We report a detailed investigation of the behavior of chemisorbed hydrogen atoms (Ha) on Pt(111) by a combination of an ex-perimental study of the Ha + Da reaction and first-principles calculations. The coverage-depen...We report a detailed investigation of the behavior of chemisorbed hydrogen atoms (Ha) on Pt(111) by a combination of an ex-perimental study of the Ha + Da reaction and first-principles calculations. The coverage-dependent adsorption and desorption behavior of Ha and Da on Pt(111) have been systematically established and can be well interpreted in terms of repulsive inter-actions between adsorbates. Ha adsorbs exclusively on the face-centered cubic (fcc) sites of Pt(111) at coverages not exceeding 1 monolayer (ML). With increasing Ha coverage,repulsive interactions between Ha increase,leading to a reduction in both the adsorption energy and the desorption activation energy. It is proposed that the lateral interactions within a Ha layer are partly induced by the local repulsive interactions due to high mobility of Ha on Pt(111). For the Ha + Da exchange reaction on Pt(111),it is found that Ha has a higher selectivity for HD formation than Da. Considering that Ha diffuses much faster than Da on Pt(111),we propose that the difference in diffusion rates between Ha and Da may determine the selectivity of Ha and Da in forming HD in the Ha + Da reaction on Pt(111).展开更多
Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to ...Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to q.Denote by N（a,k,w,q,n） the 2n-th moment of（b1··· bk c） with b1··· bk c ≡ a（mod q）,1 ≤ bi≤λiq（i = 1,...,k）,1 ≤ c ≤λk＋1 q and 2（b1＋ ··· ＋ bk ＋ c）.We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N（a,k,w,q,n）,which generalized the result of Zhang.Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N（a,k,w,q,n） in the case ofw =（1/2,1/2,...,1/2） and n = 0.In order to show our result is close to the best possible,the mean-square value of N（a,k,q） φk（q）/2k＋2and the mean value weighted by the high-dimensional Cochrane sum are studied too.展开更多
基金supported by the National Natural Science Foundation of China (NSFC20503027, NSFC20773113, NSFC20803072)the Ministry of Sci-ence and Technology of China, MOE Program for PCSIRT (IRT0756)
文摘We report a detailed investigation of the behavior of chemisorbed hydrogen atoms (Ha) on Pt(111) by a combination of an ex-perimental study of the Ha + Da reaction and first-principles calculations. The coverage-dependent adsorption and desorption behavior of Ha and Da on Pt(111) have been systematically established and can be well interpreted in terms of repulsive inter-actions between adsorbates. Ha adsorbs exclusively on the face-centered cubic (fcc) sites of Pt(111) at coverages not exceeding 1 monolayer (ML). With increasing Ha coverage,repulsive interactions between Ha increase,leading to a reduction in both the adsorption energy and the desorption activation energy. It is proposed that the lateral interactions within a Ha layer are partly induced by the local repulsive interactions due to high mobility of Ha on Pt(111). For the Ha + Da exchange reaction on Pt(111),it is found that Ha has a higher selectivity for HD formation than Da. Considering that Ha diffuses much faster than Da on Pt(111),we propose that the difference in diffusion rates between Ha and Da may determine the selectivity of Ha and Da in forming HD in the Ha + Da reaction on Pt(111).
基金Supported by National Natural Science Foundation of China(Grant Nos.11001218,11201275)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20106101120001)the Natural Science Foundation of Shaanxi Province of China(Grant No.2011JQ1010)
文摘Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to q.Denote by N（a,k,w,q,n） the 2n-th moment of（b1··· bk c） with b1··· bk c ≡ a（mod q）,1 ≤ bi≤λiq（i = 1,...,k）,1 ≤ c ≤λk＋1 q and 2（b1＋ ··· ＋ bk ＋ c）.We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N（a,k,w,q,n）,which generalized the result of Zhang.Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N（a,k,w,q,n） in the case ofw =（1/2,1/2,...,1/2） and n = 0.In order to show our result is close to the best possible,the mean-square value of N（a,k,q） φk（q）/2k＋2and the mean value weighted by the high-dimensional Cochrane sum are studied too.
