Transformation relaxation and aging in a CuZnAl shape-memory alloy studied by modulated differential scanning calorimetr
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I.
INTRODUCTION
DIFFERENTIAL scanning calorimetry (DSC) is a very useful tool for analyzing various phase transitions in materials and has been extensively used to characterize the transformations, especially the forward and reverse martensitic transformations, in various shape-memory alloys.[1–4] However, traditional DSC does have some limitations. Since DSC measures only the sum of all the thermal events, the results are often confusing and misinterpreted if multiple transitions occur in the same temperature range. In addition, DSC results are always a compromise between sensitivity and resolution, so the sensitivity and resolution are not high enough to detect some weak transitions or to separate complex transitions. More recently, a greatly enhanced version of the DSC method called modulated differential scanning calorimetry (MDSC) was introduced and has now become available in the commercial differential scanning calorimeters of TA Instruments.[5,6] The MDSC method not only can incorporate the capability of conventional DSC by offering the same information, but also overcomes the limitations of DSC and provides significant and distinct advantages over it by providing new information that permits unique insights into the structure and behavior of materials; hence, MDSC has brought a new dimension to thermal analysis.[5,7] In conventional DSC, the sample temperature is usually heated or cooled linearly at a constant rate. The measured heat flow is the total of all the thermal responses and can be simply expressed as[5]
Z.G. Wei, Postdoctoral Fellow, is with the Department of Materials Science and Engineering, Royal Institute of Technology, S-10044, Stockholm, Sweden. Manuscript received March 31, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
dQ dT 5 Cp ( ) 1 f (t, T) dt dt
[1]
where dQ/dt is heat flow, Cp the sample heat capacity, dT/dt is the heating rate, t is the time, T is the absolute temperature, and f(t, T) is a function of time and temperature which governs the kinetic response of any physical or chemical transitions observed in DSC.[5] Accordingly, the measured heat flow is, in fact, a combination of two components: (1) the reversing heat flow, which is dependent on the heat capacity and directly follows the heating rate; and (2) the nonreversing heat flow, which depends on the rate of any kinetically driven process and does not follow the heating rate. The former is called the thermodynamic component, while the latter one is called the kinetic component. Unfortunately, it is impossible to separate the two components in conventional DSC. In the updated MDSC method, a small temperature oscillation or perturbation, say, a sine wave, is superimposed on the normal isothermal, linear heating/cooling or other steps of the temperature program. By using a discrete Fourier transformation algorithm, the total calorimetric response to the perturbation is then deconvoluted into the reversing quantity and the nonreversing quantity. Accordingly, MDSC is an invaluable tool for characterizing the thermodynamic
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