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The concentration series of nonstoichiometric crystals Ca1–xYxF2+x (x = 0.01–0.14) was obtained from a melt by directional crystallization to refine the composition of the temperature maximum on the melting curves. A precision (±9 × 10−5 Å) determination of lattice parameters of the Ca1–xYxF2+x crystals with the structure of fluorite (sp. gr. Fm-3m) was performed, and a linear equation of their concentration dependence was calculated: a(x) = 5.46385(5) + 0.1999(4) x. The distribution of yttrium along the crystals Ca1–xYxF2+x, the content of which is determined by the precision lattice parameters, is studied. The congruently melting composition x = 0.105(5) of the Ca1–xYxF2+x phase is refined by the method of directional crystallization.

A specialized empirical (Spec-zd Emp) system of ionic radii (SIR) for R = Y3+, La3+, Ln3+, and F1− (R rare earth elements (REE)) was derived from the dependence of lanthanide contraction (LC) on the atomic number (Z) of lanthanides (Ln). LC decreased the radius of the cation with increasing Z. The structures of t-RF3 (LaF3-NdF3, “pseudo t-SmF3”) of the LaF3 type, 11 β-LnF3 (Ln = Sm-Lu), and β-YF3 of the β-YF3 type were studied. The empirical basis of the shortest (F-F)min and (R-F)min distances was calculated from the structural data for the RF3 complete series. The dependence of (F-F)min on Z reached saturation at Z = 67 (Ho). The base F1− radius r− = 1.2539(16) Å was calculated as the arithmetic mean of five (F-F)min in LnF3 with Ln = Ho-Lu. For the LnF3 series with Ln contributions up to 75 % wt., the dependence of (Ln-F)min on Z reflected the non-uniformity of the 4f orbital filling. SIR was calculated as the difference in the empirical constants of RF3 (ionic radii of (R,Ln)3+ (r+) and F1− (r−)), the change in which was continuous over the series and did not depend on the type of structure: r+ = (ZR-F)min − ½(F-F)min (Z = 57–71). The changes in LC in the LnF3 series were described by a third-degree polynomial. LC reduced r+ by 24% (percentage relative to less) from 1.1671(16) Å (La3+) to 0.9439(17) Å (Lu3+). In the Spec-zd Emp SIR, r+ were constants that did not require corrections for a coordination number (CN). A comparison of r+ in the Spec-zd Emp SIR with other SIRs was performed.

A lanthanide contraction(LC) of 14 lanthanides (Ln) from 58Ce to 71Lu consists of the interaction of Ln nucleus with 4f-electrons. Rare earth elements (REEs—R) include Sc, Y, La, and 14 Ln. They are located in 4–6th periods of the subgroup of group III. The electronic structure divides R into short (d- Sc, Y, La) and long (14 f-elements Ce-Lu) homologous series. The most important chemical consequence of LC is the creation of a new conglomerate of 16 RF3 by mixing fluorides of d- (Y, La) and f-elements. This determines the location of YF3 among LnF3. The location of YF3 depends on the structural (formula volumes—Vform) and thermochemical (temperatures and heats of phase transformations, phase diagrams) properties. The location of YF3 between HoF3 and ErF3 was determined by Vform at a standard pressure (Pst) and temperature (Tst). The location of YF3 according to heats of phase transformations ΔHfus and ΔHtrans is in a dimorphic structural subgroup (SSGr) D (Ln = Er-Lu), but without the exact “pseudo ZY”. According to the temperatures of phase transformations (Ttrans) in LnF3 (Ln = Dy-Lu), YF3 is located in the SSGr D between ErF3 and TmF3. The ErF3-YF3 and YF3-TmF3 phase diagrams show it to be between ErF3 and TmF3. The crystals of five β-LnF3 (Ln = Ho-Lu) and β-YF3 were obtained in identical conditions and their crystal structures were studied. Vform (at Pst and Tst) with “pseudo” atomic number ZY = 67.42 was calculated from the unit cell parameters, which were defined with ±5 × 10−4 Å accuracy. It determines the location of YF3 between HoF3 and ErF3.

The formation of materials with negative thermal expansion (NTE) based on a phase transition-type mechanism (NTE-II) in 50 T–x (temperature–composition) RF3-R’F3 (R = La-Lu) systems out of 105 possible is predicted. The components of these systems are “mother” RF3 compounds (R = Pm, Sm, Eu, and Gd) with polymorphic transformations (PolTrs), which occur during heating between the main structural types of RF3: β-(β-YF3) → t-(mineral tysonite LaF3). The PolTr is characterized by a density anomaly: the formula volume (Vform) of the low-temperature modification (Vβ-) is higher than that of the high-temperature modification (Vt-) by a giant value (up to 4.7%). In RF3-R’F3 systems, isomorphic substitutions chemically modify RF3 by forming R1−xR’xF3 solid solutions (ss) based on both modifications. A two-phase composite (β-ss + t-ss) is a two-component NTE-II material with adjustable parameters. The prospects of using the material are estimated using the parameter of the average volume change (ΔV/Vav). The Vav at a fixed gross composition of a system is determined by the β-ss and t-ss decay (synthesis) curves and the temperature T. The regulation of ΔV/Vav is achieved by changing T within a “window ΔT”. The available ΔT values are determined using phase diagrams. A chemical classification (ChCl) translates the search for NTE-II materials from 15 RF3 into an array of 105 RF3-R’F3 systems. Phase diagrams are divided into 10 types of systems (TypeSs), in four of which NTE-II materials are formed. The tables of the systems that comprise these TypeSs are presented. The position of Ttrans of the PolTr on the T scale for a short quasi-system (QS) “from PmF3 to TbF3” determines the interval of the ΔTtrans offset achievable in the RF3-R’F3 systems: from −148 to 1186 ± 10 °C. NTE-II fluoride materials exceed known NTE-II materials by almost three times in this parameter. Equilibrium in RF3-R’F3 systems is established quickly. The number of qualitatively different two-component fluoride materials with the giant NTE-II can be increased by more than ten times compared to RF3 with NTE-II.

Multicomponent fluorides of rare earth elements (REEs—R) are phase transition-type negative thermal expansion (NTE-II) materials. NTE-II occurs in RF3-R′F3 systems formed by “mother” single-component dimorphic RF3 (R = Pm, Sm, Eu, and Gd) with a giant NTE-II. There are two structural types of RF3 polymorphic modifications: low-temperature β-YF3 (β−) and high-temperature LaF3 (t−). The change in a structural type is accompanied by a density anomaly: a volume of one formula unit (Vform) Vβ− >Vt−. The empirical signs of volumetric changes ΔV/V of NTE-II materials were considered. For the GdF3-TbF3 model system, an “operating-temperature window ΔT” and a two-phase composition of NTE-II materials follows from the thermodynamics of chemical systems: the phase rule and the principle of continuity. A necessary and sufficient sign of NTE-II is a combination of polymorphism and the density anomaly. Isomorphism in RF3-R′F3 systems modifies RF3 chemically by forming two-component t− and β− type R1−xR’xF3 solid solutions (ss). Between the two monovariant curves of ss decay, a two-phase area with ΔTtrans > 0 (the “window ΔT”) forms. A two-phase composite (t−ss + β−ss) is an NTE-II material. Its constituent t−ss and β−ss phases have different Vform corresponding to the selected T. According to the lever rule on a conode, Vform is calculated from the t−ss and β−ss compositions, which vary with T along two monovariant curves of ss decay. For the GdF3-TbF3 system, ΔV/V = f(T), ΔV/V = f(ΔT) and the “window ΔT” = f(x) dependencies were calculated.

The defect structure of Ba0.69La0.31F2.31 single crystals in as-grown state and after annealing at 1173 K for 336 h was studied by X-ray diffraction analysis. Both crystals belong to the CaF2 structure type (sp. gr. Fm3¯m). They have vacancies in the main anion motif and interstitial fluorine anions in Wyckoff positions 48i and 4b. Relaxation (static displacement of some main anions to Wyckoff position 32f) is observed in the annealed crystal. It was established that annealing leads to a change in the type of displacement of the main anions in Wyckoff positions 8c from dynamic to static. Displacement of La3+ cations to Wyckoff position 32f is observed in both crystals. A model of the defect structure of Ba0.69La0.31F2.31 is proposed, according to which interstitial fluorine anions and La3+ cations are aggregated into [Ba14−nLanF64+n] clusters with the cuboctahedral anionic core formed by interstitial fluorine anions in Wyckoff positions 48i. Ba2+ cations are located in the cluster in the centers of the faces, and the La3+ cations are shifted by 0.24 Å from the vertices of the cluster along the three-fold axis towards the center of the cluster. The study establishes the relationship between the defect structure of crystals and their structurally sensitive properties, and to develop approaches to their management.

The defect structure of Ba0.69La0.31F2.31 single crystals in as-grown state and after annealing at 1173 K for 336 h was studied by X-ray diffraction analysis. Both crystals belong to the CaF2 structure type (sp. gr. Fm3¯m). They have vacancies in the main anion motif and interstitial fluorine anions in Wyckoff positions 48i and 4b. Relaxation (static displacement of some main anions to Wyckoff position 32f) is observed in the annealed crystal. It was established that annealing leads to a change in the type of displacement of the main anions in Wyckoff positions 8c from dynamic to static. Displacement of La3+ cations to Wyckoff position 32f is observed in both crystals. A model of the defect structure of Ba0.69La0.31F2.31 is proposed, according to which interstitial fluorine anions and La3+ cations are aggregated into [Ba14−nLanF64+n] clusters with the cuboctahedral anionic core formed by interstitial fluorine anions in Wyckoff positions 48i. Ba2+ cations are located in the cluster in the centers of the faces, and the La3+ cations are shifted by 0.24 Å from the vertices of the cluster along the three-fold axis towards the center of the cluster. The study establishes the relationship between the defect structure of crystals and their structurally sensitive properties, and to develop approaches to their management.

A specialized empirical (Spec-zd Emp) system of ionic radii (SIR) for R = Y[sup.3+], La[sup.3+], Ln[sup.3+], and F[sup.1−] (R rare earth elements (REE)) was derived from the dependence of lanthanide contraction (LC) on the atomic number (Z) of lanthanides (Ln). LC decreased the radius of the cation with increasing Z. The structures of t-RF[sub.3] (LaF[sub.3]-NdF[sub.3], “pseudot-SmF[sub.3]”) of the LaF[sub.3] type, 11 β-LnF[sub.3] (Ln = Sm-Lu), and β-YF[sub.3] of the β-YF[sub.3] type were studied. The empirical basis of the shortest (F-F)[sub.min] and (R-F)[sub.min] distances was calculated from the structural data for the RF[sub.3] complete series. The dependence of (F-F)[sub.min] on Z reached saturation at Z = 67 (Ho). The base F[sup.1−] radius r[sub.−] = 1.2539(16) Å was calculated as the arithmetic mean of five (F-F)[sub.min] in LnF[sub.3] with Ln = Ho-Lu. For the LnF[sub.3] series with Ln contributions up to 75 % wt., the dependence of (Ln-F)[sub.min] on Z reflected the non-uniformity of the 4f orbital filling. SIR was calculated as the difference in the empirical constants of RF[sub.3] (ionic radii of (R,Ln)[sup.3+] (r[sub.+]) and F[sup.1−] (r[sub.−])), the change in which was continuous over the series and did not depend on the type of structure: r[sub.+] = ([sub.Z]R-F)[sub.min] − ½(F-F)[sub.min] (Z = 57–71). The changes in LC in the LnF[sub.3] series were described by a third-degree polynomial. LC reduced r[sub.+] by 24% (percentage relative to less) from 1.1671(16) Å (La[sup.3+]) to 0.9439(17) Å (Lu[sup.3+]). In the Spec-zd Emp SIR, r[sub.+] were constants that did not require corrections for a coordination number (CN). A comparison of r[sub.+] in the Spec-zd Emp SIR with other SIRs was performed.

A lanthanide contraction(LC) of 14 lanthanides (Ln) from [sub.58]Ce to [sub.71]Lu consists of the interaction of Ln nucleus with 4f-electrons. Rare earth elements (REEs—R) include Sc, Y, La, and 14 Ln. They are located in 4–6th periods of the subgroup of group III. The electronic structure divides R into short (d- Sc, Y, La) and long (14 f-elements Ce-Lu) homologous series. The most important chemical consequence of LC is the creation of a new conglomerate of 16 RF[sub.3] by mixing fluorides of d- (Y, La) and f-elements. This determines the location of YF[sub.3] among LnF[sub.3]. The location of YF[sub.3] depends on the structural (formula volumes—Vform) and thermochemical (temperatures and heats of phase transformations, phase diagrams) properties. The location of YF[sub.3] between HoF[sub.3] and ErF[sub.3] was determined by V[sub.form] at a standard pressure (Pst) and temperature (Tst). The location of YF[sub.3] according to heats of phase transformations ΔHfus and ΔHtrans is in a dimorphic structural subgroup (SSGr) D (Ln = Er-Lu), but without the exact “pseudo Z[sub.Y]”. According to the temperatures of phase transformations (T[sub.trans]) in LnF[sub.3] (Ln = Dy-Lu), YF[sub.3] is located in the SSGr D between ErF[sub.3] and TmF[sub.3]. The ErF[sub.3]-YF[sub.3] and YF[sub.3]-TmF[sub.3] phase diagrams show it to be between ErF[sub.3] and TmF[sub.3]. The crystals of five β-LnF[sub.3] (Ln = Ho-Lu) and β-YF[sub.3] were obtained in identical conditions and their crystal structures were studied. V[sub.form] (at P[sub.st] and T[sub.st]) with “pseudo” atomic numberZ[sub.Y] = 67.42 was calculated from the unit cell parameters, which were defined with ±5 × 10[sup.−4] Å accuracy. It determines the location of YF[sub.3] between HoF[sub.3] and ErF[sub.3].

Multicomponent fluorides of rare earth elements (REEs—R) are phase transition-type negative thermal expansion (NTE-II) materials. NTE-II occurs in RF[sub.3]-R′F[sub.3] systems formed by “mother” single-component dimorphic RF[sub.3] (R = Pm, Sm, Eu, and Gd) with a giant NTE-II. There are two structural types of RF[sub.3] polymorphic modifications: low-temperature β-YF[sub.3] (β−) and high-temperature LaF[sub.3] (t−). The change in a structural type is accompanied by a density anomaly: a volume of one formula unit (Vform) Vβ[sub.−] >Vt[sub.−]. The empirical signs of volumetric changes ΔV/V of NTE-II materials were considered. For the GdF[sub.3]-TbF[sub.3] model system, an “operating-temperature window ΔT” and a two-phase composition of NTE-II materials follows from the thermodynamics of chemical systems: the phase rule and the principle of continuity. A necessary and sufficient sign of NTE-II is a combination of polymorphism and the density anomaly. Isomorphism in RF[sub.3]-R′F[sub.3] systems modifies RF[sub.3] chemically by forming two-component t− and β− type R[sub.1−x]R’[sub.x]F[sub.3]solid solutions (ss). Between the two monovariant curves of ss decay, a two-phase area with ΔT[sub.trans] > 0 (the “window ΔT”) forms. A two-phase composite (t−ss + β−ss) is an NTE-II material. Its constituent t−ss and β−ss phases have different V[sub.form] corresponding to the selected T. According to the lever rule on a conode, V[sub.form] is calculated from the t−ss and β−ss compositions, which vary with T along two monovariant curves of ss decay. For the GdF[sub.3]-TbF[sub.3] system, ΔV/V = f(T), ΔV/V = f(ΔT) and the “window ΔT” = f(x) dependencies were calculated.