Question

Transformation from α-Sn to β-Sn and from β-Sn to α-Sn is exactly the same in terms of the kinetics of the phase transformations.

Answer 1

• An accessible approach was designed todetermine the kinetics of β→α allotropic transformation of bulk Sn plates.
• The method proposed showed high sensitivity towards β→α transition in bulk Sn with detection limits of less than 2%.
• The kinetics of β→α transformation were found to follow Johnson-Mehl-Avrami-Kolmogorov model.
• The Avrami exponent varied according to a variety of factors.

Reliable measurements of the kinetics of β → α allotropic transformation in Sn-based solder underlie the design and development of advanced interconnects for low-temperature electronics. In this paper, a highly-accessible
and buoyancy-based method, but different from common dilatometry, was developed to consistently detect a change of the transformed fraction in bulk βSn plates (10 × 10 × 1mm) with time at −20, −40, and −60 °C.
Due to the concurrent effects of undercooling temperature and interfacial atomic diffusion, the β → α transformation in Sn plates at −40 °C proceeded most rapidly up to around 70% αSn fraction after 168 h. The transformed
fraction versus time curves yielded excellent fits to the classic Johnson-Mehl-Avrami-Kolmogorov model with a constant nucleation rate during transformation process (Avrami exponent, n of 4). Addition of nucleation agent accelerated the transformation by shortening the incubation period, but the nucleation rate decreased to zero in the following transformation (n = 3). Furthermore, coarsening grain size depressed β → α transformation and
led to the saturation of nucleation sites in the vicinity of half transformation (n decreasing from 4 to 2). The sim-ple, convenient, and reliable method proposed showed high sensitivity with detection limits of about 2%, and it could be a promising approach to study and predict solid-state phase transformation kinetics

Modern electronics manufacturing is inconceivable without solder alloys, a basic part of which consists of beta tin (βSn). βSn may transform to allotropic alpha tin (αSn) upon cooling below 13.2 °C
. This transformation is a potential devastating hazard to electronics, particularly to those operating in cryogenic environments, such as exploration instruments servicing in Antarctic expedition
(−60 °C) ,and extraterrestrial space (Mars: −153 °C) , high- sensitivity photonic detectors (−196 °C) [4], and Magnetic Resonance Imaging machine (−269 °C) [5,6]. Upon the transformation (also called as tin pest), intact, strong, and conductive solder joints can crumble into weak semiconductor powders [7]. Lead (Pb) prevents the catastrophic disaster in Sn-based solders [8], but it has
been restricted in the manufacture of electronics under the Restriction of Hazardous Substance (RoHS) [9], which arouses growing concerns about the tin pest in lead-free electronics [1,7]. Since the
matrix of most lead-free solders is Sn (commonly N 90 wt%), characterizing the βSn-to-αSn (β → α) phase transition is of fundamental importance to predict and design the reliability of the electronics systems.
The β → α transformation shows massive in nature [10], wherein the product phase αSn has a different crystal structure from but the
same composition as the parent phase βSn [11]. Massive transfor- mation endures an indefinitely prolonged incubation period [12],
and once αSn nucleated, it can rapidly proliferate to cause disintegration of bulk solders and the joints. The indefiniteness of the incubation is a serious impediment to quantify kinetics of the
transformation accurately. Previous studies of the β → α transformation focused on recognizing the influences from main factors such as exposure temperatures and microstructures using differential scanning calorimetry [13], electrical resistance measurements [14,15], and microstructural observations [16]; however, they failed to aim to reliably perform further quantitative measurements of the
kinetics. Powder X-ray diffraction (PXRD) can give a quantitative analysis of phase contents, and recently several investigators [17,18] utilize it to determine the transformation kinetics of powdered Sn
samples seeded with αSn, but without discussing the detection limit and confounding effects thoroughly. Quantitative phase analyzing by PXRD is based on the fact that the intensity of the diffracted pattern of each component in a mixture is a function of their amounts [19]. The PXRD could achieve reasonable detection limits by decreasing the intensity fluctuations in terms of improving counting statics and stabilization of diffractometers [20,21].
However, the intensity is not only dependent on the abundance, but also strongly correlated with various factors such as preferred orientation [22], microabsorption [23], and grain size [24] in samples tested. These factors are not trivial; variations in them can reduce the detection sensitivity and thus produce significant errors in final analysis results [25]. This intricate interplay raises serious doubts as to PXRD's validity for quantitative analysis of the phase
transformation kinetics of bulk Sn plates because of the complex crystallographic textures and the markedly different linear absorption coefficients of αSn (on CuKα: 1529/cm) from that of βSn (on
CuKα: 1930/cm

In this paper, we design a readily accessible approach inspired by Archimedes' principle [27], but different from typical dilatometric methods, to reliably measure the kinetics of β → α allotropic transformation of bulk Sn; and investigate the effects of exposure temperatures, alone and combined with nucleation agent and grain size, on the transformation kinetics. The proposed method can find it use in accessibly evaluating the dependence of
various alloying elements on sluggish β → α allotropic transformation of bulk solders and designing new tin pest-resistant materials

.
2. Experimental
2.1. Materials
The bulk βSn plates tested were prepared from Sn particles with a purity of 99.9999 wt% (Table 1) because high purity Sn has more potential for the transformation [1]. The Sn particles were firstly molten in a
vacuum furnace at 300 °C for 1 h and then cooled in furnace (cooling rate of ~0.03 °C/s) and in air (cooling rate of ~0.3 °C/s) to obtain Sn plates with different grain sizes. These casted bulk Sn were machined into a dimension of 10 × 10 × 1mm and then grounded to 800 grit as the specimen prepared for following measurements. Optical microscopy (OM)
was used to identify the grain sizes by chemically etching the polished surfaces using a standard solution (15 ml HCl, 85 ml deionized H2O,5 g FeCl3) for Sn.
To examine the distinct role of nucleation in the transformation kinetics of Sn plates, a nucleation agent, 99.999 wt% InSb powders of 1 mg, were added on the surface of βSn plates cooled in air. The transformation product was identified through X-ray diffraction (XRD) and scanning electron microscopy (SEM).

2.2. Measurements
Volume change can be utilized as an effective measure of transformation kinetics. The β → α transformation brings about a 26.6% swell in volume due to the density difference between βSn (7.286 g/cm3)
and αSn (5.771 g/cm3) [1]. This volume expansion causes high elastic strain energy in the interior of bulk Sn due to its geometry restraint, thus inhibiting the interior nucleation and facilitating the surface nucleation. As a result, the αSn strongly prefers the surface nucleation and also cracks to release strain energy; hence the phase transition corresponds exactly to the volume increase.
A general method for measuring volume is fluid confinement dilatometry, which had been used to perform isothermal dilatometric measurements for the transformations in Sn powders and filings [28].
However, despite the conceptual simplicity, the method is somewhat cumbersome, and suffers from inherent limitations that severely restrict its applicability. First, the method needs to evacuate the system in order
to fill it with the confining fluid. Moreover, the confining fluid must be highly thermal conductive to minimize temperature gradients in the sample cell, and should not interact with the sample. Furthermore, the
fluid must has a relatively low coefficient of thermal expansion to attain an adequate degree of stability of the measurement. Our attempts at
pushing these limits with long-term kinetics of phase transitions in bulk Sn plates failed (See Supplementary material 1) because of serious measurement errors in the volume changes arising from the unforeseen
height change of the fluid column in the capillary. Here, inspired by basic Archimedes principle of buoyancy, we chose to measure the mass of the fluid that is displaced by a Sn plate [27]. Fig. 1 shows a schematic of the measurement system, consisting of a balance for weighing and a thermostat to keep the transition products. The established measurement procedure includes two steps: low-temperature storage and weighing (Fig. 1b). After low-temperature exposure, bulk Sn samples in a container with a liquid C4H2Br4 were stored in a 0 °C refrigerator for 30 min to eliminate the errors due to temperature fluctuations. During the weighing, the measurement container was placed in an ice-water mixture at 0 °C to prevent the transformation from αSn to βSn and pertinent volumetric changes.

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