About Dr. Ron

Materials expert Dr. Ron Lasky is a professor of engineering and senior lecturer at Dartmouth, and senior technologist at Indium Corp. He has a Ph.D. in materials science from Cornell University, and is a prolific author and lecturer, having published more than 40 papers. He received the SMTA Founders Award in 2003.

Professor Michael Dickey: Prophet of Gallium Liquid Metals

North Carolina State’s Professor Michael Dickey is arguably the world expert on applications of liquid gallium metal. See his Tedx Talk and also his recent Jones Seminar at my university, Dartmouth College. Professor Dickey has found many interesting applications that may be future products. Some of the applications are, for lack of a better word, clever.

Look at these two videos and see if you agree.

Most interesting is his emphasis on the “softness” of liquid metals and how this feature will enable liquid metals to be the foundation for wearable electronics. As a company that provides high-quality jettable liquid metal and liquid metal paste technology, Indium Corporation is very interested in his work and the new applications of liquid metal. 


Dr. Ron

Join Me at SMTA PanPac 2023


I’ve gone to SMTA PanPac since 2018 and it is a terrific conference. This coming year’s conference, from January 30 to February 2, 2023, will be another great experience. The venue is striking as seen in the photo. Admittedly, it is small, but that is one of its attractions. In addition, the people that go tend to be leaders in the field. Since it is small, you will get to know everyone there.

So please submit an abstract and please come.


Dr. Ron

Square vs. Circular Apertures and the Five Ball Rule Revisited


I recently posted that circular apertures deliver much less solder paste than square apertures. One of the obvious reasons is that a circle of diameter D has only 78.5% of the area of a square of side D. However, in addition, the circular aperture has poorer release than a square aperture. In the aforementioned post, I theorized that the reason for the poorer release is that the curved surface of the circular aperture adheres to the solder paste solder balls more effectively.

I recently thought of the above situation in light of the “Five Ball Rule.” This rule states that the solder paste’s largest solder particle diameter should be such that at least five of these particle diameters would span the width of a rectangular stencil aperture.

See Figure 1 for the Five Ball Rule applied to circular and square apertures. Note that the ratio of solder balls is 19/25 = 76%, almost the theoretical maximum ratio. However, for square and circular apertures, the ‘Eight Ball Rule” is suggested. But, in some configurations the Eight Ball Rule may result in less solder paste — 40/60 = 62.5% (Figure 2). It should be remembered that this is just a surface area argument, not a volume argument. Solder paste is printed in volume and in this discussion we are just looking at one layer of paste.

Figure 1. Circular apertures provide only 76% of the solder paste that square apertures do using the Five Ball Rule.
Figure 2.  Circular apertures provide only 62.5% of the solder paste that square apertures do using the Eight Ball Rule.

However, the bottom line is that square apertures should be preferred over circular apertures.


Dr. Ron

Excel Software Tool to Determine Mass Fractions in Binary Alloy


Recently, I posted a derivation of the equations to determine the mass fractions of two metals in a binary alloy. I thought it may be helpful to develop an Excel software tool to perform these calculations.

To use the tool, you enter the densities of the two metals and the density of the alloy in the blue cells as seen in Figure 1 below. The calculated mass fraction of each metal is shown in the gray cells.

Figure 1. The data entry for the mass fraction calculator. The densities are entered into the blue cells and the mass fractions are calculated and shown in the gray cells. 

As an example, let’s assume you purchase some 14 karat gold. Unfortunately, to your eye it looks more like 10 karat gold, so you want to check it out. As a reminder, when gold is expressed in karats, the alloying metal is copper. First you need to measure the density of the gold alloy. An easy way to do this is the wet gold technique as discussed in a past blog post. From using this technique, you determine that the density of the alloy is 11.53 g/cc. The density of gold is 19.3 g/cc and that of copper is 8.96 g/cc. You will recall that 14 karat gold is (14/24) gold or a mass fraction of 0.5833.

The weight fraction of gold is shown to be 0.4167 or 10/24, as shown in Figure 1, indicating that the gold is 10 karat, not 14 karat.

Time to complain to the seller!


Dr. Ron

How to Calculate the Metal Mass Fractions in a Two-Metal Alloy System


I was surprised to see the wrong formula for metal alloy density calculations on YouTube. The wrong (Eq. 1) and correct (Eq. 2) formulas are shown in Figure 1. In many cases, Equation 1 will give an answer only a few percent off. However, in some cases it can be off by more than a factor of 1,000 as seen in a past blog post. This blog post also gives the derivation of Equation 2.

Figure 1. The wrong and right equations to calculate alloy density.

The YouTube video mentioned above did suggest one interesting task—determining the metal mass fractions of a two-metal alloy, while only knowing the alloy density. Of course, we know the densities of the two metals. The solution to this problem is seen in Figure 2.

Figure 2. Solving for the mass factions of two metals in a two-metal alloy. 

To check the result, assume we have a tin-lead metal alloy. The alloy density is 8.4 g/cc. Tin has a density of 7.29 g/cc and lead 11.34 g/cc. By plugging these numbers into the solution for x (tin), we get 63% and y = 37%. Hence, this alloy is the tin-eutectic alloy.

This technique can solve only two-metal alloy system mass fractions.


Dr. Ron

New Excel Software Tools to Practice for SMTA Certification #2: Reflow Profiling


In my last post, I shared about an Excelbased software tool called Line Balancer to help candidates for SMTA Certification prepare for the line balancing part of the program. They can use Line Balancer to check the correctness of practice line balancing problems. This post will discuss another Excel-based software tool, Reflow Profiler, to help candidates prep for the reflow profiling part of the certification.

Typically, the reflow profiling goal is to determine if the reflow profile matches the requirements of the solder paste specification.

As an example, let’s consider a reflow profile as shown in Figure 1. The solder paste specification is shown in Figure 2. We will first solve the problem by hand and then use the software.

Figure 1. A ramp-to-peak reflow profile.
Figure 2. The solder paste reflow specification

The first task is to determine if the ramp-to-peak rate matches the solder paste specification outlined in red in the specification shown in Figure 3. By measuring the change in temperature in Figure 4 from point A to B and dividing it by the change in time from those points, we see in Figure 4 that the ramp-to peak-rate is 0.857°C/sec., and is within the recommended specifications 0.5 to 1.0°C/sec.

Figure 3. The solder paste specification with the ramp-to-peak rate highlighted.
Figure 4. The reflow profile with the ramp-to-peak rate calculated.

Figure 5 shows the solder paste specification with the time above liquidus (TAL) with the peak temperature highlighted. While Figure 6 shows the reflow profile, where the TAL is measured as 60 seconds and the peak temperature at 240°C, both are consistent with the recommended values.

Figure 5. The solder paste specification with the TAL and peak temperature highlighted.
Figure 6. The reflow profile with the TAL and peak temperature identified.

Lastly, Figure 7 shows the solder paste specification with the cooling ramp rate highlighted and Figure 8 shows the reflow profile with the cooling rate calculated as -2.8°C/s, again within the specification.

Figure 7. The solder paste specification with the cooling rate highlighted.
Figure 8. The reflow profile with the cooling rate calculated.
Figure 9 shows all of the calculations performed and matched to the specification with Reflow Profiler.

If you are interested in a copy of Reflow Profiler send me an email at [email protected]

Dr. Ron

New Excel Software Tools to Practice for SMTA Certification #1: Line Balancing

I recently developed some Excel-based software to help those who are planning to take the SMTA certification exam to practice. 

In this post, I will discuss the tool that performs line balancing. In a typical SMT assembly line, the placement machines are the “gate” in the cycle time of the line. To assure that their cycle time is the lowest, the placement machines must be time balanced. For example, suppose a simple SMT assembly line has one chip shooter and one flexible placer. Let’s say that the chip shooter takes longer to place all of the chips than the flexible placer takes to assemble the simple and complex integrated circuits. So, in this case, chips should be removed from the chip shooter and be placed on the flexible placer. But how many should be moved to the flexible placer? Determining the number requires algebra, and to understand how to do it, we need a numeric example.

Let’s do an example. In an assembly line, the “gate” in the cycle time is component placement.

  • The chipshooter (CS) places passives at 60,000/hr and Simple ICs (SICs) at 4,000/hr
  • The flexible placer (FP) places complex ICs (CICs) at 3,000/hr and SICs and passives at 8,000/hr
  • The bill of material (BOM) is 354 passives, 12 SICs, and 4 CICs
  • If the FP takes less time to place the CICs and SICs than the CS takes to place all of the passives, then move some of the passives to the FP to time balance the line
  • Let’s check the situation that the FP takes: (4 CICs / 3,000/hr) + (12 SICs / 8,000/hr) = 0.001333 + 0.0015 = 0.002833hrs
  • The CS takes: 354/60,000/hr = 0.0059hrs
  • So, move chips to the FP—but how many? Let’s call the number x. The times should be equal, so:
    • 0.002833+x/8000 = (354-x)/60,000.  Solve for x to time balance the line.
    • 0.002833+x/8000 = (354-x)/60,000, multiply each side by 60,000
    • (60,000*0.002833) + (60,000x/8000) = 354 – x
    • 170 + (60/8)x = 354 – x,  gather x terms
    • 170 + ((60/8) +1)x = 354, gather numbers
    • (68/8)x = 354-170 = 184, solve for x
    • x = (8/68)*184 = 21.65 or 22 passive moved to FP

Let’s see if the times on each machine are the same.

  • CTCS= 332 passives/60,000 passives/hr =0.005533 hrs or 19.92 secs

Is the FP the same?

  • CTFP = 0.002833 + 22/8,000 = 0.005583 hrs or 20.10 secs

Why the difference?

The times can’t be exactly the same as we rounded the number of passives moved to the FP.

Figure 1. The “Line Balancer” answer to the problem

Figure 1 shows the calculations from the Excel® software tool I developed called “Line Balancer.”  Note the answers are the same. If you would like a copy, send me an email at [email protected].

Here is a problem for you to solve:

  • The chip shooter (CS) places passives at 50,000/hr and Simple ICs (SICs) at 3,000/hr
  • The flexible placer (FP) places Complex ICs (CICs) at 4,000/hr and SICs and passives at 7,000/hr
  • The bill of material (BOM) is 390 passives, 14 SICs, and 6 CICs

How many components need to be moved, and to which placement machine? What is the cycle time?

To the first person that sends me the answer, I will send them a Dartmouth hat.

Why Square Apertures Provide More Solder Paste than Circular Apertures


When comparing the volume of solder paste provided by a circular versus square aperture, consider that if the side of the square is D and the diameter of the circle is also D, the square has greater than 25% more area. (i.e., (1-0.785)/0.785 = 0.274). See Figure 1.

Figure 1. Square vs. circle areas.

However, the greater area of a square is not the only reason square apertures deposit more solder paste. The curving of the circular aperture enables more surface of the stencil to contact more of the solder particle’s area. See Figure 2. So, the solder particles will adhere to a cicular aperture more readily and not adhere to the pad, resulting in a smaller solder paste deposit. 

Figure 2. The curving of a circular aperture results in more contact area with solder particles than a square aperture

These two effects can result in dramatically different soldering results, as seen in Figure 3. Using the square aperture provides so much more solder paste; when compared to what a circular aperture provides, it is stunning in the soldering result.

Figure 3. Circular aperture/pad (left) and square aperture/pad (right), using the same Type 3 powder size, area ratio, flux chemistry (no-clean), and reflow profile (RTP)


Dr. Ron

The Only Way to Demonstrate Zero Defects is to Sample all the Product


John Foster felt very fortunate. Not only did he get his undergraduate degree summa cum laude, but was now a graduate student at Ivy University under the tutelage of the famous Professor Patty Coleman. While contemplating these pleasant thoughts, he was working on his homework in advanced statistics when Professor Coleman walked up to his desk.

“Hey, John, I have a little assignment for you. Mike Madigan, CEO of ACME, has a vendor that is guaranteeing zero defects in lots of diodes that ACME buys, yet when ACME gets the lots they find a defect rate of around 1% or more. Can you contact ACME’s quality engineer, Frank Ianonne, to see how you can help?” Patty asked. “We covered this topic in the intro stats class you took last term,” she finished.

“Sure, glad to help,” replied John.

“Thanks, I’m going to SMTA’s PanPac for the first time and have a lot going on there,” Patty said thankfully.

“Wow,” John thought, “the pressure is on.”

John contacted Frank and learned that the vendor’s sales engineer, Mike Gladstone, said that they sample 20 diodes from each 10,000-part lot. If they find no defects in in the sample of 20, they claim they can say that there are 0 defects with 95% confidence, since 19 out of 20 is 95% and they found no defects.

“Yikes,” John thought, “this can’t be right.”

He thought about this and finally came up with what he confidently felt was the answer, especially after looking at his notes from the class Professor Coleman mentioned. He contacted Frank and they set up Zoom call with Mike to discuss the issue.

On the Zoom call after introductions, Frank asked Mike how they determine that a lot has zero defects.

“I’m glad to have the opportunity to explain this to youse guys,” said Mike.

It seemed to John that his tone was arrogant.

Mike continued, “Well, you will agree that 19 out of 20 is 95%, right?”

“Yes,” responded Frank and John.

“So, if we don’t get no defects in 20 samples, we got zero defects in the lot with 95% confidence. If we had one defect in the 20 samples, we couldn’t claim to have no zero defects in the lot,” Mike said.

“Mike, look at the image I took of one defect (a red bead) out of 2000 beads.” (See Figure 1.) “If I selected 20 beads on the left side of the container, how would I know that the defect rate is 0.0005 (1 in 2000)?” asked John.

Figure 1. The red bead is one “defect” out of 2000.

There was long silence.

“Mike what is your answer?” asked Frank.

Still no answer.

“The answer is that the only way you can assure zero defects is to evaluate all of the samples,” said John.

“You’re just confusing the issue with that there photo,” Mike spit out.

“Seems quite clear to me,” said Frank.

“You Ivy League types is all the same. You confuse the issue with mumbo jumbo when any dufuss can see I’m right,” Mike screamed.

Some profanity followed and Frank cut Mike’s Zoom feed.

“I see your point John,” Frank said. “but, can you give me some math to back it up?”

“Sure,” John replied.

“Let’s consider a case where the defect rate is not zero, but quite low, say 1 in 10,000 in a very large population. When we select the first sample, the likelihood of it being good is 0.9999 (10,000-1)/10000). What is the likelihood that the second one will be good?” John asked.

“Ah, let’s see…0.9999, right?” Frank answered.

“But what is the likelihood of both events?” John asked.

“Wait, I remember from a statistics class I took a few years ago, it’s 0.9999 x 0.9999,” Frank said triumphantly.

“And the likelihood of three in a row being good?” John asked again.

“0.99993,” Frank answered confidently.

“So let’s say we sample so many times, let’s call it n times, that 0.9999n = 0.05. What does this tell us?” asked John.

“Hmm …., ” replied Frank.

“Well, how likely is this to happen if the defect rate is 1 in 10,000?” John asked.

“Wait, I see, it would only happen 0.05 or 5% of the time.” Frank responded excitedly.

“So, let’s say we didn’t know the defect rate, what could we say if we sampled n and got no defects?” queried John.

Frank was stumped.

“I’ll tell you what, think about it and we will get back tomorrow. It’s already almost 6PM. Oh, and see if you can calculate what n is. Let’s Zoom at 10AM,” John proposed.

Time flew quickly and John and Frank were Zooming again.

“John, you just about killed me, I had trouble sleeping, but I think I have it after reviewing my stats book and doing some Youtubing,” Frank began.

“Well, if we didn’t know the defect rate and wanted to see if it was at least as good as 1 in 10,000 and we sampled n such that 0.9999n = 0.05, we could say with 0.95 (1 – 0.05) confidence that the defect rate was 1 in 10,000 or less,” Frank said triumphantly.

“Precisely,” John exclaimed.

“But what is n?” John asked.

“That’s where I am stuck. We have the equation 0.9999= 0.05, but I can’t solve for n,” Frank said dejectedly.

“Hint: Logarithms,” John replied.

“That’s it, I got it,” said Frank enthusiastically.

Frank worked for a few minutes with a calculator, and came up with the solution in Figure 2.

Figure 2. The defects calculation.

“So, to show with 95% confidence that the defect rate is 1 in 10,000 or less, we would have to sample almost 30,000 components and find no defects,” Frank exclaimed.

“By looking at the equation, you can see if the defect rate was zero, 0.9999 would be replaced by 1 and the log of 1 is 0 so you would need an infinite sample,” said John.

“So, the only way to show 0 defects is to sample all of the components,” Frank said.

“Right!” replied John.


Dr. Ron

Using FMEA to Determine Your Tin Whisker Mitigation Strategy

In our last post, we discussed techniques to mitigate tin whiskers (TW). To help determine what your tin whisker mitigation strategy should be, consider using failure modes and effects analysis (FMEA). The central metric of FMEA is the risk priority number (RPN). For tin whiskers, the RPN is equal to the product of: (1) the probability of tin whiskers (P); (2) the severity, if a tin whisker exists (S); and (3) how hard it is to detect a tin whisker (D).  In equation form:


As a first example, consider a consumer product, like a mobile phone with a life of 5 years. With mitigation, on a scale of 1 to 10, P might be 2. For S, we might rate it at a 3, as a failure in the device is unlikely to cause severe harm to anyone. Detection (D) is a problem because the tin whiskers that form later cannot be detected during manufacturing; hence, we would have to rate D as a 10. So, the RPN is: 2*3*10 = 60, which is not too high. Therefore, with P and S at relatively low values, a tin whisker mitigation strategy would likely be successful for any consumer product. It should be pointed out that determining the RPN numbers would almost certainly require supporting data, brainstorming sessions, and a buy-in from the entire product team. The team would also have to determine any appropriate mitigation strategy such as avoiding bright tin coatings on component leads and perhaps using a flash of nickel between the copper and the tin (Figure 1).

Figure 1. In  mission-critical products, coatings may be required. It is almost impossible for a TW to penetrate both layers of coating as shown above.

Now consider a mission-critical product, such as certain types of military equipment. If we assume that the electronics have a service life of 40 years and that a failure could cause bodily harm or death, we could likely end up with a consensus that RPN = 10*10*10 =1000, the highest RPN possible. This situation would demand that special tactics be used to address the tin whisker risk. These tactics were discussed in my paper and presentation given at SMTA Pan Pacific 2019.


Dr. Ron