Smooth Flow in Diamond: Atomistic Ductility and Electronic Conductivity

Diamond is the quintessential superhard material widely known for its stiff and brittle nature and large electronic band gap. In stark contrast to these established benchmarks, our first-principles studies unveil surprising intrinsic structural ductility and electronic conductivity in diamond under coexisting large shear and compressive strains. These complex loading conditions impede brittle fracture modes and promote atomistic ductility, triggering rare smooth plastic flow in the normally rigid diamond crystal. This extraordinary structural change induces a concomitant band gap closure, enabling smooth charge flow in deformation created conducting channels. These startling soft-and-conducting modes reveal unprecedented fundamental characteristics of diamond, with profound implications for elucidating and predicting diamond’s anomalous behaviors at extreme conditions.

Figure 1

(a) Stress response of diamond under (11-2)[111] pure shear (PS), ${\sigma }^{\mathrm{PS}}$, and constrained shear (CS), ${\sigma }^{\mathrm{CS}}$. A normal-to-shear stress ratio of 2.475 is maintained during CS, corresponding to biaxial stress fields under Vickers indentation. Data in open symbols indicate dynamic instability revealed by imaginary phonon modes (see Fig. S1 [19] for details). Maximal strains sustained by stably deformed diamond crystal under the PS and CS loadings are labeled as ${\epsilon }_m^{\mathrm{PS}}$ and ${\epsilon }_m^{\mathrm{CS}}$, respectively, and marked by the two vertical dashed lines passing through all the panels. (b) Variation of the bond angle ${\alpha }_{143}$ between atom pairs 1-4 and 4-3 [see panel (e)] in deformed diamond crystal under the PS and CS strains. (c),(d) Variation of three key bond lengths, $d_{14}$, $d_{24}$, and $d_{34}$, in deformed diamond crystal under the PS and CS strains. (e) Structural snapshots at zero, maximal PS and CS strains, along with valence charge density showing changes in bonding strengths [3] (see Fig. S2 [19] for more details).

Figure 2

(a) Electronic band gap $E_g$ of deformed diamond along the PS and CS paths in Fig. 1 from first-principles calculations. Also shown are integrated density of states (IDOS) of electronic states within 0.3 eV on both sides of the Fermi energy under CS strains, as a measure of diamond’s ability for electronic conductivity. Stress-strain curves from Fig. 1 are shown in the background to offer a visible reference. (b),(c) Electronic density of states from Heyd-Scuseria-Ernzerhof hybrid functional calculations [19] at select PS and CS strains, highlighting band gap reduction under PS and full closure and metallization under CS. (d),(e) Electronic band structures revealing directional electron and hole conduction at CS strains of 0.22 and 0.28. Inset in (d) shows Brillouin zone with high-symmetry points.

Figure 3

Robustness of smooth structural and charge flow in diamond under CS loadings. Stress data in open symbols indicate dynamic instability revealed by imaginary phonon modes (see Fig. S3 [19] for details). (a) Creeplike smooth-flow stress responses of diamond under (11-2)[111] CS strains with a normal-to-shear stress ratio of 2.00 and 3.00, and the associated electronic band gap closure and rising IDOS, similar to those shown in Fig. 2. (b) Similar smooth-flow stress, band gap and IDOS behaviors under (12-3)[111], (10-1)[111], and (22-3)[334] Vickers CS strains. (c) Similar smooth-flow stress, band gap and IDOS behaviors under (11-2)[111] CS strains at fixed normal stress (180 and 190 GPa).