3.225 27 © H.L. Tuller-2001 Langasite : f R (T) • Temperature dependence of the resonance frequency (f R ) of a resonator device with difference mass loads. 0 100 200 300 400 500 600 700 800 1,71 1,72 1,73 1,74 1,75 1,76 1,77 Contact 1 (f Co1 ) Contact 2 (f Co2 ) Calculation f Co1 + ∆ f( ∆ m Co2 ) T [°C] f A [MHz] 3.225 28 © H.L. Tuller-2001 Ongoing Activities • Resonator (Langasite) H.Seh & H. Fritze – Defect chemistry – Oxygen diffusion/exchange studies – Bulk conductivity dependence on T and PO 2 • Active Layer (PCO) T. Stefanik – Transport-Defect chemistry correlations • Gas Sensor – Add active layer (PCO) using PLD ⇒ nanocrystalline vs microcrystalline – Sensor testing 14 1 1 3.225 1 © E. Fitzgerald-1999 Magnetic Materials • The inductor ( Law) sFaraday'(explicit 1 Theorem) s(Green' densityflux magnetic 11 (CGS) 1 tc dEV dEEdS tc BdS tc EdS t B c E B B B ∂ Φ∂ −=⋅= ⋅=×∇ ≡Φ ∂ Φ∂ −= ∂ ∂ −=×∇ ∂ ∂ −=×∇ ∫ ∫∫∫ ∫∫∫∫ l l Φ===⋅= ∂ ∂ == ∂ ∂ = ∂ ∂ = ∂ ∂ −= ∂ Φ∂ −= ∂ ∂ = ∂ Φ∂ ==Φ ∫∫ 2 2 2 1 2 1 2 1 Energy Power capacitor) for the (recall CV)(Q CVcapacitor INLILIdIdtPower t I LIVI t V CI t I LV t I L t N V t I L t LI B B EMF B B 2 3.225 2 © E. Fitzgerald-1999 The Inductor lAn cI BAN I N L nllengthnN In c B I c dSJ c dBBdS t E c J c B B 2 4)( 4 44 14 πφ π ππ π === =⋅= = =⋅=⋅=×∇ ∂ ∂ +=×∇ ∫∫∫∫ ∫ l ) 3 3.225 3 © E. Fitzgerald-1999 Insert magnetic material Magnetic dipoles in material can line-up in magnetic field MHHHB ππχ 44 +=+= B magnetic induction χ magnetic susceptibility H magnetic field strength (applied field) M magnetization HBMB H M HM µπ πχµχχ =+= +== ∂ ∂ = 14 41 MKS: B = µ 0 (H+M) = µ 0 nI + µ 0 M µ r = B/ µ 0 H = 1 + (M/H) = 1 + χ m Magnetic Permeability and Susceptibility 4 3.225 4 © E. Fitzgerald-1999 Maxwell and Magnetic Materials • Ampere’s law • For a permanent magnet, there is no real current flow; if we use B, there is a need for a fictitious current (magnetization current) • Magnetic material inserted inside inductor increases inductance 0 ==⋅ ∫ IdH l () χ π π πχπχπ lAn cI N L AIn c HAMABA B B 2 2 4 4 444~ = Φ = ===Φ L increased by ~χ due to magnetic material Material Type χ Paramagnetic +10 -5 -10 -4 Diamagnetic -10 -8 -10 -5 Ferromagnetic +10 5 2 5 3.225 5 © E. Fitzgerald-1999 Microscopic Source of Magnetization • No monopoles • magnetic dipole comes from moving or spinning electrons µ L A e- I µ is the magnetic dipole moment θµµ cosHHEEnergy −=⋅−== r r What is µ? For θ=0, 2 2 2 2 2 and ~ Lloop1forand~energysince r c e rA c e I IAHAIIH HAdSH I LIIHE B B B B ωµ π π ω µµ µ −= =−= =∴=Φ= ∴ ⋅=Φ Φ =Φ−≈−= ∫∫ Orbital Angular Momentum 6 3.225 6 © E. Fitzgerald-1999 • Classical mechanics gives orbital angular momentum as: Microscopic Source of Magnetization ll h h rr r l , 0, , 2 22 2 −== = −=−=−= =×= mL mc e LL mc e L mc e mrprL Z B ZBZQML µ µµ ω E(H=0) +µ B H -µ B H 0 Example for l=1: Spin Moment µ s spinelectronfor2 2 1 2 0 00 =±== −=−=−= gmS SgS mc e gS mc e SZ ZBz MQ s µµ h E(H=0) -(1/2)µ B g 0 H +(1/2)µ B g 0 H 3 4 7 3.225 7 © E. Fitzgerald-1999 Exchange E~-JS 1 S 2 J negative, E~+S 1 S 2 > Energy if J positive, E~-S 1 S 2 > Energy if Fe, Ni, Co > J positive! Other elements J is negative Rule of Thumb: 5.1 radius) 2(atomic distance cinteratomi 2 >≡ a r r J is a function of distance! 8 3.225 8 © E. Fitzgerald-1999 Ferromagnetism M T T C () ( ) () ( ) 1.4-1.3 0.37-0.33 ≈−∝ ≈−∝ − γχ β γ β TTT TTTM C C H B=H+4πM ‘normal’ paramagnet B r , M s H c Irreversible boundary displacement Domain rotation reversible boundary displacement Easy induction, “softer” Magentic anisotropy hardness of loop dependent on crystal direction comes from spin interacting with bonding 9 3.225 9 © E. Fitzgerald-1999 Domains in Ferromagnetic Materials B M N S Magnetic energy dVB ∫ = 2 8 1 Magnetic domain Domain wall or boundary N N N N S S S Flux closure No external field S 5 . material Material Type χ Paramagnetic +10 -5 -1 0 -4 Diamagnetic -1 0 -8 -1 0 -5 Ferromagnetic +10 5 2 5 3.225 5 © E. Fitzgerald-1999 Microscopic Source of Magnetization • No monopoles • magnetic. µ r = B/ µ 0 H = 1 + (M/H) = 1 + χ m Magnetic Permeability and Susceptibility 4 3.225 4 © E. Fitzgerald-1999 Maxwell and Magnetic Materials • Ampere’s law • For a permanent magnet, there. E. Fitzgerald-1999 Exchange E~-JS 1 S 2 J negative, E~+S 1 S 2 > Energy if J positive, E~-S 1 S 2 > Energy if Fe, Ni, Co > J positive! Other elements J is negative Rule of Thumb: 5.1 radius)