Electronic structure and dynamics of ordered clusters with ME or RE ions on oxide surface

Journal of Luminescence 131 (2011) 526–530

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Electronic structure and dynamics of ordered clusters with ME or RE ions on oxide surface N.A. Kulagin Kharkiv National University for Radio Electronics, Avenue Shakespeare 6—48, 61045 Kharkiv, Ukraine

a r t i c l e i n f o

a b s t r a c t

Available online 19 January 2011

Selected data of ab initio simulation of the electronic structure and spectral properties of either cluster with ions of iron, rare earth or actinium group elements have been presented here. Appearance of doped Cr + 4 ions in oxides, Cu + 2 in HTSC, Nd + 2 in solids has been discussed. Analysis of experimental data for plasma created ordered structures of crystallites with size of about 10–9 m on surface of separate oxides are given, too. Change in the spectroscopic properties of clusters and nano-structures on surface of strontium titanate crystals discussed shortly using the X-ray line spectroscopy experimental results. & 2011 Elsevier B.V. All rights reserved.

Keywords: ME/RE/AC ions Electronic structure Cluster Nano-structures Oxides

1. Introduction The electronic structure of molecules or clusters with ions of the iron, lanthan and actinium group elements (there are the ions with unfilled d- or f- (nl) electronic shell, shortly ME) are responsible of the compound ground properties. In particular, the oxidation state of the ions and the symmetry of surroundings strongly relate to structure of the energy bands, optical, dielectrical and other properties of solids [1–3]. It is well known that the nl ions show oxidation states up ‘‘ +2’’ to ‘‘ + 5’’ in different molecules and compounds. Thermal treatment, irradiation, variation of the compound design conditions, etc. may induce changes in oxidation state of the ions as components as impurities ones. For example, Sr2 + Ti4 + O3 crystals can contain more than 20% of Ti3 + ions upon a thermal treatment [4,5]. It should be noticed that the experimental study of the ion oxidation state for most of the doped and component ions in solids is quite complex task. For this purpose, we proposed an effective method based on the valence shift of X-ray lines related to change of oxidation state of an ion called valence shift of X-ray lines, VSXRL. This method was used for investigation of radiation and structural defects in crystals and during study of nanostructures, too [2–9]. Data presented in Refs. [5–8] show appearance of ordered nano-structures with size at about 10  9 m on surface of separate oxides after plasma treatment accompanied by changing oxidation state in doped and component ions. To understand the processes occurring in the clusters, molecules and crystals, we have developed an ab initio method for cluster electronic structure simulation. The Hartree–Fock–Pauli, HFP, method and Heitler–London, HL, approximation have been used as basis in

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this approach (see Refs. [9–13]). The self-consistent field theory for clusters permits to calculate the wave functions for the ground and exited electron configurations and to simulate the physical properties of clusters and solids. Energy of optical, and X-ray transitions spectra in clusters were calculated with high accuracy, earlier in Refs. [2,4,13]. The cluster MEn + :[L]k, consisting in the ME/RE/AC ions with its surrounding ligands, L, is the elementary grouping for the study of the energy level scheme for molecules, doped solids, etc. The number of ions in the cluster may be quite large, more than 100 and more. In this work, we consider the foundations of an ab initio approach for the MEn + :[L]k cluster and data of the electronic structure calculation in different systems. We discuss the main paths leading to a change in the oxidation state of the ions and in the electronic structure of the clusters upon plasma irradiation.

2. Method of the self-consistent field for clusters A symbiosisis of the HFP method and HL model has been used to study the electronic structure of clusters [14–16]. The theoretical values are compared to experimental ones for optical and X-ray spectra of ME ions in free state and in wide band gap crystals, too [2,4,18–20]. For the first step, we may consider the electronic structure of MEn+ :[L]k cluster, consisting in the central ME ion in the nlN ground configuration surrounded by k ligands, L, at a distance R. The electronic configuration of the ligand contains the occupied electron shells, nulu4lu þ 2 , only. The symmetry of the cluster corresponds to the symmetry of the crystallographic structure of the unit cell. HFP method operates with the main part of Breit relativistic Hamiltonian: velocity-dependence on electron mass, contact, C(nl), and spin-contact, Q(nl) interactions which were also taken into

N.A. Kulagin / Journal of Luminescence 131 (2011) 526–530

account in our approach. The calculated results closely correspond to the experimental data and data of Fock–Dirac method [17]. In the framework of the HL approximation, when the wave function of the cluster presented as anti-symmetrical set of the wave functions of the central ion, C1(nlN), and ligand one, C2 ðnuluNu Þ, relatively to the rearrangement of the electrons for the ion in the crystal. Using the one-electron approximation for the wave functions of the central field approximation, the energy of the cluster may be written as [3,18] EðMEn þ : ½Lk Þ ¼ E0 þ kE1 þ kuðEZ þ Ec þ Eex Þ,

ð1Þ

where E0 (E1) is the energy of the central ion and ligand, respectively, in the free state. The terms Ez, Ec and Eex in Eq. (1) correspond to the energy of the interaction of electrons with the strange nucleus, the Coulomb interaction and the exchange interaction for all electrons. k0 , is a numerical coefficient depending on the symmetry of the cluster. Full expressions for the terms Ez, Ec and Eex written in Refs. [2,4,18] including next integrals: ðm1 9m2u Þ – the two electrons two-centers penetrating integral of the wave functions of nl ion and n0 l0 ligand; ðm1 9rZ1 9m2u Þ – one electron two-centers matrix elements of 2 operator describing the interaction of the electron with the strange nucleus, ðm1 m2 9r12 1 9mu1 mu2 Þ—two electrons two-centers matrix element of the Coulomb or exchange interaction. Using Eq. (1) we can write the following system of equations for each ion in the cluster [2,8,18]:  2  X d 2 lðl þ 1Þ þ Yuðnl9rÞenl  enul Pðnul9rÞ, Pðnl9rÞ ¼ Xuðnl9rÞ þ 2 2 r r dr nu a n ð2Þ where enl is one-electron energy. The Coulomb and exchange potentials Yuðnl9rÞand Xuðnl9rÞ differ from the original Hartree– Fock potentials [19,21] by the following additional terms: X kk DYðnl9rÞ ¼ r=2 ½a 1 Ykk1 ðnulu,nulu9rÞ þ bkk1 Ykk1 ðnl,nulu9rÞ, ð3Þ lll’ ll’ k,k1 ,nulu

DXðnl9rÞ ¼ 

X

k

1 ½akk Ykk1 ðnl,nulu9rÞ þ blll r k1 Pðnulu9rÞ, llu

k,k1 ,nulu

Eqs. (3) describe the self-consistent field of the cluster depending on state of all electrons of the cluster. Here, the tensor 1 1 1 function, Ykk1(nl,n0 l0 9r) and the coefficients: akk , bkk , akk , bk are llu llu llu given in Refs. [2,18] and include the angular part of the matrix elements of different operators, only. v and v0 are numerical coefficients. It is easy to see that solutions of Eq. (2) depend on the wave functions of all ions in the cluster. The energy of Stark-levels of LSJ state for nl ion in crystalline field may be written as X EðnlN 9aauLSJ GÞ ¼ E0 þ fk ðlN , aauLSÞFk ðnl,nlÞ k

þ wðLSLuSu,JÞZðnlÞ þ

X Bkq Ykq ðYi Fi Þ,

ð4Þ

k,q,i

where E0 is the center of gravity of nlN configuration, Fk(nl,nl) the Slater integrals, Z(nl) the spin–orbit constant and Bkq the crystal field parameters (for d ions in a cubic field, Dq). The radial integrals are determined in Ref. [19]. As shown in Refs. [4,18], Eqs. (2)–(4) are describing the real radial distribution of the electronic density in the cluster or molecule. Using these equations, we can study the change of the electronic distribution during the transfer of the free nl-ion into the crystal for different compound. For all 3d, 5d and 5f ions, we have obtained results that closely correspond to the semi-empirically determined data for Slater (or Racah) integrals and for level energy schemes, in particular, for ions in doped oxide, fluoride and chloride crystals. For RE2 + doped ions numerical data are close to

527

experimental spectra and for RE + 3 ions results are quite good when Hartree wave functions have been used as original point for calculation. It should be noted that the radial wave functions of each electron in the cluster change under the free ion-to-crystal transition. As shown in Refs. [22–24], the radial part of the electronic density for d and f electrons changes significantly during this transition [15,16,18,19]. Eq. (2) was used successfully to calculate energies in a cluster with boundary conditions for either the free ion or the crystal with Wigner–Zeits boundary conditions [2,4,18]. When the Wigner–Zeits boundary conditions have been used @Pðnl=rÞ ¼ 0, @r r-R0

ð5Þ

for each electron wave function in the cluster the strong change in the electronic distribution in the cluster observed [18]. The so-called Roothaan’s radial wave functions were used for the ligands: O2 (F  and Cl  , too). Additional potentials (see Eqs. (3)) for clusters were introduced in our calculation procedure, which is using the numerical programmes presented in Ref. [2]. The Fourier-transformation of the ligand wave function to the center of the cluster was used for calculation of the additional terms. The main problem of HFP theory is correct calculation of wave functions of exited configurations nlN1 nuluNu for study of X-ray and inter-configuration transitions. We use orthogonalization procedure for nl and n0 l0 radial wave functions and calculated numerical results are quite correct for selected compounds [18].

3. Change of the electronic structure of the nl ions under free ion-to-cluster transition For ME ions, the values of the radial integrals during the free ion-to-crystal transition and the radial distribution of the electronic density change significantly. Calculated results for Cr3 + ion in Cr3 + :[O2  ]6 cluster are plotted in Refs. [9,18]. Total energy E and average radius of 3d shell for the ion in the cluster are increasing comparatively to the free ion values. In the contrary, the values of the Slater integrals, the spin–orbit constant and the radial integrals Fk(3d,n0 l0 ) or Gk(3d,n0 l0 ) are decreasing. Changing in the radial integrals is similar for all 3d ions and for any type of the cluster. The radial integrals value depends on the ion oxidation state and configuration of the nl ion as well as symmetry of cluster and number of the ligands. The results of calculation of different radial integrals published in Refs. [2,4,18] for the free ions with 3dN, 3dN  14s and 3dN  14p configurations and for the ions in MEn + :[L  ]k (L ¼O2  , F  Cl  ) clusters with different R. Selected theoretical and semi-empirical data for Crn + ions in oxides are given in Table 1. The first rows of Table 1 shows semi-empirical data for B, C, Dq parameters for Cr3 + as doping ion in different oxides. In the last table rows theoretical data for Cr3 + and Cr4 + ions in clusters with octahedral and tetrahedral symmetry have been presented. The theoretical energy level scheme of Cr3 + ion in cluster Cr3 + :[O2  ]6 calculated for R¼1.96 A˚ closely corresponds to the level scheme in ruby and for R¼ 1.90 A˚ in YAG garnet [12,18]. The effect of the approach is shown through the study of the radiation induced defects in ruby, garnets and other compounds [17,18]. In the g- or electron-irradiated ruby (at doses higher than 102 Gy), the following additional optical bands appear in the absorption spectra at 217, 260, 360 and 460 nm [9]. Comparison in the theoretical data in Table 1 with experimental ones permits to attribute the additional bands at 217, 360 and 460 nm to the Cr4 + ion in an octahedral environment. These optical bands are assigned as electronic transitions in Cr4 + :[O2  ]6 cluster. Transition Cr3 + -Cr4 + oxidation state upon irradiation of

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N.A. Kulagin / Journal of Luminescence 131 (2011) 526–530

Table 1 Semi-empirical and theoretical data for B, C and Dq for Crn + ions in different crystals (cm  1). Integral

a-Al2O3

Y3Al5O12

Gd3Sc5O12

Gd3Sc2Ga3O12

Cr + 3:[O  2]6

Cr + 4:[O  2]6

Cr + 4:[O  2]4

B C Dq

682 3120 1787

725 3373 1650

740 3578 1500

740 3578 1500

789 2829 1750

590 2301 1037

730 3134 950

Table 2 Radial integrals theoretical data for Cu2 + ion in 3d9 configuration in the cluster Cu2 + :[O2  ]k. Integral

˚ R ¼ 2.5 (A)

2.0

1.9

1.8

R ¼2.5

2.0

1.9

1.8

Units

DE, k¼6

0.0841 1.4477 0.8989 93,078 58,120 825.0 1.71

0.0839 1.3872 0.9013 91,987 57,495 820.8 1.43

0.0832 1.3532 0.9043 91,796 57,365 818.9 1.63

0.0723 1.3356 0.9070 91,569 57,251 815.1 1.79

DE, k ¼4 1.4547 0.8990 94,363 59,008 831.2 2.01

0.9843 1.4096 0.8996 93,503 58,410 929.1 1.89

0.0835 1.3869 0.9003 93,143 58,218 825.5 1.71

0.0844 1.3699 0.0927 93,038 58,374 822.9 1.42

a.u. a.u. a.u. cm  1 cm  1 cm  1 eV

e3d (3d9r93d) F2(3d,3d) F4(3d,3d) Z(3d) E(3d9– 43d84s)

ruby or ABO3: Cr, or A3B2C3O12: Cr compounds, and other oxide crystals doped with Cr was detected by ESR, VSXRL and others methods [18]. As shown in Refs. [10–12,18] oxide cluster Cr4 + :[O2  ]4 with tetrahedral symmetry appears in garnets after radiation or thermal treatment effect. Let us consider now, the structure of the ME ions for HTSC Cu containing superconductors (the so-called, 1-2-3 ceramics) where Cun+ ions play an important role [3,23–25]. We have studied the electronic state of the ground 3dN and excited 3dN 14s configurations of Cu3 + and Cu2+ ions. The results for Cun+ :[O2 ]k clusters are presented in Table 2 [22,23]. According to these data, the minimum value of the total energy, Emin ¼E0  DE, where (E0 ¼  1638 a.u. and DE plotted in Table 2) for Cun + :[O2 ]6 cluster is observed for Cu3 + ion ˚ Emin for Cu2 + ion is in the octahedral cluster, at R¼1.89–1.95 A. 2+ 2 observed for tetrahedral cluster Cu :[O ]4 and R¼1.85 A˚ [24]. There is important that the energy of 3d-4s transitions in Cr2+ ions ˚ k¼6 and in clusters Cu2 + :[O  2]k strongly decreases at R¼2.0 A, ˚ k¼4. R¼1.85 A, Results for MEn + in a fluorine and chlorine environment with different R and k values reported in Refs. [18,23,24]. The calculated qualitative and quantitative changes of the Slater integrals for these clusters are closely to the experimental ones. Thus, the relative change of Fk(3d,3d) is 22% for Cu2 + :[O2  ]6, 19% for the fluorine cluster (R ¼2.1 A˚ and k¼ 6) and 20% for the chlorine one (R ¼3.0 A˚ and k¼ 6). Similar results were obtained for the spin–orbit coupling constant of ME ions in the respective clusters. The Slater integrals for all 3d ions decrease under free ion-tocrystal transition by 10–30% as well as the data for Z(3d), in close agreement with experiment. The average ‘‘size’’ of the ME ions, (3d9r93d) increases by 8–22% when R decreases. Let us consider the electronic density in selected RE and AC ions in the clusters. There is well known that the 4f35d configuration is the ground configuration of Nd2 + free ion and the 4f4 is the excited one. But in solids the opposite situation observed, the ground configuration of Nd2 + in solids is the 4f4 one. The total energy of the 4f35d and 4f4 configuration of the Nd2 + ions in free state are the following: E0(4f35d)¼ 9590.5881 a.u. and E0(4f4)¼ 9590.5358 a.u. For the ion in the cluster Nd2 + :[O2 ]8, the corresponding energies are E0(4 f35d)¼  9588.4364 a.u. and E0(4f4)¼  9589.3669 a.u. The value of (4f9r94f) goes from 0.9559 to 1.1356 a.u. for 4f4 state and from 0.9000 to 0.8971 a.u. for the 4f35d one for ion in the free state and in the cluster, respectively. The average value of size of 5d shell changed from 2.4457 to 4.0262 a.u. during to the cluster transition of Nd2+ ion

ground state to 4f35d configuration. Analysis of experimental data shows that separate amount of Nd2 + appears in Y3Al5O12 crystals doped with Nd ion (see Ref. [18]). For RE ions, the best results were obtained for RE2 + :[L]k clusters. For RE3 + in the oxygen or chloride cluster, a decrease of the radial integral values by 5–10% (less than the experimental shift magnitude) was observed. As expected, fluorine cluster, leads to a small change in radial integrals. In Refs. [2,18], data for REn + :[L]k clusters that are presented depend on the method of calculation of the free ion wave functions. For clusters with 5f ions with oxidation states, AC2 + –AC4 + , results are similar to the ones obtained for 3d ion clusters. Magnitude of Fk(5f,5f) and Z(5f) for actinides in the cluster decrease by 15–25% in comparison with free ion and there is quite correct result [25].

4. Theoretical data for energy of K and L X-ray lines The procedure of the theoretical study of the X-ray spectra for nl ions is similar to the one already presented: the energy of the transition of a core electron from an initial state, n0 l0 , to a final one, n00 l00 , is the difference between the energy of the configurations N 00 00 1 N nulu1 j nl and n l j nl , where j—total electron’s momentum. For example, X-ray line determined by the following way: 1s1/2nlN2p51/2,3/2nlN (Ka1,2 lines,); 2p53/2nlN-3d93/2,5/2nlN (La1,2 lines), etc. Therefore, the energy of X-ray line, Ex, may be defined as N N EN x ¼ Enulu Enuuluu ,

ð6Þ

N 0 0 where EN nulu is the energy of nl configuration with vacancy in n l

N shell. It should be noticed that n00 l00 1 j nl —configurations are highly excited ones and calculation of their energy is a complex problem for the free ion and for clusters. For corrected calculations we used orthogonalization procedure for wave functions of N the n00 l00 1 j nl —configurations. Selected data for the ions of ME, RE and AC groups in oxidation state from 5 +2 to +4 b are given in Refs. [2,4,17]. The energy of X-ray lines for ME ions plotted in Ref. [2] and for example, in Table 3, we show the energies for selected ME, RE and AC ions. For investigation of the stability of the electronic state of any nl ion in crystals and cluster, we have used the so-called valence shift of X-ray line procedure, VSXRL. The shift of X-ray lines is due to change in ion oxidation state (change of the number of nl electrons, N). Valence shift of X-ray

N.A. Kulagin / Journal of Luminescence 131 (2011) 526–530

Table 3 Theoretical values of energy of Ka,

b

529

and La X-ray lines in selected ME, RE and AC ions (in eV).

ME

E (Ka1)

E (Kb1)

E (La1)

RE

E (Ka1)

E (Kb1)

E (La1)

Cr2 + Cr3 + Cr4 + Fe2 + Fe3 + Fe4 + RE Nd2 + Nd3 + Nd4 + Eu2 + Eu3 + Eu4 + Gd2 + Gd2 + Gd2 +

5418,21 5417,36 5416,60 6400,67 6399,90 6399,13

5949,50 5953,49 5955,99 7061,06 7063,52 7066,91

– – – – – –

52,156,939 52,155,897 52,155,007

58,580,850 58,578,564 58,576,031

7,421,563 7,426,668 7,429,100

37,337,290 37,336,610 37,335,741 40,071,174 40,070,420 40,069,405 42,921,661 42,920,521 42,920,118

42,250,942 42,248,875 42,246,471 45,371,500 45,369,567 45,367,192 48,620,131 48,618,235 48,615,998

5,370,895 5,369,708 5,368,449 5,852,357 5,848,793 5,847,622 6,062,622 6,063,971 6,060,614

Yb2 + Yb3 + Yb4 + AC U2 + U3 + U4 + Np2 + Np3 + Np4 + Bk2 + Bk3 + Bk4 +

95,912,345 95,912,037 95,911,663 98,307,960 98,307,642 98,307,262 108,277,894 108,277,543 108,277,142

108,809,007 108,808,394 108,807,659 111,517,588 111,516,963 111,516,221 122,779,219 122,778,545 122,777,775

13,639,793 13,639,528 13,639,200 13,970,953 13,970,674 13,970,346 15,339,303 15,339,005 15,338,668

line is determined as

DEx ¼ ENx ExN 7 1 , 71 (EN ) x

ð7Þ N

is the energy of X-ray lines of ions in nl and where (nlN 7 1) configuration. As shown in Refs. [2,4,18] the energy of X-ray lines strongly depends on the number of nl electrons. The value of X-ray valence shift for the MEn + to MEn + 1 transition in nd and nf ions is about 0.1–0.5 eV [26]. The highest value of VS obtained for Ka lines in 3d and 5f ions while the smallest one was observed for AC La lines. Comparing our results with the experimental data for AC ions [27], we may conclude that for Ka and Kb lines in 5f ions, the mismatch is typically of 1–3% similar to data for RE and ME ions [2,26]. For La lines in AC ions, the agreement is surprisingly good (misfit of 0.5%) but for others lines the relative deviation is worse and may reach about 6%. The change in energy of X-ray lines in nl ions with ionization of nl electrons depends on the relative shift between n0 l0 - and n00 l00 -shells [2,4]. We determined the relative concentration of the ions in different oxidation states in the crystal with a relative uncertainty of 2–10% by using a X-ray microanalyzer or a two-crystal X-ray spectrometer [2,4,18]).

5. Study of ordered nano-structures on the surface of plasma treated oxides

Fig. 1. SEM image of SrTiO3: Nd surface after plasma treatment.

2

1.0

4

0.6

1

0.4 0.2 4505

Follow to results presented in Refs. [6,7] we study clusters on the surface of strontium titanate single crystals, SrTiO3 after plasma treatment. Earlier [7,8] we observed quasi-ordered nano-structures on surface of selected oxide compounds. Selected methods of investigation of surface, in particular, scanning electron microscopy (SEM) and atomic force measurements (AFM) were used [8]. Exemplary, SEM image of the surface for SrTiO3 doped with Nd ions treated by magneto-plasma accelerator mentioned above plasma-flow with an energy density (dose) 20 J cm  2 given in Fig. 1. Nature of changed surface and unit pyramids as their properties are unknown, now. The first step for study was made by used of X-ray spectroscopy method [2,7,8]. X-ray line intensity and VS for TiKa1 and SrKa1 lines for the original and plasma-treated samples were detected by means of EDX technique with a microanalyzer Camebax. Experimental procedure discussed in Refs. [2,18]. As an example, the experimental profiles of TiKa1 X-ray line are given in Fig. 2 [8]. For the SrTiO3: Nd sample after plasma treatment at dose of about 20 J cm  2 due to relative small

3

0.8 I,a.u.

EN x

4507

4509

4511

4513

4515

E, eV Fig. 2. Profiles of TiKa1 XRL: perfect sample (1), SrTiO3: Ni (2), SrTiO3: Nd before (3) and SrTiO3: Nd after plasma treatment (4).

thickness of destroyed layer (d less than 10  6 m), study of VSXRL was made in practically parallel direction to the crystal surface. A shift in the energy X-ray line peak position indicates the change of Ti ion oxidation state (valence). The shift of TiKa1 line for doped samples to higher energy indicates decreasing oxidation state of separate part of Ti ions [5,18]. The TiKa1 line profiles studied for different samples were fitted using Lorentz functions. Calculated data for VS DEexp of TiKa1 line for as-prepared doped crystals in comparison to perfect SrTiO3 are the following: 0.35(9) eV and 0.46(9) eV for SrTiO3: Ni (Co) and SrTiO3: Nd (Sm), respectively. We determined the shift of TiKa1 line in the sample SrTiO3: Nd, after plasma treatment with energy of about 20 J cm  2 which is E(TiKa1)¼  (0.5870.09) eV. There is important that relative intensity of TiKa1 line grows together with increasing VS value. Relative concentration of Ti + n ions with changed

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N.A. Kulagin / Journal of Luminescence 131 (2011) 526–530

oxidation state can be estimated with the next simple relation [18] nþ

CðTi

Þ ¼ DEexp =DEtheor ,

ð8Þ

N71 where DEexp—is experimental VS value and DEx ¼ EN is the x Ex theoretical one. Relative concentration of Ti3 + ions, C(Ti + 3), in the doped samples changes from 19(5)% (SrTiO3: Ni) to 25(5)% (SrTiO3: Nd) assuming the ideal stoichiometric composition Sr + 2Ti + 4O3 2 of the perfect crystal. In SrTiO3: Nd sample after plasma treatment concentration of Ti3+ ions arises to 32% as compared with pure sample. The change of the intensity of TiKa1 and SrKa1 lines and variation of ratio k ¼ISr/ITi of the XRL intensities in the tested samples was observed, too. The k-value varies from 0.76 (0.73) to 0.95 and 1.00 in the tested samples in close agreement with data of the crystal density measurements [18]. The VS shift in SrKa1 line for every studied crystal was less than experimental error. Intensity of SrKa1 line for sample after plasma treatment decreases in opposite to TiKa1. Detailed investigations of TiKa1 and SrKa1 XRL intensity must be a task of additional measurements.

6. Conclusion The ab initio method used for the investigation of the electronic structure of MEn + :[L]k clusters for ions with unfilled nl shell and the numerical calculations was performed for clusters with different values of R and different types of ligands. Calculated data allow drawing several conclusions. Firstly, the available experimental data on both optical and X-ray spectra for the impurity ions of the iron, lanthan and actinium group elements can be completely described within our approach. The energy level schemes calculated for Cr3 + :[O2  ]6 cluster at R¼1.96 A˚ are close to the experimental spectra recorded in ruby. Ab initio calculated level scheme of Cr4 + ions in octahedral and tetrahedral environment corresponds to the optical spectra of ruby, perovskites and garnets after irradiation and thermal treatment. The results of the study of the valence shift of CrKa1 X-ray line make possible to assume that the additional optical absorption bands in the crystals are due to change in oxidation state of impurity. The most interesting results were obtained for copper ions where a sharp decrease in the excitation energy and an increase in the d–s interaction energy are observed for Cu2 + ion surrounded by four oxygen ions at distances corresponding to the structure of HTSC ceramics. This result has been obtained only for Cu2 + ions and is not observed for Cu3 + ions or the other MEn + :[L]k clusters

considered. This makes possible the use of X-ray lines for the investigation of changes in the valence of the ions in solids. Plasma treatment effects in appearance of systems of unit crystallites with size in order up 10  6–10  9 m depending on crystal conductivity, time and energy of plasma impulse. For certain conditions the area of created crystallites may be called as ‘‘quasi-ordered system’’. For definite conditions we discover appearance of two-level systems of crystallites when unit ones with size of about 10  9 m grown on ordered structures with size of about 10  6 m. Appearance of the nano-structures is accompanied by transition of some part of Ti4 + ions in the Ti3 + oxidation state and change of stoichiometry of destroyed surface layer.

References [1] A. Stoneham, Theory of Defects in Solid State, McGrow Hill, London, 1968. [2] N.A. Kulagin, D.T. Sviridov, Methods of Calculation of Electronic Structure of Free and Impurity Ions, Nauka, Moscow, 1986 [in Russian]. [3] K.A. Muller, Physica C 341 (2000) 11. [4] N.A. Kulagin, D.T. Sviridov, Introduction to Doped Crystals Physics, High School, Kharkov, 1990 [in Russian]. [5] N.A. Kulagin, M.F. Ozerov, Phys. Solid State 35 (1993) 2463. [6] N.A. Kulagin, ICPLC 07 Abstract Book, Alushta—Kharkov, 2007, p. IL5. [7] N.A. Kulagin, A.A. Levin, E. Langer, D.C. Mayer, I. Dojcinovic, J. Puric, Cryst. Rep. 53 (2008) 1061. [8] N.A. Kulagin, E. Hieckmann, J. Dojcilovic., Phys. Solid State 52 (2010) 2583. [9] N.A. Kulagin, D.T. Sviridov, J. Phys. (London) C17 (1984) 4539. [10] L.I. Krutova, N.A. Kulagin, V.A. Sandulenko, A.V. Sandulenko, Phys. Solid State 31 (1989) 170. [11] N.A. Kulagin, Phys. Solid State 27 (1985) 2039. [12] N.A. Kulagin, V.A. Sandulenko, Phys. Solid State 31 (1989) 243. [13] N.A. Kulagin, Phys. Solid State 44 (2002) 1484. [14] J. Slater, Consistent Field Methods for Molecules and Solid States, J. Wiley, N.Y, 1968. [15] R.D. Cowan, The Theory of Atom Structure and Spectra, University California Press, Berkely, 1981. [16] D.T. Sviridov, Yu.F. Smirnov, Theory of the Optical Spectra of the Ions of the Transition Metals, Nauka, Moscow, 1977. [17] N.A. Kulagin, J. Alloys Compds. 300–301 (2000) 348. [18] N.A. Kulagin, in: J.-C. Krupa, N.A. Kulagin (Eds.), Physics of Laser Crystals, Kluwer, AP, Brussels, 2003, p. 135. [19] B.G. Wybourne, Spectroscopic Properties of Rare Earth, J. Wiley, N.Y, 1965. [20] D.T. Sviridov, R.K. Sviridova, Yu.F. Smirnov, Optical Spectra of the Ions of the Transition Metals in Crystals, Nauka, Moscow, 1976. [21] D. Hartree, Atomic Structure Calculation, J. Wiley, London, 1957. [22] N.A. Kulagin, Phys. Solid State 27 (1987) 2039. [23] N.A. Kulagin, Sh.I. Kuliev, Phys. Solid State 31 (1991) 3382. [24] N.A. Kulagin, Physica B 222 (1995) 173. [25] N.A. Kulagin, Physica B 245 (1998) 52. [26] O.I. Sumbaev, Usp. Fiz. Nauk. 124 (1978) 281. [27] A.E. Sandstrom, in: S. Flugge (Ed.), Encyclopedia of Physics, J.Wiley, N.Y, 1957, p. 182 part XXX.