Peter Schmidt

Peter Schmidt
Michigan State University | MSU · Department of Economics

About

312
Publications
63,257
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
46,291
Citations

Publications

Publications (312)
Article
Full-text available
In this work, we present a computational protocol that is able to predict the experimental absorption and emission spectral shapes of Eu2+-doped phosphors. The protocol is based on time-dependent density functional theory and operates in conjunction with an excited-state dynamics approach. It is demonstrated that across the study set consisting of...
Article
Full-text available
The oxonitridosilicate La 7 Sr[Si 10 N 19 O 3 ]:Eu 2+ and its substitutional variants RE 8− x AE x [Si 10 N 20− x O 2+ x ]:Eu 2+ with RE = La, Ce; AE = Ca, Sr, Ba and 0 ≤ x ≤ 2 were synthesized starting from RE N, SrN/Ca 3 N 2 /Ba 2 N, SiO 2 , amorphous Si 3 N 4 and Eu 2 O 3 as doping agent at 1600°C in a radiofrequency furnace. The crystal structu...
Article
Full-text available
The nitridoberylloaluminate Ba 2 [BeAl 3 N 5 ]:Eu 2+ and solid solutions Sr 2- x Ba x [BeAl 3 N 5 ]:Eu 2+ ( x = 0.5, 1.0, 1.5) were synthesized in a hot isostatic press (HIP) under 50 MPa N 2 atmosphere at 1200 °C. Ba 2 [BeAl 3 N 5 ]:Eu 2+ crystallizes in triclinic space group (no. 2) ( Z = 2, a = 6.1869(10), b = 7.1736(13), c = 8.0391(14) Å, α = 1...
Article
Full-text available
We present the first nitridic analogs of micas, namely AE Si 3 P 4 N 10 (NH) 2 ( AE = Mg, Mg 0.94 Ca 0.06 , Ca, Sr), which were synthesized under high-pressure high-temperature conditions at 1400 °C and 8 GPa from the refractory nitrides P 3 N 5 and Si 3 N 4 , the respective alkaline earth amides, implementing NH 4 F as a mineralizer. The crystal s...
Article
We present the first nitridic analogs of micas, namely AE Si 3 P 4 N 10 (NH) 2 ( AE = Mg, Mg 0.94 Ca 0.06 , Ca, Sr), which were synthesized under high-pressure high-temperature conditions at 1400 °C and 8 GPa from the refractory nitrides P 3 N 5 and Si 3 N 4 , the respective alkaline earth amides, implementing NH 4 F as a mineralizer. The crystal s...
Article
Full-text available
The nitridosilicate CaLu[Si 4 N 7−2 x C x O x ] ( x ≈ 0.3) was synthesized by carbothermal reduction and nitridation starting from CaH 2 , Lu 2 O 3 , graphite and amorphous Si 3 N 4 at 1550°C using a radiofrequency furnace. CaLu[Si 4 N 7−2 x C x O x ] ( x ≈ 0.3) crystallizes isotypic to many previously known M II M III Si 4 N 7 compounds in space g...
Article
Full-text available
In this paper, we consider various methods for evaluating the cdf of the Skew Normal distribution. This distribution arises in the stochastic frontier model because it is the distribution of the composed error, which is the sum (or difference) of a Normal and a Half-Normal random variable. The cdf must be evaluated in models in which the composed e...
Article
Full-text available
This paper makes two contributions. The first is to propose a new family of copulas for which the copula arguments are uncorrelated but dependent. Specifically, if w1 and w2 are the uniform random variables in the copula, they are uncorrelated, but w1 is correlated with |w2 − 1/2|. We show how this family of copulas can be applied to the error stru...
Article
Full-text available
This paper proposes a stochastic frontier model with three composed errors, and therefore six error components. As in the metafrontier literature, firms belong to groups with a group-specific frontier. A firm has a level of short-run and long-run inefficiency relative to its group-specific frontier, as in existing models with two composed errors an...
Chapter
Copulas are used to create joint distributions with specified marginal distributions. The copula models the dependence between the corresponding marginal random variables. In the normal case, the multivariate normal distribution is a natural choice of joint distribution with normal marginals and its covariance matrix parameterizes the dependence be...
Article
Full-text available
Recently introduced nitridophosphate synthesis in a hot isostatic press (HIP) enabled simple access to large‐scale product quantities starting from exclusively commercially available starting materials. Within this work, we show that this method is suitable for the synthesis of highly‐condensed functional nitridophosphates, as well. Hence, the synt...
Article
Full-text available
Nitridophosphate zeolites AE3P5N10X (AE=Sr, Ba; X=Cl, Br) were synthesized under medium‐pressure conditions (150 MPa N2, 1200 °C), extending the range of the degree of condensation for nitridophosphates accessible by hot isostatic pressing from κ=1/3 to 1/2. AE3P5N10X:Eu²⁺ (AE=Sr, Ba; X=Cl, Br) reveals natural‐white to deep‐red emission. Abstract...
Article
The nitridoberylloaluminate Sr2[BeAl3N5]:Eu2+ was obtained through reaction of the binary nitrides in a hot isostatic press under a pressure of 50 MPa N2 and a temperature of 1400 °C. The crystal structure was solved and refined from single-crystal X-ray diffraction data (P1 ̅ (no. 2), Z = 2, a = 6.061(2), b = 6.982(3), c = 7.872(4) Å and α = 102.2...
Article
Full-text available
(Oxo)Nitridophosphates have recently been identified as a promising compound class for application in the field of solid‐state lighting. Especially, the latest medium‐pressure syntheses under ammonothermal conditions draw attention of the semi‐conductor and lighting industry on nitridophosphates. In this contribution, we introduce hot isostatic pre...
Article
Full-text available
Hot isostatic pressing is introduced as easy and fast synthetic access to nitridophosphate phosphors, while providing large‐scale quantities. In particular, the calcium nitridophosphate Ca2PN3:Eu²⁺ was synthesized under medium‐pressure conditions (150 MPa N2, 1200 °C), revealing single crystals with remarkable size (>100 μm) and quality. Further, C...
Article
Full-text available
A well-known result due to Waldman (J Econom 18:275–279, 1982) states that, in the standard normal/half-normal SFA model, estimated technical inefficiency will be zero if the OLS residuals are positively skewed. It is not clear how much this result generalizes. In this paper, we consider the normal/half-normal model in which the distribution of the...
Article
Full-text available
The nitridophosphates AE P 8 N 14 ( AE = Ca, Sr, Ba) were synthesized at 4−5 GPa and 1050−1150 °C applying a 1000 t press with multianvil apparatus, following the azide route. The crystal structures of CaP 8 N 14 and SrP 8 N 14 are isotypic. The space group Cmcm was confirmed by powder X‐ray diffraction. The structure of BaP 8 N 14 (space group Amm...
Article
Full-text available
Nitridophosphates exhibit an intriguing structural diversity with different structural motifs, e.g. chains, layers or frameworks. In this contribution we present the novel nitridophosphate Sr 3 P 3 N 7 with unprecedented dreier double chains. Crystalline powders were synthesized using the ammonothermal method, while single crystals were obtained by...
Article
The ortho‐oxonitridophosphate Ba2PO3N was synthesized under ammonobasic conditions (T = 1070 K, p = 120 MPa) in custom‐built high‐temperature autoclaves, starting from red phosphorus, BaO, NaN3 and KOH. Thus, single crystals of up to several hundred µm were obtained, which were used for single‐crystal X‐ray diffraction. Ba2PO3N [Pnma (no. 62), a =...
Article
Full-text available
Barium imidonitridophosphate BaP6N10NH was synthesized at 5 GPa and 1000 °C with a high‐pressure high‐temperature approach using the multianvil technique. Ba(N3)2, P3N5 and NH4Cl were used as starting materials, applying a combination of azide and mineralizer routes. The structure elucidation of BaP6N10NH (P63, a = 7.5633(11), c = 8.512(2) Å, Z = 2...
Preprint
\beta$-Si$_{6-z}$Al$_{z}$O$_{z}$N$_{8-z}$ is a prominent example of systems suitable as hosts for creating materials for light-emitting diodes. In this work, the electronic structure of a series of ordered and disordered $\beta$-Si$_{6-z}$Al$_{z}$O$_{z}$N$_{8-z}$ systems is investigated by means of ab initio calculations, using the FLAPW and the Gr...
Article
Full-text available
In the stochastic frontier model, the composed error is the sum (or difference) of a normal and a half normal random variable. Often the composed error is linked to other errors using a copula, and evaluation of the copula requires evaluation of the cdf of the composed error. There is no analytical expression for this cdf, though there are several...
Article
The oxonitridosilicates RE6−xCa1.5xSi11N20O (RE = Yb, Lu; x ≈ 2.2) were synthesized starting from REF3, CaH2, and “Si(NH)2” in a radiofrequency furnace at 1600 or 1400 °C, respectively. The crystal structure was solved and refined from single‐crystal X‐ray diffraction data of dark red Yb6−xCa1.5xSi11N20O crystals in the trigonal space group P31c (n...
Article
Recently, a number of different structurally related nitrides characterized by pairs of edge‐sharing Si-N tetrahedra forming [Si2N6]10- units, have emerged via different synthesis methods. Concurrently, upon doping with rare earth elements (e.g. Eu2+ and Ce3+) numerous applications in the field of luminescent materials were revealed, ranging from t...
Article
In this paper we consider a panel data model with individual effects that are arbitrarily correlated with the explanatory variables. The effects are composed as the sum of two different interpretable components, such as inefficiency versus heterogeneity in a production frontier setting, or ability versus socioeconomic background in an earnings func...
Article
The isotypic nitridoberyllates MBe20N14 with M = Sr, Eu, Ba have been synthesized at high temperatures under N2-atmosphere. The crystal structures were solved and refined from single-crystal X-ray diffraction data (I4/m (no. 87), Z = 2, SrBe20N14:Eu2+, a = 6.525(2), c = 12.133(4) Å; EuBe20N14, a = 6.524(8), c = 12.136(2) Å; BaBe20N14:Eu2+ a = 6.540...
Article
We report on the structure and properties of the lithium oxonitridosilicate oxide Li4Sr4[Si4O4N6]O:Eu2+ obtained from solid-state metathesis. The crystal structure was solved and refined from single-crystal X-ray data in the space group P42/ nmc (No. 137) [ Z = 2, a = 7.4833(6), c = 9.8365(9) Å, and R1(obs) = 0.0477]. The structure of Li4Sr4[Si4O4N...
Article
Narrow-band red emitting luminescent CaBa[Li2Al6N8]:Eu2+ for potential application in illumination grade white light emitting diodes (WLEDs) was synthesized by reaction of the metal hydrides and nitrides in molybdenum crucibles in a hot isostatic press. Upon irradiation with high-energy visible light (444 nm), the material exhibits intense red and...
Article
The oxonitridocarbidosilicates RE4Ba2[Si12O2N16C3]:Eu2+ ( RE = Lu, Y) were synthesized by carbothermal reactions starting from RE2O3, graphite, Ba2Si5N8, Si(NH)2, and Eu2O3. The crystal structure of Lu4Ba2[Si12O2N16C3]:Eu2+ was elucidated on a submicron-sized single crystal by a combination of transmission electron microscopy and microfocused synch...
Article
Ce3+ doped solids find broad application, e.g. in phosphor converted light emitting diodes (pcLEDs), utilizing the usually broad blue to yellow-orange emission of the respective phosphors. The red to infrared spectral range was not yet accessible with the activator Ce3+, even in nitride host materials. Here we report on the nitridolithosilicates Li...
Article
Beryllate structures are marginally investigated, but show intriguing structural relations to oxo‐ and nitridosilicates. A typical feature is the coordination of Be both in trigonal planar and tetrahedral coordination by O. A broad range of structures is accessible by variable combinations of both building units. Three novel ternary Sr‐oxoberyllate...
Article
Highly efficient phosphor‐converted light‐emitting diodes (pc‐LEDs) are popular in lighting and high‐tech electronics applications. The main goals of present LED research are increasing light quality, preserving color point stability and reducing energy consumption. For those purposes excellent phosphors in all spectral regions are required. Here,...
Article
Highly efficient phosphor‐converted light‐emitting diodes (pc‐LEDs) are popular in lighting and high‐tech electronics applications. The main goals of present LED research are increasing light quality, preserving color point stability and reducing energy consumption. For those purposes excellent phosphors in all spectral regions are required. Here,...
Article
The nitridosilicate La3−xCa1.5xSi6N11:Eu2+ (x ≈ 0.77) was synthesized in a radiofrequency furnace starting from LaF3, La(NH2)3, CaH2, Si(NH)2, and EuF3. The crystal structure was solved and refined from single-crystal X-ray data in the tetragonal space group P4bm (no. 100) with a = 10.1142(6), c = 4.8988(3) Å, and Z = 2. Thereby, the so far unknown...
Article
Oxo- and (oxo)nitridoberyllates show exceptional potential as host lattices for application in illumination grade phosphor converted (pc)LEDs due to their remarkable electronic and structural characteristics, allowing highly efficient narrow-band emission upon doping with Eu2+. Sr[Be6ON4]:Eu2+, the first example of an oxonitridoberyllate phosphor,...
Article
Red-emitting phosphors with the general sum formula Sr8[Li(2−0.5x)MgxAl(22−0.5x)N28]:Eu2+ for application in warm-white illumination grade light emitting diodes were obtained by reacting the metals, hydrides and nitrides in molybdenum crucibles in a hot isostatic press. Upon irradiation with blue light (440 nm) the materials exhibit red luminescenc...
Article
The oxonitridosilicate oxides RE26Ba6[Si22O19N36]O16:Eu²⁺ (RE = Y, Tb) were synthesized in high-temperature solid-state reactions. The compounds crystallize in a new structure type with intriguing silicate layers. The crystal structure solution is based on single-crystal X-ray data and supported by PXRD and EDX data. The optical properties of Y26Ba...
Article
The oxonitridosilicate oxides Y4Ba2[Si9ON16]O:Eu2+ and Lu4Ba2[Si9ON16]O:Eu2+ have been synthesized starting from REF3, RE2O3 (RE = Y, Lu), BaH2, Si(NH)2 and EuF3 in a radiofrequency furnace at 1550 °C. The crystal structures were solved and refined from single-crystal X-ray data supported with Rietveld refinement on X-ray powder diffraction data. B...
Article
Highly efficient narrow-band red emitting phosphors are the most desired and requested materials for developing illumination grade phosphor-converted light emitting diodes (LEDs). This study presents direct measurements of RE energy levels, critical to the color and efficiency of LED-phosphors. For the first time, we experimentally determine the en...
Article
A large band gap is a prerequisite for efficient emissions from a rare earth doped phosphor and is consequently a prerequisite for its application in high-quality lighting. We present a detailed characterization of luminescent materials Li2Ca2[Mg2Si2N6]:Eu2+ and Ba[Li2(Al2Si2)N6]:Eu2+ using soft X-ray spectroscopy and density functional theory calc...
Article
This paper considers a stochastic frontier model that contains environmental variables that affect the level of inefficiency but not the frontier. The model contains statistical noise, potentially endogenous regressors, and technical inefficiency that follows the scaling property, in the sense that it is the product of a basic (half-normal) ineffic...
Article
Increasing the luminance of white LEDs to the 200 Mnit level and beyond, opens a completely new design space for a wide range of lighting applications, by allowing significant reductions in optics and luminaire size as well as costs. Moreover, new applications, such as dynamic beam steering, are enabled by the ability to create arrays of densely pa...
Article
The nitridomagnesosilicates Li2Ca2[Mg2Si2N6]:Eu2+ and Li2(Ca1.88Sr0.12)[Mg2Si2N6]:Eu2+ show narrow-band red emission at 638 nm and 634 nm, respectively, with emission band width of 62 nm (~1513 cm-1) after excitation in the blue spectral region. Ce3+-doped samples show luminescence in the green spectral range (λem = 540 nm). The compounds were synt...
Article
Ca18.75Li10.5 [Al39N55]:Eu2+ (0.5 mol%) is prepared by hot pressing of stoichiometric amounts of Li3N, CaH2, AlN, and EuF3 (Mo-lined corundum crucibles in an isostatic press, 51.7 MPa N2, 1250 °C, 5 h).
Article
Droop, the decrease of efficiency with increased power density, became a major topic with InGaN LEDs, after its introduction in 2007. This paper provides insight into droop in localized center luminescence phosphors, exemplified here by Eu2+ doped materials. This topic is of increasing importance, as high brightness blue LEDs have reached outputs >...
Article
Highly efficient red-emitting luminescent materials deliver the foundation for next-generation illumination-grade white light emitting diodes (LEDs). Recent studies demonstrate that the hardly explored class of nitridoaluminates comprises intriguing phosphor materials, e. g. Sr[LiAl3N4]:Eu2+ or Ca[LiAl3N4]:Eu2+. Here we describe the novel material...
Article
This article is a set of comments on “Meritocracy Voting: Measuring the Unmeasurable” by Peter C. B. Phillips.
Article
In this study the band gap and electronic structure of the next-generation, red phosphor Sr[Mg3SiN4]:Eu2+ (SMS) are explored through a combination of soft X-ray spectroscopy, density functional theory calculations, and thermal quenching data for the Eu2+ 5d→4f emissions. The results will be compared to those for the high-efficiency phosphor Sr[LiAl...
Article
Eu2+- as well as Ce3+-doped Ba[Li2(Al2Si2)N6] and its related Mg-substituted compounds Ba[(Mg2-xLix) (Al4-xSix)N6]:Eu2+ (x = 0-2) with x = 1.6, 1.8 have been synthesized by metathesis reactions in tantalum ampules. Crystal structures were solved and refined from single-crystal X-ray diffraction data. All three compounds crystallize in tetragonal sp...
Article
The isotypic nitridophosphates Ba3P5N10X (X = Cl, I) have been synthesized by high-temperature reaction under pressures between 1 and 5 GPa. The crystal structures of both compounds were solved and refined using single-crystal X-ray diffraction data. Accuracy of the structure determination as well as phase purity of the products were confirmed by R...
Article
Nitridophosphates MP2N4:Eu2+ (M=Ca, Sr, Ba) and BaSr2P6N12:Eu2+ have been synthesized at elevated pressures and 1100-1300 °C starting from the corresponding azides and P3N5 with EuCl2 as dopant. Addition of NH4Cl as mineralizer allowed for the growth of single crystals. This led to the successful structure elucidation of a highly condensed nitridop...
Article
Due to the relationship between structure and luminescence properties, detailed crystal structure determination for microcrystalline phosphors is necessary for a profound understanding of materials properties. The yellow phosphor La3BaSi5N9O2:Ce3+ (λmax = 578 nm; fwhm ~ 4700 cm-1) was characterized by a combination of transmission electron microsco...
Article
Stochastic frontier models are typically estimated by maximum likelihood (MLE) or corrected ordinary least squares. The consistency of either estimator depends on exogeneity of the explanatory variables (inputs, in the production frontier setting). We will investigate the case that one or more of the inputs is endogenous, in the simultaneous equati...
Article
Ba[Mg3SiN4]:Eux (x = 0.005-0.025) is prepared by a solid state metathesis reaction of BaF2, Mg3N2, Si(NH)2, LiN3 as N source, Li as flux, and EuF3 as dopant (Ta tube in evacuated silica tube, 1050 °C, 24 h; cooling to 500 °C within 250 h).
Article
Nitridophosphates MP2 N4 :Eu(2+) (M=Ca, Sr, Ba) and BaSr2 P6 N12 :Eu(2+) have been synthesized at elevated pressures and 1100-1300 °C starting from the corresponding azides and P3 N5 with EuCl2 as dopant. Addition of NH4 Cl as mineralizer allowed for the growth of single crystals. This led to the successful structure elucidation of a highly condens...
Article
This paper proposes a test of the null of integer integration against the alternative of fractional integration. The null of integer integration is satisfied if the series is either or . We reject the null if the KPSS test rejects and a unit root test rejects . We suggest a new unit root test (a lower-tail KPSS test applied to the differenced data)...
Article
The nitridomagnesosilicate Ba[Mg3SiN4] has been synthesized in an arc welded Ta ampule. The crystal structure was solved and refined from single crystal X ray data and Rietveld refinement on the basis of powder X ray diffraction data, revealing a distorted triclinic variant of the UCr4C4 structure type (space group P‾1 (no. 2), Z = 1, a = 3.451(1),...
Article
The isotypic nitridomagnesoaluminates M[Mg2Al2N4] (M = Ca,Sr, Ba,Eu) as well as a novel nitridomagnesogallate Ba[Mg2Ga2N4] have been synthesized by high-temperature reactions in arc-welded tantalum ampules. The crystal structures were solved and refined using single-crystal X-ray diffraction or powder X-ray diffraction data, respectively. All compo...
Article
Außergewöhnlich schmalbandig emittierende rote Leuchtstoffe auf Nitridbasis bilden die Grundlage für eine neue Generation noch effizienterer Leuchtdioden.
Article
Ca[LiAl3N4]:Eu2+ is prepared by firing a mixture of Ca, LiAlH4, LiN3, AlF3, and 5 mol% EuF3 (Ta ampules, 1000 °C, 4.5 h).
Article
Full-text available
In this paper we consider a stochastic frontier model in which the distribution of technical inefficiency is truncated normal. In standard notation, technical inefficiency u is distributed as N +(μ, σ 2). This distribution is affected by some environmental variables z that may or may not affect the level of the frontier but that do affect the short...
Article
In this paper we consider a fixed-effects stochastic frontier model. That is, we have panel data, fixed individual (firm) effects, and the usual stochastic frontier analysis (SFA) composed error. Maximum likelihood estimation (MLE) of this model has been considered by and . It is subject to the “incidental parameters problem”, that is, to possible...
Article
To facilitate the next generation of high-power white-light-emitting diodes (white LEDs), the discovery of more efficient red-emitting phosphor materials is essential. In this regard, the hardly explored compound class of nitridoaluminates affords a new material with superior luminescence properties. Doped with Eu(2+), Sr[LiAl3N4] emerged as a new...
Article
Ca[LiAl3N4]:Eu2+ is an intriguing new narrow-band red-emitting phosphor material with potential for application in high-power phosphor-converted light-emitting diodes (pc-LEDs). With excitation by blue InGaN-based LEDs, the compound exhibits an emission maximum at 668 nm with a full width at half maximum of only 1333 cm–1 (60 nm). Ca[LiAl3N4]:Eu2+...
Article
The isotypic compounds M[Mg3SiN4] (M = Ca,Sr,Eu) have been synthesized by solid-state reactions in sealed tantalum ampules or in a radio-frequency furnace. The nitridomagnesosilicates crystallize in space group I41/a (No. 88). Crystal structures were solved and refined from single-crystal X-ray diffraction data (Z = 16, Ca[Mg3SiN4]:Ce3+, a = 11.424...
Article
The isotypic nitridomagnesoaluminates M[Mg2Al2N4] (M = Ca,Sr, Ba,Eu) as well as a novel nitridomagnesogallate Ba[Mg2Ga2N4] have been synthesized by high-temperature reactions in arc-welded tantalum ampules. The crystal structures were solved and refined using single-crystal X-ray diffraction or powder X-ray diffraction data, respectively. All compo...
Article
In this paper we consider parametric deterministic frontier models. For example, the production frontier may be linear in the inputs, and the error is purely one-sided, with a known distribution such as exponential or half-normal. The literature contains many negative results for this model. Schmidt (Rev Econ Stat 58:238–239, 1976) showed that the...