MPB by definition is a compositionally induced phase transition. It is not related to any specific symmetry although in literature sometimes is considered that any phase transition from tetragonal to rhombohedral symmetry is an MPB (analogy to most well known MPB of PZT). As far as I am concerned a diffuse phase transition is just a phase transition that occurs on a broad temperature range and involves a change in symmetry. So if you have a diffuse phase transition you do not have an MPB or vice versa (at least I cannot imagine a phase diagram in which both phenomenons would occur because one is excluding the other, if a very rigorous definition is considered). Probably you could specify more what you mean by your question, I might have misunderstood it. Regards, Matias.

One possibility is that the ceramic samples used to measure the structure or another physical property at the transition have a distribution of grain sizes.. This entails in principle a distribution of transition temperatures, which giving rise to a diffuse transition. If the grain size is kept the same within narrow limits a sharper transition may be expected.

I hope this comment is helpful.

Dear Prof. Gonzalo,

thank you sir for addressing another direction of the problem. Definitely I'll look into the grain size distributions of these compositions and hope to learn more things in future.

Dear Matias A,

thanks you for addressing this answer, however I did not get why MPB and DPT are mutually exclusive as per your opinion. My apologies, if I understood your statement wrongly. One more suggestion that I need from you, am I mis-correlating both the issue (MPB and DPT).

Anyways, I'm glad to interact with you and hope you will help me out as I asked you later regarding the same issue.

No problem at all! I meant that a DPT is a phase transition that normally occurs on a broad temperature. Because an MPB is a temperature independent phase transition then is not so common to have both phenomena. I would not exclude it but is not so common. The only possibility that I see now on a phase diagram that this could occur would be that you have a DPT which is tilted and occurs due to both change in T and C. If this happens, there might be a very strange triple point in which the DPT and MPB would meet but this is only a point on the phase diagram...

Some of the MPB systems have a slightly tilted MPB (like PZT and PMN-PT), so for composition around the MPB, with the increase of temperature, two phase transitions will take place in squence,1. transition from Rhombohedral phase (ferroelectric) to tetragonal (ferroelectric) phase; 2. transition from tetragonal phase (ferroelecric) to cubic phase (paraelectric), i.e., Curie point. Depending on the composition, the two phase transitions could take place at fairly close temperatures, so that the two dielectric anomalies/peak could overlap, which makes it look like a broad peak as for a DPT.

One another thing needs to be paid attetion is that some of the MPB solid solution systems have one end member typical ferroelectrics but the other end member a relaxor, like PMN-PT, PZN-PT, PIN-PT, so for those systems, with the increase of PT content in the solid solution, there is a change from relaxor to ferroelectric (at low temperature) due to the polarization of polar nano regions into polar clusters and then electric domains as a result of increasingly strong internal electric field built up as the ferroelectric PT content increases, therefore depending on the composition, these solid solution system may exhibit a relaxor ferroelectric phase transition (broad transition peak) instead of a typical ferroelectric-paraelectric phase transition. then you need to check if e vs. T above transition temperature follows Curie-Waiss law, and if there is frequency dispersion for both e' vsT, and e" vs. T. for PMB-PT, and PZN-PT, slight relaxation behaviour could still be observed at the MPB composition.

one more possiblity is that you ceramic synthesis/calcination is not completed (calcination temperature is not high enough, e.g.), that will lead to a distribution of different compositions for the grains, so that each grain has a different but close Curie points, giving rise to a broad transition peak.

Dear Dr. Zhu,

I'd appreciate your efforts to make nice comments and possibilities for the problem. I've checked your first suggestion, however I found the two phase transitions are well separated and therefore DPT is not due to overlap of these two transitions.

In my system one end member is BaTiO3 (classical ferroelectric)and other is a DPT ferroelectric, so may be your second suggestion will be very helpful. The system does not follow Curie-Weiss law above Tm, and a little frequency dispersion is there for both e' and e'', however there is no shift of Tm with frequency.

Your third suggestion, that synthesis temperature may leads to different grains with different composition, I really have to look into it carefully.

Thank you very much for your suggestions