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Ab initio simulation of magnetic and optical properties of impurities and structural instabilities of solids (I) M. Moreno Dpto. Ciencias de la Tierra y Física de la Materia Condensada UNIVERSIDAD DE CANTABRIA SANTANDER (SPAIN) TCCM School on Theoretical Solid State Chemistry. ZCAM May 2013 Importance of calculations in the study of solids (pure and doped) Goals of calculations • Reproduce experimental data but especially Total energy (eV) • Understand the microscopic origin of properties -159.8 (x2-y2)1 (3z2-r2)1 -159.9 EJT -160 -160.1 B -21.6 pm 0 30.3 pm Qq It is nice to know that computer understands the problem but I would like to understand it too (E.Wigner) EXPERIMENTAL DATA CALCULATIONS THEORETICAL BACKGROUND H=E Understanding: Is there enough experimental information? Some relevant data are often not accessible • Electronic density for different orbitals • Small changes in electronic density pressure or distortions • Equilibrium geometry excited states • Equilibrium geometry ground state of impurities in solids •Interpretation of available experimental data requires calculations •It avoids speculations! Outline I 1. Introduction. Motivation: Role of impurities in crystalline solids 2. Impurities in insulators. Localization 3. What are the calculations useful for? Microscopic origin of phenomena Relation with phenomena of pure solids 4. Substitutional Transition Metal Impurities in insulators Description of states Study of Model Systems Geometry and optical properties *keeping(I) and changing(II) the host lattice structure 5. The colour of gemstones containing Cr3+ 1. Introduction Impurities in crystalline materials In crystalline compounds there are always point defects • Foreign atoms Impurities • Intrinsic defects like vacancies 1. Introduction PURE DOPED • Crystals are often grown at high temperatures • Equilibrium Minimize G=U-TS+PV • Doped phase Entropy increase Free energy reduction • Upon cooling impurities are trapped in a crystal Properties may depend on the sample! 1. Introduction RESISTIVITY OF TWO DIFFERENT SAMPLES OF POTASSIUM V I (arbitrary units) 5 I 4 3 II 2 1 0 10 20 T (K) Mc Donald et al, Proc Roy.Soc A 202, 103(1950) • Clear differences at low temperatures • Due to the presence of impurities and other defects • For increasing the current impurities are unwanted 1. Introduction Are impurities always undesirable? p-n junction needs doped silicon ! Si B P Conduction band _ + _ + _ + Valence band 1. Introduction Impurities in insulators New properties Applications Devices Lasers Al2O3: Ti3+, Ruby Scintillators NaI: Tl+, LiBaF3:Ce3+ Storage phosphors BaFCl: Eu2+ Radiation Dosimeters Al2O3: C4+ Gemstones Emerald (Be3Al2Si6O18: Cr3+) 1. Introduction Ionic conductivity of NaCl doped with small quantities of CdCl2 (arbitrary units) 24 20 16 12 8 4 0 15 30 45 60 105 Mole Fraction Ionic conductivity increases by the presence of small amounts of Cd2+ impurities! 2. Impurities in insulators. Localization What are we going to deal with • Systems Transition metal impurities in insulators ( Gap> 4eV) •Main Goal: Understand the microscopic origin of new properties •Tools Theoretical calculations and analysis of data. 2. Impurities in insulators. Localization Microscopic insight for doped lattices More difficult than for pure compounds Translational symmetry broken However many insulators are made of ions Active electrons from the impurity are localised Transition Metal Complex MX6 z 5 4 x 3 2 1 6 Solid State Physics problem Study of a trapped molecule y 2. Impurities in insulators. Localization KZnF3: Mn2+ J.Chem.Phys 47, 692(1986) MnF64- complex MnF2 Stout J.Chem.Phys 31, 709(1959) • Broad bands • Bandwidths up to 0.5eV! 2. Impurities in insulators. Localization Electron Paramagnetic Resonance • Spectroscopy in the electronic ground state if S0 • Transitions among Zeeman sublevels when H0 • Microwave absorption • Direct observation of hyperfine interactions with close nuclei M=+1/2 S=1/2 M=-1/2 H=0 H0 2. Impurities in insulators. Localization Evidence of Localization square-planar complex NiF43- CaF2:Ni+ EPR spectrum Studzinski et al. J.Phys C 17,5411 (1984) Ni+: 3d9 ion Bo || <100> T = 20 K 5 superhyperfine lines F Ni+ I(F) =1/2 Total spin I=4(1/2)=2 2I+1=5 lines No interaction with further fluorine ions detected! 2. Impurities in insulators. Localization The concept of complex (A. Werner 1893) z A Solid State Physics problem 5 3 4 What are the properties of a molecule? 2 1 x y 6 The colour of a transition group complex is dependent to any large extent only on the ligands directly attached to the central ion while solvents or the formation of solid salts with different anions have only a very minute influence C.K Jørgensen Absorption Spectra and Chemical Bonding in Complexes (1962) 2. Impurities in insulators. Localization Pictorial description R • Active electrons are confined in the complex • Close ions to ligands lying outside the complex Chemical pressureR • Few atoms clusters (100) reproduce the properties due to the impurity. 3. What are the calculations useful for? Substitutional Impurities • Isotropic relaxation Geometry is kept • Example KMgF :Mn 3 2+ • What is the metal-ligand distance, R? • What is the origin of the colour? • Can we understand the effects due to pressure? J.Phys.: Condens. Matter 18 R315-R360(2006) 3. What are the calculations useful for? Ruby under pressure S. Duclos et al. PRB 41, 5372(1990) •The two broad absorption bands are very sensitive to pressure •The sharp emission line is little affected by pressure Why? 3. What are the calculations useful for? Electronic structure Equilibrium geometry Structural Instabilities. Static Jahn-Teller effect z 5 3 4 2 1 x y 6 • d9 ions ( Cu2+, Ag2+) in cubic sites • Local symmetry becomes tetragonal • What is the magnitude of the distortion? • Is the octahedron elongated or compressed? Why? J.Phys.: Condens. Matter 18 R315-R360(2006) 3. What are the calculations useful for? Structural Instabilities. Off-centre motion SrCl2 :Mn2+(d 5) on-centre SrCl2:Fe+ (d7) off-centre • What is the origin of the distortion? • What is the distance corresponding to the off centre displacement? • Why it does not happen for a Mn2+ impurity? 3. What are the calculations useful for? Structural Instabilities BaF2:Mn2+ a2u mode • Cube surrounding Mn2+ is distortedTd symmetry! • But no distortion when BaF2 is changed by CaF2 or SrF2 • What is the origin if there is not a Jahn-Teller effect? • Why at T>50K the system appears as cubic? Phase transition? 3. What are the calculations useful for? More examples Req Cu2+ Rax H N z CuCl4(NH3)22- in NH4Cl Tetragonal Cl- CuCl4(H2O)22- in NH4Cl Req Cu2+ O Rax H z •The four equatorial Cl- are not equivalent ! • Orthorhombic symmetry when axial NH3 H2O? What is found in pure compounds containing CuCl4X22- units (X = NH3, H2O)? • In CuCl2(NH3)2 the CuCl4(NH3)22- units have tetragonal symmetry • In Rb2CuCl4(H2O)2 the CuCl4(H2O)22- units have orthorhombic symmetry 3. What are the calculations useful for? Impurities in insulators pure ionic materials • Optical spectrum of KZnF3: Mn2+ and MnF2 are very similar • The same situation holds comparing Al2O3: Cr3+ ( ruby) with Cr2O3 • Ferroelectricity in BaTiO3 involves an off centre motion! • Perovskites like KMF3 (M:Mg,Zn,Ni) are cubic but KMnF3 is tetragonal 3. What are the calculations useful for? Structural Instabilities in pure solids KMgF3 Cubic Perovskite KMnF3 Tetragonal Perovskite P.Garcia –Fernandez et al. J.Phys.Chem letters 1, 647 (2010) 4. Substitutional Transition Metal Impurities Description Free TM ions Cr3+( 3d3) ; Mn2+( 3d5) ; Ni2+( 3d8) ; Cu2+( 3d9) Fivefold degeneracy partially removed even in cubic symmetry Octahedral Complex z eg (x2-y2; 3z2-r2) 5 10Dq d t2g (xy;xz,yz) 3 4 x 2 1 6 y 4. Substitutional Transition Metal Impurities • Direct evidence of the cubic field splitting, 10Dq • Absorption in the red region of Cu(H2O)62+ complexes blue colour 10Dq Cu2+( 3d9) eg (x2-y2; 3z2-r2) 10Dq d t2g (xy;xz,yz) Units: 103 cm-1 Holmes et al. JCP 26,1686(1957) What is the origin of the strong absorption for > 30.000cm-1? 4. Substitutional Transition Metal Impurities Ground and excited states of octahedral Cr3+( 3d3) impurities 3z2-r2 x2-y2 10Dq 10Dq 10Dq 10Dq xy 4A 3 2 (t2g ) 2E (t 3) 2g 2E 4A 4T (t 2 2 2g eg1) xy 4T (t 2 1 2g eg1) 2 Duclos et al. PRB 41, 5372(1990) •2E 4A2 depends on <xz(1),yz(2) e2/r12 xz(2),yz(1)> •4A2 4T2 is equal to 10Dq •4A2 4T1 depends on 10Dq and on interelectronic repulsion 4. Substitutional Transition Metal Impurities The Rough Crystal Field Model Main Assumptions Ligands are taken only as point charges Properties depend on the d-electrons of the impurity d-electrons feel the electrostatic potential, VCF, coming from ligands In octahedral complexes VCF exhibits cubic symmetry 6e2 Z L 35Z L e2 4 3 4 4 4 VCF (r) x y z r .. 5 R 4R 5 10Dq =5 ZLe2<r4>/3R5 4. Substitutional Transition Metal Impurities Appraisal of 10Dq =5 ZLe2<r4>/3R5 from Crystal Field (CF) model • <r4>3d = 4.26 au for Cr3+ • R = 2.39 Å for CrCl63• 10Dq (CF) = 830 cm-1 • 10Dq (Exper.) = 12800 cm-1 • CF gives 10Dq one order of magnitude smaller than the experimental value • 10Dq mainly reflects the chemical bonding inside a complex z 5 4 x 3 1 6 2 y 4. Substitutional Transition Metal Impurities Electronic levels for an isolated octahedral fluorine complex eg()3z2-r2; x2-y2 10Dq t2g()xy; xz; yz 3d (Cr3+) t1g() t1u(;) z t2u() t2g() 5 4 x 3 1 6 2 y 2p (F) t1u(;) eg() ag() 2s (F) •Unpaired electrons in antibonding t2g() and eg() levels • Allowed t1u(; ) eg() jumps: ChargeTransfer transitions 4. Substitutional Transition Metal Impurities The Cu(H2O)62+ complex 10Dq Units: 103 cm-1 What is the origin of the strong absorption for > 30.000cm-1 ? • Due to allowed charge transfer transitions •They cannot be understood within the crystal field model •They reflect the chemical bonding in the complex 4. Substitutional Transition Metal Impurities Model systems (I) Impurities in cubic lattices with the same structure • What is the metal–ligand distance for the ground state? •How varies 10Dq and the optical spectra? Example: Mn2+ in cubic fluoroperovskites 4. Substitutional Transition Metal Impurities Model systems (I) Determination of the Mn2+-F- distance, R Whole series study through DFT calculations R follows RH but R < RH Host lattice KMgF3 KZnF3 RbCdF3 CsCaF3 RH(pm) 199 203 220 226 R (pm) 206 208 213 215 Ba2+ Li+ F- K+ Mn2+-F- distance wants to be close to r(Mn2+) + r(F-) = 212 pm Mg2+ 4. Substitutional Transition Metal Impurities Model systems (I) Determination of the Mn2+-F- distance, R Variation of the Mn2+-F- distance in the series RH Distance in the pure lattice R /RH = 0.30 J.Phys.: Condens.Matter 11, L525 (1999) 4. Substitutional Transition Metal Impurities Model systems (I) Analysis of optical spectra Sharp line independent on 10Dq. 10Dq KMgF3 It is at the same place along the series 10Dq variations along the series only due to R changes! RH=1.99Å 10Dq = KR-n n = 4.7 CsCaF3 RH=2.26Å J.Chem.Phys 47, 692 (1986) 4. Substitutional Transition Metal Impurities Model systems (I) Results from Theoretical calculations R dependence of 10Dq V. Luaña et al, J Chem.Phys 90, 6409(1989) 10Dq KR-n MnF64-in KZnF3 n=5.5 Reliable theoretical calculations reproduce the experimental behaviour Calculated values of the exponent n J.Phys.:Condens.Matter 4, 9481(1992) 4. Substitutional Transition Metal Impurities Model systems (I) Experimental Evidence of 10Dq = KR-5 NiO under pressure H.G.Drickamer, J.Chem.Phys 47,1880(1967) The exponent cannot be understood through Crystal field Theory which gives 10Dq =5 ZLe2<r4>/3R5 4. Substitutional Transition Metal Impurities Model systems (II) Impurities in different host lattices Impurities (Mn2+,Ni2+,Co2+) in the LiBaF3 inverted perovskite LiBaF3 Mg2+ Li+ Ba2+ KMgF3 K+ F- Fa In LiBaF3 Mn2+ enters Li+ site with remote charge compensation Observed by Magnetic Resonance measurements An octahedral MnF64- complex is also formed Yosida et al, J.Phys.Soc.Japan 49, 127 (1980) B. Henke et al, Phys. Stat. Solidi C 2, 380 (2005) 4. Substitutional Transition Metal Impurities Model systems (II) Excitation Spectra of KMgF3: Mn2+ and LiBaF3: Mn2+ 2000 cm-1 1000 cm-1 10Dq KMgF3: Mn2+ LiBaF3: Mn2+ 400 500 600 Remarkable differences! 10Dq is 1000 cm-1 higher for LiBaF3: Mn2+ Does it reflect a different Mn2+-F- distance? (nm) 4. Substitutional Transition Metal Impurities Model systems (II) Increase of the experimental 10Dq value from KMgF3:M2+ to LiBaF3:M2+ M 10Dq (cm-1) LiBaF3:M2+ 10Dq(cm-1) KMgF3:M2+ Mn 9800 8400 Ni 8400 7800 Co 9360 8000 • Is it due to a different R value? • Difficult to accept ! RH(Å) LiBaF3 KMgF3 1.998 1.993 4. Substitutional Transition Metal Impurities Model systems (II) What at are the impurity-ligand distances for LiBaF3:M2+ from calculations? M R(Å) LiBaF3:M2+ R(Å) KMgF3:M2+ Mn 2.06 2.06 Ni 2.04 2.02 Co 2.03 2.04 R is essentially the same in both lattices What is the origin of the different 10Dq? Phys.Rev B 75, 155101 (2007); 78, 075108 (2008) Chem.Phys 362, 82 (2009) 4. Substitutional Transition Metal Impurities Model systems (II) 10Dq values 10Dq is bigger for MnF64- in LiBaF3 than in KMgF3 However R is essentially the same for both systems LiBaF3 :Mn2+ does not fit into the pattern of normal perovskites 4. Substitutional Transition Metal Impurities Model systems (II) Effect of the rest of the lattice • • • Ions are charged Long range Coulomb potential due to ions outside the complex Do the electrons in the complex feel this internal electric field? 4. Substitutional Transition Metal Impurities Model systems (II) Calculated rest of the lattice potential, VR, upon electronic levels of MnF64-complex in a cubic perovskite Energy of one electron → (-e) VR VR is very flat J.Phys.: Condens.Matter 18 R315-R360(2006) 4. Substitutional Transition Metal Impurities Is it so for every crystalline lattice? 4. Substitutional Transition Metal Impurities Model systems (II) Internal electric field on ligands in LiBaF3 •Main effects along metal-ligand directions: Raises the eg() level <100> eg* BaLiF3 KMgF3 Mn2+ eg* (10Dq)v+ R (10Dq)v F t2g* No electric field on the central ion Oh symmetry But active electrons spread over the complex. VR not flat! Additional extrinsic contribution to 10Dq from VR t2g* 4. Substitutional Transition Metal Impurities Model systems (II) What do cluster calculations say? R 10Dq = [10Dq(R)]v + R Phys.Rev 78, 075108(2008) There is a shift [10Dq(R)]v R4.6 In vacuo R Shift Extrinsic contribution Microscopic origin? 4. Substitutional Transition Metal Impurities Model systems (II) Differences in 10Dq in normal and inverted perovskites +2 KMgF3 +1 +1 LiBaF3 •First shell +1 •First shell +2 •Second shell +2 •Second shell +1 Positive charges Cube (10Dq)>0 Octahedron (10Dq)<0 +2 Phys.Rev 75, 155101 (2007) KMgF3: First shell contribution ( +1 ions) cancelled from that from second shell (+2 ions) LiBaF3: Positive first shell contribution ( +1 ions) dominates 5. The colour of gemstones containing Cr3+ Huge amount of work carried out on Cr3+ based gemstones Ruby Al2O3:Cr3+ Emerald Be3Si6Al2O18:Cr3+ d2 d1 d2 d3 Al Os Si Ol Ol Als C3 symmetry Al All d3 Os d4 Os Ol Be Al d1 O D3 symmetry •Both host lattices are ionic •In both cases Cr3+ replaces Al3+ and a CrO69- complex is formed 5. The colour of gemstones containing Cr3+ Experimental data Ruby Emerald Relative Shift 10Dq (eV) 2.24 2.00 -11% 2E 4A (eV) 2 1.79 1.82 1.7% R. G. Burns, Mineralogical applications of crystal field theory (Cambridge Univ. Press, Cambridge, 1993)) (T1; T2) 10Dq 2E 4A Ruby 2 S. Duclos et al. PRB 41, 5372(1990) • Why 10Dq and the colour are so different? 5. The colour of gemstones containing Cr3+ For explaining the colour shift if has often been assumed Active electrons are localized in the CrO69- complex But the average Cr3+-O2- distance is 6 pm smaller in ruby than in emerald L. Orgel , Nature 179, 1348 (1957) d2 d1 d2 d3 Al Os All Al d3 Ol Ol Als Os Si Os Ol d4 Be Al O d1 5. The colour of gemstones containing Cr3+ Experimental data for pure host lattices System Symmetry RH (pm) Be3Si6Al2O18 D3 190.6 Al2O3 C3 191.3 E. Gaudry, Ph. D. Thesis, Université Paris 6 (2004) • RH = average Al3+ -O2- distance ( in pm) for the host lattice • Both are nearly identical • Can it be true that R(emerald)-R(ruby) = 6 pm ?? 5. The colour of gemstones containing Cr3+ RH (Host) (Å) MgO:Cr3+ Emerald Ruby 2.11 1.906 1.913 Cr3+ Mg2+ 10Dq (eV) 2E 4A 2 (eV) 2.00 1.78 2.00 1.82 2.24 1.79 O2- • Is it true that 10 Dq only depends on the Cr3+ - O2- distance, R ? • Is R different in ruby and emerald but the Al3+ - O2- distance is the same? • Is R the same in MgO:Cr3+ and emerald although RH is very different? 5. The colour of gemstones containing Cr3+ Experimental and calculated Cr3+-O2- distances in ruby Rs(Å) Rl (Å) R=(Rs+Rl)/2 EXAFS data (a) 1.92 2.01 1.97 Calculated ( b) 1.94 2.00 1.97 Calculated ( c) 1.92 1.99 1.96 a: Gaudry et al Phys. Rev. B 67, 094108 (2003) ; b: Aramburu et al, Phys.Rev B 85, 245118 (2012) c :S. Watanabe et al. Phys. Rev. B 79, 075109 (2009) d1 d2 d3 Al Os All Ol Ol Als Os Os Ol Al 5. The colour of gemstones containing Cr3+ Experimental and calculated Cr-X distances (in Å) for emerald EXAFS data (a) Calculated (b) Calculated (a) 1.970.005 1.968 1.99 Cr-Be 2.695 2.70 Cr-Si 3.306 3.31 Cr-O a: Gaudry et al Phys. Rev. B 76, 094110 (2007) ; b: Aramburu et al, Phys.Rev B 85, 245118 (2012) d2 Al d3 Si d4 Be O d1 5. The colour of gemstones containing Cr3+ Additional Contribution to 10Dq from the internal field ER(r) Isolated complex Addition of the internal field eg* eg* (10Dq)v t2g* (10Dq)v+ R t2g* R Extrinsic contribution to 10Dq due to the internal field felt by the complex 5. The colour of gemstones containing Cr3+ eg 51.36 2.00 eV t2g 49.36 -52.22 -52.48 -56.41 -56.36 -0.86 -5.36 1.95 eV -7.31 2.26 eV -3.12 Isolated CrO69- + ER ruby + ER emerald • In ruby ER(r) produces a shift of -52.2 eV on both eg and t2g levels • However the decrease is a little higher (0.26 eV) for t2g than for eg •This explains the red color of ruby •By contrast ER(r) has no effect on emerald green Aramburu et al, Phys.Rev B 85, 245118 (2012) 5. The colour of gemstones containing Cr3+ Electrostatic potential VR(r)ER(r) MgO:Cr3+ -54 -54 -55 Cr3+ -eVR(r) (eV) Mg2+ [111] -56 -56 -57 [100] -58 -58 -59 -60 -60 [110] -61 -62 -62 O2- -63 -64 -64 0 0 Cr3+-O2- distance =2.03 Å eg 0.5 0.5 1 1.0 r (Å) 1.5 1.5 49.82 1.80 eV • t2g decreases a bit more than eg 10Dq ! t2g 48.02 -54.36 -54.57 • Mg2+ along <110> are the closest ions to the complex -4.54 2.01 eV -6.55 {VR(r) - VR(0)} First order perturbation Isolated CrO69- + (-e)VR(r) 2 2.0 3. The Isolated Complex is a True Molecule Microscopic insight eg* R dependence of 10 Dq (eg) t2g* (t2g) d Admixture of 3z2-r2; x2-y2 levels with 2p and 2s raises Admixture of xy; xz; yz 10Dq 10 Dq d p p2 p2 N 2 d s N 2 s2 p contribution J.Phys.: Condens.Matter 18 R315-R360(2006) s contribution s eg by (eg) levels with 2p raises t2g by (t2g) =(eg )- (t2g ) p p 3. The Isolated Complex is a True Molecule Description of antibonding levels. Covalency Admixture with 2p and 2s orbitals if ligands are F,O 2s 3d 2p eg N 3z 2 r 2 p p s s Octahedral complexes. Sometimes covalency measured by Fribourg-Freiburg June 2009 fs N s 3 2 ; f N p 3 2 Species (nLp)- (nLs) Species (nLp)- (nLs) Li 1.85 F 22.9 Be 2.75 F- 24.3 C 4.5 Cl 15.4 N 10.3 Cl- 15.9 O 16.7 Br 14.6 S 12.0 Br- 14.9 Units: eV 3. The Isolated Complex is a True Molecule Results from Theoretical calculations R dependence of (Np)2 f 2p covalency FeF63- a a • f nearly independent on R • All methods are coincident Phys. Rev B 61, 6525 (2000) Fribourg-Freiburg June 2009 3. The Isolated Complex is a True Molecule Results from Theoretical calculations R dependence of (Ns)2 fs 2s covalency FeF63Main Conclusions • f>> fs • But fs = AR-n(s) • n(s) 7 •Strong R dependence ! Phys. Rev B 61, 6525 (2000) Fribourg-Freiburg June 2009 4. Covalency and 10Dq: dependence on the metal-ligand distance Analysis of covalent contributions to 10Dq from ab initio calculations 10 Dq 10 Dq p 10 Dq s 10Dq p d p 3 f 4 f 10Dq s 3 d s f s Complex (10Dq)s (103 cm-1) (10Dq)p (103 cm-1) CrF63- 12.4 3.8 CrBr63- 8.9 3.8 CrI63- 6.2 2.3 • 10Dq is determined mainly by the residual 3d – nLs hybridization • The reduction of Racah parameters is controlled by the global covalency Ne2; Nt2 J.Phys.Chem A 115, 1423 (2011) (a) (b) Equidensity contours of the difference density function, , for a CrF63+ complex when the metal-ligand distance is: a) 1.75 Å, and b) 2.15 Å 3. Results. Color Shift and Polarization -e VR(r) (eV) -40 -45 Diagonal Als-Cr-All -50 d1 d2 -55 d3 Al Os All Ol Ol Als Os Os Ol -60 C3 Axis -65 -70 -75 -80 Al -85 -90 -2 Cr Als 1.5 - -1 -0.5 0 All 0.5 1 1.5 2 Å •VR(r) is asymmetric when r >1Å •It tends to decrease the energy of t2g levels increase of 10Dq 3. Results. Internal Fields in Emerald d2 -45 -45 d3 -eVR(r) (eV) -50 d4 -55 -55 Al d1 -60 Si -65 -65 d4 d2 -70 -75 -75 -2 -2 Be -1.5 -1 -1 -0.5 00 0.5 11 1.5 d3 O 22 r (Å) • Smaller variations of VR(r) in emerald •For some directions VR(r) - VR(0) >0 while for others it is negative •Is there some compensation? •What happens if only the nearest Be2+ are taken into account? d1 3. Results. Internal Fields in Emerald System Isolated CrO69- unit CrO69- + 3 Be2+ CrO69- + 3 Be2+ + 6 Si4+ CrO69- + all lattice charges 10Dq(eV) 2.00 2.20 1.93 1.95 d2 Al d3 •VR(r) - VR(0) is determined by the first shells Si • Second shell cancels the effects of the first one d4 Be O d1 • Somewhat similar to perovskite 5. Model Systems (II): Mn2+ in LiBaF3 Host lattices data RH=a/2 KMgF3 LiBaF3 1.987Å 1.998Å Cluster Calculations on Doped lattices KMgF3: Mn2+ LiBaF3 : Mn2+ R ( 21átoms) 2.06 Å 2.06 Å R ( 57átoms) 2.05 Å 2.04 Å Phys.Rev 78, 075108(2008) 1. Introduction Impurities in crystalline materials •In crystalline compounds there are always foreign atoms Impurities