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《中国物理C》(英文)编辑部
2024年10月30日

2001 Vol. 25, No. S1

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Supplement issue
Experimental Study of X-Ray Induced Dose Enhancement Effect Using Synchrotron Radiation
GUO Hong-Xia, CHEN Yu-Sheng, ZHANG Yi-Men, ZHOU Hui, HAN Fu-Bin, GUAN Ying, GONG Jian-Chen
2001, 25(S1): 1-6.
Abstract:
A multiple parallel plate Aluminum ionization chamber has been designed.Using the ionization chamber the measurement dose gradient distribution at and near the interface of Kovar/Au/Al,Pb/Al,Ta/Al has been done for 30—100keV Beijing synchrotron radiation facility x-rays and DEF(Dose Enhancement Factor)are provided.Complementary metal-oxide semiconductor (CMOS) 4069 devices are irradiated by hard x-rays in BSRF with emphasis on the relative dose-enhancement factor.Using Bi-laminate structure,the equivalent relation of total dose damage is setup by comparing the response of devices,damage enhancement factor of the device is provided.These methods are provided for X-rays radiation hardening technology as an effective evaluation approach.
New Development of XAFS Experimental Methods at BSRF
XIE Ya-Ning, LUO Jun, TAO Ye, ZHANG Jing, HU Tian-Dou
2001, 25(S1): 7-11.
Abstract:
Based on the XAFS experimental station,jointed with the user team,we have made effort to develop new experimental methods,to expand the applications of this method.Those efforts include the XAFS of melting status; the total reflection XAFS and XEOL-XAFS.The principle,the experiment and the result of each of those methods are briefly introduced and a short discusses for the results are also given in this paper.
Effect of Mn Additions on the Microstructure of Nd9Fe85-xB6Mnx Nanocomposite
YIN Shi-Long, BIAN Qing, YANG Hong-Wei, XIE Guo-Zhi, WEI Shi-Qiang
2001, 25(S1): 12-16.
Abstract:
The long-rang and local structures of the Nd9Fe85-xB6Mnx(x=0.5,1.0)nanocomposite produced at melt spinning speed of 20m/s have been investigated by X-ray absorption fine structure(XAFS) and X-ray diffraction (XRD).The crystallized samples were annealed at temperatures 700°C for 5 minutes with a high heating rate.The results show that in the initial samples,the structures of the Nd9Fe85-xB6Mnx manocomposite were strongly correlated with the addition of Mn atoms.Following the increase of Mn content,the long-range and local orders of the Nd9Fe85-xB6Mnx nanocomposite increase,and a soft magnetic phase of α-Fe and a hard magnetic phase of Nd2Fe14B were formed at the addition of 1% Mn.However,the addition of element Mn can not lead to the generation of new phases or the deeper crystallization for the Nd9Fe85-xB6Mnx nanocomposite.We consider that during the preparation,element Mn was alloyed into the main lattice of the Nd9Fe85-xB6Mnx nanocomposite with a metastable structure; through annealing,the Mn atoms were separated from the initial main lattice to the borders of crystalline grain.
EXAFS Study of ZnO/γ-Al2O3 Prepared by Co-Precipitation Method
YANG Peng-Cheng, CAI Xiao-Hai, HAO Jun-Chang, ZI Feng-Lan, XIE You-Chang, HU Tian-Dou, XIE Ya-Ning, ZHANG Jing
2001, 25(S1): 17-20.
Abstract:
The co-precipitated ZnO/γ-Al2O3 system calcined under 200°C,300°C,450°C and 800°C was studied here using XRD and EXAFS and the Zn-centered Radial Distribution Functions were obtained.The nearest Zn-O shell was fitted and a conclusion was drawn that the Zn is coordinated by 4 oxigen atoms,just like within the original ZnO crystal.The changing tendency of RDF peaks of the second Zn-centered shell with the ZnO loading was also discussed.
Synchrotron Radiation Based Angle Integrated Photoemission Experiments and Data Treatments
Kurash Ibrahim, WU Zi-Yu, QIAN Hai-Jie, Abbas M.I., SU Run, LIU Feng-Qin, XIAN Ding-Chang
2001, 25(S1): 21-27.
Abstract:
Photoemission spectroscopic experiment is one of most important method amongst the experimental methods used to study electronic structures of condensed matter as well as thin films. Data acquisition and proper treatment of the photoemission experimental data are indispensable processes to draw intrinsic information of the electronic structure of the target matter.In this paper we discuss the experimental modes under angle integrated photoemission condition and the problem for further data treatment obtained under energy distribution curve mode using synchrotron radiation photoemission spectroscopy.
Valence Band Photoelectron Investigation of Pr1-xSrxMnO3 System
Kurash Ibrahim, WU Zi-Yu, QIAN Hai-Jie, LIU Feng-Qin, XIAN Ding-Chang
2001, 25(S1): 28-32.
Abstract:
Valence band photoemission experiments on Pr1-xSrxMnO3 polycrystalline system with x ranging from 0.0 to 0.4 show that the density of states of the bands appearing in the ranges between Fermi level and ~12eV below Fermi level have a substantial change with the doping level x.These features are discussed in terms of charge transfer in the ground states of Pr1-xSrxMnO3 system.A nonlinear charge transfer with the doping amount x is evidenced and a possible second order phase transition mediated by the charge transfer is proposed.
Synchrotron Radiation Angle-Resolved Photoemission Study of the Orientational Phase Transition for K3C60
XU Ya-Bo, LI Hong-Nian, BAO Shi-Ning, LI Hai-Yang, QIAN Hai-Jie, LIU Feng-Qin, Kurash Ibrahim, JIA Jin-Feng, XUE Qi-Kun
2001, 25(S1): 33-38.
Abstract:
Synchrotron radiation photoemission spectra were measured along the [111] direction of K3C60 single crystal film at 190K,200K and 300K.Conduction band dispersions can be observed at 190K,and the band structure was nearly the same as that at 150K corresponding to the onedimensional-disordered orientaltional structure (IDDS) of K3C60.When the sample temperature increased to 220K,most subpeaks of the conduction band vanished and the dispersions could not be observed.This result coincides with the existence of an orientational phase transition occurred at 200K.The fcc nearest-neighbor antiferromagetic Ising model was found to be suitable to analyz the temperature dependence of the band structure.The phase transition is due to the onedimensional-disordered orientational structure at lower temperatures turned to be the mixture of BDS domains and disordered molecules at higher temperatures.The number of disordered molecules was deduced to be about 40 percent of the total molecular number at 220K.At room temperature,the electronic structure was drastically different from that at low temperatures because of the dynamical disorder of C60 molecules.
Measurement and Calculation of Escape Peak in SR-XRF Analysis
KANG Shi-Xiu, SUN Xia, YAO Kun, WU Zi-Qin, HUANG Yu-Ying, JU Xin, XIAN Ding-Chang
2001, 25(S1): 39-43.
Abstract:
The escape peaks in synchrotron radiation X-ray fluorescence (SR-XRD) spectra generating from Si(Li) detector can disrupt seriously the qualitative and quantitative analysis.Discrimination to escape peaks in experiments was performed.The escape peak position and intensity of 12 elements from K Kα to As Kα,for each of the 14 specimens,are measured.The differences of standard and experimental values of escape peak and the nearest major peak are compared.The errors are less than 10% in general.The ratios of intensity of escape peak and major peak are calculated using a simplified emitting distribution model of Si Kα excited by X-ray.The ratios,both calculated and experimental,descend approximately from 1% to 0.1% with the atom ordinal number increasing.
X-Ray Fluorescence Analysis of Some Plants in the King George Island,Antarctica
JU Xin, SHEN Xian-Sheng, KANG Shi-Xiu, WU Zi-Qin, SUN Li-Guang, ZHANG Li, YIN Xue-Bin, HUANG Yu-Ying
2001, 25(S1): 44-48.
Abstract:
Using synchrotron radiation X-ray fluorescence (SR XRF) analysis method without the standard reference,the distribution and absorption of heavy metal elements of some plants,such as bryophyte,algae and lichen,in the King George Island,Antarctica,were investigated.It is found that different plants are of different ability to absorb the heavy metal elements,and the same to different organs of a plant.It is helpful for us to understand the ability to monitor the environment in the Antarctica with these plants,and make them a preliminary screening.
Study of Elements in Yue Kiln Ancient Porcelain by SRXRF
FAN Dong-Yu, FENG Song-Lin, XU Qing, ZHANG Ying, FENG Xiang-Qian, LEI Yong, CHENG Lin, SHA Yin, CHAI Zhi-Fang, HUANG Yu-Ying, HE Wei, QUAN Kui-Shan, SHEN Yue-Ming
2001, 25(S1): 49-53.
Abstract:
Elemental contents of ancient porcelain were analyzed by SRXRF.The ancient porcelain manufactured from late Tang Dynasty to early Song Dynasty were excavated at Zhejiang Yue Kiln.Data of elemental contents were analyzed with clustering analysis.We also studied distribution of several elements in the porcelain.Results show that contents of Ca,Mn in glaze are higher than those in body,contrary to distribution mode of K,Ti and Fe.Most of the ancient porcelain samples bore temporal and territorial characteristics.
Collimation in Energy Dispersive X-Ray Experiment under High Pressure
LI Xiao-Dong, LIU Jing, LI Yan-Chun, YANG Shi-Shun
2001, 25(S1): 54-57.
Abstract:
A collimation system is designed to improve the orientation of diffraction beam more exactly and suppress the scattering background in the energy dispersive X-ray diffraction (EDXD) experiment in high pressure station at BSRF.During twice SR dedicated mode,the results of some experiments show that the collimation system can improve the signal-to-noise ratio very much.The quality of the data from some materials whose diffraction signal are too weak to be measured before is much better.The system provide a useful way of the megabar experiment.
Pressure-Induced Phase Transition of Nanocrystalline Zinc Sulfide
PAN Yue-Wu, QU Sheng-Chun, CUI Qi-Liang, ZHANG Wei-Wei, LIU Xi-Zhe, LIU Jing, LIU Bing-Bing, GAO Chun-Xiao, ZOU Guang-Tian
2001, 25(S1): 58-61.
Abstract:
In situ energy dispersive X-ray diffraction measurements on nanocrystalline zinc sulfide have been performed by using diamond anvil cell with synchrotron radiation.There is a phase transition which the ultimate structure is rocksalt when the pressure is up to 16.0GPa.Comparing the structure of body materials,the pressure of the phase transition of nano zinc sulfide is high.We fit the Birch-Murnaghan equation of state and obtained its ambient pressure bulk modulus and its pressure derivative.The bulk modulus of nanocrystalline zinc sulfide is higher than that of body materials,it indicate that the rigidity of nanocrystalline zinc sulfide is high.
EDXD Study of α-LiIO3 under High Pressure
ZHANG Wei-Wei, CUI Qi-Liang, PANG Yue-Wu, ZHU Pin-Wen, MA Hong-An, ZOU Guang-Tian, LIU Jing, LI Yan-Chun, LI Xiao-Dong
2001, 25(S1): 62-65.
Abstract:
X-ray diffraction studies were carried out on the α-LiIO3 under high pressure by synchrotron radiation.Some changes of patterns showed that phase transition happened in the range of 15.6GPa—23.8GPa.
Study on Vacuum ltraviolet Circular Dichroism Spectra of Several Proteins
SHENG Yi, LI Xiao-Wei, LI Dong-Mei, TAO Ye
2001, 25(S1): 66-69.
Abstract:
Beijing Synchrotron Radiation Setting(BSRF)3B1B Vacuum Ultraviolet Experimental Station and new development on Vacuum Ultraviolet Circular Dichroism spectoscopy(VUVCD)are introduced.At the same time,results on VUVCD spectra of several proteins are analyzed.
VUV Luminescent Properties of Rare Earth Fluorides and Borates
YOU Fang-Tian, YANG Zhi, LU Pei-Chao, WANG Ying-Xia, LIN Jian-Hua, TAO Ye
2001, 25(S1): 70-74.
Abstract:
The quantum cutting effect was observed in Eu3+ doped hexagonal NaGdF4.Upon VUV excitation to the 6GJ level of Gd3+,two red photons are emitted by Eu3+ through an efficient two-step energy transfer process.The quantum efficiency of this material is about 160%.Cubic NaGdF4 contains considerable amount of oxygen impurity,so that the 4f-5d transition moves to lower energy(177nm),which fits the energy of the VUV photons from discharge of inert gas; the color purity of the emission of cubic NaGdF4 is also improved by oxygen doping.The photon cascade emission of Gd3+ ions was observed in GdBaB9O16.Under the 202 nm excitation,a red and a near infrared radiative transition from 6GJ states,6GJ6IJ and 6GJ6PJ occur followed by an ultraviolet emission of 6PJ8S7/2.
Study of the Effect of Urea on the Phase Transition of Phospholipid by Synchrotron X-Ray Diffraction
YU Zhi-Wu, FENG Ying, WANG Jun, DONG Bao-Zhong
2001, 25(S1): 75-80.
Abstract:
Synchrotron X-ray diffraction and differential scanning calorimetry were used to study the effect of urea solutions on the phase behavior of Dioleoylglycero-phosphatidvlethanolamine (DOPE).It was found that urea could stabilize lamellar liquid-crystalline phase at the expense of lamellar-gel phase and non-bilayer inverted hexagonal phase.The repeat distance of DOPE multilamellar structure increases with the increasing of urea concentration.The molecular mechanisms are discussed in terms of the possible hydrogen bonds between urea and the phospholipid head groups and the Hofmeister effect of urea,where urea is taken as a waterstructure breaker.In addition,X-ray diffraction pattern of a wet rat tail collagen fiber was collected and was used as calibration standard at small-angle diffraction stations.
Preliminary Transformation on Experimental Data of Small Angle X-Ray Scattering
ZHAO Hui, LI Zhi-Hong, DONG Bao-Zhong, RONG Li-Xia, WANG Jun
2001, 25(S1): 81-84.
Abstract:
A method is introduced on preliminary processing of experimental data from Small Angle X-ray Scattering (SAXS) Experimental Station,Beijing Synchrotron Radiation Facility.That is how to transfer the scattering signal recorded by image plates' detector into data of scattering angles and their corresponding intensities.Detailed discussions are given on problems that may arise in the data-transforming process.
XRD Investigation of Self-Assembly and LB Films of Substituted Phthalocyanine and Porphyrin
LEI Sheng-Bin, WANG Jun, DONG Yu-Hui, XU Sai-Long, XU Shan-Dong, ZENG Qing-Dao, WANG Chen, BAI Chun-Li
2001, 25(S1): 85-89.
Abstract:
Using X-ray diffraction and scanning tunneling microscopy (STM),the structure self assembly and langmuir-blodgett membrane of substituted phthalocyanine and porphyrin were investigated.It is demonstrated that these molecules adsorb with its molecular plane parallel to the substrate surface on graphite,but perpendicular to the surface of Si(111) and glass.These results indicate these molecules can form organic thin films with different structure on substrate which have different polarity.
Microstructural Characterization of YBCO Thin Films Grown on YSZ
LIU Cui-Xiu, CHEN Xiang-Ming, TANG Wei-Hua, WANG Yong, XU Ming, MAI Zhen-Hong, JIA Quan-Jie, ZHENG Wen-Li, JIANG Xiao-Ming, GAO Ju
2001, 25(S1): 96-99.
Abstract:
Ultrathin films of YBa2Cu3O7-σ with good crystallinity and superconductivity were prepared by a modified off-axis sputtering with an Eu2CuO4 buffer layer.The microstructure of YBCO thin films with or without buffer layer,were studied by using scanning electron microscopy and X-ray techniques.It was found that the epitaxy and crystallinity of the grown YBCO have been significantly enhanced by using the ECO buffer layer,and the surface of the YBCO films with buffer is more smooth.The results also show that the ECO buffer can efficiently block the interaction between YBCO and yttria stabilized ZrO2 substrate.
Bragg Diffraction and Its Simulation of Ba TiO3/SrTiO3Superlattices
CUI Shu-Fan, LUO Guang-Ming, YU Wen-Xue, CHEN Xiang-Ming, LIU Cui-Xiu, LI Ming, MAI Zhen-Hong, LU Hui-Bin, CHEN Zheng-Hao, JIA Quan-Jie, ZHENG Wen-Li, JIANG Xiao-Ming
2001, 25(S1): 100-105.
Abstract:
Ba TiO3/SrTiO3(BTO/STO)superlattices were examined by using X-ray agazing grazing incidence diffraction under total external reflection conditions and ordinary Bragg diffraction.Dynamical diffraction theory was used to simulate Bragg diffractions.It is shown that,these superlattices partially relaxed.However,unlike semiconductor epilayers or superlattices,the lattice constants of BTO/STO superlattices do not completely obey the role of tetragonal distortion.The perpendicular lattice constants deviate slightly from that predicted by elasticity theory.These deviations are probably relevant to the structures of oxide materials.
Magnetoresistance and Structural Studies on Co/Cu Multilayers with the Combination of the first and Second Antiferromagnetic Oscillation Peak
TAN Wei-Shi, YOU Biao, ZHANG Jie-Qiu, WU Xiao-Shan, HU An, JIANG Shu-Sheng, WANG Jun, JIA Quan-Jie, ZHANG Wen-Li, JIANG Xiao-Ming
2001, 25(S1): 106-109.
Abstract:
The first and second antiferromagnetic oscillation peaks with respect to the spacer thichness of Cu in Co/Cu multilayers are determined.With the combination of the first and second oscillation peaks,[Co(2 nm)/Cu(t1)/Co(2 nm)/Cu(t2)]30 multilayer is fabricated and characterized.In contrast to the first and second oscillation peak samples ([Co(2 nm)/Cu(t1)]30)and ([Co(2 nm)/Cu(t2)]30),the enhancement of magnetoresistance(MR) in this combinated multilayer is observed.We believe that the enhancement of MR in the combinated sample is due to the added coupling between Co(2 nm)/Cu(t1)and Co(2 nm)/Cu(t2).
A New Method to Determine the Orientations of Crystal Defects by Synchrotron Radiation
YU Wan-Li, LUO Yong-An, WANG Ming-Zhi, ZHENG Qiu-Ju, ZHANG Hui-Jun, TIAN Yu-Lian, HUANG Wan-Xia
2001, 25(S1): 110-115.
Abstract:
A new method was put forward to determine the orientations of crystal defects by synchrotron radiation.Instead of using monochromic radiation as it was done before,a simple method was proposed using white radiation to calculate directions of crystal defects.In order to do so,at least two topographs with different beam incident directions were needed.The direction of an image of a defect should be figured out first.It can be fixed by the angles between the direction of the image and [100],[010]and [001].Suppose the direction of the topograph is [u1 v1 w1]and the direction of the image in the first topograph is [cosα11,cosβ11,cosγ11],α1111 and γ11 are the angles between the image and [100],[010] and [001],respectively,then the direction of the defect should be in thd plane with normal n1=[u1 v1 w1]×[cosα11,cosβ11,cosγ11].Similarly,in the second topograph,the normal of the plane in which the same defect lies is n2=[u2 v2 w2]×[cosα12,cosβ12,cosγ12],in which [u2 v2 w2] is the direction of the second topograph,α1212, and γ12 are the angles between the direction of the image and [100],[010] and [001].Since the defect are normal to n1 and n2,its direction n can be calculated out as n=n1×n2=[u v w].Using this method,the directions of dislocations in natural diamond were calculated and the types of the dislocations were figured out.
In Situ Observation of Domain Structure of Molybdates Gadolinum Single Crystal by Synchrotron X-Ray Topography
YUAN Qing-Xi, XU Jun, PAN Shou-Kui, HUANG Wan-Xia, TIAN Yu-Lian, JIANG Jian-Hua
2001, 25(S1): 116-120.
Abstract:
The domain structure of Gd2(MoO4)3 single crystal grown by Czochralski technique was observed first using a polarizing microscope,then using the Synchrotron X-ray topography under the conditions that the temperature of the crystal piece was increased from room temperature to 200°C and to applied DC voltage was varied from 0V to 4400V.The experiment results show that there are ferroelectric and ferroelastic domains in the crystal,but these two kinds of domains all disappeared when the temperature was increased above Curie temperature and could be transformed to a single domain when the applied DC voltage was high enough.This experimental results shows us that it is possible to make periodically poled Gd2(MoO4)3 crystal,though the presence of ferroelastic domain.
Applications for Synchrotron Radiation in Inertial Confinement Fusion Research
SUN Ke-Xu, YI Rong-Qing, HUANG Tian-Xuan, CUI Yan-Li, YANG Jia-Min, JIANG Shao-En, DING Yong-Kun, ZHANG Bao-Han, WANG Hong-Bin, WEN Shu-Huai, ZHENG Zhi-Jian, CUI Ming-Qi, ZHU Pei-Ping, ZHAO Yi-Dong, LI Gang, TANG E-Sheng
2001, 25(S1): 121-127.
Abstract:
In this paper the calibrations of different soft X-ray detector elements used experiment diagnostics of ICF in Beijing Synchrotron Radiation Facility-3W1B beam is reported.SR used special operation type with beam current 35—110mA.the storage ring electron energy 2GeV,photon energy region 50—150eV.First,property of light source was studied by transmission grating-face array CCD system.We have divided 50—1500eV energy region in seven energy section through different material prefilter with monochromaticity better 95%.The AXUV-100 photodiode produced by IRD of America as secondary standard monitored light source intensity.The successive adjust monochromatic light was contained through reflectometer target chamber and relative adjust facility.The sensitivity of XRD(Au,Al),the reflectivity of planar mirror and multi-layer mirror,the transmissivity of different material filter,the diffraction efficiency of transmission grating,the energy response curve of soft X-ray film,the quantum efficiency of face array CCD and the still property of soft X-ray streade camera et al.were calibrated.Finally,the experiment data treatment in Shenguang-Ⅱ were used by many calibration resuite,which secure data treatment accuracy.
Study on Synchrotron Radiation Lithography at BSRF
PENG Liang-Qiang, YI Fu-Ting, HAN Yong, ZHANG Ju-Fang
2001, 25(S1): 128-130.
Abstract:
It is the excellence for fabricating microstructures with high aspect ratio and great structural height by synchrotron radiation lithography.A successive exposure method with present masks is put forward in this paper.Microstructures with thickness 2.2mm have been obtained by this method.A serial of studies of the effects on aspect ratio of mask,PMMA resist,substrate,wavelength range and dose of X rays have been processed.Microstructures with aspect ratio 104 have been obtained under optimized condition.
Study on New Type LIGA Mask Fabrication Technique
CHEN Di, ZHU Jun, LEI Wei, WANG Sui, ZHANG Da-Cheng, YI Fu-Ting
2001, 25(S1): 131-134.
Abstract:
The fabrication of LIGA masks is a critical and challenging process in LIGA technique.As inductively coupled plasma (ICP) deepetching appears to be the most suitable source for deep silicon etching,we fabricated a new type LIGA mask using this technique.In comparison with other types of LIGA masks,the mask we fabricated has the advantages of its low cost and its simple fabrication process.Desired microstructures have also been fabricated using this new type LIGA mask in LIGA mask in LIGA technique.
Computer Simulation for the Real-Sized Electron-Positron Converter on BEPC-LINAC Based Slow Positron Beam
YU Run-Sheng, WANG Bao-Yi, MA Chuang-Xin, CAO Xing-Zhong, PEI Guo-Xi, WEI Long, YE Ming-Han
2001, 25(S1): 135-139.
Abstract:
This paper describes the simulation by EGS4 code for the positron converter on BEPC LINAC-based slow positron beam and the radiation shield.Results show that the slow positron yield will be 3.5×106e+/s(Ta target,1.5cm thick,φ10mm)or 4.3×106e+/s(W target,1.3cm thick,φ10mm) when the LINAC is running under the parasitic mode.Meanwhile,the slow positron yield will be 4.7×108e+/s(Ta target,1.3cm thick,φ10mm)or 5.9×108e+/s(W target,1.1cm thick,φ10mm) when the LINAC is running under the long-pulse-width mode.A 3m thick concrete wall inserted with a 1m long×1m wide×0.2m thick Fe plate is needed for the radiation shield and placed behind the positron converter.
A Double Crystal Monochromator of Sagittal Focusing at SSRF
HE Jian-Hua, XIA Shao-Jian, HOU Zheng-Chi, GONG Jin-Long, JIANG Xiao-Ming, ZHAO Yan
2001, 25(S1): 140-144.
Abstract:
A double crystal monochromator of sagittal focusing has been designed,based on the idea of the separate movements of the crystal and the independent adjustment of crystal orientations,to be able to work in both the fixed beam exit and the variable beam exit cases.Three sorts of flexure hinge mechanisms have been used to bend the focusing crystal and to adjust the crystal orientations independently.The first crystal of the monochromator is cooled directly by water feeding through the rotation axis.The performance of the monochromator has been tested off-line,and the results show that the adjusting precision of the crystal orientations is better than 0.5 arcsecond and the horizontal width of the focusing image deviates from the theoretical width by less than 25%.