Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

价电子 离子半径 价(化学) 协调数 原子半径 多面体 离子键合 化学 Atom(片上系统) 材料科学 化学物理 计算化学 结晶学 物理 热力学 电子 离子 量子力学 数学 几何学 计算机科学 嵌入式系统
作者
G. V. Gibbs,F. C. Hawthorne,Gordon E. Brown
出处
期刊:American Mineralogist [Mineralogical Society of America]
卷期号:107 (7): 1219-1248 被引量:12
标识
DOI:10.2138/am-2021-7938
摘要

Abstract Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2− and selenite (Se4+O3)2−] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
希望天下0贩的0应助angela采纳,获得10
1秒前
1秒前
1秒前
安全123完成签到,获得积分20
3秒前
李嘉图的栗子完成签到,获得积分10
4秒前
Orange应助科研通管家采纳,获得10
4秒前
地表飞猪应助科研通管家采纳,获得10
4秒前
我是老大应助科研通管家采纳,获得10
4秒前
彭于晏应助chen采纳,获得10
4秒前
领导范儿应助科研通管家采纳,获得10
4秒前
汉堡包应助科研通管家采纳,获得10
4秒前
科研通AI2S应助科研通管家采纳,获得10
4秒前
斯文败类应助科研通管家采纳,获得10
4秒前
CipherSage应助科研通管家采纳,获得10
4秒前
隐形曼青应助科研通管家采纳,获得10
4秒前
SYLH应助科研通管家采纳,获得20
5秒前
5秒前
赘婿应助科研通管家采纳,获得10
5秒前
Owen应助科研通管家采纳,获得10
5秒前
田様应助科研通管家采纳,获得30
5秒前
JamesPei应助科研通管家采纳,获得10
5秒前
5秒前
所所应助科研通管家采纳,获得10
5秒前
昏睡的蟠桃应助科研通管家采纳,获得200
5秒前
搜集达人应助科研通管家采纳,获得10
5秒前
ding应助科研通管家采纳,获得10
5秒前
Jasper应助科研通管家采纳,获得10
6秒前
在水一方应助科研通管家采纳,获得10
6秒前
6秒前
Ava应助科研通管家采纳,获得10
6秒前
6秒前
6秒前
6秒前
6秒前
6秒前
6秒前
7秒前
7秒前
如云发布了新的文献求助10
8秒前
angela给angela的求助进行了留言
8秒前
高分求助中
【提示信息,请勿应助】关于scihub 10000
Les Mantodea de Guyane: Insecta, Polyneoptera [The Mantids of French Guiana] 3000
徐淮辽南地区新元古代叠层石及生物地层 3000
The Mother of All Tableaux: Order, Equivalence, and Geometry in the Large-scale Structure of Optimality Theory 3000
Global Eyelash Assessment scale (GEA) 1000
Picture Books with Same-sex Parented Families: Unintentional Censorship 550
Research on Disturbance Rejection Control Algorithm for Aerial Operation Robots 500
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 4038657
求助须知:如何正确求助?哪些是违规求助? 3576306
关于积分的说明 11375198
捐赠科研通 3306108
什么是DOI,文献DOI怎么找? 1819379
邀请新用户注册赠送积分活动 892698
科研通“疑难数据库(出版商)”最低求助积分说明 815066