Dear Amir,

please let M be the total mass of your sample, so the individual masses of the constituents are (x, y, and z being mass fractions):

MA = M*x,  MB = M*y  and  MC = M*z;   (eq. 1)

the partial volumes of your constituents will be:

VA =  MA/rhoA;  VB = MB/rhoB  and VC = MC/rhoC with rhoA, rhoB and rhoC being the appropriate densities of your sample constituents.

The total volume Vtot is given by Vtot = VA + VB + VC

Now the total density rhotot is the equal to the total mass M  divides by the total volume Vtot: thus we will whave :

rhotot = M/Vtot = M/( VA + VB + VC)  =  M/(MA/rhoA + MB/rhoB +MC/rhoC).

Now using equation 1 you will get:

rhotot = M/Vtot = M/( M*x/rhoA +M*y/rhoB + M*z/rhoC)

           rhotot = 1/(x/rhoA + y/rhoB + z/rhoC)

You see that it is a simple calculation.    But.....there is one concern:

Your sample has to be a close  packed system without any holes or pores. In reality you will have pores or holes, (Dávid mentioned that above; we wrote the answers at the same time) so your sample volume will be:

Vsample > Vtot(from calculation) and

 rhosample <  rhotot  = 1/(x/rhoA + y/rhoB + z/rhoC)

@ Amir and Dávid: does one knows the volume fractions of the constituents as Dàvid uses in his equations?

I think for a composite the mass fractions are known more precisely than the volume fraction; just by weighting prior to mixing....

Dear Amir Mostafaei,

As I believe the density can be easily calculated by using the rule of mixtures. Keep in mind that this is just an assumption. If your composite is very porous or very contaminated, its density can deviate a lot from the theoretical value. Take a look at the attachment. 

Dear Amir,

please let M be the total mass of your sample, so the individual masses of the constituents are (x, y, and z being mass fractions):

MA = M*x,  MB = M*y  and  MC = M*z;   (eq. 1)

the partial volumes of your constituents will be:

VA =  MA/rhoA;  VB = MB/rhoB  and VC = MC/rhoC with rhoA, rhoB and rhoC being the appropriate densities of your sample constituents.

The total volume Vtot is given by Vtot = VA + VB + VC

Now the total density rhotot is the equal to the total mass M  divides by the total volume Vtot: thus we will whave :

rhotot = M/Vtot = M/( VA + VB + VC)  =  M/(MA/rhoA + MB/rhoB +MC/rhoC).

Now using equation 1 you will get:

rhotot = M/Vtot = M/( M*x/rhoA +M*y/rhoB + M*z/rhoC)

           rhotot = 1/(x/rhoA + y/rhoB + z/rhoC)

You see that it is a simple calculation.    But.....there is one concern:

Your sample has to be a close  packed system without any holes or pores. In reality you will have pores or holes, (Dávid mentioned that above; we wrote the answers at the same time) so your sample volume will be:

Vsample > Vtot(from calculation) and

 rhosample <  rhotot  = 1/(x/rhoA + y/rhoB + z/rhoC)

@ Amir and Dávid: does one knows the volume fractions of the constituents as Dàvid uses in his equations?

I think for a composite the mass fractions are known more precisely than the volume fraction; just by weighting prior to mixing....

The following correlation, based on mass fractions (wi), reasonably estimates the density (ρ) of a non porous composite constituted from its i-components: 1/ρ ≈ ∑fi·wi / ρi, Here, fi are empirical dimensionless fitting coefficients and ρi are the densities of each component. Furthermore, from mass additivity: ∑wi = 1. It is also appears reasonable to (optionally) accept ∑fi = 1, hence decreasing the number of degrees of freedom by one to facilitate the fitting procedure, typically least-squares based. In absence of (enough) experimental data, we may take either some or all fi = 1. For the last case, our previous correlation reduces to a mixture rule, what allows us to estimate (predict) the composite density solely based on that of its components: 1/ρ ≈ ∑wi / ρi. It simply expresses that both mass and volume balances were accepted to hold for the composite obtained from its components. In terms of the volume fractions for its components (vi), while accepting also volume additivity (∑vi = 1), we can alternatively express our previous density mixture rule as: ρ ≈ ∑vi·ρi. 

Appreciate all your responses. Very precise and useful.

Simply use archemedies principle

I already used that method. I need to report relative density so I need to know density of the bulk composite without any pore.

Hi Amir,

The rule of mixtures mentioned above are applicable in the case of composites with very less porosity. However for porous materials (porosity could be more than 80%) it is difficult to predict density. You may find my paper useful if your composite is porous.

http://www.sciencedirect.com/science/article/pii/S0950061817303768

I assume that x, y and z are mol-fractions. So multibly x,y,z with the according moleculat weights of the elements. This gives you different weights which you have to add. Then calculate the single percentages related total weight. Now you have the weight fractions of the elements. Look for the densities of hte elements and use the formula from gerhard Martens.Xw, yw and zw are the weight fractions which you have noe. 1/rhotot = xw/rhoA+ yw/rhoB+zw/rhoC. Thake the reciprocal value of 1/rhotot and you have the required density. Please take in consideration that this is a theoretical value, reaction like solid solution may change the theoretical value.

Thank you Christian Kühl and Md Arifuzzaman for your responses.

Dear Amir,

Dr. Martens gave the correct answer. Rule of mixture is an approximation.

Dr Gerhard Martens gave the best answer.

Dr Gerhard Martens gave an explicit answer

Dear Dr Gerhard Martens , Dr Amir Mostafaei

I want to use these calculations in my thesis and I need a reference for this formula. Can you help me find a reference?

Dear Erfan Fotoohi ,

these are just basic calculations using the definitions of the densities and mass fractions.

To my opinon there is no need for a reference in the thesis.

You may put a similar derivation of the formalism in the appendix.

Alternatively you may 'google' for 'rule of mixtures'. There will be a lot of results.

Good luck

use the following eq.

(mass1+mass2) /((mass1/density1)+(mass2/density2))

Composites theoretical density can be calculated by using "RULE OF MIXTURE" equations and Experimental density can be evaluated with the help of Archimedes Principle.

By using "RULE OF MIXTURE" ....Fellow this link.

https://www.sciencedirect.com/topics/engineering/rule-of-mixture-equation

direct calculation

https://netcomposites.com/calculator/volume-weight-fraction-calculator/

with A, B, and C materials use this link.

https://rechneronline.de/material/mix-density.php