52 Another description of covellite CuS is that it is composed of alternating CuS 3–CuS 3–CuS 3 layers and S–S layers along the c-axis. 51 The most Cu-deficient covellite CuS phase has a unique layered structure in spite of simplest stoichiometry, where its copper atoms locate in two different environments: planar trigonal CuS 3 layer are sandwiched by two tetrahedral CuS 4 layers along the c-axis, with the triple layers connected to adjacent triple layers through disulfide (S–S) covalent bonds. 50 Moreover, according to the theoretical study based on DFT theory, anilite phase was shown to be the most stable structure among the known Cu 2− xS phases. 49 In the orthorhombic unit cell of 28 copper atoms, 20 of which are in triangular coordination and 8 are in tetrahedral coordination with sulfur. 23,47,48 Anilite Cu 1.75S (Cu 7S 4) phase has an orthorhombic crystal system, where the sulfur atoms adopt approximately face-centered cubic arrangement and the copper atoms occupy the interstices. 46 The roxbyite phase is unusual in bulk forms but has been readily synthesized in NPs. Some of which have two-fold linear coordination, but mostly they have three-fold triangular and four-fold tetrahedral coordination. Other layers sandwiched between the close packed sulfur layers composed of double or split layers of Cu atoms. 45,46 It has been described that, it possesses a triclinic unit cell with 90 atoms, constructing a distorted hexagonal close packing of 32 sulfur atoms with 58 individual copper atoms occupying triangular coordination with sulfur. 44 Roxbyite phase Cu 1.81S (Cu 58S 32) is just as complex in its entirety as the structures of low chalcocite and djurleite phase. 42,43 These three structures are close related to each other, and therefore, phase identification of Cu 1.8S NPs remains a challenge. Three conference papers have come out of the work, and two journal articles are in preparation.Cu 2− xS (0 104 ☌, high chalcocite phase is at 104 ☌ 73 ± 3 ☌, low-temperature phase also has face-centered cubic symmetry of sulfur anion structure but different lattice constants and metastable rhombohedral phase obtained by cooling from 73 ± 3 ☌ resembles high chalcocite, with one copper atom located at four equivalent positions in each sulfur tetrahedron. During the period of the grant, I recruited a PhD student to work in this area, and he and I together visited our collaborator in Xi'an for a productive week in 2017. "We had three visits funded by the Exchange, though the Chinese collaborator also won significant additional funding to spend a year in another university in the UK. The Chinese collaborator is an expert in evaluating highly oscillatory integrals. This was very accurate and in some ways efficient, but the true potential of its efficiency could only be unlocked by finding a fast, yet accurate, method of evaluating highly oscillatory integrals. "Much of my work in the previous ten years had focused on a numerical method for solving high-frequency wave scattering problems. "As an engineer, the opportunity arose to work jointly with a Chinese mathematician on a problem of much interest to me, but in which a deeper mathematical knowledge would be helpful. “I applied for the International Exchanges funding as a means of enabling a new cross-disciplinary collaboration.
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