Nickel Electroforming Wall Rate & Haring-Blum Throwing Power

Negative throwing power (-10.1%) in an un-shielded sulfamate bath starves deep optical mandrel recesses while growing thick "dog-bone" nodules on outer corners!

**Nickel Sulfamate (`Ni(SO_3NH_2)_2`) Mandrel Electroforming** grows zero-internal-stress freestanding rocket thrust-chamber liners, helicopter rotor abrasion shields, and holographic stamper shims (`M_{Ni} = 58.6934` g/mol, `n = 2`, `rho_{Ni} = 8.908` g/cm³) at **Faraday Wall Growth Rate `r_{Ni} = (((J / 100) * 3,600 * 58.6934 * (eta_c / 100)) / (2 * 96,485.332 * 8.908)) * 10,000`** (`um/h` at Current Density `J` A/dm² and Cathode Efficiency `eta_c` %)! Yet average thickness **`h = r_{Ni} * t`** (`um`) means nothing if deep mandrel grooves plate thin: in a **Haring-Blum Rectangular Test Cell** (`Far-to-Near Anode Distance Ratio K = L_{far} / L_{near}`, typically `K = 3` or `5`) measuring **Plated Near-to-Far Cathode Mass Ratio `M = m_{near} / m_{far}`**, **Samuel Field’s (`1934`) Normalized Throwing Power `TP = ((K - M) / (K + M - 2)) * 100%`** spans `+100%` (perfectly uniform wall `M = 1`) through `0%` (pure primary geometric current `M = K`) down to **negative `%` (`M > K`)** whenever local hydrogen evolution drops cathode efficiency inside low-current recesses!

Verify on a Low-Stress Optical Stamper Electroforming Bath—Cathode_Current_Density `J` = 4.50 A/dm² (B2), Cathode_Efficiency `eta_c` = 98.0% (B3), Plating_Duration `t` = 6.50 h (B4), Haring-Blum_Distance_Ratio `K` = 3.00 (B5), and Measured_Near/Far_Weight_Ratio `M` = 2.15 (B6): Deposition Rate equals `54.21` um/h (E2), Electroformed Shell Wall reaches `352.3` um (`0.352` mm in E4), and Field Throwing Power equals **`+26.98%`** (E5, polarization-smoothed thickness distribution)!

Faraday Nickel Sulfamate Growth & Field-Modified Haring-Blum Throwing Power Formula

Validate `Current_Density J` in `[0.5, 30]` A/dm², `Cathode_Efficiency` in `[50, 100]`%, `Electroform_Time` in `[0.1, 500]` h, `Haring-Blum Geometry Ratio K` in `[1.5, 10]`, and `Mass_Ratio M` in `[1.0, 20]`!

=LET(jd_a, B2, ce_p, B3, tm_h, B4, kr_d, B5, mr_w, B6, IF(OR(jd_a < 0.5, jd_a > 30, ce_p < 50, ce_p > 100, tm_h < 0.1, tm_h > 500, kr_d < 1.5, kr_d > 10, mr_w < 1, mr_w > 20), "Invalid Electroform Input", ROUND(((kr_d - mr_w) / (kr_d + mr_w - 2)) * 100, 2)))

Chloride-Contaminated High-Current Bath (`M = 3.45 > K = 3.0`) Dog-Bone Corner Check

Push high current without non-conductive current-thief shields where low-CD recess efficiency sags (`M` climbs to `B6 = 3.45 > K = 3.0`): Field Throwing Power E5 flips negative to **`-10.11%`**—meaning outer mandrel edges build `3.45x` thicker than deep grooves, demanding conformal auxiliary anodes or PVC robber shields!

=IF(ISTEXT(E5), E5, ROUND((((B2 / 100) * 3600 * 58.6934 * (B3 / 100)) / (2 * 96485.332 * 8.908)) * 10000, 2))

Further reading

• Arte Sheets Lesson — Copper Electrorefining Anode Cycle, Scrap & Slime Formula
• Arte Sheets Lesson — Aluminum Sulfuric Anodizing Rule-of-720 Oxide Build Formula