A08 ESR

Packages

<< Graphics`Graphics`

<< NumericalMath`PolynomialFit`

<< Statistics`LinearRegression`

<< Graphics`MultipleListPlot`

Konstanten

h = 6.6260693*(10^(-34)); hbar = h/(2 π); 
    em = 1.60217653*(10^(-19)); 
    me = 9.10938188*(10^(-31)); μb = em hbar/(2 me);

DPPH

g-Faktor

fDPPH = 9.3301*10^9; 
    BDPPH = 3324 10^-4; δfDPPH = 10/93301; δBDPPH = 
      9/3324;

δgDPPH = Sqrt[δfDPPH^2 + δBDPPH^2];

gDPPH = h fDPPH/(μb BDPPH)

ΔgDPPH = gDPPH δgDPPH

Halbwertsbreite

δB = 0.03/2.40;

ΔB = Sqrt[2 Log[2]] 2.40

ΔΔB = δB ΔB

Vanadyl-acetylacetonat

g-Faktor

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 
      23/3358;

δgVan = Sqrt[δfVan^2 + δBVan^2];

gVan = h fVan/(μb BVan)

ΔgVan = gVan δgVan

a-Hyperfeinwechselwirkungskonstante mI=7/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3004 10^-4; mI = 7/2; δBI = 22/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=5/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3100 10^-4; mI = 5/2; δBI = 19/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=3/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3201 10^-4; mI = 3/2; δBI = 17/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=1/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3304 10^-4; mI = 1/2; δBI = 16/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=-1/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3411 10^-4; 
    mI = -1/2; δBI = 16/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=-3/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3539 10^-4; 
    mI = -3/2; δBI = 16/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=-5/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3638 10^-4; 
    mI = -5/2; δBI = 16/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante mI=-7/2

fVan = 9.3301*10^9; 
    BVan = 3358 10^-4; δfVan = 10/93301; δBVan = 23/3358; 
    BI = 3759 10^-4; 
    mI = -7/2; δBI = 16/BI 10^-4;

δaVan = 
        Sqrt[δfVan^2 + 
            Sqrt[δBVan^2 + δBI^2]];

aVan = fVan/mI (1 - BI/BVan)

ΔaVan = aVan δaVan

a-Hyperfeinwechselwirkungskonstante gesamt

Mx = (281/29^2 + 287/28^2 + 291/28^2 + 300/28^2 + 295/27^2 + 
              335/31^2 + 311/29^2 + 318/29^2)/(1/29^2 + 1/28^2 + 1/28^2 + 
              1/28^2 + 1/27^2 + 1/31^2 + 1/29^2 + 1/29^2) // N

ΔMx = 
      1/Sqrt[(1/29^2 + 1/28^2 + 1/28^2 + 1/28^2 + 1/27^2 + 1/31^2 + 
                1/29^2 + 1/29^2)] // N

Nitroxidradikal

g-Faktor

fNit = 9.3301*10^9; 
    BNit = 3323 10^-4; δfNit = 10/93301; δBNit = 
      10/BNit 10^-4;

δgNit = Sqrt[δfNit^2 + δBNit^2];

gNit = h fNit/(μb BNit)

ΔgNit = gNit δgNit

a-Hyperfeinwechselwirkungskonstante mI=1

fNit = 9.3301*10^9; 
    BNit = 3323 10^-4; δfNit = 10/93301; δBNit = 
      10/BNit 10^-4; BI = 3307 10^-4; 
    mI = 1; δBI = 18/BI 10^-4;

δaNit = 
        Sqrt[δfNit^2 + 
            Sqrt[δBNit^2 + δBI^2]];

aNit = fNit/mI (1 - BI/BNit)

ΔaNit = aNit δaNit

a-Hyperfeinwechselwirkungskonstante mI=-1

fNit = 9.3301*10^9; 
    BNit = 3323 10^-4; δfNit = 10/93301; δBNit = 
      10/BNit 10^-4; BI = 3338 10^-4; 
    mI = -1; δBI = 8/BI 10^-4;

δaNit = 
        Sqrt[δfNit^2 + 
            Sqrt[δBNit^2 + δBI^2]];

aNit = fNit/mI (1 - BI/BNit)

ΔaNit = aNit δaNit

a-Hyperfeinwechselwirkungskonstante gesamt

Mx = (44.9/3.6^2 + 42.1/2.7^2)/(1/3.6^2 + 1/2.7^2) // 
        N

ΔMx = 1/Sqrt[(1/3.6^2 + 1/2.7^2)] // N

Empfindlichkeitsmessung

N1 = 10^17; δN1 = 2/10; n = 3;

Direkte Detektion

ΔB = 10 10^-4; δΔB = 
      2/ΔB 10^-4; SR = 5; δSR = 1/SR;

E1 = N1/(n ΔB SR) // N

δE1 = 
        Sqrt[δN1^2 + δΔB^2 + δSR^2] // 
          N;

ΔE1 = E1 δE1

Lock-In-Detektion

ΔB = 2.68 10^-4; δΔB = 
      0.13/ΔB 10^-4; 
    SR = 112; δSR = 47/SR;

E1 = N1/(n ΔB SR) // N

δE1 = 
        Sqrt[δN1^2 + δΔB^2 + δSR^2] // 
          N;

ΔE1 = E1 δE1

Kupfersulfat-Einkristall

g-Faktor 0

fCu = 9.3301*10^9; 
    BCu = 2977 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 20

fCu = 9.3301*10^9; 
    BCu = 3034 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 40

fCu = 9.3301*10^9; 
    BCu = 3107 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 60

fCu = 9.3301*10^9; 
    BCu = 3126 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 80

fCu = 9.3301*10^9; 
    BCu = 3121 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 100

fCu = 9.3301*10^9; 
    BCu = 3073 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 120

fCu = 9.3301*10^9; 
    BCu = 3013 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 140

fCu = 9.3301*10^9; 
    BCu = 2966 10^-4; δfCu = 10/93301; δBCu = 
      22/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 160

fCu = 9.3301*10^9; 
    BCu = 2953 10^-4; δfCu = 10/93301; δBCu = 
      22/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 180

fCu = 9.3301*10^9; 
    BCu = 2979 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 200

fCu = 9.3301*10^9; 
    BCu = 3039 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

g-Faktor 220

fCu = 9.3301*10^9; 
    BCu = 3097 10^-4; δfCu = 10/93301; δBCu = 
      21/BCu 10^-4;

δgCu = Sqrt[δfCu^2 + δBCu^2];

gCu = h fCu/(μb BCu)

ΔgCu = gCu δgCu

Graph

ga = 2.08; gb = 2.27;

gwCu=({{0, 2239, 1, 16}, {20, 2197, 1, 16}, {40, 2146, 1, 15}, {60, 2132, 1, 15}, {80, 2136, 1, 15}, {100, 2169, 1, 15}, {120, 2212, 1, 16}, {140, 2248, 1, 17}, {160, 2257, 1, 17}, {180, 2238, 1, 16}, {200, 2194, 1, 16}, {220, 2152, 1, 15}});gwCu2=({{180, 2239, 1, 16}, {20, 2197, 1, 16}, {40, 2146, 1, 15}, {60, 2132, 1, 15}, {80, 2136, 1, 15}, {100, 2169, 1, 15}, {120, 2212, 1, 16}, {140, 2248, 1, 17}, {160, 2257, 1, 17}, {180, 2238, 1, 16}, {200, 2194, 1, 16}, {220, 2152, 1, 15}});

gvCu=({{0, 2239}, {20, 2197}, {40, 2146}, {60, 2132}, {80, 2136}, {100, 2169}, {120, 2212}, {140, 2248}, {160, 2257}, {180, 2238}, {200, 2194}, {220, 2152}});

gwCuErr = 
        Replace[gwCu, {de_, df_, dg_, dh_} -> {{de, df 10^-3}, 
              ErrorBar[dg, dh 10^-3]}, 2];
gvCu = 
        Replace[gvCu, {de_, df_} -> {de, df 10^-3}, 
          2];

FindFit[gvCu, gb + (ga - gb) Sin[(x + c) π/180]^2, {c}, 
      x]

d = 21.467973272493605`;

DisplayTogether[
      Plot[gb - 0.015 + 
          0.75 (ga - gb) Sin[(x + d) π/180]^2, {x, 0, 220}], 
      MultipleListPlot[gwCuErr], 
      ImageSize -> 
        550, 
AxesLabel -> {"δ", "g(\
δ)"}]

Regress[gvCu, {1, Sin[(x + d) π/180]^2}, x]

b = -0.13065651279930746`; Δb = 
      0.004665284193997629`; 
    a = 2.2569663571403513`; Δa = 
      0.0027537645294143285`;

gwCuErrSin = 
        Replace[gwCu2, {de_, df_, dg_, 
              dh_} -> {{Sin[(de + d) π/180]^2, df 10^-3}, 
              ErrorBar[dg/de Sin[de π/180]^2, dh 10^-3]}, 
          2];

\(\(DisplayTogether[MultipleListPlot[gwCuErrSin], 
        Plot[{b\ x\  + a, \ \((b + \ Δb)\)\ x + 
              a + Δa, \((b - Δb)\)\ x + 
              a - Δa}, {x, 0, 1}, 
          PlotStyle -> {Dashing[{ .0}], Dashing[{0.01}], 
              Dashing[{ .01}]}], 
        ImageSize -> 
          550, 
AxesLabel -> {"sin²(δ)", "g(δ)"}];\)\)