a of additive as shown in fig5 the local cte z net value will increase monotonically as one moves toward the interface in the first layer material in a fifth approach illustrated graphically in fig6 the additive material is distributed as a functional gradient non uniformly in the second layer material with additive density u03c1 z a increasing sharply as one approaches the interface in the second layer and decreasing abruptly toward 0 as one moves into the first layer material and away from the interface as shown graphically in fig6 with the distribution u03c1 z a of additive as shown in fig6 the local cte net value will increase monotonically as one moves toward the interface in the second layer material in any of fig2 6 a maximum density mass or volume fraction of the additive preferably lies in a range 0 5 40 percent of total density with smaller amounts preferred the additive density u03c1 z a and an associated additive thickness near the interface are preferably chosen in fig5 and 6 so that 1 any net decrease in emittance in the first layer and or in the second layer is relatively small and 2 the cte mismatch of the additive layer thickness with the first layer material is reduced relative to the original cte mismatch cte2 u2212 cte1 at high temperatures some of the additive material in a material layer will diffuse into an adjacent layer material as in the third and fourth.