Numerical Calculation of the Cooling Rate in the J-Quenching Technique
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I.
INTRODUCTION
DUE to the excellent properties such as outstanding mechanical strength, good resistance corrosion ability, and attractive soft magnetic properties, bulk amorphous alloy is attracting more and more attention.[1–3] However, it is very difficult to prepare bulk amorphous alloy by means of the common techniques. To explore available synthesis techniques is a key task in this field. Recently, bulk amorphous Fe40Ni40P14B6 rods with a diameter as large as ~2.5 mm were synthesized by means of a so-called J-quenching technique in our experiment.[4] In order to investigate the glass formation ability of the specimen, it is essential to determine the cooling rate of the specimen in the J-quenching experiment. In the J-quenching technique, at first, the molten sample was injected into a long needle quartz tube. Then, the entire system was put into a high-temperature furnace to keep it at a high temperature for a few minutes. After that, the entire system was taken out of the furnace and immediately quenched into water, as shown in Figure 1(a). The temperature of the sample would fall quickly below its glass transition temperature and form amorphous solid. However, the cooling rate of the specimen is too fast in this process, and it is hardly possible to measure the cooling rate of the specimen directly by a experimental method. Thus, here we will attempt to determine the cooling rate of the specimen in the J-quenching technique using the numerical calculation method. II.
CALCULATION MODEL AND METHOD
The cooling procedure in the J-quenching technique can be considered as a transient heat conduction
QIANG LI, Associate Professor, is with the School of Physics Science and Technology, Xinjiang University, Urumqi, Xinjiang 830046, People’s Republic of China. Contact e-mail: [email protected] Manuscript submitted August 29, 2008. Article published online April 21, 2009. METALLURGICAL AND MATERIALS TRANSACTIONS B
problem. It will be governed by the following heat conduction equation: @T ¼ ar2 T @t
½1
Here a is the thermal diffusivity of the medium and is defined as qCk p ; where k, q, and Cp are the thermal conductivity, density, and specific heat at constant pressure of the medium, respectively. In the J-quenching technique, the system consisted of the sample and a quartz tube can be considered as an infinitely long cylinder so that distribution of the temperature field will be independent of h and z. So the preceding transient heat conduction equation (Eq. [1]) can be simplified to @Tðr; tÞ 1@ @Tðr; tÞ ¼a r ½2 @t r @r @r The boundary conditions in the J-quenching experiment will be stated in the following section. There are two interfaces in the sketch of the calculation model, as shown in Figure 1(b). At the interface between the sample and the quartz tube, the heat flux should be continuous in the cooling process. So the following boundary condition can be given: @T @T ½3 ks ¼ kq @r r¼rb @r r¼rb Here ks and kq are the thermal conductivity of the sample and the quartz tube, respectively. The heat transfer in the
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