The Lattice Compatibility Theory: Arguments for Recorded I-III-O2 Ternary Oxide Ceramics Instability at Low Temperatures beside Ternary Telluride and Sulphide Ceramics

Some recorded behaviours differences between chalcopyrite ternary oxide ceramics and telluride and sulphides are investigated in the framework of the recently proposed Lattice Compatibility eory (LCT). Alterations have been evaluated in terms of Urbach tailing and atomic valence shell electrons orbital eigenvalues, which were calculated through several approximations. e aim of the study was mainly an attempt to explain the intriguing problem of difficulties of elaborating chalcopyrite ternary oxide ceramics (I-III-O2) at relatively low temperatures under conditions which allowed crystallization of ternary telluride and sulphides.

p-type Cu-Al-O-like ceramics have been prepared by several techniques.Pulsed laser deposition [14], sputtering [15], more information of these two techniques will be introduced in the following sections.
e subject of this paper is an attempt to explain, starting from experimental facts, why was it impossible to stabilize ternary oxides under humid condition below 450 ∘ C, while both binary and ternary sulphides were easily obtained.is paper is arranged as follows.In Section 2, we present some experimental details concerning ternary oxide ceramics fabrication.In Section 3, the fundamentals of the lattice Compatibility eory (LCT) are presented as a plausible explanation to ternary oxide ceramics unexpected instability at low temperatures.Conclusion will be appeared in Section 4.

Experimental Details
CuAlS 2 thin �lms ceramics have been deposited on glass substrates using chemical bath deposition CBD technique with CuSO 4 , (NH 2 ) 2 SC and hydrated Al 2 (SO 4 ) 3 as precursors.Commercial solutions of 0.10 M CuSO 4 (NH 2 ) 2 , and 1.0 M (NH 2 ) 2 SC, 0.1 M Al 2 (SO 4 ) 3 ⋅14H 2 O were used.A primal solution of CuSO 4 (NH 2 ) 2 with an excess triethanolamine was stirred for few minutes until colour changed, before adding a stirred Al 2 (SO 4 ) 3 solution.Substrate slides were �nally immerged in the obtained dark orange black solution for 22 hours.Removal of the slides was carried out at room temperature and was followed by a few rinsing-drying stages.CuAlTe 2 layers have been synthesized by annealing, under vacuum in an argon-rich medium, a multilayer structure of thin Cu, Al, and Te layers which were deposited by evaporation.A mixture of pure copper, aluminium, and tellurium weighed in stoichiometric ratios was sealed in a vacuum quartz tube.e tube was subjected to several 35 h annealing stages.CuAlTe 2 layers were consecutively grown by the evaporation of the obtained powder under vacuum.More details about experimental procedure can be found elsewhere [21,23,24,[26][27][28].Similar techniques and disposals have been used in order to synthesize CuAlO 2 .A wide variety of precursors, including mineral CuFeO 2 , high-purity CuO, Al 2 O 3 , and metallic Aluminium have been tried unsuccessfully in our laboratories, particularly at temperatures beyond 450 ∘ C.

Oxygen Beside Sulfur-Like Structural Disparity
3.1.Atomic Scale Patterns.In order to explain the mentioned paradox (Section 2), a quick comparative review of oxygensulfur properties is needed.While both elements have the same valence, oxygen electronegativity is 3.44, less than that of sulfur (2.58).Some other differences can be outlined: (i) O=O double bonds are stronger than S=S.
(ii) S-S single bonds are almost twice as strong as O-O.
(iii) Sulfur can expand its valence shell to hold more eight to twelve electrons.
e last difference has been illustrated by Carelli et al. [29] who stated that in combined media, "sulfur can expand its valence shell to produce a so nucleophilic center" which refers to the so-called S-nucleophilicity.is property, accounts, in the case of I-III-O 2 and I-III-S 2 compounds for the ability of sulfur to expand its valence shell from 8 to 10 or 12 electrons using its available 3d orbitals, allowing oxidation states not available to its oxygen analogs (Figure 1).
Moreover, opposite to Cu-O bonding patterns, which obey a simple oxidation state formalism, Cu-S bonding systems have a high degree of delocalization resulting in additional electronic band structures (Figure 1) and are hence covalent rather than ionic.
Moreover, calculation of atomic valence shell electrons orbital eigenvalues for sulfur, oxygen, and tellurium in delafossite structures con�rms this delocalization plausibility.Orbital eigenvalues were calculated through local density (LDA) [30] and scalar-relativistic local density (ScRLD) [31] approximations using OPIUM code [32,33].In the �rst approach, the many-electron con�guration is approximated by a set of single-particle equations while the second takes into account some of the effects of relativity, such as Darwin shi and mass-velocity term.
According to (LDA) and (ScRLD) calculations, most of Tellurium bonding in the valence region is accomplished by the 5p orbitals.e in-plane locally -type 5p orbitals (Figure 2) form a narrowband between −0.2 and −0.3 eV, which is far below the Fermi energy.is range con�rms the diffuse character of tellurium p-orbitals, which also confers to the lattice a covalent rather than ionic aspect.
(Figure 3) shows the two-dimensional arrangement with Cu + ions located between layers of B III O 2 octahedra.e structure is characterized by alternating layers of slightly distorted edge-shared B III O 2 (or B III S 2 ) octahedra sandwiching planes of close-packed A + cations (here Cu + ) in linear or "dumbbell" coordination to oxygen anions in the adjacent octahedra.
e difference in length between Cu-O and Cu-S bonds (24%) has been ascribed to the electrons being shied to the orbital 3d.All these observations plea on favor of the presence of a delocalized valence "hole" favorizing natural bonding between two opposed octahedra planes (Figure 3) at low temperatures.If we consider the results of Liang et al. [34,35], which stated that the Cu-Cu bonding character was very weak in such structures, we can conclude that the crystalline behavior of A I B III O 2 (Figure 3) and A I B III S 2 lattices depends mainly on is the status of A + ion (here Copper).According to Landolt-Börnstein [36][37][38] and Greenwood and Earnshaw [39], any formulation of copper monosulphide as Cu II S with no meaningful S-S bonds is incompatible both with the crystal structure, and the observed diamagnetism as a Cu(II) compound would have a d 9 con�guration and be expected to be paramagnetic.An alternative formulation as (Cu + ) 3 (S 2− )(S 2 ) − was proposed and supported by other studies.

Urbach Energy and Lattice Compatibility eory (LCT)
Consideration.An additional argument can also be formulated through the recently proposed Urbach energy-related Lattice Compatibility eory (LCT) [40][41][42].Urbach energy   has been determined, for the ternary oxides and telluride and sulphides samples through the equations: where  represents, for each sample, the experimentally deduced optical absorption pro�le.Urbach energy   has been de�ned as an aggregated for the evaluating of the intrinsic disorder and atomic scale dispersion inside structures as it indicates the width of the band tails of the localized states in presence of defects.e width of the localized states (band tail energy or Urbach energy   ) has been estimated from the slopes of the plots of Ln  versus energy  (Figure 4).
It can be noticed that the atomic-scale intrinsic disorder is higher in CuAlS 2 and CuAlTe 2 than in �lms, and disposals have been used in order to synthesize CuAlO 2 matrices.is result is in good agreement with the precedent analyses and with the fundaments of the Lattice Compatibility eory (LCT) [40][41][42].
Finally, additional investigation should be carried out in order to explain the need of calcination (at 1200 ∘ C [43], 800 ∘ C [44], and 900 ∘ C [45]), as un avoidable step for establishing A I B III O 2 stable structures, while A I B III S 2 are autostabilized at low temperatures apparently, thanks to the above-described valence "hole."

Conclusion
In this study, we tried to give some explanation to the intriguing problem of the impossibility of elaborating chalcopyrite ternary oxide ceramics (I-III-O 2 ) at relatively low temperatures in wet media.Contrast has been highlighted with regard to ternary telluride and sulphide ceramics.An attempt to explain this paradox has been formulated in terms of particularities of A I B III O 2 and A I B III S 2 ceramics delafossite structure and bonding interaction.

F 3 : 2 F 4 :
A I B III S 2 and A I B III O 2 ceramics Delafossite type structure (with additional sulfur orbitals).Plots of (Ln ( versus energy ℎ (as guides for evaluating   ).