On the brittleness of elementary semiconductors
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2023-01-01 |
| Journal | Физика твердого тела |
| Authors | М. Н. Магомедов |
| Institutions | Joint Institute for High Temperatures |
| Citations | 1 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Brittleness of Elementary Semiconductors
Section titled “Technical Documentation & Analysis: Brittleness of Elementary Semiconductors”Executive Summary
Section titled “Executive Summary”This research provides a critical theoretical framework for understanding the intrinsic mechanical limits of single-component covalent crystals, particularly diamond (C-dia), focusing on the Brittle-Ductile Transition Temperature ($T_{BDT}$).
- Core Mechanism: The brittleness of diamond is attributed to the “duplicity” of the interatomic potential, where the specific surface energy for plastic (irreversible) deformation ($\sigma_s$) is significantly lower than for elastic (reversible) deformation ($\sigma_e$).
- Energy Advantage: The specific surface energy for plastic fracture is shown to be more than two times lower than for elastic stretching, making brittle fracture energetically favorable at low deformation.
- Critical Temperature: Diamond exhibits an exceptionally high experimental $T_{BDT}$ range (1470 - 1615 K), confirming its superior mechanical stability compared to Si and Ge.
- Transition Indicator: The brittle-ductile transition is fundamentally linked to the metallization of paired covalent bonds on the crystal surface.
- Upper Limit Defined: Under static load conditions (infinitely low deformation speed), the theoretical upper limit for the transition temperature ratio is $T_{BDT}/T_m < 0.45$.
- 6CCVD Value Proposition: Replicating or extending this fundamental research requires ultra-high purity, low-defect Single Crystal Diamond (SCD) materials, which 6CCVD provides with precise control over orientation, surface finish, and thickness.
Technical Specifications
Section titled “Technical Specifications”The following hard data points were extracted from the analysis of C-dia (Diamond) properties, calculated at $T = 0$ K and $P = 0$ unless otherwise noted.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Melting Temperature ($T_m$) | 4235 | K | Calculated Value |
| Brittle-Ductile Transition Temperature ($T_{BDT}$) | 1470 - 1615 | K | Experimental Range (Static Load) |
| $T_{BDT}/T_m$ Upper Limit | < 0.45 | Dimensionless | Static Load Condition |
| Elastic Specific Surface Energy ($\sigma_e$) | 14025.0 x 10-3 | J/m2 | Reversible Deformation (Derived from $D_b$) |
| Plastic Specific Surface Energy ($\sigma_s$) | 6104.5 x 10-3 | J/m2 | Irreversible Deformation (Derived from $D_s$) |
| Surface Energy Ratio ($\sigma_e - \sigma_s) / \sigma_s$ | 1.297 | Dimensionless | Measure of Brittleness |
| Strong Single Bond Energy ($\Delta D/2$) | 4.75 | eV | Covalent Bond Duplicity Model |
| Weak Single Bond Energy ($d$) | 0.535 | eV | Covalent Bond Duplicity Model |
Key Methodologies
Section titled “Key Methodologies”The research utilizes an analytical, non-computer-based simulation approach based on fundamental solid-state physics models to derive the conditions for brittle fracture initiation and the $T_{BDT}$.
- Interatomic Potential Model: The Mie-Lennard-Jones potential (Equation 1) is used to model pair interatomic interaction in the single-component crystal.
- Potential Duplicity: The model introduces two potential depths: $D_b$ (for elastic/reversible deformation) and $D_s$ (for plastic/irreversible deformation), where $D_b > D_s$.
- Surface Energy Calculation: Specific face surface energy $\sigma(100)$ is calculated using the “only nearest neighbors interaction” approximation combined with the Einstein model for crystal vibration spectrum (Equation 7).
- Fracture Condition Derivation: The prerequisite for brittle fracture is defined by the energy inequality $\Delta E = E_b - E_s \ge 0$, where the energy required for brittle fracture ($E_s$) is less than that for elastic surface tension ($E_b$).
- $T_{BDT}$ Calculation: The brittle-ductile transition temperature is derived by setting the elastic and plastic surface energies equal at $T_{BDT}$: $\sigma_e(T_{BDT}) = 2\sigma_s(T_{BDT})$.
- Temperature Ratio: The final $T_{BDT}/T_m$ ratio is calculated using a derived expression (Equation 15) that incorporates the specific surface energies at $T=0$ K and $T=T_m$.
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”The findings underscore the exceptional mechanical and thermal stability of diamond, making it the ideal material for high-stress, high-temperature applications where fracture resistance is paramount. 6CCVD is uniquely positioned to supply the materials necessary to validate and extend this fundamental research.
Applicable Materials
Section titled “Applicable Materials”To study the intrinsic brittle-ductile transition properties of diamond, researchers require materials with minimal defects and controlled orientation.
- Optical Grade Single Crystal Diamond (SCD): Essential for replicating the theoretical analysis of intrinsic properties. 6CCVD provides high-purity SCD plates with controlled crystallographic orientation (e.g., (100) face, as referenced in the paper) and thicknesses ranging from 0.1 µm up to 500 µm.
- High-Purity Polycrystalline Diamond (PCD): For studies involving grain boundary effects or nanostructured materials (as mentioned in the context of glass/metastable states), 6CCVD offers PCD wafers up to 125 mm in diameter with controlled grain size distribution.
Customization Potential for Mechanical Testing
Section titled “Customization Potential for Mechanical Testing”Replicating mechanical tests at high temperatures (1470 K - 1615 K) often requires precise sample preparation and specialized interfaces.
| Research Requirement | 6CCVD Capability | Technical Specification |
|---|---|---|
| Specific Surface Orientation | Custom crystal growth and orientation control. | SCD plates available in (100), (110), and (111) orientations. |
| High-Precision Geometry | Advanced laser cutting and dicing services. | Custom dimensions and shapes for micro-beam bending tests or fracture mechanics studies. |
| Surface Condition Control | Ultra-low roughness polishing. | SCD surfaces polished to Ra < 1 nm; Inch-size PCD polished to Ra < 5 nm. |
| Interface Metallization | In-house metal deposition for contact or bonding. | Custom metalization stacks (e.g., Ti/Pt/Au, W, Cu) for high-temperature fixture attachment or thermal management. |
| Substrate Thickness | Thick substrates for high-load testing. | Substrates available up to 10 mm thickness for robust mechanical fixtures. |
Engineering Support
Section titled “Engineering Support”The theoretical analysis presented relies on complex relationships between interatomic potential, surface energy, and thermal properties (Debye temperature, Grüneisen parameter).
- Material Selection Expertise: 6CCVD’s in-house PhD team specializes in the fundamental properties of CVD diamond and can assist researchers in selecting the optimal material grade (SCD vs. PCD, specific doping levels) to isolate or study specific phenomena, such as the metallization of covalent bonds during the brittle-ductile transition.
- Global Logistics: We ensure reliable, global delivery of sensitive diamond materials, offering DDU (Delivered Duty Unpaid) as default and DDP (Delivered Duty Paid) options for seamless international research collaboration.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
It is shown that the brittleness of a single-component covalent crystal (diamond, Si, Ge) is due to the &quot;duplicity&quot; of the paired potential of interatomic interaction for elastic (reversible) and for plastic (irreversible) deformation. This leads to the fact that the specific surface energy during plastic deformation of a covalent crystal is more than two times less than the specific surface energy during elastic deformation. Therefore, with a small deformation of a covalent crystal, it is energetically more advantageous to create a surface by irreversible breaking than by reversible elastic stretching. It is indicated that the brittle-ductile transition in a single-component covalent crystal is accompanied by metallization of covalent bonds on the surface. It is shown that the brittle-ductile transition temperature (T BDT ) for single-component covalent crystals under static load has an upper limit: T BDT /T m &lt;0.45, where T m --- is the melting temperature. Keywords: interatomic covalent bond, brittleness, ductility, elementary semiconductors, brittle-ductile transition.