# Understanding formulas for PZT

In the slides i'm studying (about the production of PZT), is given the following formula for lead zirconate titanate : $$\ce{PbZr(Ti)O_3}$$ with the explanation:

It is a solid solution of two oxides: lead zirconate $$\ce{PbZrO_3}$$, and lead titanate $$\ce{PbTiO_3}$$

Later on, it's used an other formula (acceptor doping: $$\ce{K^{1+}}$$ replacing $$\ce{Pb^{2+}}$$ site)

$$\ce{(Pb_{1-x}K_x)(Ti,Zr)(O_{3-x/2}V_{O\,x/2})}$$ where $$\ce{V_O}$$ indicates oxigen vacancies

even later (acceptor doping: $$\ce{Fe^{3+}}$$ replacing $$\ce{Ti^{4+}}$$/$$\ce{Zr^{4+}}$$ site)

$$\ce{Pb\{(Ti,Zr)_{1-y}Fe_y\}(O_{3-3y/2}V_{O\,3y/2})}$$

• Now, what's the meaning of parenthesis in this context?

• Is this the standard notation to indicate solutions? In this case, which is the general rule? Because it seems that quite multiple ways were used here..

• In chemistry, much like in math, parentheses can mean a lot of things. The multiple notations for solid solutions are used more or less interchangeably. As for the oxygen vacancies in the formula, they are needed because oxygen vacancies exist in the real compound. Also, charge balance. – Ivan Neretin Jun 17 '20 at 21:33
• So you say there is not a standard way? The problem arises because for example from the first i would understand that $AB(C)D$ means: '$ABD$ in solution with $ACD$', and from the second one that $A(B,C)D$ means: '$ABD$ in solution with $ACD$', but if now i use this understandings in the third then $A((B,C)D)(EF)$ would mean: '$A$ in solution with $BD$, $CD$ and $EF$', which is certainly not the case! – Giorgio Pastasciutta Jun 17 '20 at 21:44
• Lol what's the meaning of -1? Please, if the question is found not clear just propose some improvements – Giorgio Pastasciutta Jun 17 '20 at 21:58
• Your parens/braces don't match for the Fe3+ case. But, in general, the point is to group what is on various distinctly different crystal sites. So, you have (Ti,Zr) meaning they occupy that site. But {(Ti,Zr),Fe} you now have a different charge state ion (Fe) that somehow fits onto the (Ti or Zr) site, leading to changes in the oxygen site occupancy. It is pretty clear once you know what has to go where, and can't go over there. – Jon Custer Jun 17 '20 at 22:48
• Ah ok now i start to understand, thanks! So the parenthesis used for $\{(Ti,Zr) Fe\}$ have also the meaning of substitution and they should have a comma probably? i.e. $\{(Ti,Zr), Fe\}$ – Giorgio Pastasciutta Jun 17 '20 at 22:59