The elastic behavior of low albite is investigated ab initio under hydrostatic pressure up to 16 GPa. Our calculations complement and extend previous studies confirming a highly anisotropic character of the feldspar cell compression and, more importantly, revealing a clear change of all structure deformation trends around 8–9 GPa pressure. We correlate this change to the trend of the bulk modulus of low albite as a function of pressure, which we compute in different and independent ways using (1) the Birch–Murnaghan equation of state, (2) the analytical Voigt–Reuss–Hill averaging scheme of calculated elastic constants, and (3) a pressure–volume numerical differentiation procedure. The latter, in particular, uncovers a singularity in the bulk modulus between 8 and 9 GPa pressure which is evocative of a λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}-type critical point. We find that the same behavior emerges when comparing with pressure–volume datasets from the experimental literature, where it has been so far overlooked due to the misleading use of a fourth-order Birch–Murnaghan equation of state. Indeed, we show that the equation of state must be extended up to at least the sixth power of the Eulerian strain to approximate the complex elastic behavior of feldspars. The low albite structure softens under increasing pressure between 5 and 8 GPa, as a result of the initiation of auxiliary compression mechanisms—notably, the squeezing of the crankshaft chains along b—and then abruptly resumes a stiffening trend in association with a displacive transformation of the O–O pair interactions. Whether this is an isosymmetric phase transition or a supercritical crossover, it suggests a compatibility with seismological profiles indicating a low wave-velocity anomaly in correspondence of the upper portion of the subducting Pacific plate and the disappearance of such anomaly at greater depths, assuming the alkali feldspar survives as a metastable phase. The data and methodology described here can enable the exploration of important, potentially overlooked features in other minerals, and inspire future high-pressure research in mineral physics.

中文翻译：

---

亚稳态低钠长石的从头算压缩性：揭示地球上地幔压力下的 λ 型奇点

在高达 16 GPa 的静水压力下从头研究了低钠长石的弹性行为。我们的计算补充并扩展了先前的研究，证实了长石单元压缩的高度各向异性特征，更重要的是，揭示了在 8-9 GPa 压力下所有结构变形趋势的明显变化。我们将这种变化与作为压力函数的低钠长石体积模量的趋势相关联，我们使用 (1) Birch-Murnaghan 状态方程，(2) 解析 Voigt-Reuss-Hill 以不同且独立的方式计算计算弹性常数的平均方案，以及 (3) 压力-体积数值微分程序。尤其是后者，揭示了体积模量在 8 到 9 GPa 压力之间的奇点，这让人联想到 λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{ amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} 类型的临界点。我们发现，在与实验文献中的压力-体积数据集进行比较时，会出现相同的行为，迄今为止，由于四阶 Birch-Murnaghan 状态方程的误导性使用而被忽视。事实上，我们表明状态方程必须至少扩展到欧拉应变的六次方才能近似长石的复杂弹性行为。低钠长石结构在 5 到 8 GPa 之间增加的压力下软化，由于辅助压缩机制的启动——特别是曲轴链沿 b 的挤压——然后突然恢复与 O-O 对相互作用的位移变换相关的硬化趋势。无论这是等对称相变还是超临界交叉，它都表明与地震剖面的兼容性，表明俯冲太平洋板块上部的低波速异常和这种异常在更深的深度消失，假设碱长石作为亚稳态相存在。此处描述的数据和方法可以探索其他矿物中可能被忽视的重要特征，并激发未来矿物物理学的高压研究。