For a cubic material: d_((h k l))= a/√(h^2+k^2+l^2 ) (1) d-spacing is measured from Bragg’s law. nλ=2d sin⁡θ
(2) Precision in measurement of a or d depends on precision in derivation of sin θ.

Differentiation of the Bragg equation with respect to θ provides us with the same result. nλ=2d sin⁡θ
(3) Take partial derivative of the Bragg equation: 0=2 ∆d sinθ+2 d cos ∆θ
(4) ∆d/d=-(cos θ)/(sin θ) ∆θ=-cot θ ∆θ
(5) For a cubic system:
∆a=∆d .√(h^2+k^2+l^2 ) (6) ∆a/a=∆d/d=-cot θ ∆θ
(7) The term ∆a⁄a ((or ∆d)⁄(d))is the fractional error in a (or d) caused by a given error in θ. The fractional error approaches zero as θ approaches 90°.
Values of a will approach the true value as we approach 2θ = 180° (i.e., θ = 90°). We can’t measure a value at 2θ = 180°. We must plot measured values and extrapolate to 2θ = 180° versus some function of θ.
For a cubic crystal with a lattice parameter a, a Nelson-Riley extrapolation function is used: F(θ)=K((〖cos〗^2 θ)/sin⁡θ +(〖cos〗^2 θ)/θ) (8)

Errors in measurement of interplanar spacing d and lattice parameter(s) a using modern diffractometers can occur due to:
Misalignment of the instrument Absorption of X-Rays by the specimen Displacement of the specimen from the diffractometer axis must be minimized Vertical divergence of the incident beam Use of a flat specimen instead of a curved one to correspond to the diffractometer circle.