JOURNAL OF MATERIALS SCIENCE 37 (2 0 0 2 ) 1055 – 1060 Thermal diffusivity measurement of Zn, Ba, V, Y and Sn doped Bi-Pb-Sr-Ca-Cu-O ceramics superconductors by photoacoustic technique W. M. M. YUNUS ∗ , C. Y. J. FANNY, T. E. PHING, S. B. MOHAMED, S. A. HALIM, M. M. MOKSIN Department of Physics, Faculty of Science and Environmental Studies, Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia E-mail: mahmood@fsas.upm.edu.my The simple open photoacoustic cell technique is demonstrated for measuring the thermal diffusivity of the Zn, Ba, V, Y and Sn doped Bi-Pb-Sr-Ca-Cu-O superconducting ceramic samples. It is based upon the measurement of the photoacoustic signal as a function of the modulation frequency in the region where the sample thickness, l s , equal to the thermal diffusion length of the sample, μ s . The obtained thermal diffusivity values of Ba, V, Y and Sn doped in Bi-Pb-Sr-Ca-Cu-O system increase with the increasing dopant concentration at Ca side. However, the thermal diffusivity values of Zn doped sample decrease with the increasing of dopant concentration in the system. The measured thermal diffusivity value was found to be very dependent on the dopant atom and dopant concentration. C  2002 Kluwer Academic Publishers 1. Introduction After the discovery the formation of the high Tc phase (2223) in Bi-Pb-Sr-Ca-Cu-O system, intensive exper- imental work has been done by many researchers to enhance the Tc value by addition of dopant in the sys- tem [1–3]. However, there seems to exist no systematic investigation of the thermal properties of the system in the literature. In this paper, we describe the use of the open photoacoustic cell (OPC) technique to obtain the thermal diffusivity of Bi 2 Pb 0.6 Sr 2 Ca 2-x M x Cu 3 O δ , (where M = Zn, Ba, V, Y and Sn and x = 0.02–0.10) superconducting ceramic. The theory of the photoacoustic effect in solid was first described by Rosencwaig and Gersho [4]. Apply- ing the simple one dimensional thermal diffusion model of RG, the pressure fluctuation, P th in the air chamber of the open photoacoustic cell detection given by [5–8] P th = γ P o I o (α g α s ) 1/2 2π l g T o k s f e j (ωt -π/2) sin h(l s σ s ) (1) where γ is the air specific heat ratio, P o (T o ) are the am- bient pressure (temperature), I o is the absorbed light intensity, f is the modulation frequency, l i , k i and α i are the length, thermal conductivity and thermal dif- fusivity of material i , respectively. The subscript i de- notes the sample (s) and gas (g) media. Besides that, σ i = (1 + j )a i and a i = (π f /α i ) 1/2 , is the complex ther- mal diffusion coefficient of material i . According to this model, the heat generated in the sample will dif- ∗ Author to whom all correspondence should be addressed. fuse from the sample to the gas in immediate contact with the sample. In this process, an important param- eter involved is the diffusion length of the sample μ s , which can be defined in terms of the thermal diffusivity by [9] μ s =  α/(π f ) (2) It meant that, μ s decreases with the increasing mod- ulation frequency. At very low frequency ( f < f c ) or μ s > l s for the thermally thin sample, the amplitude of the photoacoustic (PA) signal decreases as f -1.5 one increases the modulation frequency. In contrast, at high modulation frequencies ( f > f c ) or μ s < l s for a thermally thick sample, the amplitude of PA signal de- creases exponentially with the modulation frequency as (1/ f ) exp(-a √ f ), where a , is a parameter defined as a = l s √ π/α s . For a characteristic frequency, say f = f c when the diffusion length becomes equal to sample thickness. The thermal diffusivity can then be calcu- lated by applying the Equation 2 which correspond to the situation l s = μ s , one has [10, 11] α s = π f c l 2 s (3) The three phenomena considered in this technique is schematically displayed in Fig. 1. However, for a plate shaped solid samples surrounded by the air, the ther- moelastic bending of the sample cannot be neglected. This effect is essentially due to the temperature gradient 0022–2461 C  2002 Kluwer Academic Publishers 1055