app / stack designer

engine 0.1, data 2026.09.05-1

Stack designer

Case C-0412. Layer order, CTE staircase and per-interface stress against the 0.3 / 0.8 / 2.0 GPa thresholds. Headline numbers come from the engine; the layer table and per-interface bars are a mock layout pending the discrete stack engine.

CTE staircase

mock layout, R05 steps in proportion to 1 / M

Interface stress

mock bars, GPa at dT 1 200 K

direct joint, R04

2.92 GPa

equal CTE steps mock

1.12 GPa

minimax step stress, R05

0.63 GPa

Phi, R06

0.79

fracture margin at step 1, R18

36.7

membrane gate, R24

passes

Layers, top to bottom

mock layer table, total 3.7 µm between substrate and build

	Layer	Role	t, µm	CTE	M, GPa
	Al2O3, c-plane	substrate	bulk	7.0	580
	MoO2 adhesion	anchor		6.5	400
	Step 1, Mo 85 wt%	graded		6.9	445
	Step 2, Mo 70 wt%	graded		8.4	415
	Step 3, Mo 54 wt%	graded		10.1	383
	Step 4, Mo 38 wt%	graded		11.9	350
	Step 5, Mo 20 wt%	graded		13.8	315
	Cr barrier	barrier		6.2	353
	NiCr seed	seed		13.0	290
	IN718, LPBF	build	bulk	15.5	282

CTE in 1e-6 / K. M is the biaxial modulus E / (1 - nu), rule R01. Edit thickness and re-run to update G at each interface (R16).

Activity0 / 15 steps

01R01Sapphire, c-plane: M = E / (1 - nu) = 435 GPa / (1 - 0.25) = 580 GPa.
02R01Inconel 718: M = E / (1 - nu) = 205 GPa / (1 - 0.3) = 293 GPa.
03R02Delta alpha = alpha(Inconel 718) - alpha(Sapphire, c-plane) = 15.3 x 1e-6 / K - 7 x 1e-6 / K = 8.3 x 1e-6 / K.
04R03Delta T = T_process - T_op = 1 493 K - 293 K = 1 200 K.
05R04Direct joint: sigma = M_film x Delta alpha x Delta T = 293 GPa x 8.3 x 1e-6 / K x 1 200 K = 2.92 GPa.
06R05quality CGraded stack, n = 5: sigma_step = M_H Delta alpha Delta T / (n + 1) = 380 GPa x 8.3 x 1e-6 / K x 1 200 K / 6 = 0.63 GPa.
07R06Phi = sigma_step / sigma_c = 0.63 GPa / 0.8 GPa = 0.79. Passes, Phi <= 1.
08R07n_min = ceil(M_H Delta alpha Delta T / sigma_c) - 1 = ceil(4.73) - 1 = 4.
09R08Nichrome 80/20 membrane stress = E/(1 - nu) x Delta alpha x Delta T = 2.23 GPa; exceeds sigma_y 1 000 MPa, capped and shed plastically.
10R09Nichrome 80/20 plastic strain = (sigma_mem - sigma_y) / E = (2.23 GPa - 1 GPa) / 214 GPa = 0.58 %.
11R22Sapphire, c-plane / Molybdenum step 1: alpha_D = (E_bar_1 - E_bar_2) / (E_bar_1 + E_bar_2) = (464 GPa - 364 GPa) / (464 GPa + 364 GPa) = 0.121.
12R17quality CSapphire, c-plane / Molybdenum step 1: alpha_D = 0.121, edge delamination psi = 50.8° (interpolated omega table, TO VERIFY).
13R16Sapphire, c-plane / Molybdenum step 1: G = Z sigma^2 h / E_bar = 0.5 x (0.63 GPa)^2 x 0.64 µm / 364 GPa = 0.35 J / m2.
14R18quality CSapphire, c-plane / Molybdenum step 1: G_c(psi) = G_Ic [1 + tan^2((1 - lambda) psi)] = 8.5 J / m2 x 1.51 = 12.9 J / m2; margin G_c / G = 36.7. No delamination.
15R24Membrane gate: h_m sigma_y = 51 500 N / m against sum sigma_i h_i = 2 019 N / m; ratio 25.5. Passes.
awaiting input

mock: simulated measurement. quality C: placeholder value, to verifyR00 to R24