Structural and Thermal Characterization of Polymorphic Er 2 Si 2 O 7 Asghari Maqsood

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1 Key Engineering Materials Online: ISSN: , Vols. 50-5, pp doi:0.4028/ 202 Trans Tech Publications, Switzerland Structural and Thermal Characterization of Polymorphic Er 2 Si 2 O 7 Asghari Maqsood Thermal Transplant Laboratory, School of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad, Pakistan tpl.qau@usa.net Keywords: Thermal diffusivity, thermal conductivity, heat capacity, Eucken s law Abstract: The first measurement of thermal transport properties on the polycrystalline D-Er 2 Si 2 O 7 have been made in the temperature range K. Both the thermal conductivity and the thermal diffusivity follow modified Eucken s law in this temperature region. The Transient Plane Source technique (TPS) has been used to measure thermal conductivity and thermal diffusivity simultaneously. Introduction Compounds containing rare-earth ions are of technological and research interest on account of their electrical, optical, magnetic and thermal properties. Silicates of composition R 2 O 3 +2SiO 2 (R = rareearth ion) show a higher number of polymorphic forms than other rare-earth silicates []. A study of single crystal growth of R 2 Si 2 O 7 (R = Tm, Er, Ho, Dy) by Maqsood et al [2] shows that Er 2 Si 2 O 7 exist in three modifications A triclinic low temperature phase (type B), a monoclinic modification (type C) and a high temperature monoclinic modification (type D). The magnetic susceptibility measurements on the single crystals of polymorphic D-Er 2 Si 2 O 7 showed that this material became anti-ferromagnetic at.9 0.K. The experimental results are discussed by Maqsood [3] at length. Thermal transport properties of small single crystals at room temperature have been reported by Maqsood et al [4]. The idea of investigating polycrystalline sample arose for the following two reasons; first the preparation of polycrystalline sample is much easier than the single crystals. Second it is possible to measure thermal conductivity and thermal diffusivity simultaneously with the transient plan source (TPS) technique [5, 6]. Experimental Thermal transport properties are measured using Transient Plane Source Technique (TPS).This method [5] considers three dimensional heat flows inside the specimen and is regarded as an infinite medium. The technique uses a resistive element both as a heat source and a temperature sensor. The time-dependent temperature increase ΔT gives rise to a change in the electrical resistance, R(t), of the conducting pattern shown in Fig.a, and may be expressed by the following expression [6]. R t) R T ( 0 P0 T ( ) D( ) 3/ 2 r t r t C p () All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (# , Pennsylvania State University, University Park, USA-8/09/6,03:56:48)

2 256 Advanced Materials XII where: R 0 = resistance of TPS element; α = TCR of sensor T() = average temperature rise of TPS sensor; P 0 = heat liberation from sensor R = radius of TPS sensor; t = measurement time λ= thermal conductivity of sample; = thermal diffusivity of sample Cp =heat capacity; = density of sample Fig. a. TPS element [6] Fig. b. Er 2 Si 2 O 7 sample with element The samples were prepared by the solid state reaction technique. Each sample consisted of two identical disc-shaped pellets having diameter of about 22mm and thickness of 8mm. After the basic characterization of the material as indicated in Table, a TPS element was sandwiched between two identical pieces of D-Er 2 Si 2 O 7 as shown in Fig.b. To measure the thermal transport properties, a simple bridge circuit as shown in Fig.2 was used. By supplying a constant current to the TPS sensor and by monitoring the subsequent voltage increase over a short period of time (after the start of experiment), it is possible to get precise information about thermal transport properties of the material surrounding the heat source. Prior to transient recording the bridge is balanced. Then a constant current pulse is passed through the TPS sensor, which changes the bridge to the off-balance mode. Fig. 2. A block diagram of the electrical bridge circuit along with the experimental set-up: DVM, digital voltmeter; R s, standard resistance; R l, lead resistance; and R p, series resistance.

3 Key Engineering Materials Vols The beauty of this technique is that it can be used for the simultaneous measurement of thermal conductivity, thermal diffusivity, and volumetric heat capacity of insulators, conductors, liquids and high-tc superconductors. The thermal transport data were collected using the TPS technique, and the detail of the method is published by the present author at length [6-8]. The thermal conductivity, thermal diffusivity and heat capacity per unit volume of the polycrystalline D-Er 2 Si 2 O 7 were measured at atmospheric pressure as a function of temperature in the temperature range from K. The measured thermal conductivity and thermal diffusivity of D-Er 2 Si 2 O 7 at different temperatures are plotted in Fig. 3. Results and Discussion Physical Properties of D- Er 2 Si 2 O 7 are shown in Table and Fig. 3 shows the thermal transport data. Table. Physical Properties of D- (after refs. 2-4) Lattice Constants a=5.56(5)å b=0.79() Å c = 4.683(5) Å α = 90⁰ β = 96⁰(0) γ = 90⁰ Space Group Volume 28.4() Dielectric Constant at 500 Hz and at MHz 5.83 DC electrical resistivity 6.50 at 300 K (Ω-cm) Density(g/ ) 5.93 Colour pink Magnetic Properties Anti ferromagnetic ( K).9 ± 0. Specific heat at 3.4R room temperature Hardness porosity 23% DC electrical resistivity 2.72 at 500 K (Ω-cm) Activation Energy E a (ev) 0.574± 0.005

4 258 Advanced Materials XII Fig. 3. Temperature dependence of (a) thermal conductivity with the fit to least squares polynomial of second order and, A BT. (b) Thermal diffusivity with the fit to least squares polynomial of second order and R ST It is clear from the experimental plots that both the thermal conductivity and thermal diffusivity follow a modified Eucken s law of the form: and (2) The values of thermal conductivity vary between 5.5 Wm - K - and 3.2 Wm - K - in the temperature of the study. The - values lie between 2.3x0-6.2x0-6 m 2 s -. Theoretically, thermal energy in solids consists of waves that travel with the velocity of sound. They are therefore capable of transporting energy. From the kinetic theory of gases, thermal conductivity is related to the heat capacity as: C ph 3 where (3) ph : Phonon Velocity : Mean free path For the polycrystalline D-Er 2 Si 2 O 7 various ways of data processing were tested, starting from the general Eucken s rule: a T (4)

5 Key Engineering Materials Vols This law is normally applicable to simple inorganic compounds. A more complex relation of the following type is often found to be workable: n a 2 T N > - volume effect n (5) The above relation did not fit well to this material, which might be due to the fact that these models are good for those solids which have alkali and halogen ions of nearly equal masses. For the analysis of our data, an additional temperature-independent term was added to the thermal resistivity (/λ) to Eucken s rule as: A BT The physical justification of this term is the existence of numerous additional scattering centers for phonons in D-Er 2 Si 2 O 7, caused by structural and chemical imperfections and the influence of the grain boundaries. Similarly: R ST The fitted parameters are shown in Table 2. (6) (7) Table 2. Parameters A, B, R and S for the thermal resistivity /λ(t) and the inverse of thermal diffusivity / (T) of D-, and are the respective correlation coefficients. Α B R S It is clear from Table 2 that the data appear to fit very well. The equation: can be calculated from the where ρ is the density of the material (8)

6 260 Advanced Materials XII The heat capacity as a function of temperature along with mean free path is shown in Fig. 4. The above figure shows that C p increases and begins to flatten out in the neighborhood of room temperature which is the usual observation in the crystalline solids. The expected value of specific heat should be 33R at room temperature. Our experimental value of C p at 300K is 35R. Using the calorimetric method [7] the heat capacity per unit mass for small crystals of D-Er 2 Si 2 O 7 at room temperature was found to be Jg K corresponding to the molecular heat capacity of 3.4R. This confirms our present investigation. The effective mean free path increases with the decrease in temperature and lies between 200-0Å and its maximum value is equal to the average particle size i.e. 200Å, calculated using the x-ray diffraction data at room temperature. Summary The first simultaneous measurements of the thermal conductivity, thermal diffusivity and volumetric heat capacity of polycrystalline D-Er 2 Si 2 O 7 as a function of temperature (77-300K) are made using the TPS technique. The thermal conductivity and thermal diffusivity data follow a modified Eucken s law. The observed volumetric heat capacity follows a usual trend with temperature. The experimental data obtained from the volumetric heat capacity are in agreement with the calculation at room temperature. The effective mean free path varies between Å within the temperature range K. References Fig. 4. Heat capacity at constant pressure of D-Er 2 Si 2 O 7 as a function of temperature (R=8.3 Jmol-K-). The estimated error is about 0%. The variation in the effective mean free path l eff. =3/ρC P v ph of phonons with the temperature. [] J. Felshe: J. Less Common Met. Vol. 2 (970), p.. [2] Maqsood, B. M. Wanklyn and G. Garton: J. of Cryst Growth. Vol. 46 (979) p. 67. [3] A.Maqsood: J. Mater. Sci. Vol. 6 (98), p [4] Maqsood, M. Arshad and M. Maqsood: J. Phys. D: Appl. Phys. Vol. 2 (994), p [5] S.E. Gustafsson: Rev. Sci. Instrum. Vol. 62 (99), p [6] M.A. Rehman and A. Maqsood: J. Phys. D: Appl. Phys. Vol. 35 (2002), p [7] M.Maqsood,M. Arshad, M. Zafarullah and A. Maqsood: J.Supercond. Sci.Technol. Vol. 9( 996) p32. [8] M. A. Rehman and A. Maqsood: Int. J. Thermo-phys. Vol. 24 (2003), p. 867.