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arXiv 0904.0264cond-mat.mtrl-scicond-mat.stat-mech
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铁电晶体自由能的微观研究

Free energies of ferroelectric crystals from a microscopic approach

Gregory Geneste

摘要:

钛酸钡的自由能在居里温度附近作为极化的函数从Zhong、Vanderbilt和Rabe的第一原理导出的有效哈密顿量计算[Phys. Rev. Lett. 73,1861(1994)],通过与热力学积分方法耦合的分子动力学模拟。这种方法的主要特点是计算在3-D空间的自由能梯度(Px,Py,Pz)的热平均值的力作用在本地模式,这是由分子动力学的约束下得到的固定的P.一个仔细的分析状态的约束极化进行在T=280 K(~ 15-17 K低于Tc),特别是在低序参量。这些状态被发现合理均匀的小超胞尺寸(L=12和L=16),直到观察到大超胞(L=20)在低序参量的非均匀状态。然而,对于合理的超晶胞尺寸(L=12),得到的自由能曲线是非常好的协议与唯象朗道势的litterature。此外,所获得的自由能是相当不敏感的超晶胞尺寸从L=12到L=16在T=280 K,这表明界面的贡献,如果有的话,在这些尺寸在Tc附近是可以忽略不计的。该方法允许的自由能垒分离的顺电铁电相在Tc的数值估计。然而,我们的测试证明了在低温和低序参量下的相分离,与Tröster等人的结果[Phys. Rev. B 72(2005),094103]一致。

英文摘要:

The free energy of barium titanate is computed around the Curie temperature as a function of polarization from the first-principles derived effective hamiltonian of Zhong, Vanderbilt and Rabe [Phys. Rev. Lett. 73, 1861 (1994)], through Molecular Dynamics simulations coupled to the method of the Thermodynamic Integration. The main feature of this approach is to calculate the gradient of the free energy in the 3-D space (Px,Py,Pz) from the thermal averages of the forces acting on the local modes, that are obtained by Molecular Dynamics under the constraint of fixed P. A careful analysis of the states of constrained polarization is performed at T=280 K (~ 15-17 K below Tc) especially at low order parameter. These states are found reasonably homogeneous for small supercell size (L=12 and L=16), until inhomogeneous states are observed at low order parameter for large supercells (L=20). However, for reasonable supercell sizes (L=12), the free energy curves obtained are in very good agreement with phenomenological Landau potentials of the litterature. Moreover, the free energy obtained is quite insensitive to the supercell size from L=12 to L=16 at T=280 K, suggesting that interfacial contributions, if any, are negligible at these sizes around Tc. The method allows a numerical estimation of the free energy barrier separating the paraelectric from the ferroelectric phase at Tc. However, our tests evidence phase separation at low temperature and low order parameter, in agreement with the results of Tröster et al [Phys. Rev. B 72 (2005), 094103].

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