Is there any equation for density estimation for metal alloys?

If you assume that upon alloying the specific volume of individual alloying element doesn't change very much then you can easily formula the expectation value of the density alloy denoted as Dal: Let, {Xa, Da} and {Xb,Db} are volume fractions and densities of the species present in the alloy, respectively. Then you can write the following expressions by definition:

Dal= (Na Wa+NbWb)/V = (Va/V) (NaWa/Va) + (Vb/V)(NbWb/Vb) ,

Where Wa and Wb atomic weights, Na and Nb are number of atoms in an alloy of a given volume of V. Let: Xa=Va/V, Xb= Vb/V volume fractions in the alloy. Then, by definiton,

Dal= Xa Da+ Xb Db, if you define the relative volume fraction as f= Xa/Xb= Va/Vb , then you can easily obtain the following expression:

Dal = {f Da + Db)/(1+f) QED. That means all you have to know the densities of individual alloy species, and their relative volumes in the mixer before to go through the alloying processing.

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Niko Ojala

Robit Plc

Thanks Tarik. I need to try that out.

What I was after for was little bit like your second answer. Basically what I thought was an equation where one could input a chemical composition of an alloy or a metal.

What I first think was to use a simple fractions formula (like the one in your first answer), but doesn't that give wrong estimate as the densities of pure elements can change when mixed? And similarly in the second formula also? Is there any way to compensate that? Or how good the estimate is if calculated by densities of pure elements?

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Tarık Ömer Oğurtanı

Middle East Technical University

I think we can find many ways to compensate (to estimate the error) ) the change in the specific volume (which is inverse of the density) of the alloy as a function of composition if you have additional information such as i.e., XRD lattice parameter 'a' measurements (Del a/a). Otherwise, catagorically it is impossible!!!

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Uday M. Basheer

Universiti Teknologi Malaysia

You can calculate the theoretical density of the alloy metals by using the XRD diffraction analysis. I calculated the theoretical density of the 6061 aluminum alloy when exposed to friction and joining with several types of ceramics such as alumina and YSZ during my research studies. And of course I have the plastic deformation suffered by the metal alloy in every time when changed the parameters, but I calculated the theoretical density of Aluminum alloy surface by XRD and the density results were variable slightly. It is important in the subject can be determined theoretical density of the alloy in an expeditious manner using XRD analysis, if the metal alloy components are not known.

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Tarık Ömer Oğurtanı

Middle East Technical University

Dear Dr. Basheer, your are definitely right. XRD in combination with XR Fluorescence chemical analysis is very powerful tool. One can determine the chemical composition, lattice structure, short and long range order in alloys, grain size, particle size, stacking fault probability, strain distribution, dislocation densities etc. But one should have very sophisticated tailor made theories supplement by mathematical modelling and numerical methods. Best Regards

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Christian Ressel

Metals Consult, www.metals-consult.net

A. A. GORNI also relates to BOHNENKAMP within a handy practical resource he has compiled and provided for download at

http://www.gorni.eng.br/e/Gorni_SFHTHandbook.pdf

The practical approaches he quotes distinguish between ferritic and austenitic steels.

http://www.gorni.eng.br/e/Gorni_SFHTHandbook.pdf

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Carlos Araújo Queiroz

Universidade NOVA de Lisboa

We can coarsely estimate of the molar volume of an alloy of a particular composition, by simply multiplying the molar volume of the elements by their molar ratio and summing the respective contributions. This approach accepts that the alloy, taken as homogeneous, can be approximately taken as an ideal solid solution of the elements that constitute the alloy. We could, of course, apply a comparable linear mixture rule directly to densities, but that would not be consistent with the ideal solution assumption and might, therefore, result in larger errors. Improved estimates may be possible, by taking into account the often available molar volume data for related equimolar binary alloys, and/or, other possibly known data for other specific alloys from the same composition system.

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Vikash Kumar

Jadavpur University

https://www.indium.com/blog/interest-in-formula-for-calculating-alloy-density-still-keen.php

It is well explained in this link.

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