3-1 Theory introduction
3-1(a) Crystal Field Splitting
Crystal field splitting (also called as ligand field multiplet-LFM) model is to approximate the transition metal(TM) as an isolated atom surrounded by a distribution of charges, which mimic the system, molecule, or solid, around the TM. This seems to be a very simplistic model but it was successful in explaining a large range of experiments. A TM ion in the gas phase has five degenerate 3d orbitals. When the metal ion is placed in a crystal with six neighboring ions equidistant on the three axes, the crystal field is octahedral and its symmetry properties belong to the cubic group Oh. The effect of cubic crystal field is that the five 3d orbitals will loose their degeneracy and split into doubly degenerate eg state (3z2-r2 and x2-y2, point directly to ligands) with a higher energy and triply degenerate t2g state(xy,yz and zx,point between ligands) with a lower energy. (see Fig. 3-1)
Fig. 3-1 Crystal Field Splitting in octahedral symmetry
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3-1(b) Hund’s Rule
Hund's rules was refered to a set of rules formulated by German physicist Friedrich Hund around 1927, which can be used to discuss the ground state symmetries of partly-filled 3d band in TM compounds. The three rules are :
1. For a given electron configuration, the term with the maximum value of the total spin angular momentum S has the lowest energy.
2. For a given total spin angular momentum S, the term with the largest value of the total orbital angular momentum L has the lowest energy.
3. For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum J lies lowest in energy. If the outermost shell is more than half-filled, the level with the highest value of J is lowest in energy.
3-1(c) Jahn-Teller distortion (JT)
The Jahn–Teller distortion is named after Hermann Arthur Jahn and Edward Teller, who proved that orbital nonlinear spatially degenerate molecules cannot be stable, and will undergo a geometrical distortion that removes that degeneracy to lowers the overall energy. The JT effect is most often encountered in octahedral complexes of the TM. For example, in the d9 electronic configuration gives three electrons in the two degenerate eg orbitals, leading to a doubly degenerate electronic ground state. Such complexes will distort along one axes (set as z axis), and breaks the degeneracy to lower the overall energy. When such an elongation occurs, the 3z2-r2 orbital will lower its energy level from the electrostatic repulsion, and cause a energy difference ∆eg between x2-y2 orbital, see Fig. 3-2. The JT effect was arisen in such configurations, d9, low-spin d7 and high-spin d4 complexes, which all have doubly degenerate ground states.
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Fig. 3-2
Jahn-Teller distortion
3-2 Experimental Method
In the X-ray energy region, the mass photoabsorption coefficient generally decreases as the photon energy increase, but there still exist some particular raising range when the incident photon energy fortuitously satisfy the excitation and excites the core electron to outer empty shell. Depending on the energy range, X-ray is roughly separate into two parts, soft X-ray (hv<2000 eV, weak penetration, the experiment must be down in ultra high vacuum) and hard X-ray (hv>2000 eV, high penetration, the experiment can be down in the air.)
X-ray absorption spectroscopy (XAS) is a powerful tool to study the electronic states of outer electrons, the valence electron states in material. XAS can roughly separate into two regions, XANES and EXAFS. In XANES(X-ray absorption near edge structure), the edge energy increase with the increasing of elements valence in material, which come from the interaction between nucleus and outer shell electrons.
This phenomenon is quite obvious in K-edge(see Fig.3-3.). In EXAFS(Extended X-ray Absorption Fine Structure ), we can get some information about the number of
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atoms around and the distance between each surrounding atoms. In our studies, we focus on the XANES experiment to investigate the valence and spin state of transition metal ions in material.
6530 6540 6550 6560 6570 6580
0.0 quantum number n, orbital angular momentum l, and magnetic quantum number ml. The electric transition obeys the dipole selection rule △l=+1,-1, and △ml=+1,-1,0. In K-edge, the core electron is excited from 1s shell to np orbital. For the L1, L2 and L3
absorption edge, core electrons were excited from the 2s, 2p1/2 and 2p3/2 orbital. The TM L2,3-edge spectra can be describe as the transition from 2p63dn initial state to 2p53dn+1 final state, which is extremely sensitive to the symmetry of the initial state.
There are two kind of signals in XANES, total electron yield (TEY) and X-ray fluorescence yield (FY). TEY is used to study the surface state of material. As the material absorbed the X-ray photon, the core level electron was consequently emitted
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as a photoelectron. During the Coulomb interaction between the photoelectron and other electrons in the material, the photoelectron from inner material is undetectable.
On the other hand, fluorescence yield is used to study the bulk state. As the absorption occurred, a core hole was created. The resulting core hole is filled by capture of an electron from another shell by emission of a fluorescent photon. Since the fluorescent photon has no Coulomb interactions with other electrons, inner material signals were obtained.
Fig. 3-4 Photoabsorption of an x-ray into a core level followed by photoelectron emission, filling of the core hole by an electron in another level, accompanied by fluorescence photon.
The XAS experiments were performed at the BL.20A H-SGM beamline, BL.11A Dragon beamline, and BL. 17C at the National Synchrotron Radiation Research Center (NSRRC) in Taiwan.
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3-2-1(b) NSRRC BL.20A H-SGM beamline equipment
Fig. 3-5 NSRRC BL.20A H-SGM beamline equipment
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3-2-1(c) NSRRC BL.17C equipment
Fig. 3-6 NSRRC BL.17C equipment
3-2-2 X-ray diffraction 3-2-2(a) Bragg diffraction
To study the crystal structure, we did experiments by using X-ray diffraction (XRD). Diffraction occurs as the incidence of X-ray to the material, according to the Bragg's law, Where d is the spacing between the planes in the atomic lattice, θ is the
angle between the incident ray and the scattering planes, n is an integer and λ is the wavelength of incident wave. e.g. λ(Kα1)= 1.5406 Å for copper target.
2d sinθ=nλ
3-2-2(b) XRD experiments
The θ-2θ scans, also called normal scans, are always satisfy the Bragg’s law, which the angle from incident beam to sample surface (θ) always keep half the angle from incident beam to detector (2θ).
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3-2-2(c) Rietveld refinement
Rietveld refinement is a technique for characterizing the crystalline materials.
The x-ray diffraction of powder samples results in a pattern characterised by reflections (peaks in intensity) at certain positions. The height, width and position of these reflections can be used to determine many aspects of the materials structure.
The Rietveld method, which was able to deal reliably with strongly overlapping reflections, uses a least squares approach to refine a theoretical line profile until it matches the measured profile, and Rietveld method.
Where Wi is the weight, Wi=1/Yi(obs), Yi(obs) is the real peak intensity (counts) from experiment and Yi(cal) is the theory calculated peak intensity.
function, Phkl is the prefer orientation function and Yib is the background signal.
In the Rietveld method, three factors can be used to determine the accuracy:
The Weighted Profile R-factor
2 2
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3-3 Theoretical calculation in XTLS
The theoretical calculations of transition metal L2,3 XAS line shape is calculated by the XTLS software compiled by Dr. A. Tanaka[8], and the input file parameters were provided by Dr. Z. Hu.
In XTLS calculations, full atomic mutiplet effect and ligand field mutiplet effect are considered. The full atomic mutiplet effect includes the 3d-3d and 2p-3d Coulomb and exchange interactions inside transition metal ions, while the ligand field mutiplet effect includes the hybridization of transition metal 3d orbital with the O 2p ligands, and the local crystal field. Fig. 3-7 shows the changeable parameters in XTLS.
Fig. 3-7 Input file of XTLS software.
In the first part, parameter U3d3d and U3d2p represent the Coulomb and exchange interactions between 3d-3d and 2p-3d electrons inside transition metal ions.
Parameter Dlt represents the charge transfer energy, in transition metal L2,3-edge XAS spectra (2p→3d), the transition can be describe as α|2p63dn> + β|2p63dn+1L＞→α’
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|2p53dn+1> +β’ |2p53dn+2L>, where L denotes a charge transfer from ligand and create a ligand hole, and Dlt is the energy difference between |2p63dn> and |2p63dn+1L> state.
In the second part, parameter pds is the hybridization coefficient between TM 3d and ligand 2p orbitals. In the third part, parameter AOh is the local crystal field on TMO6
coordination with an octahedral symmetry, and parameter Deg is the energy splitting
∆eg from the distorted TMO6 octahedral. Fig. 3-8 shows setting of the initial and final electronic states, which depend on the transition metal ions. Other parameters are mentioned in M. W. Haverkort [9]. In the calculation result, XTLS gives first 16 states spectra, including the energy and angular momentum information of each state.(see Fig. 3-9)
Fig. 3-8 Initial and final electronic states setting in XTLS.
Fig. 3-9 Detailed information of each states given by XTLS.
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