5-Cg-2015-010694R2-With Cover

Page 1 of 16 Crystal Growth & Design 1 2 3 4 Kinetics of the β→α transformation of tin: Role of α–tin 5 6 nucleation 7 8 9 10 11 Guang Zeng1, Stuart D. McDonald1, Qinfen Gu2, Syo Matsumura3 and Kazuhiro Nogita1* 12 13 14 15 1 Nihon Superior Centre for the Manufacture of Electronic Materials (NS CMEM), School of 16 17 Mechanical and Mining Engineering, The University of Queensland, St Lucia, QLD 4072, 18 19 Australia; 20 21 22 2 Powder Diffraction Beamline, The Australian Synchrotron, Clayton, VIC 3168, Australia; 23 24 3 Department of Nuclear Engineering and Quantum Physics, Kyushu University, Fukuoka 819- 25 26 0395, Japan 27 28 29 30 31 ABSTRACT The role of α-Sn nucleation on the kinetics of the β→α phase transformation is investigated in this 32 study, using in situ variable temperature synchrotron powder x-ray diffraction (PXRD). In the entire thermal history 33 34 of α→β→α transformation, the population of α-Sn at the onset of the β→α transformation was varied by controlling 35 the α→β transformation under isothermal conditions. The degree of α-Sn nucleation is found to have a strong 36 37 influence on the kinetics of the β→α phase transformation. By introducing an impingement factor c=2, the 38 transformation curves yield good fits to the modified Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. Inceases 39 40 in annealing time at 45 ºC resulted in insufficient nucleation at the commencement of the reaction at the kinetically 41 optimal temperature of -45 ºC and additional nucleation is required. 42 43 44 45 46 1. Introduction 47 48 The crystallography, mechanical properties and physical properties of tin have been the subjects 49 1-5 50 of considerable interest from experimental and calculation/modeling studies . The β→α 51 transformation in tin has been of great theoretical and practical interest for over 100 years 2, 3, 5-14. 52 53 It is the only known solid-state transformation in which a metallic material (β-Sn) transforms 54 12-15 55 into a non-metallic semi-conductive solid (α-Sn) . The significant density change (27.0% at - 56 5, 14 57 100°C to 26.1% at 50°C) that is induced by this transformation can lead to the blistering of 58 59 60 ACS Paragon Plus Environment 1 Crystal Growth & Design Page 2 of 16 1 2 3 the free surface of the tin, cracking and even complete disintegration. This phenomenon has been 4 5 traditionally known as “tin pest” 5 because the blisters that form on the surface of the tin have an 6 7 appearance similar to those which occur on the skin of animals and humans afflicted by some 8 14 9 diseases . This blistering and cracking is the result of the combination of the large increase in 10 14, 16 11 volume as the β-Sn transforms to α-Sn and the very low ductility of the α-Sn . With the 12 widespread adoption of lead-free solders by the electronics industry there has been renewed 13 14 interest in tin pest because of concern that these Sn-rich alloys might be susceptible to this 15 14 16 phenomenon . It has been concluded that commercial lead-free solder made with standard purity 17 5, 17 18 Sn have less potential for "tin pest" than high purity Sn due to impurity effects . However, it is 19 still difficult to predict "tin pest" and the deep understanding required to exercise any practical 20 21 control of the β→α transformation is lacking5. 22 23 Previous studies have confirmed that the β→α transformation is a nucleation and growth process 24 25 2, 5, 18. The equilibrium transformation temperature is 13.2°C but in practice the reaction occurs 26 27 only with significant undercooling and after a considerable incubation period2, 3, 6, 10, 13. The 28 13 29 nucleation of α-Sn is particularly difficult so the majority of the time for the β→α 30 31 transformation is taken up by the incubation period with the subsequent growth being relatively 32 rapid 5. It has been reported that the kinetics of the transformation can be greatly accelerated by 33 34 the introduction of heterogeneous nuclei, known as seeding 13. Seeding can be achieved by 35 36 pressing into the β-Sn, powdered crystals of α-Sn or other crystals that are isomorphic with α-Sn 37 6, 13 38 with similar lattice parameters such as CdTe, InSb and Ge . Once nucleated the growth 39 kinetics of the β→α transformation are determined mainly by the impurities and alloying 40 41 additions in the tin, the shape and size of the sample, the tin grain size, the temperature and the 42 43 thermo mechanical history prior to transformation 5, 9-11, 19-23. The kinetics of the β→α 44 5 24 45 transformation have been intensively investigated by methods such as XRD , DSC , 46 2 9 8-12, 19-26 47 dilatometry , electrical resistance measurement and microstructural observation . 48 Despite these investigations over the past 60 years the kinetics of the transformation are still not 49 50 well understood, and this may be due to the difficulty in identifying the quantity of any α-Sn 51 52 particles within the β-Sn as potential nucleation sites for the transformation. 53 54 X-ray powder diffraction is one of most powerful methods of obtaining quantitative phase 55 27 56 information from multicomponent mixtures . The variable temperature in situ synchrotron 57 58 PXRD that is now available provides a method of studying the transformation more precisely 59 60 ACS Paragon Plus Environment 2 Page 3 of 16 Crystal Growth & Design 1 2 3 than has been possible in the past. In our recent study of the transformation using this method, 4 5 data sufficient to plot a temperature, time, transformation (TTT) diagram for the β→α 6 7 transformation were obtained 5. This TTT diagram has a typical “C” shape with a “nose” at - 8 9 50°C and is reasonably consistent with the results of the 1957 kinetic study by Burgers and 10 2 11 Groen who used dilatometry. In that study the samples were of similar purity (99.99%) and had 12 a thermal history of previous β→α transformations. It should be noted that in our study where 13 14 samples were annealed for 10 minutes at 50°C prior to cooling, the β→α transformation kinetics 15 28-30 16 were a good fit with the Johnson-Mehl-Avrami-Komolgorov (JMAK) model with an Avrami 17 18 exponent of 3, which implies that the transformation occurred by three-dimensional growth from 19 pre-existing nuclei5. However, as the annealing time at 50°C was increased to 20 minutes, the 20 21 kinetics failed to fit the JMAK equation and additional nucleation was required for the β→α 22 17 23 transformation to commence . In our recent study, additions of 1 wt.% Pb, Cu, Ge, or Si, in the 24 17 25 form of powder mixtures, all inhibited the β⟶α transformation . The method used minimised 26 27 the effects of element solubility and residual stresses and the primary effect of the additive was 28 assumed to be that of intimate physical contact. Of the addition elements studied, Pb and Cu 29 30 show the strongest ability to suppress the β⟶α transition. Ge and Si also inhibited the β→α 31 17 32 transformation despite having a similar crystal structure to α-Sn . The kinetics of the β→α 33 4-6, 17 34 transformation is largely determined by the nucleation of α-Sn . The presence of pre-existing 35 α-Sn has been proven to greatly accelerate the formation and growth of the α-Sn phase from β- 36 37 Sn. However, it has not been quantitatively or accurately investigated in previous studies. In this 38 39 study, high purity α-Sn samples were in situ annealed during powder diffraction at 45°C for 40 41 various durations, aiming to control the amount of α-Sn remaining after α⟶β transformations of 42 43 varying degrees of completeness. Afterwards, the influences of α-Sn nucleation on the β⟶α 44 transformation in tin were examined. 45 46 47 2. Experimental Section 48 49 To prepare α-Sn samples for powder XRD experiments, high purity 99.99% tin cylinders (20mm 50 51 diameter and 10mm height) were cast and then kept for 180 days at -45ºC. During this time, the 52 cylinders converted to α-Sn powder. The samples used in this study are identical to those used in 53 54 previous studies5, 31. 55 56 57 58 59 60 ACS Paragon Plus Environment 3 Crystal Growth & Design Page 4 of 16 1 2 3 Samples of ~0.15g of the powder mixtures were loaded into quartz capillaries (0.3 mm in 4 5 diameter) and stored at -20 ºC in preparation for experiments at the the Powder Diffraction 6 7 beamline at the Australian Synchrotron. During powder x-ray diffraction (PXRD), the 8 9 temperature of the samples was controlled using a Cryostream (Oxford Cryosystems, Cryostream 10 11 Plus) with temperature accuracy within +/- 0.5 ºC. High-resolution PXRD data were collected in 12 the 2 theta range of 10 to 80 degrees using a Mythen-II detector with a 18 keV beam. A LaB6 13 14 standard (NISTLaB6 660b) was used at room temperature for wavelength calibration. The 15 16 calibrated wavelength was 0.6887 Å. Differential Scanning Calorimetry (DSC) study at a heating 17 18 rate of 6ºC/min indicated that 46.7 % of α-Sn was transformed to β-Sn at the point of 45ºC 19 during continuous linear heating, as shown in Figure 1a 17.

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