Solder equation

There are some heatsinks for radially-leaded diodes that solder to one of the leads. These are also available from the transistor heatsink manufaeturers. In this situation the thermal equation (see Figure A-6b) beeomes... 

The coefficient of hydride bed effective heat transfer aef is proportional in general to layer effective thermal conductivity and inversely proportional to layer thickness. The analysis of this equation shows that the heat transfer coefficient is less than a smaller coefficient of heat emission and, consequently, it is meaningless to increase strongly one of them without changing the other. The experimental results show that for the soldered and diffusion welded connections of sorber case and heat-conducting insertion R = (0.5-1.5)-10 5 (m2 K)/W. If contact between insertion and a case is tight fit, then R increases in 10-100 times and influence of contact resistance becomes comparable with influence of reduced heat emission of a hydride bed. 

Interpreting Chemical Equations The combustion of propane (CsHg) provides energy for heating homes, cooking food, and soldering metal parts. Interpret the equation for the combustion of propane in terms of representative particles, moles, and mass. Show that the law of conservation of mass is observed. 

The composition and pH of water also affect the oxidation of lead metal. Modern drinking water treatment is highly effective at removing lead from water before it is pumped to the consumer most water contamination comes from corrosion in distribution systems, that is, lead pipes and lead-based solder (408). Under acidic or neutral conditions in the presence of oxygen, metallic lead is readily oxidized to Pb ", as can be seen from the equations below and from Figure 21 (48, 408, 409). 

Nearly a century after Fairbaim, in 1938, two ideas emerged from the new engineering of airframes which were to focus on the paradoxical notion embodied in Equations (15.1) and (15.2). Volkersen derived a stress analysis for the deformation of a lap joint, showing that infinite stresses could arise at the ends of a lap joint, and Chadwick measured the peel strength of soldered joints, raising the conundrum that a joint is much weaker in peeling than it is when overlapped. How can strength be different when the same adhesive is employed ... 

The energy conversion at the level of the soldered joints is done without losses and obeys a coupling (variable in the case of real junctions) that is the same for each soldered joint (as it has been assumed for writing Equation J9.2) ... 

If there is no physical reason to check whether or not the asymptotic solution is unique and stable, one may employ a simplified way used by the author first for the problem of flux-driven grain ripening in the zone of reaction copper-molten solder [1]. Here, we apply this approach to classical ripening in the 3D closed system (LSW case). The size distribution in classical LSW theory satisfies the well-known equation... 

Analysis of the maximnm deflection calculation formula reveals (as expected) that components with some compliance built into their component mounting and electrical terminations (such as the DIP and PGA) can be subjected to about twice the vibrational deflection as an SMT CLCC, provided component size, PB size, and PB thickness are equivalent.The latest equation for maximum deflection calculations is rated for 10 million stress reversals when subjected to harmonic (sinusoidal) vibration, and 20 million stress reversals when subjected to random vibration. It must be understood that this equation is a first approximation for predicting solder joint life. There are many factors that must be included for a more rigorous analysis and prediction. A more thorongh discussion is found in Barker. ... 

When a lead, component, or PCB is immersed into solder during a solderability test, the following can be derived from the component solder interface Equation 42.1... 

The Au concentration in the finished reflowed solder joint can be estimated using the following equation ... 

Effect of Lead-Free Conversion, The acceleration factor equation (Eq. 59.14) is specifically derived from experimental data for Pb/Sn solder joints. What remains to be conclusively demonstrated is an eqnivalent acceleration transform for lead-free solder joints. Several studies have been performed, but there are no acceleration transforms accepted industrywide for lead-free solders. One of the acceleration transforms proposed is discnssed in this section. A more comprehensive list of other field hfe prediction studies can be fonnd in the appendix of IPC-9701-A. ... 

FEA is a numerical technique used to solve complex boundary value problems. It involves discretizing a complex geometry into smaller simpler geometries that can be represented by a set of differential equations. These equations can then be solved numerically to determine the deformation of the overall structure subjected to structural, thermal, or other loading conditions. FEA is a powerful numerical tool that has been used to assess the reliability of solder joints. FEA can be employed to ... 

If you want a liquid to wet a surface (that is, 0 — 0, therefore cos 0 1), a balance is required between the numerator and denominator of equation 22.17 that is, Tsv 7(s should be approximately equal to -y . For example, solders are alloys whose liquids wet other metals because surface tensions have the appropriate values. By the same token, detergents and soaps help water wet solids (like synthetic fabrics) because they reduce the surface tension of water to the appropriate point. 

We present here for the first time a simple and accurate way to combine the physics of failure equations for reliability prediction from accelerated life testing. We show that a matrix approach allows the reliability physics equations to be fit proportionally to the results of monitored accelerated life testing in order to extrapolate failure rate one would expect given actual operating parameters. This methodology can be extended to include radiation effects, frequency and even packaging and solder joint effects to give a complete system reliability evaluation framework. 

Solderability or wettability depends on the wetting characteristics of a solid surface by a liquid or molten solder. The angle d between a solid surface and the tangent to the liquid surface at the contact point specifies the conditions for minimum energy according to the following equation ... 

For rehability life prediction of solder interconnects through creep fatigue interactions under thermomechanical loading conditions, time and path dependent creep models are needed. A modified Coffin-Mason type equation is typically assumed to relate the number of cycles to failure to the creep strain energy density. Work is ongoing to evaluate the materials constants in the Coffin-Mason equation for SAC (Ref 106-107). 

J.H. Lau, S.W. Ricky Lee, D. Shangguan, D. Lau, and T. Kung, Thermal-Fatigue Life Prediction Equations for Lead-Free Solder Joints on Lead-Free Printed Circuit... 

AH, J/mol and T, K. Studies were performed under the auspices of the National Center for Manufacturing Sciences (NCMS) consortium, which examined the compression creep of bulk 96.5Sn-3.5Ag solder (Ref 69). There was an inadequate amount of data to be fit to the sinh law equation. However, the data were fit to the power law equation the resulting expression appears below as Eq 14 ... 

The test methodologies, whether tension/ compression tests on bulk solders or shear tests on solder joints, have their merits for specific study objectives. Tension and compression tests on bulk solder provide critical input data for constitutive models. The finite element analysis within those models can account for geometric effects on creep deformation in an actual joint configuration (included spatially varying stress state). However, length-scale effects of small joints, or elemental contamination that alters the intrinsic mechanical and physical properties of the solder, require an entirely new set of constitutive equations because finite element analysis cannot account for these effects. Thus, in the latter circumstance, the most accurate creep data would be results obtained from tests on actual joints. 

The 150 °C (302 °F) 24 h anneaUng treatment was more effective at stabilizing the solder microstructure over the entire test temperature regime. A relatively good correlation was obtained with a single sinh law equation for dddt, (Eq 23) ... 

Q. Zhang, et al. performed shear creep tests on 95.5Sn-3.9Ag-0.6Cu solder joints (Ref 73). The gap thickness was 0.180 mm (0.007 in.). The tests were performed at three temperatures 25, 75, and 125 °C (77, 167, and 257 T). The shear stresses ranged from 4 to 30 MPa (0.58 to 4.35 ksi). Initially, the authors observed the power law breakdown effect when the steady-state creep rate, shear stress and temperature were assessed with the power law function. Subsequently, the authors obtained a more consistent fit when all of the steady-state creep data were analyzed with the sinh law equation ... 

It was observed that the creep data were readily fit to the two-term or two cell version of Eq 28. Qualitatively, two-terms for Eq 28 is suitable because the creep behavior of lead-free solders is usually a combination of bulk diffusion and fast diffusion processes as has been demonstrated by the apparent activation energy values cited previously. Values of the parameters used in Eq 28 are listed in Table 3 for a number of Pb-free solders and the Sn-Pb baseline alloy. Clech validated the resulting equations, using creep and stress-strain test results that are independent of those data used to establish the parameters in Table 3. 

The creep behavior of solder can also be expressed by an equation of the following form (Ref 7) ... 

Coffln-Manson type equations are commonly used to predict the low-cycle fatigue life of solder. The general form of the Coffin-Manson equation is as follows ... 

J. Lau, W. Dauksher, and P. Vianco, Acceleration Models, Constitutive Equations, and Reliability of Lead-Free Solders and Joints, 53rd Electronic Components and Technology Conference, 2003, p 229-236... 

Two common equations used for the steady state creep of solders are the Garofalo-Arrhenius and the Norton, given respectively as ... 

Originally developed for the low-cycle fatigue of traditional structural materials such as steel and nickel alloys, the Cofifln-Manson equation (Ref 21-23), has found application in the evaluation of solder joint fatigue fife ... 

---