In the potassium-rich part of the binary system Na₄B ₈O₁₄-K₄B₈O₁₄ solid solutions have been found that can be described with the formula (Na _1-xK_x)₄B₈O₁₄ with 0.45 ≤ x <1.0. The crystal structures of (Na_0.25K _0.75)₄B₈O₁₄ and (Na _0.45K_0.55)₄B₈O₁₄ were refined at room temperature by the Rietveld method. The solid solutions crystallize like K₄B₈O₁₄ in the triclinic crystal system, space group P-1, with K partially substituted for Na. An ordered distribution of the alkali atoms over the four cation sites at room temperature has been discovered, The structure of (Na_0.25K_0.75) ₄B₈O₁₄ was also refined for data collected at 300 and 500 °C. The refinements show that sodium and potassium atoms are less ordered at higher temperatures.