Energy Level Diagram of 3d² Configuration in Tetrahedral Crystal Field and Its Applications to Cr^{4 +} /Mn^{5 +} ‐Doped Luminescent Materials

Abstract

Tanabe–Sugano diagram is a successful guideline for the energy levels of 3dn electrons for half a century. However, it is developed only under the regular octahedral crystal field. With the surging research interests in the near‐infra‐red luminescence of 3d block transition‐metal elements, it becomes an urgent demand to know the energy level diagram of Cr4 + and Mn5 + with 3d2 configuration, which are usually embedded in the tetrahedral site due to the smaller ionic size. Although the Tanabe–Sugano diagram of 3d8 configuration in octahedron is usually used as a substitution for that of 3d2 configuration in tetrahedron, the result mismatches with the crystal field strength and emission profile. In this work, irreducible tensor operator method is applied to derive the full analytical expressions of 3d2 energy levels in the tetrahedral crystal field, based on which the Tanabe–Sugano diagram of 3d2 configuration in tetrahedron is built for the first time. Also provided is a set of formulas for fast estimation of Dq/B$Dq/B$ values, which shows consistency between the crystal field strength and the emission profile among Cr4+, Mn5+‐doped luminescent materials. As it is hoped, this work could provide more deep insights into the luminescence of 3d2 elements.

Sharp-Line Near-Infrared Emission from Tetrahedron-Occupied Ni2+ in Ca2GeO4

“…Song and Liu reported the crystal-field strength D q and Racah parameters A , B , and C of 3 d 2 and 3 d 8 energy levels . Thanks to their work, the luminescence of Ni 2+ is possible to be studied in detail.…”

“…Song and Liu reported the crystal-field strength Dq and Racah parameters A, B, and C of 3d 2 and 3d 8 energy levels. 31 Thanks to their work, the luminescence of Ni 2+ is possible to be studied in detail. The Tanabe−Sugano d 8 diagram describing tetrahedrally coordinated Ni 2+ is visualized in Figure 5.…”

Efficient and stable near-infrared Y2Mg2Al2Si2O12:Cr3+ phosphor: analysis of the luminescence source by a site elimination strategy

“…S4b, ESI†). 26,33,41,42 Therefore, both [Mg1O 6 ] and [Al2O 4 ] are likely to be occupied by Cr 3+ to form the broadband emission near 850 nm (denoted as Cr2).…”

Valence state control of Cr4+-activated Li2SrGeO4for NIR-II light source to distinguish deuterium and non-deuterium reagents

“…3a. The energy of Cr 4+ in tetrahedron can be roughly estimated via eqn (S1) (ESI†), 39,43 from which the value of E[ 3 T 1 ( 3 P)] can be calculated from the energy 3 A 2 → 3 T 1 ( 3 P) of 460 nm, and the value of E[ 3 T 1 ( 3 F)] can be read as the average value of 650 nm, 671 nm, and 721 nm from the PLE spectrum of LSGO:0.5%Cr 4+ . Finally, the Dq / B value can be calculated to be 1.65, which is much less than the crossing point of 3 T 2 and 1 E levels in the Tanabe–Sugano energy level diagram of 3d 2 in the tetrahedral crystal field (Fig.…”