It depends on how many materials are making up your supperlattice. General speaking, no there is not any optimum volume fraction.

Yes, you can. search for mechanical properties of the composite with spherical grains. It may help you.

Dear Kaustav Barat,

one may consider the total linear, anisotropic elastic stiffness as the main spring properties of a superalloy. For the case of a single crystal these are three independent elastic constants, due to the cubic anisotopy of the crystal lattice. In case of a polycrystalline superalloy, it is more complicated as the total elastic properties of the material further depend on the grain structure or texture of the material.

However, let's consider the usual case for casted single crystalline Nickel-based superalloys, e.g. for the turbine blade application. Then, the microscructure is as such, that we have the cubic fcc-γ matrix, which is precipitation-strengthened by γ'-precipitate-particles. The volume-fractions of the respective γ'-preciptation-phase (orderd L12 -crystal structure) can be quite high up to 70% in commertial superalloys of this type.

In our research group at Metals and Alloys at the University of Bayreuth, we have measured the anisotropic elastic stiffnesses for sevaral different commertial and non-commertial single crystalline Nickel-based superalloys, with microstructures of this type, from room-temperature until round about 1000°C using resonance ultrasound spectroscopy. Furthermore, we also measured the anisotropic elastic stiffness of some selected and carfully prepared single-phase, single-crystalline matrix alloys. In one case (the commertial alloy PWA1483) my colleges even manage to manufacture a respective single-phase γ'-single-crystal.

Coming back to your original question, of how the elastic stiffnesses of the superalloy relates to the precipitation-volume-fraction and whether there is an optimum value or such, I can answer the following: With the regard to the high-termperature resonance ultrasound measurements, we have made quite good experience with using a simple mixture rule that relates the resulting total elastic stiffness of the two-phase microstructure with the respective elastic stiffnesses of the two individual phases and the precipitation volume fraction. For further details on this, I would like to refer to our recent paper on this, which you may also find on research gate under:

Article Phase-Field Modeling of Precipitation Growth and Ripening Du...

Within this article you will find the respective information in the text around Fig. 1.

I hope you find this information helpful.

Best Regards,

Michael Fleck

thanks michael, thanks a lot

Dear Michael, I have gone through your paper, it is a good attempt indeed however this gamma prime ripening with positive and negative misfit stresses are challenging problem and still being attempted. I have a superalloy where except gamma mu and eta phases are also present. A two step ageing treatment has been recommended by the manufacturer and before doing that I want to check some microstructural justification of a two step heat treatment, As from the basics we know that double ageing gives rise to a new population of smaller precipitates, however this gives rise to a bimodality in superalloys, As you work in Dr. Glatzel's group and being one of the finest specialist in this field in Europe you should attempt this appearance of bimodality by phase field simulation. This is little complex problem as you may have to deal a nucleation and ripening problem simultaneously. I want to check whether this is the microstructure gives better spring property or the use of this microstructure is there in some other applications.

Give my earnest regards to Dr. Glatzel, 6 years ago we did some work with one of the postdoc in his group.

Thanks and regards

Kaustav

Dear Kaustav,

what you tell about the microstructural effect of a two step heat treatment sounds very interesting! Can you reccomend certain specific journal articles or other research work, which adress this relation between the resulting bimodal precipitation microstructure and the imposed precipitation heat treatment. At best for the case of a γ/γ'-microstructur in nickel-based superalloys.

I would be very much interested in performing a simulation study on the formation of a bimodal precipitation microstructure. Only one boundary condition I have to impose for the moment, and that is that we have to restrict to a two-phase system consisting of just one matrix and one precipitate-phase.

Best regards,

Michael

thanks michael, it will be a nice study, my internet is not working prpoerly today, tomorrow i will give you the materials and if possible will chalk out something, i will be rather happy if my idea helps you