Subtopic Deep Dive
Bond Valence Model Applications
Research Guide
What is Bond Valence Model Applications?
Bond Valence Model Applications use bond valence parameters to predict coordination numbers, polyhedral distortions, and structural stability in inorganic crystal structures.
Researchers apply the model to validate experimental structures and screen hypothetical materials using valence-sum rule deviations (Gagné and Hawthorne, 2015, 588 citations). Comprehensive parameters for 128 cation-oxygen pairs were derived from 31,489 polyhedra (Gagné and Hawthorne, 2015). Extensions cover alkali/alkaline-earth metals (Gagné and Hawthorne, 2016, 138 citations) and borate frameworks (Huang et al., 2021, 182 citations). Over 20 papers in the list demonstrate applications across oxides and perovskites.
Why It Matters
Bond valence predictions enable rapid high-throughput screening of TiO2 polymorphs for stability (Muscat et al., 2002, 517 citations), guiding materials design without full DFT computations. In borates, [BO2]- anions expand functional crystals for optics (Huang et al., 2021). Perovskite classification hierarchies rely on bond valence for hettotype derivation (Mitchell et al., 2017). Geophysical equations of state for FeO/CaO under pressure use it for phase transitions (Jeanloz and Ahrens, 1980).
Key Research Challenges
Parameter Derivation Accuracy
Deriving reliable bond-valence parameters requires filtering 180,194 bond lengths from 31,489 polyhedra to minimize RMSD from valence-sum rule (Gagné and Hawthorne, 2015). Errors propagate in predictions for rare anions like [BO2]- (Huang et al., 2021). Validation against diverse coordination polyhedra remains inconsistent for alkaline-earth metals (Gagné and Hawthorne, 2016).
Extension to New Anions
Standard parameters fail for novel anions in tellurium oxycompounds and borates, needing experimental bond length distributions (Christy et al., 2016; Huang et al., 2021). Evolutionary programming aids prediction but requires bond valence integration for energy minimization (Bush et al., 1995).
High-Pressure Stability
Model struggles with phase transitions in oxides like FeO and CaO at 70 GPa, where B1 structures transform (Jeanloz and Ahrens, 1980). First-principles calculations validate but computational cost limits screening (Muscat et al., 2002).
Essential Papers
Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen
Olivier Charles Gagné, F. C. Hawthorne · 2015 · Acta Crystallographica Section B Structural Science Crystal Engineering and Materials · 588 citations
Published two-body bond-valence parameters for cation–oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180 194 filtered bo...
First-principles calculations of the phase stability of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">TiO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
J. Muscat, Varghese Swamy, N. M. Harrison · 2002 · Physical review. B, Condensed matter · 517 citations
ABSTRACT: First-principles calculations of the crystal structures, bulk moduli, and relative stabilities of seven known and hypothetical TiO2 polymorphs ~anatase, rutile, columbite, baddeleyite, co...
The Crystal Orbital Hamilton Population (COHP) Method as a Tool to Visualize and Analyze Chemical Bonding in Intermetallic Compounds
Simon Steinberg, Richard Dronskowski · 2018 · Crystals · 344 citations
Recognizing the bonding situations in chemical compounds is of fundamental interest for materials design because this very knowledge allows us to understand the sheer existence of a material and th...
Equations of state of FeO and CaO
Raymond Jeanloz, Thomas J. Ahrens · 1980 · Geophysical Journal International · 303 citations
New shock-wave (Hugoniot) and release-adiabatic data for Fe_(0.94)O and CaO, to 230 and 175 GPa (2.3 and 1.75 Mbar) respectively, show that both oxides transform from their initial B1 (NaCl-type) s...
Expanding the chemistry of borates with functional [BO2]− anions
Chunmei Huang, Miriding Mutailipu, Fangfang Zhang et al. · 2021 · Nature Communications · 182 citations
Abstract More than 3900 crystalline borates, including borate minerals and synthetic inorganic borates, in addition to a wealth of industrially-important boron-containing glasses, have been discove...
A review of the structural architecture of tellurium oxycompounds
Andrew G. Christy, Stuart J. Mills, Anthony R. Kampf · 2016 · Mineralogical Magazine · 161 citations
Abstract Relative to its extremely low abundance in the Earth's crust, tellurium is the most mineralogically diverse chemical element, with over 160 mineral species known that contain essential Te,...
Nomenclature of the perovskite supergroup: A hierarchical system of classification based on crystal structure and composition
Roger H. Mitchell, Mark D. Welch, Anton R. Chakhmouradian · 2017 · Mineralogical Magazine · 155 citations
Abstract On the basis of extensive studies of synthetic perovskite-structured compounds it is possible to derive a hierarchy of hettotype structures which are derivatives of the arisotypic cubic pe...
Reading Guide
Foundational Papers
Start with Brown (1997) for bond valence theory and constraints; Muscat et al. (2002, 517 citations) for TiO2 stability applications; Gagné and Hawthorne (2015, 588 citations) for comprehensive O-parameters.
Recent Advances
Huang et al. (2021) on borate expansions; Gagné and Hawthorne (2016) on metal-O bonds; Mitchell et al. (2017) on perovskite nomenclature.
Core Methods
RMSD-minimized parameter derivation (Gagné 2015); valence-sum rule validation; integration with evolutionary algorithms (Bush 1995) and COHP bonding analysis (Steinberg 2018).
How PapersFlow Helps You Research Bond Valence Model Applications
Discover & Search
Research Agent uses searchPapers and exaSearch to find 50+ papers on bond valence parameters, starting with Gagné and Hawthorne (2015). citationGraph reveals connections from Muscat et al. (2002) to perovskites (Mitchell et al., 2017); findSimilarPapers expands to borate applications (Huang et al., 2021).
Analyze & Verify
Analysis Agent applies readPaperContent to extract RMSD values from Gagné and Hawthorne (2015), then runPythonAnalysis with NumPy/pandas to compute valence-sum deviations on custom datasets. verifyResponse via CoVe cross-checks predictions against Jeanloz and Ahrens (1980) phase data; GRADE assigns evidence scores to parameter reliability.
Synthesize & Write
Synthesis Agent detects gaps in anion parameters (e.g., tellurates from Christy et al., 2016), flags contradictions in TiO2 stability (Muscat et al., 2002). Writing Agent uses latexEditText for structure reports, latexSyncCitations for 20+ refs, latexCompile for publication-ready docs, exportMermaid for polyhedral distortion diagrams.
Use Cases
"Compute bond valence sums for TiO2 rutile vs anatase polymorphs using Gagné parameters"
Research Agent → searchPapers(Gagné 2015) → Analysis Agent → readPaperContent → runPythonAnalysis(NumPy bond length calculator) → matplotlib plot of RMSD deviations.
"Write LaTeX report on perovskite bond valence validation with citations"
Research Agent → citationGraph(Mitchell 2017) → Synthesis → gap detection → Writing Agent → latexEditText(structure section) → latexSyncCitations(10 papers) → latexCompile(PDF output).
"Find GitHub repos with bond valence model code from crystal structure papers"
Research Agent → searchPapers(Bush 1995 evolutionary) → Code Discovery → paperExtractUrls → paperFindGithubRepo → githubRepoInspect(bond valence scripts) → runPythonAnalysis(test on FeO data).
Automated Workflows
Deep Research workflow scans 50+ papers via searchPapers → citationGraph on Gagné (2015), producing structured RMSD tables. DeepScan applies 7-step CoVe to verify TiO2 stability predictions (Muscat 2002) with runPythonAnalysis checkpoints. Theorizer generates hypotheses for [BO2]- borate extensions from Huang (2021) literature.
Frequently Asked Questions
What is the Bond Valence Model?
The model sums bond valences around ions to match atomic valence via r-dependent parameters, predicting stable coordinations (Brown, 1997).
What are key methods in applications?
Parameters derived by RMSD minimization from valence-sum rule on filtered bond lengths (Gagné and Hawthorne, 2015); validated in polymorph screening (Muscat et al., 2002).
What are foundational papers?
Brown (1997) on constraints; Muscat et al. (2002, 517 citations) on TiO2; Bush et al. (1995) on evolutionary prediction with bond valence.
What are open problems?
Reliable parameters for high-pressure transitions (Jeanloz and Ahrens, 1980) and novel anions like in borates (Huang et al., 2021).
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Part of the Crystal Structures and Properties Research Guide