Crystal structures of η′′-Cu_3+xSi and η′′′-Cu_3+xSi

The binary phase diagram of Cu–Si is unexpectedly complex in the vicinity of Cu_3+xSi. The low-temperature region contains three closely related incommensurately modulated phases denoted, in order of increasing temperature of stability, η′′′, η′′ and η′. The structure analysis of η′ has been reported previously [Palatinus et al. (2011). Inorg. Chem. 50, 3743]. Here the structure model for the phases η′′ and η′′′ is reported. The structures could be solved in superspace, but no superspace structure model could be constructed due to the complexity of the modulation functions. Therefore, the structures were described in a supercell approximation, which involved a 4 × 4 × 3 supercell for the η′′ phase and a 14 × 14 × 3 supercell for the η′′′ phase. Both structures are very similar and differ only by a subtle symmetry lowering from η′′ to η′′′. A comparison of the structure models of η′′ and η′′′ with the reported structure of η′ suggests that the reported structure model of η′ contains an incorrect assignment of atomic types.

Computing details

For both structures, data collection: Bruker SAINT, v. 8.34A; cell refinement: Bruker SAINT, v. 8.34A; data reduction: Bruker SAINT, v. 8.34A, SADABS (Sheldrick 1996); program(s) used to solve structure: Supeflip (Palatinus and Chapuis, 2007); program(s) used to refine structure: Jana2006 (Petricek et al., 2014).

(eta1)

Crystal data

Cu3.313Si	Dx = 7.563 Mg m^−3
Mr = 238.6	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P31c	Cell parameters from 1361 reflections
Hall symbol: -P 3;-2c	θ = 5.6–28.9°
a = 16.2448 (4) Å	µ = 33.35 mm^−1
c = 44.017 (8) Å	T = 743 K
V = 10060 (2) Å^3	Irregular, metallic gray
Z = 192	0.16 × 0.13 × 0.09 mm
F(000) = 21132

Data collection

KappaCCD (Bruker-Nonius) diffractometer	624 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.240
phi–scan	θmax = 30.4°, θmin = 2.7°
Absorption correction: multi-scan SADABS (J.Appl.Cryst.48 (2015). )	h = −23→22
Tmin = 0.420, Tmax = 0.746	k = −23→23
25292 measured reflections	l = −62→61
4996 independent reflections

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.150	282 constraints
wR(F^2) = 0.159	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.35	(Δ/σ)max = 0.003
4996 reflections	Δρmax = 13.76 e Å^−3
6 parameters	Δρmin = −14.71 e Å^−3

Special details

Refinement. In reality incommensurately modulated structure. Model obtained by solution of a large supercell. Coordinates fixed to values from solution, isotropic displacement parameters refined, but fixed to be constant in each crystallographicaly independent layer. Reflections limited only to main reflections and satellites of the incommensurate structure.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Cu02001	0.330488	0.420553	0.021641	0.0264 (4)*
Cu02002	0.350199	0.147312	0.024788	0.0264 (4)*
Cu02003	0.670782	0.090332	0.023323	0.0264 (4)*
Cu02004	0.829669	0.916623	0.024926	0.0264 (4)*
Cu02005	0.552851	0.152952	0.02612	0.0264 (4)*
Cu02006	0.333333	0.666667	0.024115	0.0264 (4)*
Cu02007	0.148419	0.355504	0.027323	0.0264 (4)*
Cu02008	0.376704	0.004008	0.027971	0.0264 (4)*
Cu02009	0.15083	0.551475	0.029966	0.0264 (4)*
Cu02010	0.908029	0.081561	0.03121	0.0264 (4)*
Cu02011	0.666667	0.333333	0.030443	0.0264 (4)*
Cu03001	0	0	0.053569	0.0190 (3)*
Cu03002	0.252709	0.259815	0.054954	0.0190 (3)*
Cu03003	0.503812	0.258787	0.055481	0.0190 (3)*
Cu03004	0.266695	0.510891	0.054993	0.0190 (3)*
Cu03005	0.510899	0.002051	0.055946	0.0190 (3)*
Cu03006	0.242529	1.000112	0.056445	0.0190 (3)*
Cu04001	0.085396	0.419295	0.0794	0.0184 (4)*
Cu04002	0.329906	0.16564	0.082023	0.0184 (4)*
Cu04003	0.332862	0.418198	0.083294	0.0184 (4)*
Cu04004	0.086941	0.169049	0.085457	0.0184 (4)*
Cu04005	0.580291	0.165754	0.084993	0.0184 (4)*
Cu04006	0.333333	0.666667	0.087867	0.0184 (4)*
Cu05001	0	0	0.110209	0.0190 (3)*
Cu05002	0.242312	0.487496	0.110366	0.0190 (3)*
Cu05003	0.753774	0.243312	0.110687	0.0190 (3)*
Cu05004	0.741411	0.003101	0.111305	0.0190 (3)*
Cu05005	0.492342	0.499552	0.111525	0.0190 (3)*
Cu05006	0.26031	1.000511	0.112133	0.0190 (3)*
Cu06001	0.431454	0.088662	0.135467	0.0264 (4)*
Cu06002	0.215952	0.609382	0.13746	0.0264 (4)*
Cu06003	0.155029	0.312704	0.139101	0.0264 (4)*
Cu06004	0.610446	0.217592	0.140302	0.0264 (4)*
Cu06005	0.089034	0.42884	0.141128	0.0264 (4)*
Cu06006	0.319242	0.156851	0.142699	0.0264 (4)*
Cu06007	0.663512	0.089342	0.142678	0.0264 (4)*
Cu06008	0.335895	0.428034	0.144527	0.0264 (4)*
Cu08001	0.666667	0.333333	0.189642	0.0264 (4)*
Cu08002	0.180621	0.085933	0.189741	0.0264 (4)*
Cu08003	0.333333	0.666667	0.190937	0.0264 (4)*
Cu08004	0.410102	0.561712	0.189282	0.0264 (4)*
Cu08005	0.082127	0.172119	0.190433	0.0264 (4)*
Cu08006	0.414749	0.087143	0.192505	0.0264 (4)*
Cu08007	0.209613	0.357023	0.19302	0.0264 (4)*
Cu08008	0.596519	0.150357	0.193481	0.0264 (4)*
Cu08009	0.619849	0.996459	0.194364	0.0264 (4)*
Cu08010	0.791224	0.145781	0.196653	0.0264 (4)*
Cu08011	0.091353	0.4131	0.1986	0.0264 (4)*
Cu09001	0.252089	0.005236	0.220901	0.0190 (3)*
Cu09002	0	0	0.221725	0.0190 (3)*
Cu09003	0.508636	0.245179	0.222373	0.0190 (3)*
Cu09004	0.251688	0.509733	0.222295	0.0190 (3)*
Cu09005	0.487196	−0.000996	0.222368	0.0190 (3)*
Cu09006	0.755764	−0.002912	0.222933	0.0190 (3)*
Cu10001	0.162238	0.081119	0.25	0.0184 (4)*
Cu10002	0.166464	0.583232	0.25	0.0184 (4)*
Cu10003	0.666667	0.333333	0.25	0.0184 (4)*
Cu10004	0.167464	0.334928	0.25	0.0184 (4)*
Cu10005	0.415734	0.084171	0.253736	0.0184 (4)*
Si01001	0.247476	0.999989	0.999102	0.034 (9)*
Si01002	0.741725	0.250617	0.999076	0.034 (9)*
Si01003	0.5	0	0	0.034 (9)*
Si01004	0	0	0	0.034 (9)*
Si04001	0.417857	0.081404	0.078661	0.007 (3)*
Si04002	0.162522	0.331268	0.081425	0.007 (3)*
Si04003	0.670239	0.083253	0.084013	0.007 (3)*
Si04004	0.918313	0.081666	0.084644	0.007 (3)*
Si04005	0.167356	0.584488	0.085588	0.007 (3)*
Si04006	0.666667	0.333333	0.089863	0.007 (3)*
Si07001	0.75241	1.001434	0.166893	0.007 (3)*
Si07002	0.495708	0.00157	0.165441	0.007 (3)*
Si07003	0.253651	1.992831	0.167731	0.007 (3)*
Si07004	0.247227	0.499751	0.167169	0.007 (3)*
Si07005	0.494207	0.243647	0.165664	0.007 (3)*
Si07006	0	0	0.168619	0.007 (3)*
Si10001	0.582914	0.165828	0.25	0.034 (9)*
Si10002	0.08296	0.16592	0.25	0.034 (9)*
Si10003	0.333333	0.666667	0.25	0.034 (9)*
Si10004	0.332432	0.166216	0.25	0.034 (9)*
Si10005	0.081915	0.416604	0.254474	0.034 (9)*
Cur1a	0.004825	−0.127275	0.135	0.0264 (4)*	0.1667
Cur1/1a	0.143912	0.035854	0.135	0.0264 (4)*	0.1667
Cur1/2a	0.084117	0.149434	0.135	0.0264 (4)*	0.1667
Cur1/3a	−0.091925	0.056501	0.135	0.0264 (4)*	0.1667
Cur1/4a	−0.14093	−0.114515	0.135	0.0264 (4)*	0.1667
Cur1b	−0.004825	0.127275	0.135	0.0264 (4)*	0.1667
Cur1/1b	−0.143912	−0.035854	0.135	0.0264 (4)*	0.1667
Cur1/2b	−0.084117	−0.149434	0.135	0.0264 (4)*	0.1667
Cur1/3b	0.091925	−0.056501	0.135	0.0264 (4)*	0.1667
Cur1/4b	0.14093	0.114515	0.135	0.0264 (4)*	0.1667

(eta2)

Crystal data

Cu3.311Si	Dx = 7.519 Mg m^−3
Mr = 238.5	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3	Cell parameters from 2251 reflections
Hall symbol: -P 3	θ = 5.6–28.2°
a = 56.9800 (3) Å	µ = 33.35 mm^−1
c = 44.055 (2) Å	T = 393 K
V = 123870 (6) Å^3	Irregular, metallic gray
Z = 2352	0.16 × 0.13 × 0.09 mm
F(000) = 258780

Data collection

KappaCCD (Bruker-Nonius) diffractometer	1471 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.139
phi–scan	θmax = 29.3°, θmin = 2.0°
Absorption correction: multi-scan SADABS (J.Appl.Cryst.48 (2015). )	h = −77→77
Tmin = 0.420, Tmax = 0.746	k = −77→77
25518 measured reflections	l = −60→59
4920 independent reflections

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.119	6777 constraints
wR(F^2) = 0.137	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.93	(Δ/σ)max = 0.001
4920 reflections	Δρmax = 12.91 e Å^−3
6 parameters	Δρmin = −17.54 e Å^−3

Special details

Refinement. In reality incommensurately modulated structure. Model obtained by solution of a large supercell. Coordinates fixed to values from solution, isotropic displacement parameters refined, but fixed to be constant in each crystallographicaly independent layer. Reflections limited only to main reflections and satellites of the incommensurate structure.