Some basic information on density – grain size relationship is in reference: https://link.springer.com/article/10.1007/s11837-015-1795-8
About thermal conductivity see references: https://www.sciencedirect.com/science/article/pii/S0272884210001951 https://www.sciencedirect.com/science/article/pii/0025541675901342
Dear Kanta Maan Sangwan, the references of Dr. Glodenau are sufficient for a start. In general grain size increase moderately with density up to about 93% of the relative density. Above this density pores, which impede grain growth, close and grain growth increase dramatically. Thermal conductivity increase with density increase. There are numerous equation to describe the behavior. Look for the early work of Loeb for more details Article Thermal Conductivity: VIII, A Theory of Thermal Conductivity...
Dear Kanta Maan Sangwan,
If you allow me to say, you should firstly separate your question into two parts: in one hand, the relation between density and grain size and, in the other one, the relation between density and conductivity (either electrical, thermal,...). I will make some comments only for the first part.
I presume you are working with ceramics. If that is the case, to produce ceramic materials you start with a compacted powder which has porosity. In a short way, the next step is firing. Upon heating the sample, sintering processes take place in the material and the first stage of sintering is the formation of interparticle necks. If your starting compaction is such that the number of interparticle necks is low (this means high porosity, low density), the system will hardly densify and grain growth will not take place. On the contrary, if the initial number of interparticles is high, densification can take place and also the grain growths. Porosity hinders grain growth (it is a discontinuity of matter) and conversely grain growth hinders the decrease of porosity (retards densification). Since this depends on the system under analysis, you may arrive to a situation where the material is dense with a small grain size or the material is dense with a large grain size. The good thing is to avoid grain growth during the densification process. In other words, you must analyse your material in order to solve your problem.
I hope I could help you in some way and best wishes for your work.
Hello Kanta
Let me focus this question from the very basics of materials science. First, be very cautious using terms like grain, monocrystal, particle, etc. because they are not well defined and even have different meanings depending on usage in Europe or the USA.
A monocrystal(MC) is that portion of crystalline matter contructed by well aligned uninterrupted perfect unit cells. A monocrystal can be joint to a second MC by a thin structure known as interface, interfaces as well as surfaces are always defects of the material. You can tell one MC from the neighbor MC because the direction of the unit cell is different (low angle, large angle). At these sites there is a mismatch and therefore void spaces that lower the overall density. How can you attain the maximun density? By growing or having a perfect macroscopic monocrystal. At this point you have no mismatches, no voids and perfect packing. When you have a particle comprising many small monocrystals, each one with its own particular alignment (a polycrystalline particle) there are many interfaces that lessen the density. Now you can see that the highest density is for a perfect huge monocrystal (not easy to achieve). That is the reason for the high cost of large jewel diamonds, rubies, etc. The transparency of these monocrystals is due to the small number of grain interfaces that scatter the light. Large fine diamonds are transparent but diamond powder is white (opaque) if no impurities are included.
Now, for phenomena like conductivity, there are various mechanisms. If the conductivity interesting you runs through the bulk then increasing density i.e. minimizing interfaces improves conductivity. On the other hand, if the conduction proceeds by defects and interfaces, the lower the density the higher the conductivity. Doping is a defect as well as vacancies. There are specific equations for these type of materials.
Hope this helps a bit in you question.
Edgar
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