Most piezoelectric materials exhibit a positive longitudinal piezoelectric effect (PLPE), while a negative longitudinal piezoelectric effect (NLPE) is rarely reported or paid much attention. Here, utilizing first-principles calculations, we unveil the origin of negative longitudinal piezoelectricity in ferroelectric hafnia by introducing the concept of weighted projected bond strength around cation in the c direction (WPB_c), which is proposed to quantitatively characterize the asymmetric bonding stiffness along the strain direction. When the WPB_c is anti-parallel to the direction of bulk spontaneous polarization, the polarization decreases with respect to tensile strain and leads to a negative piezoelectricity. Furthermore, to confirm the influence of WPB_c on the piezoelectric effect and understand how the value of WPB_c influences the piezoelectric coefficient e₃₃, we acquire both the piezoelectric coefficient of doped hafnia and the corresponding bonding environment around each cation. The finding reveals that the more negative piezoelectric coefficient can be achieved through a concurrent achievement of the more negative average WPB_c and the lower standard deviation (STD) of WPB_c. In addition, the Sn-doped hafnia with the lowest average WPB_c and smaller STD-WPB_c is identified to have the highest piezoelectric coefficient (−2.04 C/m²) compared to other dopants, showing great potential in next-generation electromechanical devices.

大多数压电材料表现出正纵向压电效应（PLPE），而负纵向压电效应（NLPE）却很少报道或受到太多关注。在这里，利用第一性原理计算，我们通过引入 c 方向上阳离子周围的加权投影键强度 (WPB _c ) 的概念，揭示了铁电二氧化铪中负纵向压电的起源，该概念被提出来定量表征沿应变方向的不对称粘合刚度。当WPB _c 与体自发极化方向反平行时，极化相对于拉伸应变减小并导致负压电。此外，为了确认WPB _c 对压电效应的影响并了解WPB _c 的值如何影响压电系数e ₃₃ ，我们获得了掺杂二氧化铪的压电系数以及每个阳离子周围相应的键合环境。研究结果表明，通过同时实现更负的平均WPB _c 和更低的WPB _c 标准偏差(STD)，可以实现更负的压电系数。此外，具有最低平均WPB _c 和较小STD-WPB _c 的Sn掺杂二氧化铪被认为具有最高的压电系数（-2.04 C/m ²