Yes, Vegard's law applies to composite materials, but only with respect to components that form solid solutions with each other.

As a counterexample, if you have a composite of components that do not dissolve in each other, such as an organic polymer - e.g. polyethylene - and an inorganic filler - e.g. mica - the lattice parameters of the two components will remain unchanged after mixing. The XRD patterns may change however, because the processing can cause texturing and a change in the relative intensity of various peaks.

Emanuel Cooper Thank you for your clarification and for taking the time to respond. I truly appreciate your expertise and willingness to share your knowledge.

I want to estimate the properties of LSM-GDC LaSrMnO-GdCeO composite using Vigard's law. I found in many papers that they form solid solutions from LSM with GDC and LSM with YSZ, and they characterize some properties such as electrical conductivity. Please do you think Vigard's law can be applied to these composite materials?

Hicham Helal I'd really refer to it as Vegard's rule rather than Vegard's law. It's simply a predicted linear interpolation of (for example) lattice parameters for 2 or more completely soluble phases. You can compare the theoretical prediction with known systems. Big differences between theory and practice mean that there's some complex interaction between the components (e.g. reaction) that would need to be understood.

I agree with Alan F Rawle . In addition, Vegard's law is likely to work if the two crystalline solids have the same crystallographic structure, and if there is just an interplay between two ions that can occupy the same crystallographic site. I think Hicham Helal 's case is more complicated. For instance, La and Sr can substitute for Y in YSZ but surely not to the same extent, and I'm not sure what if anything can substitute for Mn. Also consider that, with so many ions involved, there may be additional phases accessible at some component ratios.

Emanuel Cooper Hicham Helal In my Ph.D I used this rule for Pd-Au and Pd-Ag alloys. Both these systems are fully miscible in each other. I could guess at incomplete alloying (peak distortion in the XRD pattern plus deviations from Vegard’s rule). In this instance, I’d just use the rule to compare theory and practice and comment on the differences. I wouldn’t use it alone without any experimental data to compare against.

Thank you so much Alan F Rawle and Emanuel Cooper

I appreciate your time and your responses, this is very kind of you