I think your conclusion on the literature search is not true, at least not for pure iron. If you compare the lattice parameters of pure iron at the transition temperatures, the density is lower for the gamma phase both at the alpha-gamma and the gamma-delta transitions. Corresponding figures (plotting lattice parameters) are contained in the textbooks by Gottstein and Mittmeijer. I do not recall the original reference. Note however, that the density different is far smaller than expected from packing densities, being of caused by the coordination number dependence of the atomic radii. However, in case of bcc-fcc/hcp polymorphism this is not always true. I I recall a search indicating that indeed in some cases at the transition temperature the bcc phase may have a lower density, in contrast to the case of iron.

The lattice parameter of austenite is larger than that of ferrite, as you stated. However, its closed packed structure and its 4 atoms per unit cell makes its density greater. There could be changes which can reduce this difference which are dependent on the alloying elements. However, it wont be larger than that of austenite.

Please find enclosed a link to a book on steels and phase transition.

Steels: Processing, Structure, and Performance, Second Edition

https://books.google.co.il/books?id=ETJ7CgAAQBAJ&pg=PA266&lpg=PA266&dq=Steels:+Processing,+Structure,+and+Performance,+Second+Edition+austenite+density&source=bl&ots=Nwi92WQIlZ&sig=jX81MIksqiTupGzm21lIjjedtqg&hl=iw&sa=X&ved=0ahUKEwiFifqjyonQAhVEWxoKHVzcAwcQ6AEIHjAA#v=onepage&q=Steels%3A%20Processing%2C%20Structure%2C%20and%20Performance%2C%20Second%20Edition%20austenite%20density&f=false

https://books.google.co.il/books?id=OrlG98AHdoAC&pg=PA374&lpg=PA374&dq=can+density+of+ferrite+be+higher+than+austenite&source=bl&ots=huSLRED8zq&sig=P6k9goDIUCy-bwj-uVzPsTtVQtQ&hl=iw&sa=X&ved=0ahUKEwjZiLzOvInQAhXGuhQKHXgBBS8Q6AEIRjAF#v=onepage&q=ferrite%20density&f=false

I did not spend any time for literature search but simply took the lattice parameters from a data base. Therefore my comment regarding possible lattive parameter variations. Anyway..what puzzles me: you wrote "the density is lower for gamma"...despite "the density difference is far smaller than expected trom packing density" which is exactly what I pointed out and caused this question. 

Also at room temperature fcc phase can be stabilized by an amount of Ni in the range of more than 6% as in iron meteorites. Then we have a phase containing bcc and fcc, and since Ni and Fe do not have a remarkable difference in size...I would expect a higher density for fcc already because of the ccp arrangement.

@ Ravit: the 1.8% difference I referred consider of course the twice higher amount of atoms per unit cell. However, the theoretical packing density of bcc is approx. 68% whereas for fcc it is 74%, which is roughly and relatively a  -10%  lower density for bcc than for fcc.

In other words and for my simple understanding and conclusion, using the packing model as ideal case during fcc-bcc transformation the material should expand by about 10% in density, i.e. approx. 2% (2³ approx. 10) increase in lattice parameters at transformation temperature. The only alternative (again, from my point of view) would be that the "atomes shrink" in their diameter.     

sorry, I have to correct my previous entry: the density is (a bit) higher in the gamma phase, the molar volume is lower.... The differences are very small, and therefore, the additions of alloying elements cannot be neglected I think...

...in case of Fe-Ni meteorites alpha contains up  to 6% Ni and fcc can have remarkably more Ni (known is up to 40% but this is quite rare). However, Ni is also more havy so that the higher density of the fcc phase is perhaps more the result of the higher Ni concentration than of the packing difference? (Sorry, I've never thought about it before...I am no materials scientist...)

I completely agree with you.

As I stated before, these changes are probably due to the alloying elements in each phase.

I based my answer on the molar weight of the alloying element which can contribute to the difference in theoretical densities (nMw/(VNA)). The density of Ni is indeed high, about 8.9 gr/cm^3, but not the highest, such as in the case of Mo about 10.3 gr/cm^3, a ferrite stabilizer, which can make a great contribution to theoretical density of ferrite. The only problem with these substitutional atoms is that their amount is limited by the atoms per unit cell (2 compared with 4).

Therefore I proposed an austenitic Fe-Ni steel. as I already pointed out, I am no material scientist, but is there no low-alloyed steel with Ni like in iron meteorites? 

What are the numbers in data bases refering to gamma-Fe? They are not all measured at high temperature, are they? Let's assume 12% Ni in Fe then statistically two unit cells contain one Ni (1 of 8 atoms). Considering 56 (Fe) and 59 (Ni) as atomic  weight it would explain a increase in mass (and density) by 3/60 which means about 5%. The atomic radii should be 1.17A (Fe) and 1.15A (Ni), i.e., Ni should tend to cause a contraction but - as far as I understand this - this is more against the observed trend that bcc (pure Fe) has a higher density than expected from the simple geometrical assumption: 74% packing density fcc and 68% packing density bcc. 

From this follows for the density rho:

rhofcc=(cama+cbmb+...+cpmp) *Nfcc/Vfcc  

or

rhobcc=(crmr+csms+...+cvmv) *Nbcc/Vbcc  .  

c are the concentrations, m the atomic weights, N the number of atomic positions in the unit cell, and V is the unit-cell volume. 

Assuming pure iron at transition temperature

rhofcc=mfcc*4/Vfcc    ~ 0.74

rhobcc=mbcc*2/Vbcc  ~ 0.68

Adding Ni to fcc mfcc becomes higher and the difference to rhobcc even bigger. Considering the slightly smaller Ni diameter, Vfcc shrinks and rhofcc is getting even more bigger and the difference to rhobcc increases.

I think the key to this answer, besides alloying element effect, is thermal expansion (happening in austenite-iron phase). The austenite phase is created at high temperature (at plain carbon above 723 oC) depending on carbon content and depending on additional alloying elements at alloyed steels. Even though, FCC phase is the most efficiently packed, it is not in fact the most dense (as you mentioned). The same number of atoms takes up more volume (causing reduction in density) probably due to the extra energy contained in the metal at those temperatures.     

As indicated above, the densities of alpha/gamma and gamme/delta at the the transformation temperatures are more similar at the transformation temperatures than suggested by the packing densitiy. It is well known in crystal chemistry that what we call "atomic radius" depends on the coordination number, i.e. it reduces with reducing coordination number. This is a trend which counteracts the effect of increasing packing densty with increasing coordination number. I attach a table from Mittemeijers materials science textbook, which I think I have compiled originally, and which I still use in my lectures. Comparison of the cubic, lattice parameters is senseless because there is a different number of atoms per unit cell. The atomic distances decrease somewhat (see above) with coordination number and cause, that the aomic volumes (proportional to the inverse pyknometric densities) are vey close.... That is of course only the case, if the type of chemical bonding is quite similar. The relative change iin densities is much larger, in case of a change in the type of chemical bonding (alpha/beta tin and graphite/diamond). An generally, do not forget, that a given temperature, introduction of magnetic long-range order expands the volume.

Dear Andreas, I guess something with your image of the table happened. Could you perhaps post it again?

Since you sent it to me already...it reflects that there is a small increase of density for the shown close-packed strucure instead of bcc for the example of iron.

For me it suggests that the calculation of spherical packing is certainly elegant but looks more convincing as it finally is since the resulting geometrical differences are far away from being practically relevant, especially when we consider that the given lattice parameters are not comparable since either measured at different temperatures (thermal expansion) or at samples of different chemical compositions (to stabilize a high-temperature phase at room temperature). In so far, the diagram posted by A. Leineweber is the only acceptable way to demonstrate experimentally the very small increase of density during the change of fcc and bcc. However, a rough estimation results in a density variation which is about ten times smaller than geometrically expected. I only hope that the observed tendency is at least correct and not only specific for Fe.

Dear all,

now hopefully the correct attachment with the table... Please refer to discussions above.

I guess Andreas Leineweber has given the key already twice: the coordination number  has an influence on the atomic radius. Or stated differently: More of the space is filled with spheres in the fcc but the spheres are less dense.

Hi there,

I should also add that the number of vacancies is different in both cases which is highly dependent on the temperature. They are found experimentally, but not in the model already mentioned.

I think this is another effect which influences the density, but this is easy to discover since you know thr relative mass, the lattice parameter and the number of atoms per unit cell. The last one is then changed.

It is actually possible to calculate and measure the volume change associated with the transformation. The volume change in general depends on: (a) the fraction of the phases; (b) lattice parameters; and (c) thermal expansion coefficients. The effective contribution of these factors decide the nature of the volume change. In general, the austenite formation leads to contraction and vice-versa. However we have observed expansion as well in some cases (this work is currently under consideration). You may would like to refer the paper from our group:

Article Bainite Transformation During Continuous Cooling: Analysis o...