structural analysis of agxcu1−xi (0≤x≤0.5) by solid 63cu nmr and x-ray diffraction methods

$: Structural analysis of AgxCu1−xI (0≤x≤0.5) by solid 63Cu NMR and X-ray diffraction methods$
Structural analysis of AgxCu12xI �0 # x # 0:5� by solid63Cu NMRand X-ray diffraction methods

J. Kimuraa, T. Idaa, M. Mizunoa, K. Endoa,* , M. Suharaa, K. Kiharab

aDepartment of Chemistry, Faculty of Science, Kanazawa University, Kakumamachi, Kanazawa 920-1192 JapanbDepartment of Earth Sciences, Faculty of Science, Kanazawa University, Kakumamachi, Kanazawa 920-1192 Japan

Received 15 June 1999; accepted 12 July 1999

Abstract

63Cu NMR and X-ray diffraction methods have been used to investigate the temperature dependence of the nuclear chemicalshifts and the diffraction patterns, respectively, for mixed crystal AgxCu12xI �0 , x , 0:5�: We indicate from the X-raydiffraction method that the lattice constants increase gradually a little with the temperature, except for the range of theg-to-a 0 phase transition. For NMR experiments, the chemical shifts show a linear dependence of temperature to the high-field in thelower range of about 150–350 K, and the shift increases nonlinearly with the higher temperature (350–500 K). The high-fieldshifts above 350 K seem to depend on the cation disorder which occurs with the fact that a part of the tetrahedral cations move tothe qausi-stable interstitial octahedral sites. The observed high-field shifts are explained by Cu chemical shielding calculationsof TdCuI32

4 andOhCuI526 species, as obtained by the finite perturbation theory in an ab initioGaussian 94 program using

double-z basis set for Cu and I atoms. In the case of the nonlinear temperature dependence of the shift, we introduce the shiftmodel as proposed by Negita and coworkers: The shift is also due to the cation which moves to the qausi-stable interstitialoctahedral sites.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: AgxCu12xI �0 # x # 0:5�; 63Cu NMR; Theoretical Cu NMR shieldings

1. Introduction

It is well known that the CuI and AgI crystals formcomplete solid-solution, since the crystal latticesresemble each other and the atomic radii in the crys-tals are slightly different. The AgxCu12xI crystal in thea-phase is considered as a superionic conductor, afterNoelting [1] investigated the phase diagram of theAgI–CuI system. Recently, Kusakabe and coworkers[2,3] indicated from the X-ray diffraction and differ-ential scanning calorimetry (DSC) methods that the

crystal structure of AgxCu12xI �0 , x , 0:5� in thetemperature range of 300–723 K consists ofg,�g 1 a 0�; and a 0-phases. The most probable crystalstructure in thea 0-phase is an anti-fluorite one inwhich a part of cations are occupied at octahedralsites. Therefore, the occupation probability of a cationat the octahedral site rapidly increases with increasingsilver ion concentration. We will, here, investigate thesolid structure of AgxCu12xI �0 , x , 0:5� from thetemperature (150–523 K) dependence of63Cu NMRchemical shieldings.

Solid-state NMR is a powerful tool to examine thedynamic and static structure of crystals. There wereseveral studies [4–9] on the solid CuI, AgI andAgxCu12xI using NMR methods. Becker and

Journal of Molecular Structure 522 (2000) 61–69

MOLSTR 11170

0022-2860/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0022-2860(99)00365-8

www.elsevier.nl/locate/molstruc

* Corresponding author. Tel.:181-76-264-5924, fax:181-76-264-5742.

E-mail address:[email protected] (K. Endo).

coworkers [4,5] indicated that the nucleus chemicalshifts of CuI and AgI changes linearly with tempera-ture (170–800 K). An anomalous increase in NMRrelaxation rates of CuI was observed in the tempera-ture range of insulator-to-superionic conductor phasetransition by Boyce and Huberman [6]. We analyzedthe crystal structure of AgxCu12xI at room tempera-ture using 63Cu and 109Ag MAS NMR and X-raydiffraction methods [7,8]. The63Cu NMR chemicalshifts were shown to depend mainly on the 3d-holeon the Cu atom. We indicated that observed109Aglow-field shifts with decreasing lattice constants wasexplained theoretically by the chemical shieldingswhich are dominated by the paramagnetic terms oftetrahedral AgI32

4 complexes by decreasing the bondlength between Ag and I atoms. Recently, weobserved two types of63Cu NMR signals forAgxCu12xI �0:75 , x , 1:0� in theg-to a-phase tran-sition(440–475 K) [9]. We indicated from the Cuchemical shielding calculations of Cu-complexesusing theGaussian 94 program [10] that the low-field signal is due to the Cu nucleus at the tetrahedralposition, while the high-field signal results from theCu ion mainly at the octahedral 6(b) position andpartially at the tetrahedral 12(d) site.

In the present work, we will examine the tempera-ture dependence of the NMR chemical shifts and thediffraction patterns for mixed crystal AgxCu12xI �0 ,x , 0:5� by 63Cu NMR and X-ray diffraction methods,respectively. The observed high-field shifts in thetemperature range of 350–523 K will be confirmedby theoretical Cu chemical shieldings ofTdCuI32

4

andOhCuI526 species, as calculated by ab initioGaus-

sian 94 program [10] using the double-z basis set forCu and I atoms.

2. Experimental

The CuI and AgI used here were purchasedcommercially. A complete solid-solution of mixedAgxCu12xI �0 , x , 0:5� crystals in which solid solu-tion was complete were prepared at 923 K by meltannealing method in a vacuum vessel to preventoxidation.

Solid 63Cu NMR measurements of AgxCu12xI wereperformed at a frequency of 79.4 MHz using Chemag-netics CMX-300 spectrometer. 400–800 Transients

were accumulated using 3.0–5.5m(908) pulse. Thespectra were obtained using a wide bore probe and4k data points were collected over band widths of650 kHz. All measurements were carried out in thetemperature range of 150–523 K. Solid CuI (non-annealing) at room temperature (293 K) was used asan external reference. All chemical shifts for63Cu aredefined by

ssam� �nsam2 nref�=nref; �1�wheren samis the resonance frequency of a sample andn ref is the reference frequency. Shifts defined in thismanner are positive for lower shielding.

The X-ray diffraction method was performed byRigaku RINT 1200. The sample chamber was keptunder nitrogen atmosphere in the range of 293–723 K. The values of the lattice constants for mixedAgxCu12xI �0 , x , 0:5� crystals were obtainedwithin errors of^0.01 A. The Cu/Ag ratios in themixed AgxCu12xI crystals were estimated using theX-ray fluorescence method.

3. Computation

We used the lattice constants of AgxCu12xI �0 ,x , 0:50� crystals as the structural data of tetrahedralCuI32

4 complexes in theg-phase from our X-raydiffraction measurements. For each complex, coordi-nations of tetrahedral CuI32

4 ; and octahedral CuI526

were estimated as {Cu(0, 0, 0), I(2c/4, 2c/4, 2c/4),I(2c/4, c/4, c/4), I(c/4, 2c/4, c/4), I(c/4, c/4, 2c/4)},and {Cu(0, 0, 0), I(c/2, 0, 0), I(2c/2, 0, 0), I(0,c/2, 0),I(0, 2c/2, 0), I(0, 0,c/2), I(0, 0,2c/2)}, respectively,where c denotes the unit lattice constant in theg-phase. The Cu chemical shielding constants wereobtained from calculations of the finite perturbationmethod in theGaussian 94 program [10] using thedouble-z basis set for Cu and I atoms. The ab initioMO calculations were performed on a DEC VT-Alpha533 workstation.

4. Results and discussion

4.1. Phase transition ofAgxCu12xI by X-raydiffraction method

We first examined X-ray diffraction patterns for

J. Kimura et al. / Journal of Molecular Structure 522 (2000) 61–6962

AgxCu12xI �0 , x , 0:5� at various temperatures, todetermine the lattice constants in each crystal phase.Fig. 1a shows the phase transition diagram from ourX-ray diffraction measurements. The area for theg-to-a 0 phase transition is more narrow than that of thephase diagram, as indicated from the heat capacitymeasurements[1]. The difference is due to themeasurement methods: Our X-ray diffraction detectsthe density of atoms directly in theg- anda 0-phases,while the heat capacity measurement does macro-scopic observables.

In the AgxCu12xI; we showed powder X-raydiffraction patterns of the Ag0.3Cu0.7I crystal at severaltemperatures in Fig. 1b. In the figure, the pattern at533 K indicated zincblende structure, while the resultat 623 K showed anti-fruorite structure in which a partof cations occupy the octahedral site. These structurescorrespond to the g and a 0 crystal phases,

J. Kimura et al. / Journal of Molecular Structure 522 (2000) 61–69 63

Fig. 1. Results of AgxCu12xI �0 , x , 0:5� by X-ray diffraction method: (a) phase transition diagram; (b) diffraction profiles of Ag0.3Cu0.7Icrystal in the temperature range of 533–623 K; (c) the diffraction patterns in the 2u range of 24.5–25.08.

Fig. 2. Lattice constants of AgxCu12xI �x� 0;0:1; 0:3;0:5� in thetemperature range of 300–725 K from X-ray diffraction measure-ment.

respectively, as indicated by Kusakabe and coworkers[2]. In the temperature ranges of 533–593 K, thecrystal seems to beg 1 a 0 phase.

As seen in Fig. 1c, we observed the decrease oflattice constant for the (111) plane of Ag0.3Cu0.7I inthe temperature range. Then, the temperature depen-dence of the lattice constant for AgxCu12xI wasplotted in Fig. 2. The lattice constants ing and a 0

crystal phases increase linearly with rising in tempera-ture, while the lattice constant in theg 1 a 0 crystalphase decreases with the rise. The temperature-depen-dency of the lattice constants in each phase may corre-spond to the results of the specific heat using DSC [3].In the g-to-g 1 a 0 phase before the transition, theanomalous excess specific heat is due to the cation

disorder which can be produced by the fact that aproportion of the tetrahedral cations move to the octa-hedral site. In theg 1 a 0- to-a 0 phase after the transi-tion, the specific heat of�dCp=dT , 0� is owing to thejumps of mobile cations between two different tetra-hedral and octahedral sites.

4.2. Temperature dependence of63Cu NMR chemicalshift

We investigated the temperature dependence of63Cu NMR in theg phase of AgxCu12xI; since thetemperature unit of our NMR instrument is limitedin the range of 150–523 K. The spectra of threetypes of mixed AgxCu12xI �x� 01; 0:3; 0:5� were


Fig. 3. 63Cu NMR spectra of AgxCu12xI �x� 0:1; 0:3;0:5� in the temperature range of 300–500 K.

Table 1Observed Cu chemical shifts of AgxCu12xI �0 , x , 0:50�; calculated Cu chemical shielding constant ofTdCuI32

4 andOhCuI526 complexes

using thegaussian 94 program using the double-z basis set

Cu complexesRCu–I (A) sdia(ppm) spara(ppm) s total(ppm) Shift (ppm) Crystal Observed shift (ppm)

Ag0.5Cu0.5ITdCuI23

4 (2.73) 2406 2744 1662 2146 (293–375 K) 250, 2110OhCuI25

6 (3.10) 2404 2307 2097 2581 (375–500 K) 2110, 2125Ag0.3Cu0.7I

TdCuI234 (2.69) 2406 2785 1621 2105 (293–375 K) 240, 280

OhCuI256 (3.07) 2404 2341 2064 2548 (375–500 K) 2100, 2120

Ag0.1Cu0.9ITdCuI23

4 (2.65) 2406 2854 1552 236 (293–375 K) 220, 260OhCuI25

6 (3.04) 2404 2376 2028 2512 (375–500 K) 270, 290CuI

TdCuI234 (2.62) 2406 2890 1516 0 (293–500 K) 0, 250

shown in Fig. 3. We observed symmetrical andbroader signals which shifted to the high-fieldwith increasing temperature in the range of 173–348 K. As seen in Fig. 3, the spectra above 398 Kshows asymmetrical and more narrow than onesbelow 348 K. The asymmetrical spectrum mayresult from local AgI lattice units in the solid-solution. The spectrum in NMR seems to dependon the cation disorder which occurs with the factthat a part of the tetrahedral cations move to theoctahedral interstitial site.

4.2.1. Correlation between Cu–I bond-lengths and Cuchemical shieldings ofAgxCu12xI �0 , x , 0:5�

We examine a relation between Cu–I bond lengthsand Cu chemical shieldings of AgxCu12xI �0 , x ,0:5� to analyze the temperature dependence of the Cuchemical shieldings from experimental and theore-tical viewpoints. From X-ray diffraction measure-ments, the lattice constants of AgxCu12xI�0 , x , 0:5� increase with rising temperature. Onthe contrary, the Cu NMR signal was seen to shift tothe high-field with increasing temperature. We will,thus, plot the experimental relation between Cu–Ibond lengths and Cu chemical shieldings in the zinc-blende structure of AgxCu12xI �0 , x , 0:5�: For thetheoretical correlation, we can calculate Cu chemicalshieldings versus Cu–I bond length forTdCuI32

4

complexes by ab initio MO program.Table 1 showed the theoretical Cu nuclear shielding

constants and chemical shifts of the Cu complexes asobtained by the finite perturbation method using agaussian94 program with the observed chemicalshifts in the temperature range of 293–523 K. Thecalculated and observed shifts were given relative tothe reference molecules,TdCuI32

4 �RCu–I � 2:62 �A�and CuI at 293 K, respectively.

In Fig. 4, we plotted the63Cu chemical shifts versusCuI bond length for AgxCu1–xI �x� 0; 0:1;0:3;0:5�with the theoretical correlation (as indicated with asolid line) between Cu chemical shifts and CuI bondlengths of TdCuI32

4 complex as calculated by the


Fig. 4. Correlation between63Cu NMR chemical shifts and CuIbond length of AgxCu12xI �x� 0; 0:1; 3;0:5�; the solid line denotesthe theoretical correlation between Cu chemical shifts and CuI bondlength of TdCuI32

4 complexes as calculated by theGaussian 94program using the double-z basis set.

Table 2The change in atomic orbital densities ofTdCuI32

4 andOhCuI526 complexes using thegaussian 94 using the double-z basis set

Orbital TdCuI324 RCu–I (2.62 A) TdCuI32

4 RCu–I (2.65 A) OhCuI256 RCu–I (3.04 A) Td\CuI32

4 RCu–I (2.73 A) OhCuI256 RCu–I (3.10 A)

Cu3dxx1yy 2 0.0482 2 0.0449 0.0000 2 0.0348 0.00003dzz 2 0.0482 2 0.0449 0.0000 2 0.0348 0.00003dxy 2 0.0165 2 0.0134 2 0.0057 2 0.0052 2 0.00573dyz 2 0.0165 2 0.0134 2 0.0057 2 0.0052 2 0.00573dzx 2 0.0165 2 0.0134 2 0.0057 2 0.0052 2 0.00574s 0.1836 0.1757 0.0720 0.1524 0.11394px 0.1306 0.1243 0.0601 0.1067 0.05294py 0.1306 0.1243 0.0601 0.1067 0.05294pz 0.1306 0.1243 0.0601 0.1067 0.0529I5s 0.0000 0.0000 0.0001 0.0000 0.00005px 2 0.0282 2 0.0276 0.0001 2 0.0260 2 0.00065py 2 0.0282 2 0.0276 0.0001 2 0.0260 2 0.00065pz 2 0.0282 2 0.0276 0.0001 2 0.0260 2 0.0006

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Table 3Contributions to the paramagnetic term of the Cu shielding constants from the p and d atomic orbitals forTdCuI32

4 andOhCuI526 complexes

Contribution TdCuI324 RCu–I (2.62 A) TdCuI32

4 RCu–I (2.65 A) OhCuI256 RCu–I (3.04 A) Td\CuI32

4 RCu–I (2.73 A) OhCuI256 RCu–I (3.10 A)

d-contribution (2a2/3Ed) unit 2 2.189 2 1.950 2 0.257 2 1.278 2 0.257p-contribution (2a2/3Ep) unit 2 0.231 2 0.220 2 0.106 2 0.189 2 0.094

Gaussian 94 program with the double-z basis set.Although the observed results are steepest slope tothe theoretical line, we think the high-field shift ofthe signals with temperature is due partially to theCu–I bond length. As indicated in previous studies[11–13], the high-field shifts are considered to dependupon the coordination structures of metal complexes:The tetrahedral metal complexes are at a lower fieldwith octahedral metal complexes at a higher field.Then, the observed Cu high-field shifts result fromCu ion at the octahedral interstitial site in the zinc-blende structure as considered by the calculatedshielding constants of theOhCuI52

6 complex at thesame interstitial position in Table 1. In the table, theCu chemical shielding constants are explained mainlyby the paramagnetic term.

In Table 2, we summarized the change in valenceatomic orbital densities of the Cu ions and I forTdCuI32

4 and octahedral CuI526 complexes. The

change of the density was evaluated relative to densi-ties of each atomic orbital in the neutral atom. In the

table, the density increases in the 4s and 4p AOs of Cuatoms and the density decreases in the s and p AOs ofiodine atoms indicate electron transfers from theiodines to Cu atoms. Back donations to iodines alsoproduce holes in the 3d orbitals of the Cu atom coin-cident with the bonding axes of Cu iodide complexes.

As reported earlier for solution109Ag and 63CuNMR studies [11–13], the chemical shifts ofcopper–iodide complexes can be governed by theparamagnetic term. This will be explained by thefollowing equation for63Cu chemical shieldings:

spara� �22a2=3��k1=r3lpPe

T=Ep�1 �k1=r3ld3DhT=Ed��;�2�

wherePeT andDh

T are the total densities of the p elec-trons and d holes, respectively.

Contributions to the paramagnetic term for Cushieldings can be estimated from EP,d and k1/r3lp,d asparameters in Eq. (1). We assume thatEp 6 Ed;

k1=r3l4p � 0:59 a:u: and k1=r3l3d � 5:00 for Cu (the


Fig. 5. 63Cu NMR chemical shifts of AgxCu12xI �x� 0; 0:1; 0:3;0:5� in the temperature range of 100–523 K.

terms are obtained from the SCF functions byClementi and coworkers [14]). Thus, we showed thecontributions to the paramagnetic shielding constantsof the Cu for TdCuI32

4 and OhCuI526 complexes in

Table 3. From the table, we see that for the Cucomplexes the d contributions are larger than the pcontributions.

4.2.2. Analysis of the nonlinear temperaturedependence of Cu chemical shielding

For the four types of AgxCu12xI solid-solution crys-tals �x� 0;0:1;0:3; 0:5�; we plotted the peak of eachspectrum as the shifted value in Fig. 5. It can be seenin the figure that the temperature dependence of thechemical shifts for each solid-solution crystal haslinear and nonlinear parts in the temperature rangesof 100–350 and 350–500 K, respectively. In the caseof the linear dependence, we propose the high-fieldshift of the signals is due partially to the Cu–I bondlength with temperature, although in theg phase ofCuI the increase of vibrational overlap with tempera-ture was shown to be responsible for experimental Cuhigh field shifts as interpreted in the framework of asimple tight binding description of chemical bonding[4]. For the nonlinear part, the spectra seem to corre-spond to asymmetrical and more narrow spectraabove 398 K, as seen in Fig. 3. The asymmetricalspectrum results from local AgI lattice units in thesolid-solution: The spectrum in NMR depend on thecation disorder which occurs with the fact that a partof the tetrahedral cations move to the octahedral inter-stitial site, as indicated in Section 4.2.1.

In order to explain the nonlinear temperaturedependence of chemical shifts for AgxCu12xI �x�0:1;0:3; 0:5�; we use the shift model as proposed by

Negita and co-workers [15];

sCu�T� � s0�T�1 �srtr 1 sttt�=�tr 1 tt�� s0�T�1 sr 1 �st 2 sr �tt=�tr 1 tt�; �3�

wheres0�T� denotes the chemical shielding constantof the linear temperature dependence in the limit, ands r, and s t correspond to the chemical shieldingconstants in the respective equilibrium migrationswhen the average resident time of movement for Cunuclei from tetrahedral sites to octahedral interstitialpositions ist r, and in the jumping of Cu nucleus whenthe time for a single migration is given ast t, respec-tively. We can assume the timet r varies withtemperature astr � t0 exp�Ea=RT�; where Ea is theactivation energy for migrations of cations, andt0

means the resident time at infinite temperature. Thetime t r is considered to be the similar value to thecorrelation timet c as obtained from measurementsof the Cu spin–lattice relaxation. Thet t varies withtemperature, while we can assumet t is a constantsince the temperature dependence is considerablyweak.

Let us analyze the temperature dependence ofAgxCu12xI �x� 0:1;0:3; 0:5� using the model of Eq.(3). In the first step, we will consider a linear tem-perature dependence of chemical shieldings,sCu(T),as �s0�T�1 sr � a 1 bT� below 350 K. For theexperimental results of AgxCu12xI �x� 0:1;0:3;0:5�in Fig. 5, we obtain the slope b��20:22;20:26;20:25 ppm=K� and the shieldingvalue of intersection at 0 K,a� �41;36; 27 ppm�;respectively. Then, we performed the curve-fittingfor the nonlinear temperature dependence of theshieldings withtt=t0; andDs � st 2 sr as parametersusing knownEa in Eq. (3). In the equation, we used thevalues of Ea at the initial states as 50 kJ/mol forAgxCu12xI �x� 0:1;0:3;0:5� solid-solutions asobtained from the temperature dependence of the Cuspin–lattice relaxation time. The parameters wereobtained in Table 4.

In Fig.5, the curves as simulated with solid lines arein good agreement with the experimental results. It isinteresting that when the value oft0 is estimated asthe order of 10215 s using the Bloembergen–Purcell–Pounds (BPP) equation for temperature dependenceof Cu spin–lattice relaxation rates of AgxCu12xI �x�0:1; 0:3�; we can obtain the order of 10210 , 1028 s for


Table 4Dynamic parameters as obtained by analyzing the temperaturedependence of Cu chemical shielding constants using Eq. (3)

Eaa (kJ/mol) t t/t0 st 2 sr (ppm)

Ag0.1Cu0.9I 50 7:1 × 106 20Ag0.3Cu0.7I 50 1:5 × 107 43Ag0.5Cu0.5I 49 2:0 × 107 40

a Values at the initial state were obtained from the temperaturedependence of Cu spin–lattice relaxation time.

the time of single migration (t t) for Cu ion from tetra-hedral to octahedral interstitial sites.

5. Conclusion

We investigated local atomic structures of mixedcrystal AgxCu12xI �0 , x , 0:5� in the temperaturerange of 150–520 and 300–750 K by63Cu NMRand X-ray diffraction methods, respectively. Fromthe X-ray diffraction method, the lattice constantsincrease gradually a little with the temperature, exceptfor the range of theg-to-a 0 phase transition. On thecontrary, the chemical shifts in NMR experimentsshow a linear dependence of temperature to thehigh-field in the lower range of about 150–350 K,and the shift increases nonlinearly with the highertemperature (350–500 K). The high-field shiftsabove 350 K seem to depend on the cation disorderwhich occurs with the fact that a part of the tetrahedralcations move to the qausi-stable interstitial octahedralsites. The observed high-field shifts are explained byCu chemical shielding calculations ofTdCuI32

4 andOhCuI52

6 species, as obtained by the finite perturba-tion theory in an ab initioGaussian 94 program usingthe double-z basis set for Cu and I atoms. In the caseof the nonlinear temperature dependence of the shift,we introduced the shift model as proposed by Negitaand coworkers: The shift is also due to the cationwhich moves to the qausi-stable interstitial octahedralsites.

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structural analysis of agxcu1−xi (0≤x≤0.5) by solid 63cu nmr and x-ray diffraction methods

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