SOR
434 lines
20 KiB
Python
434 lines
20 KiB
Python
import math
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"""
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Hall Effect Experiment Data Processor
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霍尔效应实验数据处理计算器 (直接输入 VH 版)
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参考了表面张力系数计算器的高精度与不确定度修约逻辑。
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═══════════════════════════════════════════════════════
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公式说明:
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═══════════════════════════════════════════════════════
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1. 霍尔电压 (Hall Voltage):
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直接测量输入 VH。
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VH > 0 → P 型 (空穴导电)
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VH < 0 → N 型 (电子导电)
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2. 霍尔效应基本公式 (Hall Effect):
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VH = KH · Is · B
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其中:
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KH = 1 / (n · e · d) — 霍尔灵敏度 [V/(A·T)]
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RH = 1 / (n · e) — 霍尔系数 [m³/C]
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Is : 工作电流 (霍尔电流) [A]
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B : 磁感应强度 [T]
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d : 霍尔元件厚度 [m]
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n : 载流子浓度 [m⁻³]
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e : 元电荷 = 1.602×10⁻¹⁹ [C]
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3. 电导率 σ 计算 (Conductivity):
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σ = Is · L / (Vσ · b · d)
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线性回归 Vσ vs Is，斜率 R_slope = Vσ/Is (即样品电阻 [Ω])，则:
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σ = L / (R_slope · b · d) [S/m]
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其中:
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L : 电压电极间距 (霍尔片长度) [m]
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b : 霍尔片宽度 [m]
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d : 霍尔片厚度 [m]
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4. 载流子浓度 n 与迁移率 μ (Carrier Concentration & Mobility):
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n = 1 / (KH · e · d) = 1 / (RH · e) [m⁻³]
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μ = σ / (n · e) = σ · RH = σ · KH · d [m²/(V·s)]
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5. 螺线管中心磁场 (Solenoid Field):
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B = μ₀ · (N / L_sol) · Im
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其中:
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μ₀ = 4π×10⁻⁷ T·m/A (真空磁导率)
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N : 螺线管总匝数
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L_sol : 螺线管有效长度 [m]
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═══════════════════════════════════════════════════════
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不确定度传递公式:
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═══════════════════════════════════════════════════════
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(a) 线性回归斜率不确定度:
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u(k) = |k| · √[(1/r² − 1) / (n − 2)]
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其中 r 为相关系数, n 为数据点数
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(b) 电导率 σ 的不确定度:
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σ = L / (R_slope · b · d)
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u_r(σ) = √[(u_R/R)² + (u_L/L)² + (u_b/b)² + (u_d/d)²]
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(c) 霍尔灵敏度 KH 的不确定度:
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KH = slope₁ / B
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u_r(KH) = √[(u_slope₁/slope₁)² + (u_B/B)²]
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(d) 载流子浓度 n 的不确定度:
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n = 1 / (KH · e · d)
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u_r(n) = √[u_r(KH)² + (u_d/d)²]
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(e) 载流子迁移率 μ 的不确定度:
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μ = σ · KH · d
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u_r(μ) = √[u_r(σ)² + u_r(KH)² + (u_d/d)²]
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(f) 修约规则:
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不确定度保留一位有效数字 (四舍六入五凑偶)
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结果末位与不确定度对齐
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"""
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# ═══════════════════════════════════════════════════════
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# 通用工具函数
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# ═══════════════════════════════════════════════════════
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from utils import (
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scientific_round,
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linear_regression,
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input_float
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)
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def print_regression(label, k, b, r, u_k, x_unit, y_unit):
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"""格式化打印线性回归结果"""
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print(f"\n [{label}] 线性回归结果:")
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print(f" y = {k:.6f} · x + ({b:.6f})")
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print(f" 斜率 k = {k:.6f} {y_unit}/{x_unit}")
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print(f" 截距 b = {b:.6f} {y_unit}")
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print(f" 相关系数 r = {r:.6f}")
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print(f" 斜率不确定度 u(k) = {u_k:.4e}")
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# ═══════════════════════════════════════════════════════
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# 主程序
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# ═══════════════════════════════════════════════════════
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def main():
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print("════════════════════════════════════════════════════════════")
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print(" 霍尔效应实验数据处理计算器 (直接输入VH版)")
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print(" Hall Effect Experiment Data Processor")
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print("════════════════════════════════════════════════════════════")
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# ──────────────────────────────────────────────────
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# 物理常量
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# ──────────────────────────────────────────────────
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e_charge = 1.602e-19 # C (元电荷)
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mu_0 = 4.0 * math.pi * 1e-7 # T·m/A (真空磁导率)
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print(f"\n 物理常量:")
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print(f" e = {e_charge} C")
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print(f" μ₀ = {mu_0:.4e} T·m/A")
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# ──────────────────────────────────────────────────
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# 霍尔元件参数
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# ──────────────────────────────────────────────────
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print("\n" + "━" * 58)
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print(" 霍尔元件几何参数")
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print("━" * 58)
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d_mm = input_float(" 厚度 d (mm)", 0.095)
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b_mm = input_float(" 宽度 b (mm)", 0.235)
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L_mm = input_float(" 长度 L (mm)", 0.27)
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# 转换为国际单位 m
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d = d_mm * 1e-3
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b = b_mm * 1e-3
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L = L_mm * 1e-3
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print(f"\n d = {d_mm} mm = {d:.4e} m")
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print(f" b = {b_mm} mm = {b:.4e} m")
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print(f" L = {L_mm} mm = {L:.4e} m")
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# ──────────────────────────────────────────────────
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# 螺线管参数 (计算磁场)
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# ──────────────────────────────────────────────────
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print("\n" + "━" * 58)
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print(" 螺线管参数 (B = k_sol · Im)")
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print("━" * 58)
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print(" 选择输入方式:")
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print(" 1 - 直接输入 B/Im 比值 k_sol (T/A)")
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print(" 2 - 输入匝数 N 和有效长度 L_sol")
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mode = input(" 请选择 (默认 1): ").strip() or "1"
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if mode == "2":
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N_turns = input_float(" 螺线管总匝数 N", 2000)
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L_sol_mm = input_float(" 螺线管有效长度 (mm)", 200)
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L_sol_m = L_sol_mm * 1e-3
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k_sol = mu_0 * N_turns / L_sol_m
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print(f" k_sol = μ₀·N/L = {mu_0:.4e} × {N_turns:.0f} / {L_sol_m:.4f}")
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else:
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k_sol = input_float(" 磁场常数 k_sol = B/Im (T/A)", 0.00209)
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print(f" ★ 螺线管常数: k_sol = {k_sol:.6e} T/A")
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# ══════════════════════════════════════════════════
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# 第一部分: VH 与 Is 的关系
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# ══════════════════════════════════════════════════
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print("\n")
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print("▓" * 58)
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print(" 第一部分: VH 与 Is 的关系")
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print(" 条件: 探头在螺线管中心, Im 恒定")
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print("▓" * 58)
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Im_fixed_mA = input_float(" 固定励磁电流 Im (mA)", 600)
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Im_fixed_A = Im_fixed_mA * 1e-3
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B_fixed = k_sol * Im_fixed_A
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print(f" 对应磁场 B = k_sol × Im = {B_fixed:.6f} T")
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n_pts_1 = 10
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Is_1 = [0.20 * (i + 1) for i in range(n_pts_1)] # mA: 0.20 ~ 2.00
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print(f"\n 测量要求: 请依次输入各 Is 下对应的霍尔电压 VH (mV)")
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print(f" 请注意正负号以判断导电类型。\n")
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VH_signed_1 = []
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VH_abs_1 = []
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for Is_val in Is_1:
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vh = input_float(f" Is = {Is_val:.2f} mA → VH (mV)")
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VH_signed_1.append(vh)
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VH_abs_1.append(abs(vh))
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# 打印数据表
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print(f"\n{'─' * 46}")
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print(f" VH - Is 数据表 (Im = {Im_fixed_mA:.0f} mA, B = {B_fixed:.4f} T)")
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print(f"{'─' * 46}")
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print(f" {'Is(mA)':>7} │ {'VH带符号(mV)':>12} {'VH绝对值(mV)':>12}")
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print(f" {'─' * 42}")
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for i in range(n_pts_1):
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print(f" {Is_1[i]:>7.2f} │ {VH_signed_1[i]:>12.3f} {VH_abs_1[i]:>12.3f}")
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print(f"{'─' * 46}")
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# 线性回归: VH(mV) vs Is(mA) —— 使用绝对值 VH
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slope_1, intercept_1, r_1, u_slope_1 = map(float, linear_regression(Is_1, VH_abs_1))
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print_regression("VH-Is", slope_1, intercept_1, r_1, u_slope_1, "mA", "mV")
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# 注: 斜率单位 mV/mA = V/A
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# 判断导电类型 (由带符号 VH 的正负判定)
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VH_sign_avg = sum(VH_signed_1) / len(VH_signed_1)
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if VH_sign_avg > 0:
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carrier_type = "P 型 (空穴导电)"
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sign_str = "VH > 0"
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else:
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carrier_type = "N 型 (电子导电)"
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sign_str = "VH < 0"
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print(f"\n ★ 导电类型判定: {sign_str} → {carrier_type}")
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input("\n 按回车继续...")
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# ══════════════════════════════════════════════════
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# 第二部分: VH 与 Im 的关系
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# ══════════════════════════════════════════════════
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print("\n")
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print("▓" * 58)
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print(" 第二部分: VH 与 Im 的关系")
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print(" 条件: 探头在螺线管中心, Is 恒定")
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print("▓" * 58)
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Is_fixed_mA = input_float(" 固定工作电流 Is (mA)", 1.50)
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Is_fixed_A = Is_fixed_mA * 1e-3
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Im_start = input_float(" Im 起始值 (mA)", 100)
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Im_step = input_float(" Im 步长 (mA)", 50)
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Im_end = input_float(" Im 终止值 (mA)", 600)
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Im_2 = []
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val = Im_start
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while val <= Im_end + 0.01:
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Im_2.append(val)
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val += Im_step
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n_pts_2 = len(Im_2)
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print(f"\n 共 {n_pts_2} 个数据点: Im = {Im_start:.0f} ~ {Im_end:.0f} mA, 步长 {Im_step:.0f} mA")
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print(f" 测量要求: 请依次输入各 Im 下对应的霍尔电压 VH (mV)\n")
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VH_signed_2 = []
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VH_abs_2 = []
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for Im_val in Im_2:
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vh = input_float(f" Im = {Im_val:.0f} mA → VH (mV)")
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VH_signed_2.append(vh)
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VH_abs_2.append(abs(vh))
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# 打印数据表
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print(f"\n{'─' * 46}")
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print(f" VH - Im 数据表 (Is = {Is_fixed_mA:.2f} mA)")
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print(f"{'─' * 46}")
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print(f" {'Im(mA)':>7} │ {'VH带符号(mV)':>12} {'VH绝对值(mV)':>12}")
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print(f" {'─' * 42}")
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for i in range(n_pts_2):
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print(f" {Im_2[i]:>7.0f} │ {VH_signed_2[i]:>12.3f} {VH_abs_2[i]:>12.3f}")
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print(f"{'─' * 46}")
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# 线性回归: VH(mV) vs Im(mA)
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slope_2, intercept_2, r_2, u_slope_2 = map(float, linear_regression(Im_2, VH_abs_2))
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print_regression("VH-Im", slope_2, intercept_2, r_2, u_slope_2, "mA", "mV")
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input("\n 按回车继续...")
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# ══════════════════════════════════════════════════
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# 第三部分: 零磁场 Vσ 测量 (电导率)
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# ══════════════════════════════════════════════════
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print("\n")
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print("▓" * 58)
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print(" 第三部分: 零磁场 Vσ 测量 (电导率计算)")
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print(" 条件: Im = 0, 开关置 Vσ 档")
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print("▓" * 58)
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# Is 范围与第一部分相同
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Is_3 = list(Is_1) # 0.20 ~ 2.00 mA
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Vsigma = []
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print(f"\n 输入各 Is 下的电压降 Vσ (mV):\n")
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for Is_val in Is_3:
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vs = input_float(f" Is = {Is_val:.2f} mA → Vσ (mV)")
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Vsigma.append(vs)
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# 打印数据表
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print(f"\n{'─' * 36}")
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print(f" Vσ - Is 数据表")
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print(f"{'─' * 36}")
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print(f" {'Is(mA)':>8} │ {'Vσ(mV)':>10}")
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print(f" {'─' * 26}")
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for i in range(len(Is_3)):
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print(f" {Is_3[i]:>8.2f} │ {Vsigma[i]:>10.4f}")
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print(f"{'─' * 36}")
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# 线性回归: Vσ(mV) vs Is(mA)
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slope_3, intercept_3, r_3, u_slope_3 = map(float, linear_regression(Is_3, Vsigma))
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print_regression("Vσ-Is", slope_3, intercept_3, r_3, u_slope_3, "mA", "mV")
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print(f" 注: 斜率 = Vσ/Is, 单位 mV/mA = V/A = Ω (样品电阻)")
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# ══════════════════════════════════════════════════
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# 第四部分: 物理量计算
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# ══════════════════════════════════════════════════
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print("\n")
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print("▓" * 58)
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print(" 第四部分: 物理量计算与不确定度分析")
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print("▓" * 58)
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# ─── 4.1 电导率 σ ───
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# σ = L / (R · b · d)
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# R = slope_3 (mV/mA = V/A = Ω)
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R_sample = slope_3 # Ω
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sigma = L / (R_sample * b * d) # S/m
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# 不确定度 (此处仅传递回归斜率的不确定度，几何参数视为已知常量)
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u_r_R = abs(u_slope_3 / slope_3) if slope_3 != 0 else 0.0
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u_r_sigma = u_r_R # 简化: 仅考虑斜率不确定度
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u_sigma = abs(sigma) * u_r_sigma
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print(f"\n ── 4.1 电导率 σ ──")
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print(f" 样品电阻 R = Vσ/Is (斜率) = {R_sample:.6f} Ω")
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print(f" σ = L / (R · b · d)")
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print(f" = {L:.4e} / ({R_sample:.6f} × {b:.4e} × {d:.4e})")
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print(f" = {sigma:.4f} S/m")
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print(f" u_r(σ) = u(k₃)/k₃ = {u_r_sigma * 100:.2f}%")
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sigma_final, u_sigma_final = scientific_round(sigma, u_sigma)
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print(f" ★ σ = {sigma_final} ± {u_sigma_final} S/m")
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# ─── 4.2 霍尔灵敏度 KH (由 VH-Is 线性回归) ───
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# VH = KH · Is · B → slope₁ = KH · B → KH = slope₁ / B
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# slope₁ 单位: mV/mA = V/A
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KH = slope_1 / B_fixed # V/(A·T)
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u_r_slope1 = abs(u_slope_1 / slope_1) if slope_1 != 0 else 0.0
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u_r_KH = u_r_slope1 # B 视为无不确定度
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u_KH = abs(KH) * u_r_KH
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print(f"\n ── 4.2 霍尔灵敏度 KH (VH-Is) ──")
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print(f" KH = slope₁ / B")
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print(f" = {slope_1:.6f} / {B_fixed:.6f}")
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print(f" = {KH:.4f} V/(A·T)")
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print(f" u_r(KH) = {u_r_KH * 100:.2f}%")
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KH_final, u_KH_final = scientific_round(abs(KH), u_KH)
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print(f" ★ |KH| = {KH_final} ± {u_KH_final} V/(A·T)")
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# ─── 交叉验证: 由 VH-Im 线性回归求 KH ───
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# VH = KH · Is · k_sol · Im → slope₂ = KH · Is · k_sol
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# KH = slope₂ / (Is_fixed_A · k_sol)
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KH_check = slope_2 / (Is_fixed_A * k_sol)
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print(f"\n ── 交叉验证: KH (VH-Im) ──")
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print(f" KH' = slope₂ / (Is · k_sol)")
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print(f" = {slope_2:.6f} / ({Is_fixed_A:.4e} × {k_sol:.6e})")
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print(f" = {KH_check:.4f} V/(A·T)")
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deviation_pct = abs(KH - KH_check) / abs(KH) * 100 if KH != 0 else 0
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print(f" 两种方法偏差: {deviation_pct:.2f}%")
|
||
|
||
# ─── 4.3 霍尔系数 RH ───
|
||
RH = abs(KH) * d # m³/C
|
||
|
||
print(f"\n ── 4.3 霍尔系数 RH ──")
|
||
print(f" RH = |KH| × d = {abs(KH):.4f} × {d:.4e}")
|
||
print(f" RH = {RH:.4e} m³/C")
|
||
|
||
# ─── 4.4 载流子浓度 n ───
|
||
# n = 1 / (RH · e)
|
||
n_carrier = 1.0 / (RH * e_charge)
|
||
|
||
# u_r(n) = u_r(KH) (d 视为精确)
|
||
u_r_n = u_r_KH
|
||
u_n = n_carrier * u_r_n
|
||
|
||
print(f"\n ── 4.4 载流子浓度 n ──")
|
||
print(f" n = 1 / (RH · e)")
|
||
print(f" = 1 / ({RH:.4e} × {e_charge})")
|
||
print(f" = {n_carrier:.4e} m⁻³")
|
||
|
||
n_final, u_n_final = scientific_round(n_carrier, u_n)
|
||
print(f" ★ n = {n_final} ± {u_n_final} m⁻³")
|
||
|
||
# ─── 4.5 载流子迁移率 μ ───
|
||
# μ = σ / (n · e) = σ · RH
|
||
mu = sigma / (n_carrier * e_charge)
|
||
mu_check = sigma * RH # 验证
|
||
|
||
u_r_mu = math.sqrt(u_r_sigma ** 2 + u_r_KH ** 2)
|
||
u_mu = abs(mu) * u_r_mu
|
||
|
||
print(f"\n ── 4.5 载流子迁移率 μ ──")
|
||
print(f" μ = σ / (n · e)")
|
||
print(f" = {sigma:.4f} / ({n_carrier:.4e} × {e_charge})")
|
||
print(f" = {mu:.4e} m²/(V·s)")
|
||
print(f" 验证: μ = σ · RH = {sigma:.4f} × {RH:.4e} = {mu_check:.4e} m²/(V·s)")
|
||
|
||
mu_final, u_mu_final = scientific_round(mu, u_mu)
|
||
print(f" ★ μ = {mu_final} ± {u_mu_final} m²/(V·s)")
|
||
|
||
# ══════════════════════════════════════════════════
|
||
# 第五部分: 结果汇总
|
||
# ══════════════════════════════════════════════════
|
||
print("\n")
|
||
print("╔══════════════════════════════════════════════════════════════╗")
|
||
print("║ 实 验 结 果 汇 总 ║")
|
||
print("╠══════════════════════════════════════════════════════════════╣")
|
||
print(f"║ ║")
|
||
print(f"║ 导电类型: {carrier_type:<47}║")
|
||
print(f"║ ║")
|
||
print(f"╟────────── 线性回归 ────────────────────────────────────────╢")
|
||
print(f"║ VH-Is: k₁ = {slope_1:>10.6f} V/A r = {r_1:>9.6f} ║")
|
||
print(f"║ VH-Im: k₂ = {slope_2:>10.6f} V/A r = {r_2:>9.6f} ║")
|
||
print(f"║ Vσ-Is: k₃ = {slope_3:>10.6f} Ω r = {r_3:>9.6f} ║")
|
||
print(f"╟────────── 物理参数 ────────────────────────────────────────╢")
|
||
print(f"║ 电导率 σ = {str(sigma_final):>12} ± {str(u_sigma_final):<10} S/m ║")
|
||
print(f"║ 霍尔灵敏度 KH = {str(KH_final):>12} ± {str(u_KH_final):<10} V/(A·T) ║")
|
||
print(f"║ 霍尔系数 RH = {RH:>12.4e} m³/C ║")
|
||
print(f"║ 载流子浓度 n = {str(n_final):>12} ± {str(u_n_final):<10} m⁻³ ║")
|
||
print(f"║ 载流子迁移率 μ = {str(mu_final):>12} ± {str(u_mu_final):<10} m²/(V·s) ║")
|
||
print(f"║ ║")
|
||
print(f"╟────────── 不确定度 ────────────────────────────────────────╢")
|
||
print(f"║ u_r(σ) = {u_r_sigma * 100:>6.2f}% ║")
|
||
print(f"║ u_r(KH) = {u_r_KH * 100:>6.2f}% ║")
|
||
print(f"║ u_r(n) = {u_r_n * 100:>6.2f}% ║")
|
||
print(f"║ u_r(μ) = {u_r_mu * 100:>6.2f}% ║")
|
||
print(f"║ ║")
|
||
print("╚══════════════════════════════════════════════════════════════╝")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main() |