The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to address specific aspects of the performance of X-ray powder diffraction instruments. This report describes SRM 1878b, the third generation of this powder diffraction SRM. SRM 1878b is intended for use in the preparation of calibration standards for the quantitative analyses of α-quartz by X-ray powder diffraction in accordance to National Institute for Occupational Safety and Health Analytical Method 7500, or equivalent. A unit of SRM 1878b consists of approximately 5 g of α-quartz powder bottled in an argon atmosphere. It is certified with respect to crystalline phase purity, or amorphous phase content, and lattice parameter. Neutron powder diffraction, both time of flight and constant wavelength, was used to certify the phase purity using SRM 676a as an internal standard. A NIST-built diffractometer, incorporating many advanced design features was used for certification measurements for lattice parameters.