B04 Supraleitung

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<< Statistics`LinearRegression`

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a) Bestimmung der Übergangstemperatur

Zinn (Sn)

SnTC=({{4, 638, 1, 2}, {2, 630, 1, 2}, {-3, 620, 1, 2}, {-10, 616, 1, 2}, {-42, 612, 1, 2}, {-62, 608, 3, 2}, {-166, 604, 2, 2}, {-298, 602, 10, 2}, {-440, 600, 10, 2}, {-495, 598, 5, 2}, {-503, 596, 1, 2}, {-529, 594, 3, 2}, {-548, 592, 2, 2}, {-554, 590, 1, 2}, {-557, 588, 1, 2}, {-560, 586, 1, 2}, {-564, 584, 1, 2}, {-566, 582, 1, 2}, {-568, 580, 1, 2}, {-569, 578, 1, 2}});

SnTCErr = 
        Replace[SnTC, {de_, df_, dg_, dh_} -> {{df, de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[SnTCErr, PlotJoined -> True, 
        ImageSize -> 550];

Indium (In)

InTC=({{0, 440, 1, 2}, {0, 436, 1, 2}, {0.3, 432, 1, 2}, {0.4, 430, 1, 2}, {0.4, 428, 1, 2}, {0.4, 426, 1, 2}, {0.7, 424, 1, 2}, {1, 422, 1, 2}, {0.5, 420, 1, 2}, {0.7, 418, 1, 2}, {1.2, 417, 1, 2}, {2.4, 416, 1, 2}, {58, 415, 6, 2}, {267, 414, 20, 2}, {453, 413, 20, 2}, {647, 412, 10, 2}, {835, 411, 20, 2}, {892, 410, 6, 2}, {915.5, 409, 2, 2}, {924, 408, 1, 2}, {931, 406, 1, 2}, {934, 405, 1, 2}, {935, 404, 1, 2}, {938, 405, 1, 2}, {940, 400, 1, 2}});

InTCErr = 
        Replace[InTC, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[InTCErr, PlotJoined -> True, 
        ImageSize -> 550];

b) Bestimmung des kritischen Feldes

Indium (In) bei T=3K

InT3=({{854, 0.01, 2, .01}, {846, 0.52, 2, .01}, {834, 0.63, 2, .01}, {776, 0.78, 2, .01}, {726, .85, 2, .01}, {697, .87, 2, .01}, {638, .92, 2, .01}, {574, .96, 2, .01}, {529, .99, 2, .01}, {515, 1, 2, .01}, {476, 1.03, 2, .01}, {405, 1.09, 2, .01}, {404, 1.14, 2, .01}, {440, 1.15, 2, .01}, {150, 1.20, 2, .01}, {-35, 1.23, 2, .01}, {-35, 1.30, 2, .01}, {-29, 1.78, 2, .01}, {-25, 2.11, 2, .01}, {-8, 2.50, 2, .01}, {-7, 3.03, 2, .01}, {-7, 3.51, 2, .01}, {-5, 4.01, 2, .01}, {-4, 4.76, 2, .01}, {-1, 5.25, 2, .01}, {-0.2, 5.83, 2, .01}, {-0, 5.95, 2, .01}});

InT3Err = 
        Replace[InT3, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[InT3Err, PlotJoined -> True, 
        ImageSize -> 550];

Indium (In) bei T=2.5K

InT25=({{825, 0.01, 2, .01}, {825, 0.26, 2, .01}, {823, 0.99, 2, .01}, {820, 1.14, 2, .01}, {817, 1.26, 2, .01}, {815, 1.30, 2, .01}, {788, 1.61, 2, .01}, {741, 1.84, 2, .01}, {664, 2.03, 2, .01}, {585, 2.13, 2, .01}, {540, 2.19, 2, .01}, {490, 2.27, 2, .01}, {444, 2.32, 2, .01}, {388, 2.38, 2, .01}, {371, 2.43, 2, .01}, {320, 2.51, 2, .01}, {304, 2.56, 2, .01}, {369, 2.67, 2, .01}, {-17, 2.75, 2, .01}, {-29, 2.86, 2, .01}, {-28, 2.94, 2, .01}, {-26, 3.16, 2, .01}, {-24, 3.59, 2, .01}, {-13, 3.82, 2, .01}, {-7, 4.30, 2, .01}, {-5, 4.87, 2, .01}, {-2, 5.84, 2, .01}, {-2, 5.94, 2, .01}, {-3, 5.94, 2, .01}});

InT25Err = 
        Replace[InT25, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[InT25Err, PlotJoined -> True, 
        ImageSize -> 550];

Indium (In) bei T=2K

InT2=({{820, .01, 2, .01}, {820, .27, 2, .01}, {820, .66, 2, .01}, {820, 1.12, 2, .01}, {820, 1.30, 2, .01}, {818, 1.52, 2, .01}, {814, 1.80, 2, .01}, {812, 1.92, 2, .01}, {800, 2.17, 2, .01}, {786, 2.36, 2, .01}, {740, 2.71, 2, .01}, {705, 2.85, 2, .01}, {687, 2.90, 2, .01}, {595, 3.07, 2, .01}, {508, 3.22, 2, .01}, {462, 3.30, 2, .01}, {380, 3.43, 2, .01}, {353, 3.51, 2, .01}, {271, 3.62, 2, .01}, {395, 3.79, 2, .01}, {333, 3.83, 2, .01}, {-19, 4.06, 2, .01}, {-18, 4.14, 2, .01}, {-17, 4.37, 2, .01}, {-16, 4.78, 2, .01}, {-3, 5.03, 2, .01}, {-0, 5.26, 2, .01}, {1, 5.79, 2, .01}, {1, 5.94, 2, .01}, {0, 5.94, 2, .01}});

InT2Err = 
        Replace[InT2, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[InT2Err, PlotJoined -> True, 
        ImageSize -> 550];

Indium (In) bei T=1.7K

InT17=({{828, 0.01, 2, .01}, {828, 0.32, 2, .01}, {828, 1.21, 2, .01}, {826, 1.78, 2, .01}, {820, 2.17, 2, .01}, {813, 2.42, 2, .01}, {807, 2.57, 2, .01}, {803, 2.65, 2, .01}, {798, 2.72, 2, .01}, {789, 2.80, 2, .01}, {780, 2.89, 2, .01}, {728, 3.14, 2, .01}, {714, 3.21, 2, .01}, {702, 3.26, 2, .01}, {690, 3.30, 2, .01}, {664, 3.39, 2, .01}, {638, 3.46, 2, .01}, {609, 3.52, 2, .01}, {589, 3.57, 2, .01}, {548, 3.65, 2, .01}, {508, 3.73, 2, .01}, {472, 3.80, 2, .01}, {445, 3.87, 2, .01}, {420, 3.90, 2, .01}, {396, 3.95, 2, .01}, {383, 3.99, 2, .01}, {356, 4.06, 2, .01}, {343, 4.09, 2, .01}, {323, 4.16, 2, .01}, {264, 4.23, 2, .01}, {265, 4.28, 2, .01}, {362, 4.33, 2, .01}, {400, 4.40, 2, .01}, {376, 4.46, 2, .01}, {147, 4.55, 2, .01}, {10, 4.60, 2, .01}, {-17, 4.71, 2, .01}, {-16, 4.84, 2, .01}, {-13, 5.33, 2, .01}, {1, 5.94, 2, .01}, {-1, 5.94, 2, .01}});

InT17Err = 
        Replace[InT17, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[InT17Err, PlotJoined -> True, 
        ImageSize -> 550];

Zinn (Sn) bei T=3K

SnT3=({{504, .01, 2, .01}, {504, .28, 2, .01}, {502, .52, 2, .01}, {499, .72, 2, .01}, {499, .98, 2, .01}, {500, 1.10, 2, .01}, {516, 1.30, 2, .01}, {479, 1.53, 2, .01}, {454, 1.68, 2, .01}, {431, 1.77, 2, .01}, {405, 1.86, 2, .01}, {364, 1.99, 2, .01}, {295, 2.13, 2, .01}, {215, 2.26, 2, .01}, {-4, 2.36, 2, .01}, {-0, 2.50, 2, .01}, {-2, 2.86, 2, .01}, {-1, 3.23, 2, .01}, {-1, 4.18, 2, .01}, {-1, 5.14, 2, .01}, {-4, 5.94, 2, .01}});

SnT3Err = 
        Replace[SnT3, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[SnT3Err, PlotJoined -> True, 
        ImageSize -> 550];

Zinn (Sn) bei T=2.5K

SnT25=({{500, .01, 2, .01}, {500, .25, 2, .01}, {500, .45, 2, .01}, {490, 1.24, 2, .01}, {487, 1.35, 2, .01}, {483, 1.52, 2, .01}, {482, 1.55, 2, .01}, {480, 1.61, 2, .01}, {475, 1.78, 2, .01}, {468, 2.00, 2, .01}, {472, 2.27, 2, .01}, {461, 2.41, 2, .01}, {444, 2.55, 2, .01}, {451, 2.76, 2, .01}, {421, 2.99, 2, .01}, {379, 3.16, 2, .01}, {336, 3.34, 2, .01}, {316, 3.41, 2, .01}, {300, 3.49, 2, .01}, {279, 3.55, 2, .01}, {268, 3.60, 2, .01}, {272, 3.64, 2, .01}, {260, 3.68, 2, .01}, {198, 3.77, 2, .01}, {73, 3.83, 2, .01}, {3, 3.90, 2, .01}, {5, 3.98, 2, .01}, {5, 4.09, 2, .01}, {4, 4.32, 2, .01}, {4, 4.75, 2, .01}, {4, 5.26, 2, .01}, {4, 5.94, 2, .01}, {1, 5.94, 2, .01}});

SnT25Err = 
        Replace[SnT25, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[SnT25Err, PlotJoined -> True, 
        ImageSize -> 550];

Zinn (Sn) bei T=2K

SnT2=({{493, .01, 2, .01}, {492, .85, 2, .01}, {488, 1.28, 2, .01}, {486, 1.49, 2, .01}, {479, 1.83, 2, .01}, {470, 2.12, 2, .01}, {466, 2.28, 2, .01}, {462, 2.45, 2, .01}, {457, 2.59, 2, .01}, {453, 2.73, 2, .01}, {452, 2.79, 2, .01}, {452, 2.89, 2, .01}, {451, 3.11, 2, .01}, {442, 3.39, 2, .01}, {431, 3.57, 2, .01}, {426, 3.64, 2, .01}, {397, 3.85, 2, .01}, {407, 3.95, 2, .01}, {403, 4.05, 2, .01}, {352, 4.32, 2, .01}, {302, 4.61, 2, .01}, {278, 4.71, 2, .01}, {250, 4.80, 2, .01}, {245, 4.93, 2, .01}, {160, 5.12, 2, .01}, {19, 5.22, 2, .01}, {0, 5.27, 2, .01}, {2, 5.34, 2, .01}, {1, 5.50, 2, .01}, {0, 5.64, 2, .01}, {1, 5.84, 2, .01}, {1, 5.94, 2, .01}, {1, 5.94, 2, .01}});

SnT2Err = 
        Replace[SnT2, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[SnT2Err, PlotJoined -> True, 
        ImageSize -> 550];

Zinn (Sn) bei T=1.7K

SnT17=({{503, .01, 2, .01}, {497, .01, 2, .01}, {498, .53, 2, .01}, {493, 1.40, 2, .01}, {483, 2.11, 2, .01}, {474, 2.51, 2, .01}, {463, 2.92, 2, .01}, {455, 3.29, 2, .01}, {437, 3.99, 2, .01}, {401, 4.32, 2, .01}, {360, 4.78, 2, .01}, {334, 4.90, 2, .01}, {281, 5.14, 2, .01}, {274, 5.18, 2, .01}, {267, 5.26, 2, .01}, {240, 5.40, 2, .01}, {227, 5.49, 2, .01}, {200, 5.53, 2, .01}, {180, 5.58, 2, .01}, {149, 5.63, 2, .01}, {47, 5.72, 2, .01}, {4, 5.81, 2, .01}, {5, 5.84, 2, .01}, {7, 5.94, 2, .01}, {1, 5.94, 2, .01}});

SnT17Err = 
        Replace[SnT17, {de_, df_, dg_, dh_} -> {{df, -de}, 
              ErrorBar[dh, dg]}, 2];

MultipleListPlot[SnT17Err, PlotJoined -> True, 
        ImageSize -> 550];

Zinn (Sn) Bestimmung von BC0

SnBC0=({{0, 1, 0, 0}, {99, (3.01/3.722)^2, 9, 0.01}, {168, (2.49/3.722)^2, 18, 0.01}, {216, (2.01/3.722)^2, 14, 0.01}, {242, (1.72/3.722)^2, 13, 0.02}});

SnBC0Err = 
        Replace[SnBC0, {de_, df_, dg_, dh_} -> {{df, de}, 
              ErrorBar[dh, dg]}, 2];

SnBC0Reg=({{1, 0}, {(3.01/3.722)^2, 99}, {(2.49/3.722)^2, 168}, {(2.01/3.722)^2, 216}, {(1.72/3.722)^2, 242}});

Regress[SnBC0Reg, {1, x}, x]

a = 305.9347474121157`; Δa = 3.2991124054323544`; 
    b = -308.68904369368147`; Δb = 
      5.56273699032591`;

DisplayTogether[MultipleListPlot[SnBC0Err], 
        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];

Indium (In) Bestimmung von BC0

InBC0=({{0, 1, 0, 0}, {54, (3.01/3.408)^2, 6, 0.01}, {107, (2.49/3.408)^2, 5, 0.01}, {153, (2.01/3.408)^2, 5, 0.01}, {176, (1.72/3.408)^2, 5, 0.02}});

InBC0Err = 
        Replace[InBC0, {de_, df_, dg_, dh_} -> {{df, de}, 
              ErrorBar[dh, dg]}, 2];

InBC0Reg=({{1, 0}, {(3.01/3.408)^2, 54}, {(2.49/3.408)^2, 107}, {(2.01/3.408)^2, 153}, {(1.72/3.408)^2, 176}});

Regress[InBC0Reg, {1, x}, x]

a = 234.5185616521839`; Δa = 2.123779360275571`; 
    b = -234.0480977273146`; Δb = 
      3.2932862981124074`;

DisplayTogether[MultipleListPlot[InBC0Err], 
        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];

Zinn (Sn) theoretische Berechnung von BC0

MSn = 118.7; ρSn = 7.3 10^6; γSn = 1.78 10^-3; 
    TCSn = 3.722; μ0 = 1.256637 10^-6;

BC0 in Tesla:

BC0Sn = 
      TCSn Sqrt[μ0 ρSn γSn/(2 MSn)]

BC0 in Gauss

0.03086827524501584` 10^4

Fehler in Gauss:

Sqrt[(0.01/7.30)^2 + (0.001/
                3.722)^2] 308.68275245015843`

Indium (In) theoretische Berechnung von BC0

MIn = 114.8; ρIn = 7.3 10^6; γIn = 1.69 10^-3; 
    TCIn = 3.408; μ0 = 1.256637 10^-6;

BC0 in Tesla:

BC0In = 
      TCIn Sqrt[μ0 ρIn γIn/(2 MIn)]

BC0 in Gauss

0.0280042114368284` 10^4

Fehler in Gauss:

Sqrt[(0.01/7.30)^2 + (0.001/
                3.722)^2] 280.042114368284`