From One Engineer to Another

Interest in Formula for Calculating Alloy Density Still Keen

Thursday, August 17, 2006 by Dr. Ron Lasky [Dr. Ron Lasky]

Alistar writes

Dear Dr. Ron,

Can you send me the answer to your question of 14th Feb. 2005, which follows;

If the density of silver is 10.5 g/cc and the density of tin is 7.31 g/cc. What is the density of an alloy of 96% tin/4% silver.

Hint: The answer is not obtained by multiplying the densities by the percentages and adding together. This question requires thinking about the definition of density. Out of 150 people given this question on a certification test, only 2 got it right.

The correct answer is 7.40 g/cc (7.399927 exactly) Bob Jarrett was the first one with a correct answer. If anyone wants the technique explained or a copy of an Excel spreadsheet that perfroms these calculations send me an email (rlasky@indium.com)

Thanks in advance,

Alistair

Dear Alistair,

An easy way to understand this (proposed by Bob Jarrett) is to consider the 96% tin, 4 % silver example.

Lets assume I have 1 g of this alloy, 0.96 g is tin and 0.04 g is silver.

The volume of the tin is 0.96 g/7.31g/cc = 0.131327cc

The volume of the silver is 0.04g/10.5g/cc = 0.00381cc

So 1 g of the alloy has a volume of 0.131327 + 0.00381 cc = 0.135137 cc

Hence it's density is 1g/0.135137cc = 7.39989g/cc

The general formula is:

1/Da = x/D1 + y/D2 + z/D3

Da = density of final alloy

D1 = density of metal 1, x = mass fraction of metal 1

same for metals 2 and 3

Formula continues for more than 3 metals.

I have developed an Excel spreadsheet (shown calculating the density of SAC 305) that calculates density automatically. If anyone wants a copy, send me an email at rlasky@indium.com.

Cheers

Dr Ron

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Comments for Interest in Formula for Calculating Alloy Density Still Keen

Thursday, March 1, 2007 by karthick prabhu.c:
its a very nice formula but still i have some doubts... will you please send me the exact formulae for calculating...the alloy density.. for various metal compositions... thanking you in advance
Sunday, May 27, 2007 by SWAPAN KUMAR BOSE:
Dear Sir, This formula is very good and useful.Will you pl. send me a copy of Exel Spreadsheed that calculates density automatically devoloped by you. Thanking You in advance. With Regards, Skb.
Tuesday, June 12, 2007 by Ajay Pareek:
DearSir, This fourmula is very good and useful,plese send me a copy . Thanking you
Monday, November 12, 2007 by Dr. Perumal:
Thanks for giiving us the information about density calculations. Could you send us the Excel spreadsheet. Thanks in advance.
Thursday, November 29, 2007 by student:
Dear sir thanks for this formular.However, could you send all formation about density for me please. thanks.
Thursday, January 10, 2008 by Gerry Chen:
Good idea! could you send me the excel spreadsheet.Thanks.
Thursday, February 14, 2008 by Rochelle:
Sir, Thank you for the information. Kindly send the excel file. Thanks a lot
Monday, March 17, 2008 by John Teets:
Please send me a copy of the spreadsheet for the density calculator. We manufacture fine diameter wire using precious metals and this will be a great help with alloys that are not standard. Thanks.
Friday, March 28, 2008 by Tarek El-Ashram:
Thank you for this method of calculating the density of an alloy, but what about if there is intermetallics or vacancies.
Wednesday, April 2, 2008 by T.P.yadav:
Please send me the density of ZrFe2 alloys thank you
Thursday, April 17, 2008 by Tommy Fan :
Dear Dr. Lasky, Can you also give me the Excel spreadsheet of the calculating the density Thank you Tommy Fan
Wednesday, May 7, 2008 by John:
Hopefully this post works. Trying for the fifth time this time in a different browser. This is from density = mass / volume. First find the volume of each item. D = M / V 10.5 = .04 / V V silver = .0038095 D = M / V 7.31 = .96 / V V tin = .13133 Now find the combined density D= M / V D= M1+M2 / V1+V2 D= .04+.96 / .0038095+.13133 D= 7.399 When you have 2 components, the combined density will be between the individual components density. You can use as many components as you like. You can use whatever units for measurement you like, but they all have to match.
Tuesday, July 29, 2008 by Ramesh:
Dear Sir, Is there a possibility to obtain a copy of the excel sheet that calculates density automatically. Thank You in advance. With Regards, Ramesh
Monday, September 1, 2008 by Edward:
Dear Sir, Thank you for the equations, but I have a question, what if after alloying they form a different phase? Will this equation still apply? Also, could you still send me a copy of the excel spread sheet or any information you have on densities of alloys? Thanks in advance. Regards, Edward
Wednesday, November 19, 2008 by BELUR RAGAVAN RAVI:
DEAR SIR, GOOD DAY. I SHALL BE MUCH OBLIGED IF YOU WILL SEND ME A COPY OF EXCEL SPREAD SHEET AT YOUR EARLIEST CONVENIENCE. I THANK YOU FOR YOUR SERVICE BY PROVIDING SIMPLE METHOD TO CALCULATE ALLOY DENSITY. THANKING YOU AGAIN. WISH YOU GOOD LUCK FOR EVERY GOOD THING YOU LOVE TO ENJOY. KIND REGARDS, B.R.RAVI.
Monday, December 1, 2008 by carwaterguide.blogspot.com:
Im excitedly waiting all the changes in technology and availability of vehicles in the near future!!!
Sunday, January 11, 2009 by essam:
how can deduce the density of the elements in alloy if the alloy density known and the atomic mass number of its content- like (Al-si) alloys
Monday, April 6, 2009 by narendra patidar:
thanks alot for your explaination.but i also want to get the copy of this formula so that i can try the density of different element thanks narendra patidar
Wednesday, October 14, 2009 by Liliana Vera:
Dear Dr. Ron, could you send me the excel spreadsheet? thank you
Wednesday, March 17, 2010 by CARMEN:
Dr. Ron, Thank-you for your quick response, yes it did help, we were doing it the same way, the problem is when we send it out for analyzing we get different results!!! is it the mixing, the temperature ? we pour into 6 cupcakes and send 1 out for testing. also can you send me a copy of your Excel Spreadsheet that performs the Alloy Density of the materials, thanks again carmen
Wednesday, May 12, 2010 by Ken Endo:
Dr. Ron, Thanks for your helpful post. I get close (-1.1%) with your formulas for an alloy I am working with. I think the crystal lattice packing factor for some of the individual elements is throwing off the result since it is different than the alloy. I tried to take this into account, but I get an error on the opposite side (+1.6%) of the actual. Any thoughts on if your formula can be made more acccrate by taking element and alloy crystal lattice packing factors into account?
Wednesday, August 25, 2010 by P.Jayakumar:
I would like to calculate voulme of the 96S tin-silver solder having the dia of 1.2mm with the length 15.5mm. Pls answer to me

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