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In literature (Ref.), the second quartic coefficient, was determined by fitting the P-E curves along [001] and [011] directions in the paraelectric phase. Neglecting the high-power terms, Phkl = κhkl Ehkl + λhkl E hkl 3, and - Βhkl = λhkl ε4. As determined λ001 and λ011 both have positive values above TC. Keeping in mind that the birefringence are proportional to the square of the polarization, Δn P2 = κ2 E2 +2κλ E4 +, one would expect that the nonlinear coefficient d2 in Δn= d1 E2 + d2 E4 + have the same sign as λ for both directions as κ001 = κ011. However, the birefringence measurements evidenced positive d2 [001] whereas negative d2 [011] over the same temperature interval, contradicting to that predicted by λ values.
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