has become an invaluable computational tool. 

The major advantage of the reactive flux method is that it enables one to initiate trajectories at the barrier top. instead of at reactants or products. Computer time is not wasted by waiting for the particle to escape from the well to the barrier. The method is based on the validity of Onsager s regression hypothesis/ which assures that fluctuations about the equilibrium state decay on the average with the same rate as macroscopic deviations from equilibrimn. It is sufficient to know the decay rate of equilibrimn correlation fimctions. There isn t any need to determine the decay rate of the macroscopic population as in the previous subsection. 

In this central result the choice of the point q(0) is arbitrary. This means that at time t = 0 one can initiate trajectories anywhere and after a short induction time the reactive flux will reach a plateau value, which relaxes exponentially, but at a very slow rate, It is this independence on the initial location which makes the reactive flux method an important nmnerical tool. 

In the very short time limit, q (t) will be in the reactants region if its velocity at time t = 0 is negative. Therefore the zero time limit of the reactive flux expression is just the one dimensional transition state theory estimate for the rate. This means that if one wants to study corrections to TST, all one needs to do munerically is compute the transmission coefficient k defined as the ratio of the numerator of Eq. 14 and its zero time limit. The reactive flux transmission coefficient is then just the plateau value of the average of a unidirectional thermal flux. Numerically it may be actually easier to compute the transmission coefficient than the magnitude of the one dimensional TST rate. Further refinements of the reactive flux method have been devised recently in Refs. 31,32 these allow for even more efficient determination of the reaction rate. 

To summarize, the reactive flux method is a great help but it is predicated on a time scale separation, which results from the fact that the reaction time (1/T) is very long compared to all other times. This time scale separation is valid, only if the reduced barrier height is large. In this limit, the reactive flux method, the population decay method and the lowest nonzero eigenvalue of the Fokker-Planck equation all give the same result up to exponentially small corrections of the order of For small reduced barriers, there may be noticeable differences between the different definitions and as aheady mentioned each case must be handled with care. 

As shown by TalkneP there is a direct connection between the Rayleigh quotient method and the reactive flux method. Two conditions must be met. The first is that phase space regions of products must be absorbing. In different terms, the trial function must decay to zero in the products region. The second condition is that the reduced barrier height pyl" 1. As already mentioned above, differences between the two methods will be of the order e P. ... 

Drozdov and Tucker have recently criticized the VTST method claiming that it does not bound the exact rate constant. Their argument was that the reactive flux method in the low barrier limit, is not identical to the lowest nonzero eigenvalue of the corresponding Fokker-Planck operator, hence an upper bound to the reactive flux is not an upper bound to the true rate. As aheady discussed above, when the barrier is low, the definition of the rate becomes problematic. All that can be said is that VTST bounds the reactive flux. Whenever the reactive flux method fails, VTST will not succeed either. 

The main advantage of the VTST method is that it can be applied also to realistic simulations of reactions in condensed phases.The optimal planar coordinate is determined by the matrix of the thermally averaged second derivatives of the potential at the barrier top. VTST has been applied to various models of the CP-i-CHsCl Sn2 exchange reaction in water, a system which was previously studied extensively by Wilson, Hynes and coworkers.Excellent agreement was found between the VTST predictions for the rate constant and the numerically exact results based on the reactive flux method. The VTST method also allows one to determine the dynamical source of the friction and its range, since it identifies a collective mode which has varying contributions from differ-... 

Droppo, J. G Jr., Concurrent Measurements of Ozone Dry Deposition Using Eddy Correlation and Profile Flux Methods, J. Geo-phys. Res., 90, 2111-2118 (1985). 

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