text:
Home»Donald Trump»In Kansas gubernatorial race, even Democrats tout their ties to Donald Trump
In Kansas gubernatorial race, even Democrats tout their ties to Donald Trump
Topeka, Kansas—One of the toughest gubernatorial races in the United States is going on in Kansas. Incumbent Democrats take note of her track record against Republicans who are trying to link her with President Biden.
To win re-election in a state where Donald Trump defeated Joe Biden 56% to 41% in 2020, Gov. Laura Kelly is trying to recreate the voter coalition she envisioned four years ago. She is one of her four states' Democratic governors who voted for Trump.
Leading political news from campaigns to the Capitol.
Her Republican opponent, Attorney General Derek Schmidt, is trying to urge conservatives in the state to vote for him as part of a broader rejection of Democrats.
Due to their different strategies, the two contenders mostly babbled at each other in what analysts considered a toss-up.
"There are two races going on," said Bob Beattie, a political science professor at Washburn College in Topeka. Republicans want voters to think about Joe Biden."
An Emerson College poll released in September showed Kelly leading 45% to 43%, within margin of error.
Gov. Laura Kelly, who is campaigning for re-election, has emphasized bipartisan support.
Dominic Williams of The Wall Street Journal
Kansas voters have shown their willingness to move away from the right this year. In August, a state constitutional amendment to end protections for abortion rights fell from his 59% to hers 41% support. This comes just over a month after the US Supreme Court overturned the Roe v. Wade case.
With early voting taking place last week, Kelly attended a roundtable at a National Guard base in Topeka to discuss strategies for easing the struggles of interstate military families.
"Since my first run for governor, I have focused on specific issues, such as education and infrastructure," she said after the event. "It's not that I'm ignoring national issues…but I think people in Kansas want me to focus on what I can actually control."
She has emphasized economic development projects, funding for schools, and the elimination of state sales taxes on food, which she signed into law in May after passing a Republican-controlled Congress.
Attorney General Derek Schmidt is rallying conservatives in Kansas to elect him governor.
Mr. Schmidt, who has heavily campaigned in rural areas, has tried to convince Republicans and moderates that the opposition is too liberal for a state of three million people.
"We have Democrat Joe Biden in the governor's office here," he said Friday. "It's a philosophy…against overspending, overregulation, failure to help law enforcement, and heavy-handedness in dealing with problems."
Schmidt has criticized Kelly for closing schools early in the pandemic and not cutting taxes further amid high inflation. In his ads, he supports tighter security at the Mexican border and pledges to oppose what he calls the transgender agenda.
He campaigned with Florida Republican Gov. Ron DeSantis and posted a video showing his support from Trump.
Kelly has touted bipartisan support, including two former Republican governors. One of her in her campaign ads shows her meeting with Trump when he was president.
Others have her standing in the middle of the driveway, sipping coffee in the middle of the diner counter, declaring, "The middle is the best place."
Mr. Schmidt is trying to connect Mr. Kerry to Mr. Biden, but he is also trying to connect Mr. Kelly with former Republican Governor Sam Brownback, who stepped down as one of the nation's least popular governors in 2018.
In Johnson County, the state's most populous county, which includes the politically competitive Kansas City suburb, several registered Republicans said they voted for Kelly.
Governor Kelly and Schmidt shake hands before a debate in Overland Park, Kansas.
Ebert Nelson/Associated Press
"She had to negotiate to get people together. I think that's a great skill," said former federal manager Charles Bartlow. "All my life I've been looking for someone who was a patriot."
Some Kerry supporters cited Mr. Brownback's tax cut budget cuts as something they didn't want to revisit.
Mike Mann, manager of a restaurant company in the city of Lawrence, home to the University of Kansas, of just under 100,000 people, said he voted for Schmidt because of the economy and because he thought Kelly should vote. said. We lifted pandemic restrictions to schools sooner.
Some voters said they supported Mr. Schmidt simply by being against abortion. "I like the governor, but I don't like her stance on abortion, otherwise I would have voted for her," said William Sherrill, Lawrence's nurse. 's wife, Regina Sherrill, said the results of the August poll gave the couple more motivation to vote in this election.
share thoughts
What do you think the outcome of the Kansas gubernatorial election will be? Join the conversation below.
The outcome of the election could hinge on how many votes are cast for Dennis Pyle, an independent state senator who is considered one of Kansas' most conservative legislators. He has his 3% support in the Emerson poll, which could reduce right-wing support for Mr. Schmidt.
Pyle told the nonprofit Kansas Reflector in August that both Kelly and Schmidt were too liberal, calling them "two beans in a pod."
write destination Elizabeth Findell (Elizabeth.Findell@wsj.com)
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text:
Q: KnockoutJS data-bind setter Having a problem with HTML data-bind setter. I want it to set to model(exerciseCategories) intervals value.
If I bind to intervals from model it is the right value but is not observable.
If I bind it to $parent.intervals it is default value (1) from viewModel but it is observable.
I want both :). What am I doing wrong?
Something like this does work but displays [object Object]:

   <input data-bind='value: $parent.intervals(intervals)' />

What I've got is - HTML
            ...

                <select data-bind='options: exerciseCategories , optionsText: "category", optionsCaption: "Izberite...", value: exerciseType'></select>

                <select data-bind='options: exercises, optionsText: "title", optionsCaption: "Izberite...", value: $parent.exercise'></select>

                    <input data-bind='value: $parent.intervals' />

            ...
 JavaScript
    var exerciseCategories = [
    {
        exercises: [{
            title: 'Aerobic exercise #1',
            intervals: 2
        }],
        category: 'Aerobics'
    }];

        var Exercise = function () {
                var self = this;

                self.exerciseType = ko.observable();
                self.exercise = ko.observable();
                self.intervals = ko.observable(1);
            };

A: Doing $parent.intervals(intervals) you are invoking the intervals observable function passing intervals as a parameter, and obviously you'll receive the ko.observable object as a result.
I got your excerpt working. Take a look at this http://jsfiddle.net/MhHc4/
HTML
Categories:
<select data-bind='options: exerciseCategories , optionsText: "category", optionsCaption: "Izberite...", value: selectedCategory'></select>

selectedCategory() debug:

Exercises:
<select data-bind='options: selectedCategory() ? selectedCategory().exercises : [], optionsText: "title", value: selectedExercise'></select>

selectedExercise() debug:

<input type="text" data-bind="attr : { value : selectedExercise() ? selectedExercise().intervals : 0 }"/>

Javascript
var exerciseCategories = [{
    exercises: [{
        title: 'Aerobic exercise #1',
        intervals: 2
    }],
    category: 'Aerobics'
}];

var ExerciseViewModel = function () {
    var self = this;

    self.exerciseCategories = ko.observable(exerciseCategories);
    self.selectedCategory = ko.observable();
    self.selectedExercise = ko.observable();
    self.intervals = ko.observable(1);
};
ko.applyBindings(new ExerciseViewModel());

HTH

redpajama_set_name: RedPajamaStackExchange


text:
Agència d'Orissa (o Agència dels Estats d'Orissa) fou una entitat administrativa britànica creada el 1905 amb els Estats tributaris d'Orissa, i que va existir fins al 1933 quan es van reunir tres agències per formar l'agència dels Estats Orientals (l'agència dels Estats d'Orissa, l'agència dels Estats de Chhattisgarh i l'agència dels Estats de Bengala).

Referències
 Unió dels estats d'Orissa (pàg. 47-50)

Orissa

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text:
History of Wood & Biomass Pellets
From Sweden throughout Europe
The use of biomass pellets for energy dates back to the 1970s when alternatives to fossil fuels were sought in the wake of the energy crises of the decade. At this time, the technology used to produce animal feed pellets was modified to accommodate denser, woody materials. One of the industry's early movers was Sweden due to its prominent timber industry, desire for increased energy independence and its commitment to environmental conservation.
Wood pellet production planning in Sweden started in the late 1970s with the decision to build a pellet plant in Mora. The plant started production in November 1982 and immediately ran into problems because costs were much higher than had been calculated. Equipment was developed for converting oil boilers to pellet-fired boilers. In practically all cases, however, they were highly inefficient, not least because of the poor pellet quality. During this first year the raw material was usually bark. Pellets often had an ash content of 2.5% to 17%. The plant in Mora was closed 1986.
In 1984 a pellet plant was built in Vårgårda. The plant's last owner was the Volvo group. It was closed in 1989. In 1987 the first plant for pelletizing dried material was built in Kil. It was designed for an output of 3,000 metric tons a year. This plant is still in operation and is the oldest commercial plant in Sweden.
In the early 1990s the Swedish government came up with a proposal for taxation of mineral fuel. At this time it also limited carbon dioxide emissions. In a short time period the prospect of burning fossil fuels became unprofitable with biofuels stepping in to fill the energy void. This marked a turning point and the use of wood pellets started to grow rapidly.
Similarly ambitious clean energy programs emerged elsewhere in Europe. As a result, Europe leads the world in biomass pellet consumption to this day. The level of sophistication has risen on the continent to such an extent that manufactured pellets can be delivered in bulk via tanker trucks and deposited directly in residential storage areas, similar to the way gas stations are restocked with gasoline. In addition to residential heating, European power plants increasingly use biomass pellets to generate electricity as well as for energy in other industrial applications.
The wood pellet fuel industry became established in the mid-1980s with the introduction of the residential wood pellet stove. This appliance was capable of reducing particulate emissions well below the new requirements of the U.S.'s Environmental Protection Agency (EPA) for wood stoves and of providing consumers with a new level of automation and convenience for heating with wood. Sales of pellet stoves increased rapidly in the early 1990s, reaching a peak in 1994 before leveling off and declining somewhat due to competition with natural gas stoves.
Pellet fuel sales followed the demand curve produced by residential pellet stoves. Residential use has accounted for approximately 95% of sales during this period, the balance being industrial use.
In 1984 there were two pellet plants operating in the Pacific Northwest of the US. The majority of pellet plants are owned by small companies established specifically for that purpose. However, recently many large facilities have come online in response to rising demand in Europe, which has emerged as a key export destination for Canadian and American made pellets.
The raw material used is commonly sawdust. Shavings and chips are used to a lesser extent. The industry is a mix of stand-alone plants, whose only business is pellet production, and plants that are part of other wood-processing companies. The stand-alone firms buy their raw materials on the open market and tend to be larger producers. The add-on operations usually process only the residues generated by the company's wood processing activities.
The wood pellet industry has a history of slow plant start-ups. Many plants have required six to eighteen months after starting to normalize operations. The long start- up periods were due to a variety of factors including: variations in raw materials, inadequate design and engineering, use of worn-out or improperly sized equipment and inexperience on the part of management and production workers. Nonetheless, conditions continue to improve as the industry matures, firms more extensively research the process before entering the business, improved equipment, better overall plant design and installation by equipment/engineering firms, and the information and assistance provided by other pellet producers.
In addition to large production facilities, individuals—particularly in rural areas—have found it beneficial to produce their own pellets using small-scale machinery. These practical, often mobile pellet presses confer a certain level of energy self-reliance to the user as well as a means to derive economic benefit from readily available waste materials.
We are glad to inform you that the machines in our company are produced according to countries or areas.
In order to provide better service and products with you,it's our honor to have the below info about you.
1,Where will your Project Build?
2,How much your Budget?
3,What is your Raw materials___? their size length___width___Thickness___and mositure percent___?
4,Do you need only the Pellet Mill or a Complete Pellet Production lines?
5,What is the Capacity(Ton/Hour) you need?
6,What's your use about the pellet,for burning or feeding animals?
Any other DETAIL request,just let us know.
(Send your Inquiry) We will reply in 30 Mins!
Tags: biomass pellets, build a pellet plant, History of Wood & Biomass Pellets, Pellet fuel, Wood pellet production
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Acorn Controls' water tempering system provides usable tempered water immediately in an emergency, where time delays in receiving proper irrigation of hazardous material exposure can increase the severity of trauma and/or injury. Acorn Controls offers tank and valve size options that are able to supply multiple showers, eye/face washes and eyewashes simultaneously. All of Acorn Controls' water tempering systems, when located in a reasonable proximity to possible work place exposure, provide an environment conducive to quick and proper length of treatment, in accordance with ANSI Z358.1, Appendix B6.
5 x 5 feet all-stainless steel constructed skid for corrosive environments.
120 and 300 gallon tanks options available.
120 gallon NON-ASME or ASME compliant tank with ET71-2 tempering valve.
300 gallon ASME tank will include ET71-3 tempering valve.
Utilizes Acorn Controls ET71 Series tempering valves which are IAPMO certified per ASSE 1071 and CSA B125.3.
Electrical components in NEMA 4 standard, or optional NEMA 7 classifications.
15 feet (4.5 m), 10 gage, 4 wire power cord with 3 inch, 4 blade twist-lock connector.


Earlier today we showed you a tech-enabled shower cabin, the Frame made by Jacuzzi, and now we have an equally tech-friendly mirror that would certainly fit with the Frame. The Cybertecture Mirror is a concept mirror that will not only show how you look today, but also display useful details such as weather forecasts and flight information or show you even TV shows or exercise programs. Not to mention that it will probably be able to display all sorts of other interesting things by the time it becomes available to the public. The Cybertecture Mirror is expected to arrive in stores next spring but will set you back a cool $8,000 so better think twice before mounting one in your bathroom, or anywhere else in your home.


text:
Mooladhanam (, translation: Capital) is a 1969 Indian Malayalam-language film, directed by P. Bhaskaran, written by Thoppil Bhasi and produced by M. Azim. The film stars Sathyan, Prem Nazir, Sharada and Jayabharathi in the lead roles. The film had musical score by G. Devarajan. Cinematography was handled by P. R. Ramalingam.

The film is set amidst the Communist movement in Kerala during the 1960s.

Cast

Prem Nazir as Mammootty
Sathyan as Ravi
Sharada as Sharada
Ambika Sukumaran as Malathy
Jayabharathi as Nabeeza
Adoor Bhasi as Kuruppu
Manavalan Joseph as I.D Kasimpilla
Sankaradi as Hassanar
Sreelatha Namboothiri as Chinnamma
C.A. Balan
K. P. Ummer as Madhu
Kottayam Chellappan as Sharada's Brother
Paravoor Bharathan as Nanu

Soundtrack
The music was composed by G. Devarajan and the lyrics were written by P. Bhaskaran.

References

External links

1969 films
1960s Malayalam-language films
Films directed by P. Bhaskaran


The Story Of The Extraordinary People Who Changed Our World.
In the remote desert of New Mexico, "The Manhattan Project" is materializing-the World War II effort to build the atomic bomb. Oscar-winner Paul Newman (Hud, Nobody's Fool) stars as General Leslie Groves, the military man in charge of a massive project that will produce two weapons: "Fat Man" and "Little Boy." Dwight Schultz (The Temp, Star Trek: First Contact) is J. Robert Oppenheimer, the brilliant scientist attempting to bring the startling mission to fruition. And Bonnie Bedelia, John Cusack, Laura Dern and Natasha Richardson co-star in this "stunning...profoundly moving" film (Michael Medved, Sneak Previews) that re-creates one of history's most compelling chapters...one that resulted in the mushroom-shaped specter that changed the world forever.


text:
In Search of the Origins of Daniel Murphree
Daniel Murphree may have been an immigrant, perhaps from Ireland. We know there were many other Irish who immigrated into North Carolina prior to the Revolution. However, that doesn't explain why we first find him in an area heavily populated with native-born Americans and relatively few immigrants. The fact that the Bertie County area of North Carolina was settled mainly by Virginians forces us to consider the possibility that he may have been a second-generation American, descended from some earlier immigrant to Virginia or some other colony.
In fact, that is a distinct possibility.
Variations on the Surname
The spellings we know today — Murphy and Murphree — were relatively uncommon in the first hundred years of Virginia records. The Virginia colonial patent books show an impressive number of immigrants whose names are rendered as diversely as Merfree, Morfrey, Murfrey, Murfrye and even Murferry in addition to the more obvious Murfree and Murphree. Early county records also render the surname mainly as Murfrey, Murfery, Murfree, and Murfry and rarely as Murphree. To my consternation, I also found numerous cases where the same person appears in records with the name spelled both with and without the "r" that distinguishes Murphry from Murphy. In the Isle of Wight records cited below, for instance, Murfrey was on several occasions rendered as Murfy or Murphy.
A Few Early Virginians
One of the earliest of the name was Edward Murfrey who, with a partner named Thomas Vaughn, patented a large tract in York (later Westmoreland) County in 1643. An Edward Murferry, likely the same person, was claimed as a headright in a 1649 patent for land in York County. However by 1649 Edward Murfrey, like many immigrants of the time, had died without heirs and his land descended to his partner Vaughn. Even earlier, a James Merfee was a headright for a 1637 patent in New Norfolk County. And a James Morfrey was claimed as a headright in a 1658 patent for land in New Kent County. Within a generation or two the numbers of these immigrants increased significantly. By the early 1700s the patent books contain the names of several persons named Murfrey, Murphry, Murphrey and similar variants on the name.
Narrowing the Search by Geography
Let's narrow our focus to Murphrees in the counties on the south side of the James River which were prime suppliers of the early population of northeastern North Carolina — especially the counties of Lower Norfolk, Nansemond, and Isle of Wight. (Nansemond County, now defunct and largely replaced by the city of Suffolk, originally lay between Lower Norfolk and Isle of Wight.) In 1700 these counties bordered North Carolina above what was then Chowan and Bertie. In fact, the border between Nansemond and Isle of Wight (the part that later became Southampton County) was about 25 miles north-northeast of where we first find Daniel Murphree in 1743. An obvious migration path into Bertie County at that time would have been down the Blackwater (or the Nottoway) into the Chowan River, then just a few miles west to the Cashie River and Wahton Swamp.
Murphree Immigrants South of the James
The earliest of these is one "Danll. Murfery" — a name that commands immediate interest — who was one of 14 headrights claimed by John Marshall in a 1665 patent for land in Isle of Wight County, Virginia.1 That is, of course, much too early to be our man, but the similarity of names is intriguing. Unfortunately, the deed records for Isle of Wight are missing for nearly another twenty-five years, and essentially all the court records of the time are also lost. Thus it is no surprise that we can find no further mention of Daniel Murfery in Isle of Wight records.
A John Murfrey was settled in Nansemond County by 1680. In that year John Murfrey patented land adjacent to land he already owned and on which his "dwelling house" stood, for transportation of himself.2 His land is mentioned in at a subsequent patent, which helps us to place it as just west of the present-day city of Portsmouth. Unfortunately, Nansemond records are non-existent so we have no idea how long he may have been living there by 1680. Five years later a John Murfrey Junr. , apparently his son, patented 650 acres in Nansemond County in right of his wife Susanna, orphan of Thomas Francis.3 Ten years later in 1695, as plain John Murfrey (no "Junr."), he received 80 acres adjoining that patent.4
In 1711 John and Benjamin Goodwin patented a tract in Nansemond County which adjoined the lands of John Yeates and Daniel Murfrey.5 Since the county's records were burned in 1866, we do not know when or how Daniel Murfrey acquired that land. John Yeates received his own patent at the same time, but his grant mentioned only a Lewis Powell as an adjoining landowner. We can locate the land on Knott's Creek just west of the present-day city of Portsmouth and within walking distance of the land that John Murfrey had patented back in 1680. Whether this was the same Daniel Murfrey claimed as a headright in 1665 is anyone's guess. It seems unlikely, as no such person was listed as a landowner among the 1704 quit rents. Whoever Daniel Murfrey was, he must have acquired the land after 1704.
Finally, an Alexander Murfrey was living in adjacent Lower Norfolk County in 1691 when a patent to Hugh Campbell mentioned him as an adjoining landowner.6 He was still a landowner there as late as the 1704 Quit Rents. The only other Murphree in the 1704 Quit Rents for Virginia was a Wm. Marfry in Isle of Wight (more on him in a moment). Whether the aforementioned Murphrees died or left the area by 1704, or whether they were simply omitted from the list, is unknown.
The Search (Continued)
A highly plausible theory is that Daniel Murphree was descended from a Murphree of Nansemond County. This is explored in the next page: Nansemond Murfreys and the Queen Connection
Another alternative, that I think is less likely, is that he was related in some way to a Murfrey family in Isle of Wight County.
Virginia Patent Book 5, p252. [↩]
Virginia Patent Book 7, p37. [↩]
Virginia Patent Book 10, p28. [↩]


text:
\section{Introduction}
Ultra-high-temperature ceramics (UHTCs) form a family of materials defined by an extreme temperature range
of operation, which includes transition metal carbides, nitrides and diborides. UHTCs are very actively
researched for extensive application in various aerospace fields (as thermal protection systems in hypersonic or
atmospheric reusable re-entry vehicles, propulsion components, combustion chambers, engine intakes and rocket
nozzles), in energy (in nuclear fission and fusion, energy harvesting, concentrated solar power), in materials
processing (as high-temperature electrodes, high-speed machining tools, molten metal containment), in
microelectronics (as conductors, barrier layers, lattice-matched substrates for semiconductors), just to name a
few.~\cite{Padture2016,Zeng2017,Fahrenholtz2017,Cahill2019} Typically, UHTCs are characterised by the
exceptional combination of mechanical, thermal and electrical properties, coupled with melting temperatures in
excess of 3000~$\degree$C. These features allow UHTCs to work in extreme environments as high-temperature and
aggressive atmosphere. However, the attack of the chemical agents usually found in real-life hybrid-fuel
rockets, namely O$_2$, H$_2$O and CO, still pose huge challenges to the structural integrity of many
components. In fact, these induce changes in the surface chemistry, causing corrosion and facilitating
rapid ageing. For this reason, a comprehensive understanding of the UHTCs surface reactivity is essential for
improving their structural stability and thus ultimately the safety of UHTC-based parts.

Several experimental investigations have been conducted to unveil the primary surface reactions of various
UHTCs, although most of these studies are only focused on adsorption intermediates or dissociation products. For
instance, dissociative adsorption of O$_2$ was observed on ZrB$_2$(0001) by using high-resolution electron
energy loss spectroscopy (HREELS)~\cite{Aizawa2002a}. Belyansky and Trenary~\cite{BELYANSKY1999191} have
scrutinized the surface activity of the HfB$_2$(0001) and Hf(0001) surfaces, with the help of X-ray
photo-emission spectroscopy (XPS) and RAIRS (reflection adsorption infrared spectroscopy). Molecular adsorption
of CO was found on HfB$_2$(0001), while its dissociative adsorption was observed only on Hf(0001). In addition,
the adsorption of O on the 3-fold hollow site of HfB$_2$(0001) was measured by an impact-collision ion
scattering spectroscopy (ICISS) study~\cite{HAYAMI1994}. Similar studies have been carried out for carbides as
well. For instance, the oxidation process of ZrC was investigated with angle resolved photo-emission
spectroscopy (ARPES)~\cite{Kato_2000}, which identified carbon depletion with the concomitant Zr partial
oxidation in the form of ZrO$_x$ (1 $\leq$ $x$ $\leq$ 2). Furthermore, at an oxygen-modified ZrC(100) surface,
the dissociation of H$_2$O into hydroxyl (OH) and atomic O species was discovered by a combination of
ultraviolet photoelectron spectroscopy (UPS) and XPS measurements.~\cite{KITAOKA200123}

As an alternative to experiments, atomistic simulations provide a powerful tool to explore surface reactions in
more details. For example, by using density functional theory (DFT) calculations, Say\'{o}s et al.
~\cite{Gamallo2013} proposed that the adsorption of atomic O on the ZrB$_2$ (0001) surface takes place
predominantly at the hollow and B-B bridge sites. Zhou et al.~\cite{Sun2019,Sun2016} emphasized the effects of
the valance electron concentration on the surface stability and oxygen adsorption. The theoretical study of
oxidation of ZrB$_2$ (0001) surface from Cheng et al~\cite{Cheng2018} suggested that the initial oxygen coverage
has only little effect on the oxidation reaction. The similar feature was also claimed for H$_2$O adsorption on
TiO$_2$~\cite{Valdes2019}. Cristol et al.~\cite{Osei-Agyemang2014a} performed a statistical thermodynamics study
of O$_2$, H$_2$ and H$_2$O on a bare and ZrO-modified ZrC (100) surface. They suggested that the oxygen
modification activates the (100) surface, and water adsorbs strongly either as atomic O with H$_2$ release or
into surface OH and H groups. Despite these early studies, a systematic investigation of the surface activity of
UHTCs, looking on an equal footing at O$_2$, CO and H$_2$O, is still missing. This is not ideal, since the
reaction kinetic and its atomic characteristics are both required to effectively guide the tailoring of UHTC
materials against oxidation and corrosion.

Among the UHTC family ZrB$_2$ stands out because of its excellent chemical stability, high hardness and
strength, great thermal-stress resistance and good electrical and thermal conductivities.
~\cite{Fahrenholtz2007}. In this work, we study in detail the surface activity of ZrB$_2$ with the most common
chemical agents: O$_2$, H$_2$O and CO. These are among the most abundant chemical agents in the combustion gas
of hybrid-fuel rockets. The paper is organised as follows. A brief review of the atomic models (surface slabs,
adsorption sites and adsorbate geometries) and the calculation details are provided in section 2. Then, an
examination of atomic adsorption of O, H, OH and C on Zr-terminated (0001)$_\mathrm{Zr}$ and B-terminated
(0001)$_\mathrm{B}$ surfaces, and the related surface distortions are introduced in section 3. The adsorption
and dissociation mechanism of O$_2$, H$_2$O and CO are separately presented in sections 4, 5 and 6, while a
comparison of the surface reactivity for the three molecules is discussed in section 7. Finally section 8
contains the main concluding remarks. Supplementary Information (SI) complements the materials included here.

\section{Methodology}
\subsection{Surface models}
In order to investigate the ZrB$_2$ reactivity we construct 2$\times$2$\times$7 (0001) surface slabs, whose
structure is reported in Fig.~\ref{fig1}(a) and \ref{fig1}(b). In particular, we consider both Zr [see
Fig.~\ref{fig1}(a)] and B [see Fig.~\ref{fig1}(b)] terminations, which are denoted respectively as
(0001)$_\mathrm{Zr}$ and (0001)$_\mathrm{B}$. These are selected, since they can be easily stabilized in either
a Zr- or a B-rich chemical environment, as validated both in experiments and theory
~\cite{0953-8984-20-26-265006,Suehara2010,Zhang2018}. Our surface slab models are deliberately built up with a
symmetric termination so as to reduce spurious dipole effects. In general, periodic boundary conditions are
applied in the $x$-$y$ plane, while a vacuum region of around 26~\AA\ is added along the $z$ direction
(perpendicular to the surface) to avoid the artificial surface-surface interaction between the periodic
replicas.

\subsection{Adsorption sites}
The inequivalent adsorption sites over the (0001)$_\mathrm{Zr}$ and (0001)$_\mathrm{B}$ surfaces are identified
within the smallest structural unit of each surface, namely the threefold Zr-triangle and the six-member B ring
depicted by the dotted lines in Figs.~\ref{fig1}(a) and \ref{fig1}(b), respectively. For (0001)$_\mathrm{Zr}$
there are three  inequivalent adsorption sites, an hollow site (\textbf{H1}), a bond bridge one (\textbf{B1})
and the atop (\textbf{A1}). Similarly, four sites are identified at the (0001)$_\mathrm{B}$ surface, two hollow
positions (\textbf{H2} and \textbf{H3}), one bond-bridge site (\textbf{B2}) and one atop (\textbf{A2}). An
additional possible adsorption site, denoted as \textbf{B$^{\ast}$} in Fig.~\ref{fig1}(b), always relaxes to the
\textbf{H2} position so that is deemed unstable and it is excluded from further study.

\subsection{Adsorbate geometries}
Besides the inequivalent adsorption sites the adsorbates can also be distinguished from each other by the way
they approach the surface, namely by their adsorption geometry. Broadly speaking one can separate between the
situations in which all the molecule atoms lay parallelly with the surface plane (lateral geometry, \textbf{L}),
or when they are perpendicular to the surface (vertical geometry, \textbf{V}). These two situations are
illustrated for H$_2$O in Fig.~\ref{fig1}(c). Furthermore, for hetero-molecules like CO the adsorption geometry
can be further characterised by the alignment of the molecule with respect to the crystalline axes for the
\textbf{L} case and by the specific atom closest to the surface in the \textbf{V} situation. Thus, for CO we
have two inequivalent lateral orientations, denoted as \textbf{L($x$)} and \textbf{L($y$)} in
Figs.~\ref{fig1}(d1) and \ref{fig1}(d2), respectively (for the Zr-terminated surface), and two inequivalent
vertical ones, \textbf{V(C)} and \textbf{V(O)} [see Figs.~\ref{fig1}(d3) and \ref{fig1}(d4)]. The different
adsorption states \textbf{H1\_L(x)}, \textbf{H1\_L(y)}, \textbf{H1\_V(C)} and \textbf{H1\_V(O)} will be
examined in detail in section 6.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.85]{Fig1.jpg}
\caption{Surface slab models of (a) (0001)$_\mathrm{Zr}$ and (b) (0001)$_\mathrm{B}$ slab with side (left-hand
side panels) and top (right-hand side panels) views. The inequivalent adsorption sites (hollow: \textbf{H};
bond-bridge: \textbf{B}; atop: \textbf{A}) are marked by red circles on the top views. Note that two different
hollow sites (\textbf{H2} and \textbf{H3}) are found on (0001)$_\mathrm{B}$, while the \textbf{B}$^{\ast}$
position is unstable and relaxes into \textbf{H2}. The adsorbate geometries are labelled according to the
adsorption sites, the approaching ways and the near-end species and/or alignment axis. The approaching geometry
can be either lateral, \textbf{L}, or vertical, \textbf{V}. These two options are illustrated for H$_2$O
in panel (c), and further for CO adsorbing on the hollow site of (0001)$_\mathrm{Zr}$ in (d1) \textbf{H1\_L(x)},
(d2) \textbf{H1\_L(y)}, (d3) \textbf{H1\_V(C)} and (d4)  \textbf{H1\_V(O)}.  Colour code: Zr green; B grey; C
brown; O red; H pink.}
\label{fig1}
\end{figure}
The adsorption energy is then simply calculated as,
\begin{align}\label{Etot}
   \Delta E_\mathrm{ads}=E^\mathrm{sub}+E^{x}-E^{x/\mathrm{sub}} \:,
\end{align}
where, $E^{x/\mathrm{sub}}$, $E^\mathrm{sub}$ and $E^{x}$ are, respectively, the DFT total energies of the
surface slab including the $x$ adsorbent, the clean surface and the adsorbent either in gas phase or as an
isolated atom. The value of $\Delta E _\mathrm{ads}$ (eV/atom) measures the reactivity of the various surface
sites and the binding strength of the various adsorbate-adsorbent pairs.

\subsection{DFT calculation details}
All the calculations are performed using the plane-wave basis-projector augmented-wave method
(PAW)~\cite{Blochl1994} as implemented in the VASP~\cite{Kresse1999} code. The generalized gradient
approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)~\cite{Perdew1996} parametrization is adopted to
evaluate the exchange and correlation energy. Recently, it has been shown that, in general, dispersion
interactions strongly influence adsorption geometries and binding energies~\cite{Saqlain2018}.
Here we include these by mean of the DFT-D2 correction~\cite{Grimme.2006}, which has been proved adequate
in the description of transition-metal diborides~\cite{Zhang2018}. The calculated adsorption energies are
compared to those obtained with rPBE+D2 and rPBE+D3 in Fig.~S1 of the SI, showing little variations with the
details of the PBE functional and the van der Waals corrections chosen. For all surface calculations the
Brillouin zone is sampled by using the Monkhorst-Pack method with a $k$-mesh of 8$\times$8$\times$1. The
plane-wave kinetic energy cutoff is set to 500~eV. Geometry optimization is performed until the energy and the
forces are converged within 10$^{-7}$~eV and 0.01~eV/\AA, respectively, and dipole corrections~\cite{Makov1995}
are applied [see the electrostatic potential profile after dipole correction in Fig.~S2 of the SI].
Lastly, note that spin-polarization must be included when computing the total energy of the isolated species O,
C, OH, O$_2$ and H, while it is not relevant for the slab calculations.

The minimum energy paths for the molecules dissociation are refined by using the nudged-elastic band (NEB)
method~\cite{Henkelman2000,Henkelman2000a}. Thereafter, the transition states (TS) are located by using the
climbing-image NEB algorithm with a force threshold of 0.01~eV/\AA. During the relaxation of each reaction path,
the adsorbent atoms on the first layer of the slab are allowed to move away from their high-energy and
high-stress positions. This scheme enables us to probe the surface dissociation process, to assess whether there
are kinetic bottlenecks in the surface reaction, and to monitor the accompanying distortions of the adsorbents.

\section{Atomic adsorption}\label{AtomicAds}
The fingerprint of chemisorption, namely a positive $\Delta E_\mathrm{ads}$ according to Eq.~(\ref{Etot}), is
observed for all the chemical species investigated, namely for O, C, H and OH, on both (0001)$_\mathrm{Zr}$ and
(0001)$_\mathrm{B}$. These are presented as a radial distribution in the polar diagram of Fig.~\ref{fig2}(a),
where the binding strength of a particular adsorbent grows with the distance from the center of the diagram and
the corresponding adsorption sites are marked along the rim.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.25]{Fig2.jpg}
\caption{(a) Polar diagram of the adsorption energies, $\Delta E_\mathrm{ads}$ (eV/atom), for the chemical
species O, C, OH and H. Here H1, B1 and A1 (green shadow) are adsorption sites on (0001)$_\mathrm{Zr}$,
and H2, H3, B2 and A2 (grey shadow) are on the (0001)$_\mathrm{B}$ surface. Our results in black are compared
with those from Say\'{o}s's~\cite{Gamallo2013} in blue, Zhou's~\cite{Sun2016} in green and
Xiao's~\cite{ZENG201728} in red (note the latter two are shifted by half of the binding energies of O$_2$ and
H$_2$, respectively). (b) The disturbance of the adsorbent surface, $\Delta_\mathrm{max}$ (\AA), are measured by
the maximum displacement of the first atomic layer on the surface.}
\label{fig2}
\end{figure}

The rank of the relative adsorption strength for the different atomic species involved is O $\geq$ C $\geq$ OH
$\geq$ H on (0001)$_\mathrm{Zr}$ (O is the most strongly bonded species), which transforms into C $\geq$ O
$\geq$ OH $\geq$ H on (0001)$_\mathrm{B}$ (C is the most strongly bonded species). In more detail we find for O
the following $\Delta E_\mathrm{ads}$, 9.06, 3.44, 5.81, 8.59, 6.86, 6.43 and 5.42 (in eV/atom), respectively,
at the sites \textbf{H1}, \textbf{H2}, \textbf{H3}, \textbf{B1}, \textbf{B2}, \textbf{A1} and \textbf{A2}. These
values agree well with those from references~\cite{Gamallo2013,Sun2016}. Furthermore, $\Delta E_\mathrm{ads}$
for H is also in good agreement with that found by Xiao and coworkers~\cite{ZENG201728}. Note that the $\Delta E_\mathrm{ads}$ values extracted from Ref.~\cite{Sun2016} and Ref.~\cite{ZENG201728} and reported in Fig.~2(a)
are shifted by half of the binding energies of O$_2$ and H$_2$, respectively, due to the different reference
states chosen in such works. At the same time in the case of the Zr (0001) surface we can only compare with
results relative to metallic Zr~\cite{ZENG201728}, since those for ZrB$_2$ are not available in literature. To
the best of our knowledge $\Delta E_\mathrm{ads}$ information for C and OH on the (0001)$_\mathrm{Zr}$ and
(0001)$_\mathrm{B}$ surfaces of ZrB$_2$ are reported here for the first time.

We find the hollow and bond-bridge sites to be energetically more favourable than the atop ones. This is
generally true for both Zr- and B-terminated surfaces and for all the chemical species considered here.  In
fact, we compute $\Delta E_\mathrm{ads}$ on the hollow and bond-bridge sites of the (0001)$_\mathrm{Zr}$ surface
to range in the 3.22-9.06~eV/atom interval. These values are reduced to 1.52-7.39~eV/atom on the
(0001)$_\mathrm{B}$ surface. In contrast, the A1/A2 atop sites are significantly less preferred, presenting even
lower $\Delta E_\mathrm{ads}$ values. The tendency of O to adsorbe preferentially on hollow and bond-bridge
sites has been validated by experiments~\cite{HAYAMI1994} and other DFT-based calculations~\cite{Gamallo2013}.
Here we extend the same information to C and OH.

Importantly, the chemical adsorption can induce a disturbance in the adsorbent surfaces. The maximum
displacement of the outmost surface layer resulting from the adsorption, $\Delta_\mathrm{max}$ (\AA), is
computed and shown in Fig.~\ref{fig2}(b). At variance with $\Delta E_\mathrm{ads}$, the (0001)$_\mathrm{B}$
surface atoms display $\Delta_\mathrm{max}$ values, for all the chemical species investigated, larger than those
of (0001)$_\mathrm{Zr}$. We find that on (0001)$_\mathrm{Zr}$, the OH adsorbate causes the strongest
disturbance, $\Delta_\mathrm{max}$ $\sim$ 0.16~\AA; while on (0001)$_\mathrm{B}$, it is the C adatom to give the
largest $\Delta_\mathrm{max}$ of 0.55~\AA. This fact can be explained by the light weight of B and the strong
chemical affinity between B and C (the existence of a stable B$_4$C compound with a melting point around
2800~K). In general, we find the (0001)$_\mathrm{B}$ surface to exhibit more prominent atomic disturbances than
the (0001)$_\mathrm{Zr}$ counterpart.

In the following sections, we will discuss the adsorption mode of each molecule by examining the adsorption
thermodynamics, the geometry of the adsorbate-adsorbent systems, the dissociation pathways and the associated
activation energies. The adsorption and dissociation behaviour of the various molecules on B and Zr-terminated
surfaces will also be compared.

\section{Adsorption and dissociation of O$_2$}
\subsection{Adsorption mechanism}
As a general feature our results indicate that molecular O$_2$ is prone to dissociative adsorption when
laterally landing on the Zr- or B-terminated surfaces, but tends to adsorbe in the molecular form if vertically
approaching. These two cases are distinguished by the filled and the open symbols in the polar diagrams of
Fig.~\ref{fig3}(a) and (b), where we present the different adsorption energies of O$_2$ over
(0001)$_\mathrm{Zr}$ and (0001)$_\mathrm{B}$. The figure shows that all the dissociative adsorption starts from
lateral geometries (left halves of the polar diagrams), while most of the molecular adsorption events
originate from the vertical setups (right halves of the polar diagrams). Although dissociative adsorption of
O$_2$ has been observed in experiments~\cite{Aizawa2002a} in the past, the simple classification of the various
adsorption mechanisms based on the surface-approaching geometry is suggested here for the first time.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.75]{Fig3.jpg}
\caption{Adsorption energies ($\Delta E_\mathrm{ads}$, eV/atom) for O$_2$ on the (a) (0001)$_\mathrm{Zr}$ and
(b) (0001)$_\mathrm{B}$ surfaces. Molecular (O$_2$) and  dissociative (2O) adsorptions are distinguished by
using open and filled symbols, respectively. The initial adsorption sites are marked along the rim of the polar
diagrams, while the approaching geometries of the O$_2$ molecule are encoded as background color. These are
further mapped as a function of the adsorption distance ($d$, \AA) and the change in the interatomic length
($\Delta_l$, \AA) in panel (c). The definitions of $d$ and $l$ are shown in the inset ($\Delta_l$ is the change
in $l$ due to the adsorption). The distortion of the adsorbent surfaces ($\Delta_i$) is plotted in panel (d) as
a function of the surface atoms index (see inset and main text). (Color code: Zr = green spheres; B: grey
spheres; O: red spheres).}
\label{fig3}
\end{figure}

As expected, the dissociated adsorption of O$_2$ is normally accompanied by a large variation of the O$_2$
geometry. In fact, the O-O interatomic length, $l$, of the dissociated O adatoms increases largely when compared
to the equilibrium bond length of 1.48~\AA, see $\Delta_l$ in Fig.~\ref{fig3}(c), indicating the O-O bond
breaking. The dissociated O adatoms then relax away from their initial adsorption location, and tend to finally
adsorb on the hollow (\textbf{H}) and bond-bridge (\textbf{B}) sites. This agrees well with the energetic
preference of the \textbf{H} and \textbf{B} sites discussed in section~\ref{AtomicAds}. Such behaviour has
also been identified by Cheng et al. in Ref~\cite{Cheng2018}.

At the same time, the dissociative adsorption of O$_2$ results in strongly bonded O adatoms on the
Zr-/B-surfaces, a feature clearly demonstrated by both the large adsorption energies, $\Delta E_\mathrm{ads}$,
and the short adsorption distances, $d$;  see Fig.~\ref{fig3}(c). In fact, $\Delta E_\mathrm{ads}$ for
dissociative adsorption on the Zr (B) surface is in the range 5.5-6.2 (2.5-4.1) eV/atom. These results can be
compared with with values of 6.57-7.08~eV/atom, reported for ultra-soft-pseudopotential calculations at the
GGA-PW91 level in Ref.~\cite{Cheng2018} for dissociative adsorption of O$_2$ on Zr surface. In contrast,
molecular adsorption of O$_2$ on the Zr-terminated (B-terminated) surface has a much lower $\Delta E_\mathrm{ads}$ range, 1.6-3.1 (0.5-2.1)~eV/atom. The $d$ values distribute within the narrow range of 1.1-1.3
(1.1-1.2)~\AA~ for dissociated adatoms on Zr (B) surface, bond lengths that are considerably shorter than those
associated to molecular adsorbates (these can be as large as 2.0~\AA). The strong chemisorption of the O adatoms
on the ZrB$_2$ surfaces, with the corresponding large energy gain associated to the formation of the O-Zr and
O-B bonds, makes dissociative adsorption thermo-dynamically more favorable than molecular adsorption.

An important feature to note is that dissociative adsorption comes with sometimes severe surface distortions or
even surface reconstruction. In Fig.~\ref{fig3}(d) the displacement of each surface atoms are plotted against
their atom index. Dissociative adsorption of O$_2$ on (0001)$_\mathrm{Zr}$ activates surface reconstruction with
an atomic displacement of 0.17~\AA at the most. In contrast, dramatic effect is found for the \textbf{H3\_L(y)}
and \textbf{H3\_L(x)} on (0001)$_\mathrm{B}$ adsorbate-adsorbent systems, which present displacements as large
as 1.04~\AA. In these cases the two O adatoms position themselves as first nearest neighours on the bond-bridge
site after the O$_2$ dissociation. One B atom is then found to move above the original (0001)$_\mathrm{B}$
plane, thus breaking of the six-member ring symmetry of the (0001)$_\mathrm{B}$ surface; see the
\textbf{H3\_L(y)} illustration in the inset of Fig.~\ref{fig3}(d). These results suggest that the dissociative
adsorption of O$_2$ can trigger the reconstruction of the B-surface and therefore the easy formation of boron
oxides. Note that the melting temperature of B$_2$O$_3$, the most common among the boron oxides, is only 723~K.
This means that the formation of boron oxides during a high-temperature corrosion process will likely result in
significant B mass loss.

\subsection{Dissociation kinetics}
When an O$_2$ molecule approaches the surface in a lateral configuration dissociative adsorption takes place
without activation barrier, so that this is the most efficient reaction channel. However, in an O$_2$ gas one
cannot exclude situations where the molecule attacks ZrB$_2$ with a vertical geometry. For this reason we have
performed kinetic simulations for a number of candidate reactions involving both the vertical and lateral
channel. For each one of them, the reactants (precursors) acting as the initial states are chosen from the
adsorbed intermediates, while the dissociation products serving as the final states (FS) are selected among
dissociated adatoms. More specifically, we explore the following O$_2$ reaction paths (paths labelled with
`a' are for reaction on the Zr-terminated surface, while those with `b' are for the B-terminated one):
\begin{equation}\nonumber
\begin{array}{l}
\left\{
\begin{array}{lllr}
\mathbf{O_2: H1\_V(O)} & \rightarrow & \mathbf{2O_{[ad, H1]} (1NN)} & \;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a1)} \\
\mathbf{2O_{[ad, H1]} (1NN)}  & \rightarrow &  \mathbf{2O_{[ad, H1]} (2NN)} & \;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a2)} \\
\end{array}
\right. \\
\\
\left\{
\begin{array}{lllr}
\mathbf{O_2: H2\_V(O)}  & \rightarrow & \mathbf{O_2: B2\_L(y)} & \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b1)} \\
\mathbf{O_2: B2\_L(y)}  & \rightarrow & \mathbf{2O_{[ad, B2]} (1NN)} & \;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b2)} \\
\mathbf{2O_{[ad, B2]}(1NN)}  & \rightarrow & \mathbf{2O_{[ad, B2]} (2NN)} & \;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b3)} \\
\end{array}
\right.
\end{array}
\end{equation}

When O$_2$ approaches the (0001)$_\mathrm{Zr}$ surface with the vertical geometry \textbf{H1\_V(O)}, it
dissociates into two O adatoms after having tilted so to assume a lateral configuration [path (a1) of
Fig.~\ref{fig4}]. The so-produced O adatoms can occupy two adjacent hollow sites, thus forming a first nearest
neighbour (1NN) pair, or they can diffuse further away from each other along the surface to take a second
nearest-neighbour (2NN) position, as described by the (a2) path [see Fig.~\ref{fig4}]. Both these paths are
characterised by the absence of a kinetic barrier. However, if the O adatoms diffuse towards the atop sites
(energetically less favorable than the hollow ones), an energy barrier of 0.59~eV is found. In
Ref.~\cite{Cheng2018} an activation barrier of 0.16~eV was determined for the vertical channel starting from
the \textbf{A1} site. The dissociation path for vertical adsorption discussed here, namely the combination of
paths (a1) and (a2), appears, however more energetically and kinetically advantageous.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Fig4.jpg}
\caption{Dissociation paths of O$_2$ on the (0001)$_\mathrm{Zr}$ surface via the (a1) and (a2) paths; and on the
(0001)$_\mathrm{B}$ one along the paths (b1), (b2) and (b3). In this second case one transition state (TS1),
with energy barrier 0.38~eV, is observed. Colour code: Zr = green; B grey; O = red.}
\label{fig4}
\end{figure}

Turning now our attention to the dissociation of O$_2$ on (0001)$_\mathrm{B}$, we note that this is weakly
activated. The vertical configuration \textbf{H2\_V(O)} can firstly rotate into the lateral \textbf{B2\_L(y)},
as illustrated by path (b1). Thereafter, the O$_2$ adsorbate dissociates into two O-adatoms located at the
\textbf{B2} sites. This second step, path (b2), comes with a low activation barrier of 0.38~eV, a value in
close agreement with the previously calculated one of 0.27~eV from Say{\'o}s et al.~\cite{Gamallo2013}. Then,
the two O adatoms can occupy either the 2NN or the 1NN \textbf{B2} sites, by moving without energy barrier
along path (b3). Notably, the 1NN \textbf{B2} adsorbate geometry promotes a strong distortion of the B surface
by breaking the six-member B ring. For this reason the 2NN-\textbf{B2} configuration is more energetically and
kinetically favorable.

\section{Adsorption and dissociation of H$_2$O}
\subsection{Adsorption mechanism}
In general we find that water exhibits the characteristics of chemisorption on the (0001)$_\mathrm{Zr}$
surface, while physisorption dominates for the (0001)$_\mathrm{B}$ one.
In more detail, when a H$_2$O molecule approaches the (0001)$_\mathrm{Zr}$ surface in a vertical position with
the O atom closer to the surface, then the typical $\Delta E_\mathrm{ads}$'s are between 207~meV/atom and
368~meV/atom, as illustrated in Fig.~\ref{fig5}(a). These values reduce by approximately a factor of four in
situations where it is the hydrogen side of the molecule to form contact to the surface, and the $\Delta E_\mathrm{ads}$ range is now 34-94~meV/atom. The only exception to this trend is for the \textbf{B1\_V(H, x)}
geometry for which we compute a $\Delta E_\mathrm{ads}$ of 368~meV/atom. It must be noted that \textbf{B1\_V(H, x)}  is a highly symmetric structure, with the two protons taking the \textbf{H1} sites and the oxygen sitting
on the \textbf{B1} site.

In contrast, if the H$_2$O molecule is adsorbed on (0001)$_\mathrm{B}$, we will notice that both lateral and
vertical configurations result in weakly bonded absorbates, with the $\Delta E_\mathrm{ads}$'s clustering
around the 39-118~meV/atom interval. Only four configurations are observed with relatively large adsorption
energies, all above 200~meV/atom. These are all initiated with the O atom placed over the \textbf{H3} site, but
they consistently relax towards the \textbf{A2} one, a position that offers a more balanced adsorption
configuration for both O and H.
 %
\begin{figure}[h!]
\centering
\includegraphics[scale=0.75]{Fig5.jpg}
\caption{Adsorption energies, $\Delta E_\mathrm{ads}$ (eV/atom), for H$_2$O on the (a) (0001)$_\mathrm{Zr}$ and
(b) (0001)$_\mathrm{B}$ surfaces. Molecular (H$_2$O) and dissociative (2H-O) adsorptions are distinguished by
using open and filled symbols, respectively.  The adsorption sites are marked along the rim of the polar
diagrams, while the approaching configurations of the H$_2$O molecules are encoded as background color. The
distortion of the H$_2$O geometry is analysed in panel (c) where the deviation of one H-O bond length,
$\Delta_l$(O-H1), from its equilibrium value is plotted against the other, $\Delta_l$(O-H2), and the color
scale maps the change in bond angle, $\Delta_\theta$. The inset zooms in the mild-distortion region. The
distortion of the adsorbent surfaces, $\Delta_i$, is plotted in panel (d) as a function of the surface atoms
index (see main text).}
\label{fig5}
\end{figure}

Then we move to discuss the possibility of dissociative adsorption. This is observed on the
(0001)$_\mathrm{Zr}$ surface, although for significantly less configurations and with a much lower energy gain
than what found for O$_2$. In fact, only the \textbf{H1\_L(y)} configuration presents a clear evidence of
dissociative adsorption with a $\Delta E_\mathrm{ads}$ of 1.88~eV/atom; see Fig~\ref{fig5}(a). In fact,
in this case the final relaxed configuration shows an increase in the O-H bond length of more than 2.2~\AA,
while the bond angle decreases by about 50\degree~[see the blue symbol in Fig.~\ref{fig5}(c)]. No other
approaching geometry of H$_2$O on (0001)$_\mathrm{Zr}$ displays significant signs of molecular configuration
change, with the bond lengths and bond angle remaining close to that of H$_2$O in the gas phase [see grey
symbols in the inset of Fig.~\ref{fig5}(c)]. A somewhat intermediate situation is found for H$_2$O attacking
the (0001)$_\mathrm{B}$ surface. In this case, three lateral configurations, namely \textbf{H2\_L(y)},
\textbf{B2\_L(x)} and \textbf{B2\_L(y)}, display significant bond-length expansion (0.2-0.5~\AA) and bond angle
contraction [green symbols in Fig.~\ref{fig5}(c)]. These distortions, however, are not large enough to define
the O-H bond breaking.

The disturbance of the surface atoms caused by the adsorption of H$_2$O is found to be minor when compared to
O$_2$ adsorption [see Fig.~\ref{fig5}(d)]. In fact, we find that the maximum displacement of the surface atoms
is always less that 0.21~\AA, while it was 1.04~\AA~for O$_2$. This is consistent with the $\Delta E_\mathrm{ads}$'s for water being significantly smaller (in absolute value) than that of O$_2$. To summarise,
our results indicate that H$_2$O adsorption is less active than O$_2$ adsorption, it is characterised by modest
adsorption energies and small geometry distortions of both the molecule and the surface.

\subsection{Dissociation kinetics}
Given the more complex structure of H$_2$O with respect to that of O$_2$, its surface dissociation kinetic is
also more complex. Here we consider the following potential reaction paths, where again `a'-labelled paths are
for (0001)$_\mathrm{Zr}$, while `b'-labelled ones are for (0001)$_\mathrm{B}$.
\begin{equation}\nonumber
\begin{array}{l}
\left\{
\begin{array}{lllr}
\mathbf{H_2O: B1\_V(O)} & \rightarrow & \mathbf{OH_{[ad, H1]} + H_{[ad,H1]}} & \;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a1)} \\
\mathbf{OH_{[ad, H1]} + H_{[ad,H1]}}  & \rightarrow &  \mathbf{2H_{[ad, H1]} + O_{[ad,H1]}} & \;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a2)} \\
\end{array}
\right. \\
\left\{
\begin{array}{lllr}
\;\mathbf{H_2O: B1\_V(O)}  & \;\;\;\;\;\;\rightarrow &  \mathbf{O_{[ad,B1]} + H_2(g)} & \;\:\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a3)} \\
\end{array}
\right. \\
\left\{
\begin{array}{lllr}
\;\mathbf{H_2O: A1\_L(y)}  & \:\;\;\;\;\;\;\;\rightarrow &  \mathbf{2H_{[ad, H1]} + O_{[ad,H1]}} & \:\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a4)} \\
\end{array}
\right. \\
\\
\left\{
\begin{array}{lllr}
\mathbf{H_2O: A2\_L(y)}  & \rightarrow & \mathbf{OH_{[ad, B2]} + H_{[ad, A2]}} & \;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b1)} \\
\mathbf{OH_{[ad, B2]}} + \mathbf{H_{[ad, A2]}}  & \rightarrow & \mathbf{2H_{[ad, A2]} + O_{[ad,B2]}} & \;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b2)} \\
\end{array}
\right. \\
\left\{
\begin{array}{lllr}
\;\mathbf{H_2O: A2\_L(y)}  & \;\;\;\;\;\;\;\rightarrow & \mathbf{2H_{[ad, B2]} + O_{[ad,B2]}} & \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b3)} \\
\end{array}
\right.
\end{array}
\end{equation}

On (0001)$_\mathrm{Zr}$, we primarily explore the dissociation of H$_2$O starting from \textbf{B1\_{V(O)}}, an
energetically preferred adsorbate geometry. Our results are illustrated in Fig.~\ref{fig6}. When the molecule
moves along the (a1) path, it tilts and rotates so to first lose one proton, thereby forming an intermediate
state with the OH and H groups absorbed at two adjacent hollow sites. This intermediate state can further
dissociate into a final one, in which H and O adatoms all sit at hollow sites. We denote this second channel as
(a2). Two transition states, named TS1 and TS2, are detected for such combined (a1)+(a2) dissociation path,
with energy barriers, $E_\mathrm{b}$, of 0.09~eV and 0.64~eV, respectively. In an alternative path, (a3), a
H$_2$O molecule approaching with the \textbf{B1\_{V(O)}} geometry directly dissociates into atomic O by
releasing the two protons in the form of a H$_2$ gas molecule. The associated transition state, before H$_2$
release, has two protons separated by a distance of 1.09~\AA, while the O atom is adsorbed on the surface at
a distance of about 1.56~\AA. The activation barrier for such path is, however, very high, 2.16~eV, making such
a path available only at extremely elevated temperatures. Finally, a lateral channel initiated at the
\textbf{A1$\_${L(y)}} structure can be activated by the expansion of the H-O-H bonds along path (a4). This is
characterised by an energy barrier, at the TS4 transition state, of 0.94~eV. Thus, we conclude that on
(0001)$_\mathrm{Zr}$ the (a1) path, with the low activation energy of 0.09~eV, is the most kinetically
favourable and dominates the dissociation of H$_2$O into the OH and H groups. Notably, this is the same
dissociation reaction experimentally observed for H$_2$O on ZrC(001)~\cite{KITAOKA200123}.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Fig6_L.jpg}
\caption{Dissociation of H$_2$O on the (0001)$_\mathrm{Zr}$ surface. The initial states considered are
\textbf{B1\_{V(O)}} and \textbf{A1\_{L(y)}}. Along the (a1)+(a2) path the reaction proceeds by first producing
an OH group and a H atom and then by dissociating OH, so that the final state has two H and one O at adjacent
hollow sites. Along path (a3) a H$_2$O molecule approaching as \textbf{B1\_{V(O)}} releases an H$_2$ molecule,
leaving an O atom on the surface. The vertical path (a4) also exhibits direct dissociation into two H and one O
adatom, but these are placed at 2$^{nd}$ nearest neighbors positions. Four transition states are determined
with the following energy barriers, TS1: 0.09 eV, TS2: 0.65 eV, TS3: 2.16 eV, TS4: 0.94 eV. Colour code: Zr =
green; O = red; H = pink.}
\label{fig6}
\end{figure}

Moving now to the (0001)$_\mathrm{B}$ surface, the dissociation of H$_2$O is studied starting from the stable
adsorbate geometry \textbf{A2\_{L(y)}} along the two reaction paths illustrated in Fig.~\ref{fig7} [see also
reaction path list]. When going along (b1)+(b2) there is a first dissociation into an OH group and a H atom,
followed by the the decomposition of OH. The final dissociated geometry has O on the bond-bridge site and the
two H on the atop ones. For this reaction there are two activation barriers of 0.44~eV and 0.91~eV,
corresponding to a single deprotonation of H$_2$O and OH, respectively. The relatively high barrier for OH
deprotonation, together with the fact that the energy of fully dissociated configuration is higher than the one
in which the OH group remains intact on the surface, make this decomposition channel unlikely. In an
alternative path, (b3), one O and two H adatoms are released simultaneously, ending up at three \textbf{B2}
sites. A transition state, TS3, with an energy barrier of 1.10~eV is identified along this path. TS3 is
characterised by the water molecule placed with the O atom at the bond-bridge site and the two H ones moving
toward the adjacent bridge positions (see Fig.~\ref{fig7}) with elongated O-H bonds. As such, also for the
(0001)$_\mathrm{B}$ surface we conclude that the dissociation of H$_2$O is likely to proceed by sequential
single deprotonations.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Fig7.jpg}
\caption{Dissociation of H$_2$O on the (0001)$_\mathrm{B}$ surface initiated at the \textbf{A2\_{L(y)}}
geometry. We identify two main reaction channels, one involving sequential single deprotonation, (b1)+(b2), and
one associated to a double deprotonation, (b3). Three transition states are identified along these paths with
the energy barriers, TS1: 0.44 eV, TS2: 0.91 eV, TS3: 1.10 eV. Colour code: B = grey; O = red; H = pink.}
\label{fig7}
\end{figure}

\section{Adsorption and dissociation of CO}
\subsection{Adsorption mechanism}
In this section we investigate the energetics of CO adsorption. In general, our calculations show that CO can
be chemisorbed on both ZrB$_2$ surfaces with typical adsorption strengths falling in between those of O$_2$ and
H$_2$O. In fact, we find $\Delta E_\mathrm{ads}$'s on the Zr-terminated (B-terminated) surface within the range
1.22-2.81~eV/atom (0.51-2.51~eV/atom), see Figs.~\ref{fig8}(a) and \ref{fig8}(b).
\begin{figure}[h!]
\centering
\includegraphics[scale=0.75]{Fig8.jpg}
\caption{Adsorption energies, $\Delta E_\mathrm{ads}$ (eV/atom), for CO on the (a) (0001)$_\mathrm{Zr}$ and (b)
(0001)$_\mathrm{B}$ surfaces. Molecular (CO) and dissociative (C + O) adsorptions are distinguished by using
open and filled symbols, respectively. The adsorption sites are marked along the rim of the polar diagrams,
while the approaching configurations of the CO molecules are encoded as background color. The insets illustrate
the preferred final configurations of the adsorbates. Note that on (0001)$_\mathrm{B}$, \textbf{H3\_L(x)},
\textbf{H3\_L(y)} and \textbf{A2\_L(y)} all transform into \textbf{B2\_V(C)}, so that their corresponding
$\Delta E_\mathrm{ads}$ are the same (red dashed boxes). In panel (c) we map $\Delta E_\mathrm{ads}$ as a
function of the adsorption distance, $d$ (\AA), and the change in interatomic lengths, $\Delta_l$ (\AA).
The distortion of the adsorbent surfaces, $\Delta_i$ (\AA), is plotted in panel (d) as a function of the
surface atoms index (see main text). Colour code: Zr = green; B = grey; C = brown; O = red.}
\label{fig8}
\end{figure}

On (0001)$_\mathrm{Zr}$ the lateral CO configurations are in general more energetically stable than the
vertical ones, similarly to what found for O$_2$ and H$_2$O adsorption. It is worth mentioning that the initial
geometries \textbf{H1\_L(x)} and \textbf{B1\_L(y)} can rotate into tilted structures and finally settle with O
on the \textbf{B1} and C on the \textbf{H1} site. The top view of the final configuration of \textbf{H1\_L(x)}
is illustrated in the inset of Fig.~\ref{fig8}(a). Note that the \textbf{B1} and \textbf{H1} adsorption sites
are energetically rather similar, therefore in competition for adsorption.

In contrast, on (0001)$_\mathrm{B}$ it is the vertical adsorption to be more energetically favourable. Furthermore, we find that when CO is landing on the surface in a lateral configuration it can always rotate to
assume a vertical structure during the geometry relaxation. For example, we find that \textbf{H3\_L(x)},
\textbf{H3\_L(y)} and \textbf{A2\_L(y)} all transform into \textbf{B2\_V(C)}. As such their adsorption
energies, $\Delta E_\mathrm{ads}$ turn out to be all the same, as highlighted by the red dashed boxes of
Fig.~\ref{fig8}(b), while their final adsorbate geometry is shown in the inset. In the same way, we find that
the lateral configurations \textbf{H2\_L(x)} and \textbf{H2\_L(y)} all relax into the tilted \textbf{H2\_V(C)}
one. We believe that such strong preference for vertical geometries is associated to the chemical affinity
difference between C-B and O-B.

Importantly, for CO we do not find any evidence of direct dissociative adsorption on either (0001)$_\mathrm{Zr}$ or (0001)$_\mathrm{B}$, a fact that holds true for both lateral and vertical approaching
geometries. The relative small variations in bond length of the various configurations are presented in
Fig.~\ref{fig8}(c). In order to complete our adsorption energy study we have also specifically constructed two
dissociated configurations, namely \textbf{O$_\mathbf{[ad, H1]}$-C$_\mathbf{[ad,H1]}$} and
\textbf{O$_\mathbf{[ad, B2]}$-C$_\mathbf{[ad, B2]}$}, whose
geometries are illustrated in the insets of Fig.~\ref{fig8}(c). These present $\Delta E_\mathrm{ads}$ values
rather close to those found for molecular adsorbates, as it can be noted by comparing the empty and filledsymbols in Figs.~\ref{fig8}(a) and \ref{fig8}(b). Such close energetics between molecular and dissociated
adsorbates is indicative of a weak thermodynamic driving force to break the C-O bond during the surface
adsorption.

Finally, the atomic distortions of the surface atoms due to the adsorption of CO are displayed in
Fig.~\ref{fig8}(d) as a function of the surface atom index. For molecular adsorption we find that B atoms move
within the interval 0.004-0.38~\AA, while the range for Zr is significantly more narrow, 0.008-0.13~\AA. Large
distortions are found only for dissociated configurations on the B-terminated surface, 0.65~\AA, while they
remain modest on the Zr-terminated one, 0.16~\AA. Thus, we conclude that the surface distortions caused by CO
is much less severe than that associated to O$_2$, but more pronounced than that of H$_2$O. This is consistent
with the same ranking found for the adsorption energies. As such, there is compelling evidence that O$_2$ is
the most active chemical molecule on ZrB$_2$ surfaces, followed by CO and lastly by H$_2$O.

\subsection{Dissociation kinetics}
Since molecular CO can be adsorbed both laterally and vertically on (0001)$_\mathrm{Zr}$, and only vertically on
(0001)$_\mathrm{B}$, we decide to examine the following dissociation paths,
\begin{equation}\nonumber
\begin{array}{l}
\left\{
\begin{array}{lllr}
\mathbf{CO: H1\_V(C)} & \rightarrow & \mathbf{CO: B1\_L(y)} & \:\;\:\;\;\;\;\:\;\;\;\;\:\;\;\;\;\:\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a1)} \\
\mathbf{CO: B1\_L(y)}  & \rightarrow &  \mathbf{C_{[ad, H1]} + O_{[ad,H1]}} & \:\;\:\;\;\;\;\:\;\;\;\;\:\;\;\;\;\:\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(a2)} \\
\end{array}
\right. \\
\left\{
\begin{array}{lllr}
\;\mathbf{CO: B2\_V(C)}  & \rightarrow &  \mathbf{C_{[ad,B2]} + O_{[ad,B2]} (2NN)} & \;\;\;\:\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{(b1)} \\
\end{array}
\right.
\end{array}
\end{equation}

On (0001)$_\mathrm{Zr}$ we start by taking \textbf{H1\_V(C)} as initial CO geometry. This is thermodynamically
less stable than the lateral configuration, \textbf{B1\_L(y)}, and in fact our NEB calculation reveals that
\textbf{H1\_V(C)} can transform into \textbf{B1\_L(y)} without any activation barrier [see path (a1) in
Fig.~\ref{fig9}]. Then, the lateral adsorbate \textbf{B1\_L(y)} can decompose into two final adatoms,
\textbf{C$_\mathbf{[ad,H1]}$} and  \textbf{O$_\mathbf{[ad,H1]}$}, located at 2$^\mathrm{nd}$ nearest-neighbour
positions. The decomposition takes place along the (a2) path of Fig.~\ref{fig9}. Along such reaction trajectory
one encounters a transition state, TS1, where the two adatoms are in a 1$^\mathrm{st}$ nearest-neighbour
position. The transition state corresponds to the saddle point of the O migration and the associated activation
barrier is 0.90~eV.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{Fig9.jpg}
\caption{Dissociation of CO over (0001)$_\mathrm{Zr}$ (green line) and (0001)$_\mathrm{B}$ (grey line) along
the paths (a1)+(a2) and (b1), respectively. Two transition states, TS1 and TS2, are identified respectively for
(0001)$_\mathrm{Zr}$ and (0001)$_\mathrm{B}$ with energy barriers 0.90~eV and 2.01~eV. Colour code: Zr = green;
B = grey; C = brown; O = red.}
\label{fig9}
\end{figure}

In contrast, on (0001)$_\mathrm{B}$ the preferred adsorption geometry is vertical. In fact, any lateral
configuration investigated rotates to a vertical position upon DFT relaxation, namely it cannot be stabilised
even as metastable state. As representative configuration we then take \textbf{B2\_V(C)}, which possesses the
lowest adsorption energy on (0001)$_\mathrm{B}$ [see (b1) channel in Fig.~\ref{fig9}]. The final state
considered is made of two adatoms, \textbf{C$_\mathbf{[ad,B2]}$} and \textbf{O$_\mathbf{[ad,B2]}$}, occupying
2$^\mathrm{nd}$ nearest-neighbour positions. Such reaction path contains a transition state, TS2, in which the
B hexagonal structure is broken and the CO molecule effectively replaces on B atom. The activation barrier at
the transition state is rather large, namely 2.01~eV.

As noted before, the chemical activity of CO is located in between that of O$_2$ (the most reactive species)
and that of H$_2$O (the less reactive species), and it can result in surface reconstruction, similarly to the
O$_2$ case. However, the dissociation kinetics of CO shows a behavior totally different from that of O$_2$. In
fact bond breaking in O$_2$ can take place without kinetic activation, while that of CO demands an activation
energy of 0.90~eV on (0001)$_\mathrm{Zr}$ and 2.01~eV on (0001)$_\mathrm{B}$. Therefore, we conclude that
ZrB$_2$ oxidation can dominate at relatively low temperatures, while corrosion caused by CO requires elevated
temperatures to be active.

\section{Discussion}

ZrB$_2$, a strongly bonded compound presenting alternating Zr and B atomic planes, is likely to present a grain
structure dominated by (0001)$_\mathrm{Zr}$ and (0001)$_\mathrm{B}$ facets, which are also the most
energetically stable open surfaces under a broad range of growth conditions. These surfaces undergo corrosive
attack in the aggressive atmosphere, containing O$_2$, H$_2$O and CO, typical of real-life combustion in
aerospace applications. Here we investigate the first steps in the corrosion process, namely we focus on the
initial surface reactions involving molecular adsorption and dissociation. Our calculations confirm that
(0001)$_\mathrm{Zr}$ generally promotes strongly bound adsorption and weakly activated dissociation. Therefore,
the transition-metal-terminated (0001)$_\mathrm{Zr}$ surface is found to be more chemical active than its
(0001)$_\mathrm{B}$ counterpart. This is not a surprise given the high reactivity of early transition metals.

Turning our attention to the (0001)$_\mathrm{B}$ surface, this is characterised by a substantial reconstruction
upon both CO and O$_2$ dissociation. The limiting kinetic process in the first case is determined by a large
activation barrier of 2.01~eV. In contrast, O$_2$ dissociation requires a much more modest activation energy,
0.38~eV, so that the formation of boron oxides is likely to be determined by the O$_2$ supply. The final
reaction product, B$_2$O$_3$, has a relatively low melting point ($\sim$700~K), while evaporation takes place
above 1500~K. Thus, we expect that at intermediate temperatures B layers can be easily depleted due to the
presence of O$_2$, a mechanism similar to the C loss observed in ZrC~\cite{Kato_2000}. This appears to be the
most efficient mechanism for B depletion during combustion.

Furthermore, also at the (0001)$_\mathrm{Zr}$ surface the dominant reaction is the dissociative adsorption of
O$_2$, which proceeds spontaneously without activation. Importantly, the dissociated O adatoms can easily
diffuse at the surface with migration paths presenting a barrier of 0.59~eV, but with the presence of
barrier-less migration trajectories as well. When these results are combined together we can unambiguously
suggest that the initial oxidation process of ZrB$_2$ can proceed rapidly. A possible strategy for limiting the
corrosion may then be that of inserting additives into the ZrB$_2$ matrix. Alternatively one can develop
appropriate surface treatments, such as pre-oxidation. This may form a protective ZrO$_2$ layer over ZrB$_2$.
Importantly, ZrO$_2$ has high thermal stability (melting temperature, $T_m$ $\leq$ 2900~K), and the interface
attachment between ZrB$_2$ and ZrO$_2$ can be controlled by controlling the ZrO$_2$ polymorphism.

\section{Conclusion}

In this work, we have presented a thorough atomistic modelling of the adsorption and dissociation of O$_2$,
H$_2$O and CO over two of the most stable ZrB$_2$ surfaces. Several conclusions can be drawn from our results.
Firstly, all the chemical species investigated, namely O, C, OH and H, display strong chemisorption on ZrB$_2$,
with O and C showing the largest adsorption energies. In general, the preferred adsorption sites on both
Zr- and B-terminated surfaces are the hollow and bridge ones. Secondly, we have found that O$_2$ dissociative
adsorption prevails when the molecule laterally approaches the surface, while molecular adsorption dominates
for vertical geometries. The same trend is also found for the other molecules, with the exception of CO on
(0001)$_\mathrm{B}$. Thirdly, we have determined that the chemical activity of the various adsorbents follows
the ranking: O$_2$, CO and H$_2$O, with O$_2$ being the most active agent. H$_2$O is the less reactive of the
molecules studies and tends to be chemisorbed on (0001)$_\mathrm{Zr}$ and physisorbed on (0001)$_\mathrm{B}$.
The kinetic barriers for dissociation are instead ordered as O$_2$, H$_2$O and CO, with CO presenting
anactivation barrier of 0.90~eV on (0001)$_\mathrm{Zr}$ and of 2.01~eV on (0001)$_\mathrm{B}$. This makes O$_2$
the most aggressive chemical agent for ZrB$_2$. Finally, we have determined that the Zr-surface is chemically
more active than the B-terminated one, at least to the chemical agents studied here. Considering the low
melting point of the B-containing products, the B-surfaces are likely to be destroyed under O$_2$ and/or CO
attack, a mechanism likely to determine B mass lost during combustion.

As it stands, our work offers a complete view of the microscopic mechanism for reaction of O$_2$, CO and H$_2$O
on ZrB$_2$ surfaces. This is important to determine the first steps in the corrosion process. Future work on
the effects of the intermediate products and of the temperature is necessary for defining a complete picture of
oxidation and corrosion in UHTC materials.

\section*{Acknowledgement}
This research was supported by the European Union's Horizon 2020 ``Research and innovation programme''
under the grant agreement No.685594 (C$^3$HARME). Computational resources have been provided by the Irish
Center for High-End Computing (ICHEC) and the Trinity Centre for High Performance Computing (TCHPC). Y.Z.
would like to thank the support from the internal grant of Yanshan University and the 100 Talents Programme of
Hebei province.

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text:
Armstrong Flooring, Inc.
PURSUANT TO SECTION 13 OR 15(d)
Date of Report (Date of earliest event reported): May 3, 2019 (May 2, 2019)
of incorporation )
File No.)
2500 Columbia Avenue P.O. Box 3025
If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.
Common Stock, $0.0001 par value AFI New York Stock Exchange
Results of Operations and Financial Condition
On May 3, 2019, Armstrong Flooring, Inc. (the "Company") issued a press release announcing its first quarter 2019 financial results. The full text of the press release is attached hereto as Exhibit 99.1.
The information in Item 2.02 of this Current Report on Form 8-K, including Exhibit 99.1, is being furnished herewith and shall not be deemed "filed" for the purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the "Exchange Act"), or otherwise subject to the liabilities of that section, nor shall it be deemed incorporated by reference into any filing under the Securities Act of 1933, as amended (the "Securities Act"), or the Exchange Act, except as expressly set forth by specific reference in such filing.
Departure of Directors or Principal Officers; Election of Directors; Appointment of Principal Officers
(b) Effective May 2, 2019, pursuant to a mutual agreement between the Company and Donald R. Maier, Mr. Maier's employment with the Company ceased and he resigned as a member of the Board of Directors of the Company (the "Board"). Mr. Maier will not stand for re-election to the Board at the Company's upcoming annual meeting of stockholders. In connection with Mr. Maier's separation, the Company entered into a separation agreement under which Mr. Maier agreed to a general release of claims in favor of the Company. In exchange for this release and in accordance with the terms of the Company's Severance Pay Plan for Executive Employees (the "Severance Plan"), the Company will pay Mr. Maier a lump sum cash payment of $100,000 within 3 business days of his execution of the separation agreement, and a lump sum cash payment of $2,768,138 on or within 5 business days following his execution of a supplemental release. Mr. Maier will be eligible to receive a pro-rated bonus under the Company's 2019 Annual Incentive Plan based on actual achievement of the corporate performance metrics for 2019. Pursuant to the separation agreement, in accordance with the terms of the Severance Plan and the Company's 2016 Long-Term Incentive Plan, and subject to the effectiveness of the supplemental release, (i) Mr. Maier will be paid an amount equal to six months' of the COBRA premium in effect under the Company's health plans applicable to Mr. Maier and his dependents, less the monthly premium cost then in effect for such coverage for active employees and (ii) the vesting of 34,027 of Mr. Maier's Restricted Stock Units will be accelerated and an aggregate of 122,416 of Mr. Maier's Performance Stock Units and Performance Shares, relating to grants made in 2017 and 2018, will remain eligible to vest based on satisfaction of the applicable Company performance metrics, in each case representing a pro-rata portion of Mr. Maier's total outstanding awards. All awards previously made to Mr. Maier in 2019 and all earlier awards not vesting in accordance with the terms described in the prior sentence have been forfeited. Mr. Maier will continue to be bound by non-competition restrictions and other restrictive covenants for two years following the separation pursuant to the separation agreement.
The foregoing description of the separation agreement does not purport to be complete and is qualified in its entirety by reference to the separation agreement, which is filed as Exhibit 10.1 hereto and is incorporated by reference herein.
(c) Effective May 2, 2019, Larry S. McWilliams, the Company's Chair of the Board, age 62, has been appointed to the position of Interim Chief Executive Officer of the Company. Mr. McWilliams will have oversight of global executive functions and will serve as the Company's principal executive officer on an interim basis. Mr. McWilliams will focus on the Company's near-term strategic priorities and facilitate the Company's management transition while the Company seeks a permanent Chief Executive Officer.
Mr. McWilliams has served as a member of the Board since March 30, 2016. Previously, Mr. McWilliams had served as President and Chief Executive Officer of Keystone Foods, a supplier of proteins and distribution services (2011 to 2012), Senior Vice President at Campbell Soup Company (2001 to 2011), President of Campbell International (2005 to 2010), President of Campbell USA (2004 to 2005) and President of Campbell Soup North America (2003 to 2004). Mr. McWilliams has also held positions at Coca-Cola (1995 to 2001) and the Pillsbury Company (1993 to 1995). Since 2010, Mr. McWilliams has also served on the Board of Directors of Armstrong World Industries, Inc. and has served as its Chair since 2018. In addition, Mr. McWilliams previously served on the boards of Godiva Chocolatiers International and Bob Evans Farms, Inc. Mr. McWilliams formerly served on the Board of Governors of St. Joseph's University Food Marketing Council and the Grocery Manufacturers' Association's Industry Affairs Council.
There are no familial relationships between Mr. McWilliams and any director, executive officer, or person nominated or chosen by the Company to become a director or executive officer of the Company. Additionally, there have been no transactions since the beginning of the Company's fiscal year in which Mr. McWilliams, or his immediate family members, had or will have a direct or indirect material interest.
In connection with his appointment as Interim Chief Executive Officer, and effective as of May 2, 2019, Mr. McWilliams will receive (i) an annual base salary of $700,000 to be paid in accordance with the Company's regular payroll policies during his tenure and (ii) a grant of restricted stock units with a value of $160,000, with the number of shares to be subject to the grant determined by the NYSE closing price of the Company's common shares on the grant date. The grant will be scheduled to vest on the date of the Company's 2020 annual meeting of stockholders based on continued services to the Company, or sooner as may be provided for under the terms of the Company's 2016 Long Term Incentive Plan, as amended and restated. Mr. McWilliams will not participate in the Company's Annual Incentive Plan and, while in the role of Interim Chief Executive Officer, will not receive the cash and equity-based compensation paid to non-employee directors of the Company.
In addition, effective May 2, 2019, the Company appointed James C. Melville, age 67, as the Lead Independent Director of the Board. Mr. Melville has served as member of the Board since March 30, 2016. Mr. Melville will continue to serve as the Chair of the Nominating and Governance Committee and as a member of both the Finance and Management Development and Compensation Committees of the Board. Mr. Melville is a member of the Minneapolis, Minnesota-based law firm of Kaplan, Strangis and Kaplan, P.A., where he has practiced in the corporate, governance, mergers and acquisitions, securities and financial areas since 1994. Mr. Melville has been designated a Board Leadership Fellow by the National Association of Corporate Directors (NACD). Mr. Melville has served on the Board of Directors of Armstrong World Industries, Inc. since 2012.
There are no familial relationships between Mr. Melville and any director, executive officer, or person nominated or chosen by the Company to become a director or executive officer of the Company. Additionally, there have been no transactions since the beginning of the Company's fiscal year in which Mr. Melville, or his immediate family members, had or will have a direct or indirect material interest.
For his role as Lead Independent Director of the Board, Mr. Melville will receive an additional annual cash retainer of $25,000.
Section 7 – Regulation FD
Item 7.01 Regulation FD Disclosure.
On May 3, 2019, the Company issued a press release announcing that it will report its first quarter 2019 financial results via a live webcast and conference call on May 7, 2019 at 10:00 a.m. Eastern Time. The live webcast and accompanying slide presentation will be available in the Investors section of the Company's website at www.armstrongflooring.com. To participate in the call, please dial 877-407-0789 (domestic) or 201-689-8562 (international). A replay of the conference call will be available for 90 days, by dialing 844-512-2921 (domestic) or 412-317-6671 (international) and entering the passcode 13689555. The full text of the press release is attached hereto as Exhibit 99.1.
In connection with the actions described in Item 5.02 above, the Company also issued a press release. The full text of the press release is attached hereto as Exhibit 99.2.
The information in Item 7.01 of this Current Report on Form 8-K, including Exhibits 99.1 and 99.2, is being furnished herewith and shall not be deemed "filed" for the purposes of Section 18 of the Exchange Act, or otherwise subject to the liabilities of that section, nor shall it be deemed incorporated by reference into any filing under the Securities Act or the Exchange Act, except as expressly set forth by specific reference in such filing.
The Company's Amended and Restated Certificate of Incorporation provides that the size of the Board shall be fixed from time to time by the Board. The size of the Board is currently fixed at nine (9) members. However, the Board has taken action to reduce the size of the Board to eight (8) members, effective immediately, and to further reduce the size of the Board to seven (7) members following the certification of the results of the vote at the upcoming annual meeting of stockholders. The immediate reduction in the size of the Board will eliminate the vacancy that will exist as a result of Mr. Maier's resignation from the Board and withdrawal of his name from re-election, and the reduction to seven (7) members will eliminate the vacancy that will exist as of the upcoming annual meeting of stockholders that was previously disclosed in the Proxy Statement. The Board is permitted, however, under its Amended and Restated Certificate of Incorporation, to expand the size of the Board and appoint directors to fill such newly created vacancies. The Board continues to search for qualified director candidates.
Financial Statements and Exhibits
(d) Exhibits
Exhibit No.
10.1 Separation Agreement between Armstrong Flooring, Inc. and Donald R. Maier, dated May 2, 2019
99.1 Press Release of Armstrong Flooring, Inc., dated May 3, 2019
/s/ Christopher S. Parisi
Christopher S. Parisi
Senior Vice President,